Le Risque de Valeur Résiduelle Trois études quantitatives

Transcription

UNIVERSITÉ PARIS OUEST - NANTERRE LA DÉFENSE
THÈSE
pour obtenir le grade de
Docteur de l’Université
de Paris Ouest - Nanterre La Défense
Discipline : Sciences Économiques
présentée et soutenue publiquement par
Sylvain Prado
Le 21 juin 2010
Le Risque de Valeur Résiduelle
Trois études quantitatives
Directrice de thèse : Mme Valérie Mignon
Jury :
Mme Sandrine Lardic,
Maître de conférences à l’Université Paris Ouest - Nanterre La Défense
Mr Jean-François Lemettre,
Professeur à l’Université Paris Sud (Rapporteur)
Mme Valérie Mignon,
Professeur à l’Université de Paris Ouest - Nanterre La Défense
Mr Jamel Trabelsi,
Maître de Conférences à l’Université de Strasbourg (Rapporteur)
ii
L’Université de Paris Ouest-Nanterre La Défense n’entend donner aucune approbation ni
improbation aux opinions émises dans les thèses ; ces opinions doivent être considérées comme
propres à leurs auteurs.
Remerciements
Je tiens à remercier :
Valérie Mignon pour sa compréhension, pour avoir encadré mon travail avec beaucoup de
compétences, pour m’avoir donné les moyens de réaliser et de mener à bout cette thèse.
Evguenia pour son appui, ses conseils, et l’aide indispensable fournie dans la réalisation de
cette thèse.
Jean-François Lemettre et Jamel Trabelsi pour avoir accepté de rédiger les rappors sur cette
thèse, ainsi que Sandrine Lardic pour sa participation au jury.
Christophe Bourgoin et Hacène Ouzia pour l’aide sur LaTeX et grâce à qui le lecteur a entre
ses mains un travail bien plus lisible que lors de ma première mise en page.
L’intérêt de l’entreprise GE Capital à l’égard de mon travail, et plus particulièrement Pierre
Olivier Bard, qui a contribué à un climat favorable à ma démarche intellectuelle.
Tous ceux avec qui j’ai eu le plaisir de collaborer au sein de GE : les équipes AMO monde,
Europe, allemandes, espagnoles, francaises, italiennes et britanniques.
Tous ceux qui m’ont fourni un retour constructif sur mon travail : Kamel Mathout pour la
relecture de mes premiers travaux, le laboratoire Economix lors du séminaire lunch, l’université
de Brunel à Londres lors de la conférence QASS, l’université de Limerick lors de la Irish Society
of New Economists Annual Conference.
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REMERCIEMENTS
Résumé
Malgré son poids économique et ses avantages, l’activité de leasing reste méconnue. Le leasing fait l’objet d’un nombre limité de travaux académiques, notamment sur une problématique
qui lui est propre, le risque de valeur résiduelle. Dans l’activité de leasing, le bailleur prend le
risque de ne pas récupérer su¢ samment de capital lors de la revente de l’actif. Le risque de
perte à la revente à la …n de la période contractuelle, ainsi que la tari…cation sont fortement
impactés par le prix estimé de revente de l’actif (la valeur résiduelle). La thèse vise à fournir une
contribution académique aux professionnels en charge de la gestion de ce risque dans le secteur
du leasing. Trois thèmes sont abordés : la valorisation des actifs, la couverture des risques de
valeur résiduelle, et la dimension macro-économique.
Dans le premier chapitre, nous appliquons la méthode des prix hédoniques à un portefeuille européen de leasing, a…n d’estimer la distribution des prix de revente d’automobiles.
L’approche hédonique estime le prix d’un bien par la valorisation de ses attributs. Suite à une
discussion sur les prix hédoniques, nous proposons un modèle opérationnel pour le marché de
l’automobile d’occasion. Le modèle est appliqué à quatre pays européens (l’Allemagne, l’Espagne, la France et la Grande-Bretagne), et les distributions sont calculées sur deux modèles
de véhicules (Audi A4 et Ford Focus) permettant la comparaison des pro…ls de dépréciation et
des risques de valeur résiduelle.
Mots-clés : modèles hédoniques, valeur résiduelle, marché automobile. Classi…cation
JEL : C51, G12, G32, D12.
Dans le deuxième chapitre, nous proposons un modèle statistique pour couvrir le risque
de valeur résiduelle en utilisant la technique des copules gaussiens. A la suite d’une discussion
sur la problématique du risque de valeur résiduelle et des modèles de risque de crédit existants,
un nouveau produit dérivé est proposé et analysé : le Collateralized Residual Value (CRV).
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RÉSUMÉ
Le modèle est appliqué à un portefeuille européen de location longue durée d’automobiles. Nos
résultats indiquent que ce produit …nancier est facile à adapter et à mettre en œuvre en fonction
des caractéristiques du contrat et de la corrélation entre les actifs le composant.
Mots-clés : risque de valeur résiduelle, risque de crédit, produits dérivés de crédit, modèle
factoriel, copules. Classi…cation JEL : C10, G13.
Le dernier chapitre répond à deux questions cruciales dans le secteur du leasing automobile : Quelles sont les interactions entre les automobiles neuves et d’occasion ? Pouvons-nous
utiliser ces interactions a…n d’estimer le prix de revente des véhicules ? Les voitures neuves
d’aujourd’hui seront les voitures d’occasion de demain, et l’on suppose une forme de compétition entre le marché du neuf et le marché de l’occasion. C’est pourquoi il existe quelques
idées préconçues et de nombreuses théories sur les interactions entre le premier marché et le
second marché. Nous proposons de développer la ré‡exion par une analyse macro-économique
des marchés automobiles Français, Britanniques et Nord-Américains. Les di¤érents concepts
sont répertoriés et statistiquement contrôlés. Nos résultats indiquent que les relations entre les
di¤érents marchés semblent limitées en France et au Royaume-Uni, alors que le marché NordAméricain est confronté à un mécanisme dit de ‘Scitovscky’. Dans tous les cas, les relations ne
sont pas assez fortes pour expliquer complètement les comportements des marchés.
Mots-clés : Second marché, marché automobile, prix, causalité, corrélation cycliques, VAR.
Classi…cation JEL : C32, E31, E37.
Summary
Leasing, by its volume and its attributes, constitutes a signi…cant mean of …nancing in the
world. Leasing, however, sparked o¤ a limited academic interest, many of its features have been
unexplored and particularly on a critical point, the residual value risk. In the leasing industry
the lessor faces a risk, at the end of the contract, in not recovering su¢ cient capital value from
resale of the asset. The risk of loss on sales at the end of the contract term, as well as pricing,
are critically impacted by the forecasted resale price of the asset (residual value). The thesis
aims to provide an academic contribution directed at asset analysts in charge of residual value
in the leasing industry. Three topics are discussed : asset valuation, residual value risk hedging,
and macro economy perspective.
In the …rst chapter, we apply the Hedonic methodology to European auto lease portfolios,
in order to estimate the resale price distribution. The Hedonic approach estimates the price
of a good through the valuation of its attributes. Following a discussion on Hedonic prices,
we propose an operational model for the automobile resale market. The model is applied to
four European countries (France, Germany, Spain and Great Britain), and distributions are
calculated on two vehicle versions (Audi A4 and Ford Focus) allowing a comparison of market
depreciation patterns and residual value risks.
Keywords : Hedonic model, residual value, automotive market. JEL Classi…cation :
C51, G12, G32, D12.
In the second chapter, we propose a model to hedge residual value risk using the Gaussian
copula methodology. After discussing residual value risk and credit risk modelization, a new
derivative product is introduced and analyzed ; the Collateralized Residual Values (CRV). The
model is applied to an European auto lease portfolio of operating lease contracts pertaining to
a major company. Our results indicate that the …nancial product is easy to customize, and to
implement through the contract characteristics and the level of correlation.
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SUMMARY
Keywords : residual value risk, credit risk, credit derivatives, factor modeling, copula. JEL
Classi…cation : C10, G13.
In the third chapter, we aim at answering two critical questions of the Auto lease industry.
What are the interactions between the new and the second-hand car markets ? Can we use the
interactions to estimate the car prices of tomorrow ? Everybody knows that the new cars of
today are used cars of tomorrow and some people assume a competition between new and
used markets. There are numerous, preconceived ideas and academic theories regarding the
interactions between primary and secondary markets. To investigate the relations, we provide
a macroeconomic analysis of the French, the British and the US car markets. Our results
indicate that the relations appear limited for France and the UK, whereas the US market faces
a Scitovscky mechanism. Furthermore, they illustrate that the interrelations are not strong
enough to fully explain and forecast market patterns.
Keywords : second-hand market, automotive market, prices, causality, cyclical correlations,
VAR. JEL Classi…cation : C32, E31, E37.
Table des matières
Remerciements
iii
Résumé
v
Summary
vii
Introduction Générale
xiii
General Introduction
xxiii
1 The European used-car market at a glance
1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.2 The Hedonic theory underlies our model . . . . . . . . . . . . . . . . . . . . . .
4
1.2.1
Goods attributes constitute the Hedonic theory. . . . . . . . . . . . . . .
4
1.2.2
An identi…cation problem appears in Hedonic models. . . . . . . . . . . .
5
1.2.3
Used cars are durable commodities. . . . . . . . . . . . . . . . . . . . . .
7
1.3 Some characteristics of the model are discussed. . . . . . . . . . . . . . . . . . .
8
1.3.1
Coe¢ cients interpretation depends on used market substitution to new
market. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
1.3.2
Others products interact with price. . . . . . . . . . . . . . . . . . . . . .
9
1.3.3
Multicollinearity is a main issue in Hedonic models. . . . . . . . . . . . . 10
1.3.4
Which functional form ? . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3.5
Unobserved tastes create heteroscedasticity. . . . . . . . . . . . . . . . . 11
1.4 We use the Hedonic model to estimate the distribution of resale price. . . . . . . 12
1.4.1
Ohta and Griliches have an empirical approach. . . . . . . . . . . . . . . 12
1.4.2
Statistical models are slightly di¤erent by country. . . . . . . . . . . . . . 13
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TABLE DES MATIÈRES
1.4.3
We estimate the distribution of resale price. . . . . . . . . . . . . . . . . 14
1.4.4
An adjustment removes uncertain variables e¤ects. . . . . . . . . . . . . 14
1.5 We apply the methodology to four European countries. . . . . . . . . . . . . . . 15
1.5.1
Models are created according to the information usually available in the
leasing industry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.5.2
The regression provides a Hedonic price assessment of the European markets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.5.3
The analysis on Ford focus and Audi A4 give additional informations. . . 16
1.6 Conclusion and extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.7 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.7.1
Appendix A : Methodological aspects. . . . . . . . . . . . . . . . . . . . 19
1.7.2
Appendix B : Regression equations and notations . . . . . . . . . . . . . 22
1.7.3
Appendix C : Regression results . . . . . . . . . . . . . . . . . . . . . . . 25
1.7.4
Appendix D : Pivot Point results . . . . . . . . . . . . . . . . . . . . . . 27
1.7.5
Appendix E : Graphical analysis : . . . . . . . . . . . . . . . . . . . . . . 28
2 Hedging residual value risk using derivatives
37
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.2 Leasing
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.2.1
Main characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.2.2
Residual value risk versus competitiveness . . . . . . . . . . . . . . . . . 44
2.3 Model pre requisites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.3.1
CDO are a subclass of ABS . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.3.2
Default, default, default.... . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.3.3
Basic elements on Copulas . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.3.4
Speci…c pre requisites, the Gaussian copula . . . . . . . . . . . . . . . . . 51
2.3.5
The initial one factor model is used for CDO pricing . . . . . . . . . . . 52
2.4 A modi…ed model : The leasing model . . . . . . . . . . . . . . . . . . . . . . . 55
2.4.1
There is a similarity between credit risk and residual value risk. But there
are also dissimilarities and speci…cally in Auto Lease. . . . . . . . . . . . 56
2.4.2
Homogeneous equipment type model . . . . . . . . . . . . . . . . . . . . 58
2.4.3
Heterogeneous equipment type model : a portfolio of three di¤erent assets 60
2.4.4
Collateralized Residual Values . . . . . . . . . . . . . . . . . . . . . . . . 62
TABLE DES MATIÈRES
xi
2.5 Empirical analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.5.1
Correlation to the one sector factor . . . . . . . . . . . . . . . . . . . . . 66
2.5.2
Fair Market Value and Residual Value setting . . . . . . . . . . . . . . . 71
2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
2.7 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3 A Family Hitch
81
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.2 Academic researches in the second-hand market are legion. . . . . . . . . . . . . 82
3.2.1
Why secondary markets exist ? . . . . . . . . . . . . . . . . . . . . . . . 83
3.2.2
The Akerlof e¤ect and the car durability are linked. . . . . . . . . . . . . 85
3.2.3
Optimal durability and Time inconsistency are two areas of research. . . 87
3.2.4
Scitovsky’s mechanisms are part of a Keynesian framework. . . . . . . . 88
3.2.5
There are implied mechanisms behind the academic theories. . . . . . . . 90
3.3 The macroeconomic times series need clari…cations. . . . . . . . . . . . . . . . . 91
3.3.1
Three countries are compared through four time series. . . . . . . . . . . 91
3.3.2
How to connect the academic literature with a time series analysis ? . . . 93
3.3.3
We work on macroeconomic time series, a limited information. . . . . . . 96
3.3.4
What do the series look like ? . . . . . . . . . . . . . . . . . . . . . . . . 98
3.4 The econometric analysis shows di¤erent results by country. . . . . . . . . . . . 99
3.4.1
The unit root tests undermine the advanced mechanisms. . . . . . . . . . 100
3.4.2
The correlation analysis provides a one-month period perspective. . . . . 102
3.4.3
The Granger causality tests elaborate the assessments of the correlation
analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
3.4.4
The Hodrick-Prescott …lter reveals economic cycles. . . . . . . . . . . . . 104
3.4.5
Vector Autoregressive (VAR) models clarify the previous results. . . . . . 106
3.5 To conclude, an interdependence ? . . . . . . . . . . . . . . . . . . . . . . . . . . 108
3.6 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
3.6.1
Appendix 1 : Data sources . . . . . . . . . . . . . . . . . . . . . . . . . . 111
3.6.2
Appendix 2 : Median Age and Average Sales price in the US . . . . . . . 112
3.6.3
Appendix 3 : Raw data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
3.6.4
Appendix 4 : Growth rate and seasonally adjusted times series . . . . . . 115
3.6.5
Appendix 5 : Granger Test . . . . . . . . . . . . . . . . . . . . . . . . . . 118
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TABLE DES MATIÈRES
3.6.6
Appendix 6 : Correlation Analysis . . . . . . . . . . . . . . . . . . . . . . 120
3.6.7
Appendix 7 : Hodrick-Prescott Filter, cycles and trends . . . . . . . . . . 121
3.6.8
Appendix 8 : Hodrick-Prescott Cycles Correlations . . . . . . . . . . . . 124
Conclusion Générale
133
Bibliographie
137
Introduction Générale
"(. . . ) le principe véritable de la fécondité irremplaçable de la recherche empirique : Faire sans savoir complètement ce que l’on fait, c’est se donner une chance
de découvrir dans ce que l’on a fait quelque chose que l’on ne savait pas."
P. Bourdieu, Homo Academicus, Les Editions de Minuit, 1984, p17.
L’activité de leasing est peu connue bien qu’elle constitue une part importante de l’économie
mondiale.
L’International Accounting Standard for Lease, ou IAS171 dé…nit un contrat de leasing
comme «un accord par lequel le bailleur cède au locataire, en échange d’un paiement ou une série
de paiements, le droit d’utiliser un actif pendant une période de temps convenue» . Cependant,
la législation peut être di¤érente selon les pays, les contrats peuvent être adaptés pour répondre
aux besoins d’un client et tout type d’équipement peut, en théorie, faire l’objet de leasing. Ainsi
le mot ‘lease’comprend un large éventail de contrats.
Dans l’ensemble, le leasing est un instrument …nancier pour l’achat de matériel. Dans un
contrat de leasing, le bailleur fournit un équipement qui doit être utilisé par un locataire sur une
période dé…nie en échange de paiements spéci…és. Le bien loué peut être tout type de matériel
(imprimante, scanner, camions, avions...) utilisé par le locataire à des …ns commerciales. Le
bailleur achète l’équipement et il est le propriétaire légal de l’actif. Pour utiliser l’équipement,
le locataire verse des paiements périodiques au bailleur tout au long de la période du contrat.
1
Au sein de l’Union européenne, toutes les sociétés cotées sont tenues d’adopter l’IAS17. La norme équivalente
aux USA est le SAF13.
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INTRODUCTION GÉNÉRALE
L’ensemble du marché du leasing mondial2 a été estimé à plus de 633 milliards de dollars
en 2006. L’Europe et L’Amérique du Nord ont représenté 41% et 38% du marché mondial.
Le ‘World Leasing Yearbook 2009’ a rapporté un montant global d’équipement en leasing
de plus de 760 milliards de dollars pour 2007. Les associations européennes de leasing ont
enregistré un volume de crédit-bail neuf au-dessus de 330 milliards d’Euros et une contribution
au …nancement, en moyenne, de 18% du total des investissements européens pour 2008. Par
ailleurs, le leasing a impliqué plus de 16 millions d’automobiles en Europe3 .
D’une manière générale, les contributions academiques traitant du sujet sont quasiment
toutes liées à la comparaison entre le leasing et l’acquisition d’un équipement par le crédit.
Certains papiers analysent les avantages …scaux résultant du choix entre un contrat de leasing
et le recours à un emprunt4 . Un deuxième groupe d’articles académiques discutent du ‘Leasing Puzzle’. Les théories en …nance et en economie suggèrent que les contrats de leasing et
les emprunts sont des substituts. Ainsi, une augmentation du leasing devrait conduire à une
diminution de la dette. De plus, les théories …nancières standard gèrent les ‡ux de trésorerie
provenant des contrats de leasing de la même manière que ceux provenant des crédits. Mais
Ang et Peterson (1984) ont constaté empiriquement que le leasing et la dette apparaissent, en
fait, comme des compléments pour les entreprises. Un accroissement du leasing est associé à un
accroissement de la dette. Ne pouvant avancer une explication concluante, ils quali…èrent leur
découverte d’énigme non résolue de la …nance ou de ’Leasing Puzzle’. À la suite de leur article
fondateur, plusieurs recherches académiques ont tenté de reproduire et de véri…er les résultats5 .
Le ‘Puzzle’nous amène au troisième domaine de recherche qui couvre tous les articles liés
aux incitations au leasing et à ses avantages. Lasfer et Lévis (1998), par exemple, ont reformulé
le problème. En théorie, le leasing ne procure aucune valeur ajoutée par rapport à l’achat d’un
équipement au travers d’un crédit : les deux moyens de …nancement sont associés à un même
taux d’intérêt, ont un statut …scal similaire et prévoient le même prix de revente de l’actif.
Toutefois, dans la pratique, ces conditions ne sont pas toujours satisfaites et il existe plusieurs
2
White Clarke Global Leasing Report (2008).
Leaseurope Association Website.
4
Voir Smith et Wakeman (1985), Brick, Fung et Subrahmanyam (1987), Mackie-Mason (1990), Goodacre
3
(2002).
5
Voir Marston et Harris (1988), Lewis et Schallheim (1992), Krishnan et Moyer (1994), Branson (1995),
Beattie, Goodacre et Thomson (1999), Yan (2006).
xv
motifs pour le leasing6 . Pour les grandes entreprises, leur étude révèle que les responsables
…nanciers utilisent le leasing comme un instrument pour minimiser le coût après impôt du
capital. Pour les petites entreprises, le leasing apparaît comme une opportunité de croissance et
de survie. Les petites entreprises ont des di¢ cultés pour accéder au marché du crédit. De ce fait,
le leasing facilite le …nancement de la formation de capital …xe. En d’autres termes, les petites
entreprises à fort potentiel de croissance ou avec de faibles béné…ces sont plus susceptibles de
faire appel à ce mode de …nancement. En conséquence, sans le leasing de nombreux projets
n’auraient jamais pu voir le jour.
Drakos et Goulas (2008) avancent que l’incertitude d’un investissement pour une entreprise
est exacerbée par l’irréversibilité du capital. En permettant la séparation de l’utilisation d’un
équipement avec les engagements associés à son acquisition7 , le leasing facilite le désengagement de projets infructueux. Schmitt et Stuyck (2002)8 , Schmitt (2003)9 et Schmitt (2004) ont
démontré que le leasing est une activité relativement peu risquée et que les recommandations de
Bâle 2 pour le montant des réserves en capital devrait être réduit pour les entreprises de leasing.
Au total, le leasing apparaît comme un instrument …nancier sûr. En outre, le fait de louer des
biens plutôt que de les vendre peut contribuer à réduire les problèmes environnementaux10 . La
pratique du leasing limite la production de déchets et incite à la création d’un schéma d’utilisation du matériel en boucle fermée. Pour certains équipements et certains types de contrats, les
fabricants peuvent prendre conscience des problèmes opérationnels, ainsi que des coûts associés
à la gestion des produits en …n de vie. Ainsi, ils peuvent redessiner les produits en conséquences
a…n de limiter les externalités négatives en …n de vie. En restant dans le circuit commercial, les
équipements sont moins susceptibles d’être jetés aux ordures ou stockés quand ils deviennent
6
Lasfer et Lewis ont énuméré trois principales motivations pour la location. D’abord, la location peut réduire
les taxes …nancières. Deuxièmement, le leasing pourrait être avantageux …nancièrement pour les entreprises en
di¢ culté a…n d’obtenir un accord et l’accès aux équipements, car les bailleurs ont des créances de premier rang
sur l’actif. En…n, le leasing peut réduire le coût d’agence parce qu’il ne constitue pas un investissement complet
pour le locataire.
7
L ’hétérogénéité du capital et les di¤érents degrés d’irréversibilité associés expliqueraient ainsi les divers
recours au leasing par les entreprises.
8
Schmitt et Stuyck ont analysé des contrats de leasing en défaut sur une période de 1976 à 2000 dans six pays
d’Europe au sein de douze grandes entreprises. Ils ont constaté que le taux de recouvrement était comparables
à celui des obligations de premier rang.
9
L’estimation de la fonction de distribution des pertes et la Value at Risk dans le secteur du leasing révèlent
que l’activité présente un risque relativement faible. Voir aussi Pirotte et Vaessen (2008).
10
Voir Fishbein, McGarry et Dillon (2000).
xvi
obsolescents.
Malgré le peu d’études sur le sujet, nous devons également souligner que l’intervention des
sociétés de leasing crée un attrait supplémentaire pour ce mode de …nancement. Les sociétés
de leasing ne sont pas seulement des intermédiaires et leur expertise produit une valeur ajoutée dans la démarche de leasing. Elles sélectionnent le matériel approprié en fonction de sa
capacité à améliorer le rendement du locataire et prennent en compte divers facteurs tels que
les caractéristiques du matériel, sa durée de vie économique, la …scalité, et la valeur résiduelle
(voir infra). Les sociétés de leasing ont aussi des compétences en …nance, en risque de crédit,
et en négociation pour l’acquisition d’équipement. D’une manière generale, elles facilitent les
échanges entre les fournisseurs d’équipement et les utilisateurs11 .
Pour les sociétés de leasing, le risque de perte à la revente à la …n de la durée du contrat,
ainsi que la tari…cation, sont fortement impactés par le prix de revente estimé de l’actif.
Dans cette thèse, nous étudions un dé… crucial pour le bailleur : le risque de valeur résiduelle.
Les trois paramètres essentiels d’un contrat de leasing sont le prix de l’équipement original,
la durée du contrat et la valeur résiduelle. Ils déterminent la compétitivité et, en même temps,
l’exposition à un risque attaché à la valeur de l’actif. La valeur résiduelle est la valeur estimée de
l’actif à la …n du contrat car le bailleur doit estimer la valeur au prix du marché de l’équipement
à la …n de la période contractuelle.
Ces trois paramètres dé…nissent l’essentiel du niveau de dépréciation (qui peut être compris
comme l’écart entre le prix de l’équipement d’origine et la valeur résiduelle) et du montant de
loyer payé par le locataire pour utiliser l’équipement. La part de la dépréciation dans le loyer
(qui, généralement, en constitue la plus grande partie) peut être calculée par le montant total de
dépréciation divisé par le nombre de paiements12 . De plus, plusieurs éléments sont inclus dans
11
Parmi les nombreuses études relatives aux avantages du leasing, nous devons aussi mentionner Kichler et
Haiss (2009), qui expliquent la contribution du leasing à la croissance économique des économies d’Europe
centrale et orientale, ainsi que la thèse de Brage et Eckerstom (2009), qui comparent les di¤érents avantages du
leasing en Suède et au Japon.
12
Par exemple, dans un contrat de leasing automobile avec un prix d’équipement d’origine de 12000 $, une
valeur résiduelle de 7200 $ et une période de bail de 24 mois, le paiement mensuel de l’amortissement (à
l’exclusion des taux d’intérêt et impôts) est de 200 $ par mois (
12000 7000
24
).
xvii
les paiements e¤ectués par le locataire tout au long du contrat : les intérêts sur l’investissement
du bailleur, les frais de service (y compris les coûts d’exploitation, l’assurance, le conseil, les
réparations) et les taxes. La …gure A illustre les mécanismes en jeu dans le calcul des paiements
d’un contrat de leasing13 .
Figure A : La dépréciation dans un contrat de leasing
de l’equipement - Valeur residuelle
Loyer = ( Prix d’achat
) + Taux d’intérêt + Taxes + Frais de Services.
nombre total de paiements
Quand la valeur résiduelle augmente, l’écart avec le prix initial de l’équipement diminue et
le montant du loyer diminue aussi. Une valeur résiduelle élevée permet au locataire de payer
un montant plus bas pour utiliser l’équipement. Le contrat proposé par le bailleur devient plus
compétitif.
Cependant, ce qui contribue au succès d’une société de leasing peut entraîner des di¢ cultés
lorsque les conditions du marché changent. Le bailleur prend le risque de ne pas être en mesure
13
A des …ns de simpli…cation, nous n’avons pas mentionné un quatrième élément : les options de …n de contrat.
Di¤érentes options peuvent être disponibles pour le locataire : la période de location peut être prolongée, le
contrat peut être renouvelé, les équipements peuvent être rachetés ou rétrocédés.
xviii
de récupérer su¢ samment de capital lors de la revente de l’actif. Il existe un risque de valeur
résiduelle. Comme cela est illustré par la …gure B, la courbe de la valeur de marché révèle un
gain ou une perte à la revente, en fonction du niveau de valeur résiduelle.
Figure B : La valeur marché d’un actif
Le bailleur fait ainsi face à un dilemme. Plus la valeur résiduelle est basse, plus le risque
de perte à la revente est faible. Mais, en même temps, le loyer augmente et le bailleur perd
sa compétitivité. Inversement, plus le risque de valeur résiduelle est élevé et plus le contrat de
leasing est compétitif.
Nous apportons une perspective académique à la pratique de la gestion du risque de valeur
résiduelle.
Dans une société de leasing, le département de gestion d’actifs est en charge du risque
de valeur résiduelle et estime les prix de revente des équipements en leasing. Au cours des
sept dernières années, j’ai travaillé sur l’analyse de la valeur résiduelle au sein de General
Electric Capital, une des plus grandes entreprises de leasing dans le monde14 . Grâce à ma
position européenne au sein du groupe, j’ai eu la possibilité de rencontrer des analystes de
14
L’actif total de GE Capital Commercial Finance était de plus de 230 milliards de dollars en 2008.
xix
gestion d’actifs à travers di¤érents pays. J’ai aussi eu un aperçu des pratiques aux États-Unis,
en Nouvelle-Zélande, en Australie et au Japon. J’ai vécu une situation qui est partagée par
les professionnels dans de nombreux domaines : les équipes de gestion d’actifs reproduisent
des méthodes et des processus opérationnels, créés par leurs prédécesseurs, en les améliorant
par tâtonnement15 . Il y a une transmission du savoir-faire par l’application d’un minimum de
théorie. Plus spéci…quement, peu de travaux académiques16 et très peu de modèles statistiques
sont dédiés au risque de valeur résiduelle. Par exemple, bien que les volumes …nanciers soient
du même ordre de grandeur (Figure C)17 , le …nancement structuré des CDO (Collateralized
Debt Obligation) a attiré bien plus de recherche académique que le leasing.
Figure C : Le volume de leasing dans le monde
Néanmoins, les analystes de gestion d’actifs n’ont pas attendu la théorie et les apports académiques pour estimer la valeur d’un équipement en …n de période contractuelle. Ils doivent en
e¤et proposer un prix pour établir un contrat. Notre objectif général est d’enrichir la littérature
sur le sujet et ainsi d’apporter ‘un peu de la théorie à la pratique’18 . L’objet de toute théorie
15
Par exemple, la situation est semblable dans l’industrie des produits …nanciers dérivés. “Option hedging,
pricing, and trading (. . . ) is a rich craft with traders learning from traders (or traders copying other traders)
and tricks developing under evolution pressures, in a bottom-up manner.” Haug et Taleb (2009).
16
Les rares contributions sont mentionnées dans le deuxième chapitre.
17
Sources : White Clark Global rapport de leasing, World Leasing Yearbook 2009, SIFMA.
18
Le leasing se situe entre la …nance et l’ingénierie. Cela pourrait explique le peu de travaux académiques
xx
est de modéliser un phénomène a…n de mieux le comprendre et de faciliter son exploitation.
Or le point de vue académique ajoute un contrôle théorique sur les outils et les hypothèses
utilisées par les spécialistes. De plus, la position académique fournit une approche libérée de
tous préjugés créés par l’appartenance aux métiers du leasing.
Une analyse de la valeur résiduelle comporte plusieurs éléments parmi lequels : les caractéristiques techniques de l’actif, la composition du portefeuille d’équipement et la courbe
de dépréciation. C’est pourquoi nous pouvons béné…cier de la littérature déjà en usage dans
d’autres domaines, comme les modèles économétriques des prix hédonique ou la litterature en
macroéconomie.
Les sections empiriques de la thèse se concentrent sur les contrats de leasing automobile.
L’automobile constitue un vaste marché et permet de collecter de nombreuses informations sur
le comportement de dépréciation des actifs. Le niveau élevé de la valeur résiduelle des voitures
à la …n du contrat, par comparaison avec d’autres types d’équipements, augmente le risque de
pertes et constitue un dé… majeur pour les sociétés de leasing.
Deux types de contrats de location d’automobiles peuvent être dé…nis. Les contrats de
location courte durée concernent les automobiles louées à des clients privés ou professionnels
pour une période de temps relativement courte, a…n de répondre à des besoins occasionnels.
En revanche, la location longue durée couvre les contrats pour les entreprises qui externalisent
leurs besoins en ‡otte de véhicules à une société de leasing. En plus des véhicules nécessaires, la
société de leasing fournit généralement des services connexes, comme la maintenance, la gestion
du carburant et l’assurance. La thèse se concentre principalement sur la location longue durée.
La thèse s’organise en trois chapitres. Dans le premier chapitre, nous étudions la valorisation
et le comportement de dépréciation d’un actif : l’automobile. Dans le deuxieme chapitre, nous
proposons une nouvelle façon de couvrir le risque de valeur résiduelle. Dans le troisième chapitre,
nous étudions la relation entre les marchés du neuf et de l’occasion.
Dans le premier chapitre, nous appliquons la méthode des prix hédoniques à un portefeuille européen de leasing, a…n d’estimer la distribution des prix de revente d’automobiles.
sr le sujet. En e¤et, le …nancement d’équipements nécessite di¤érents domaines d’expertise : la …nance et une
connaissance du secteur industriel où les agents opèrent.
xxi
L’approche hédonique estime le prix d’un bien par la valorisation de ses attributs. Suite à une
discussion sur les prix hédoniques, nous proposons un modèle opérationnel pour le marché de
l’automobile d’occasion. Le modèle est appliqué à quatre pays européens (l’Allemagne, l’Espagne, la France et la Grande-Bretagne), et les distributions sont calculées sur deux modèles
de véhicules (Audi A4 et Ford Focus) permettant la comparaison des pro…ls de dépréciation et
des risques de valeur résiduelle.
Le deuxième chapitre propose un modèle statistique pour couvrir le risque de valeur
résiduelle en utilisant la technique des copules gaussiens. A la suite d’une discussion sur la
problématique du risque de valeur résiduelle et des modèles de risque de crédit existant, un
nouveau produit dérivé est proposé et analysé : le Collateralized Residual Values (CRV). Le
modèle est appliqué à un portefeuille européen de location longue durée d’automobiles. Nos
résultats indiquent que ce produit …nancier est facile à adapter et à mettre en œuvre en fonction
des caractéristiques du contrat et du niveau de corrélation. Le deuxième chapitre s’adresse
aux professionnels du leasing intéressés par un nouvel outil …nancier, ainsi qu’aux acteurs des
marchés …nanciers concernés par de nouvelles opportunités d’investissement autour du risque
de valeur résiduelle.
Les équipes de gestion d’actifs doivent prendre en considération les facteurs macroéconomiques pouvant in‡uencer les prix de revente des actifs. Le dernier chapitre analyse un
élément crucial de cette question. Les voitures neuves d’aujourd’hui seront les voitures d’occasion de demain, et l’on suppose une forme de compétition entre le marché du neuf et le marché
de l’occasion. C’est pourquoi il existe quelques idées préconçues et de nombreuses théories sur
les interactions entre le premier marché et le second marché. Nous proposons de développer la
ré‡exion par une analyse macro-économique des marchés automobiles Français, Britanniques
et Nord-Américains. Les di¤érents concepts sont répertoriés et statistiquement contrôlés a…n
de répondre à deux questions : Quelles sont les interactions entre les automobiles neuves et
d’occasion ? Pouvons-nous utiliser ces interactions a…n d’estimer le prix de revente des véhicules ? Nos résultats indiquent que les relations entre les di¤érents marchés semblent limitées
en France et au Royaume-Uni, alors que le marché Nord-Américain est confronté à un mécanisme dit de ‘Scitovscky’. Dans tous les cas, les relations ne sont pas assez fortes pour expliquer
complètement les comportements des marchés.
xxii
General Introduction
"(. . . ) the real principle of the irreplaceable empirical research creativity : doing,
without knowing exactly what we are doing, gives the opportunity to discover, in
what we do, something we did not know."
P. Bourdieu, Homo Academicus, Les Editions de Minuit, 1984, p17.
The leasing industry appears as a little known area and a great business.
The International Accounting Standard for Leases, or IAS1719 , de…nes a lease as "an agreement whereby the lessor conveys to the lessee, in return for a payment or series of payments,
the right to use an asset for an agreed period of time". Legislation may be di¤erent across
countries, contracts can be adjusted to meet the needs of a customer, and any sort of good can,
in theory, be leased ; therefore, the term ‘lease’includes a large variety of contracts.
On the whole, a lease is a …nancial instrument for the procurement of an equipment. In a
leasing contract, a lessor provides equipment for usage on a de…ned period of time to a lessee
for speci…ed payments. The asset leased could be any kind of equipment (i.e. printers, trucks,
aircrafts. . . ) used by the lessee for business purposes. The lessor purchases the equipment and
has the legal ownership of the asset. To use the equipment the lessee makes periodic payments
throughout the contract to the lessor.
The entire Global leasing market20 was estimated to be more than $ 633 billion in 2006.
Europe and North America accounted for 41% and 38% of the world market. The ‘World
19
All listed companies in the European Union are obliged to adopt the International Standards. The equivalent
standard in the USA is FAS 13.
20
White Clarke Global Leasing report (2008).
xxiii
xxiv
GENERAL INTRODUCTION
Leasing Yearbook 2009’reported a total global amount of equipment leased to be more than
$ 760 billion for 2007. The European leasing associations reported a new leasing volume above
e 330 billion and a contribution to …nancing, on average, of 18% of total European investment
for 2008. Furthermore, leasing involved more than 16 million cars in Europe21 .
Broadly speaking, almost all academic contributions on the leasing subject are related to
the comparison of leasing over lending and purchasing. Researches can be divided into three
groups.
Firstly, some papers analyze tax advantages regarding the choice between leasing and regular
debt22 . The second group of academic articles discusses the ‘Leasing Puzzle’. Theories in Finance
and Economics suggest that leases and debt are substitutes ; an increase of leasing should lead to
a decrease of debt ; moreover, standard …nance theories manage cash ‡ows from lease obligations
as an equivalent to cash debt ‡ows. Ang and Peterson (1984) found empirically that lease and
debt appear as complements for companies. They argued that greater leasing is associated
with greater debt. They could not …nd a conclusive explanation and they called their …nding
the unsolved puzzle in Finance or the “Leasing Puzzle”. Following their seminal article, the
academic contributions have been numerous to reinvestigate the results23 .
The ‘Puzzle’leads to the third area of research covering every article related to the incentives and advantages of leasing. Lasfer and Levis (1998), for instance, rephrased the problem.
In theory, leasing provides no added value to the purchase of equipment when a lessee or a
purchasing …rm, lend or borrow at the same rate of interest, have a similar tax status and
expect the same resale price of the asset at the end of the contract. In practice, however, these
conditions are not satis…ed and there are several motives for leasing24 . For large …rms, their
study reveals that …nancial managers use leasing as an instrument to minimize the after tax
21
22
Leaseurope Association Website.
See Smith and Wakeman (1985), Brick, Fung and Subrahmanyam (1987), Mackie-Mason (1990), Goodacre
(2002).
23
See Marston and Harris (1988), Lewis and Schallheim (1992), Krishnan and Moyer (1994), Branson (1995),
Beattie, Goodacre and Thomson (1999), Yan (2006).
24
They listed three main motives for leasing : First, leasing can reduce …nancial taxes. Second, it could be
advantageous …nancially for distressed companies to get an agreement and access to the equipment because
lessors have …rst claims over the asset. Finally, leasing can reduce the agency cost because it does not constitute
an investment for the lessee.
xxv
cost of capital. For small companies, leasing appears as an opportunity for growth or survival.
They have di¢ culties to access the debt market and leasing facilitates the …nancing of …xed
capital formation. In other words, small companies with potential important growth rates or
low pro…ts are more likely to lease. As a consequence, without leasing many projects would not
have been undertaken.
Drakos and Goulas (2008) mention the uncertainty in entrepreneurship exacerbated by the
irreversibility of capital. By allowing the separation of usage to the commitment of equipment
ownership25 , leasing facilitates a possible disengagement in unsuccessful projects. Schmitt and
Stuyck (2002)26 , Schmitt (2003)27 and Schmitt (2004) demonstrate that leasing is a relatively
low risk activity and that Basel 2 requirement should be reduced for leasing contracts. All in
all, leasing appears as a safe …nancial instrument ; furthermore, leasing can reduce environmental problems28 . The practice of leasing products, rather than selling them, prevents waste
generation and creates a pattern of closed loop material use. For speci…c equipment and leasing
contracts, manufacturers become more aware of operating problems and cost management for
products at life end. Consequently, they may redesign their products accordingly. Staying in
a commercial channel, the equipment is less likely to be stored or discarded when it becomes
obsolete.
Besides the lack of elements on the subject, we should also highlight that leasing companies’
interventions create additional attractiveness. Leasing companies are not only intermediaries ;
their expertise produces a real added value in the leasing process. They select the appropriate
equipment based on its ability to improve the leasing cash ‡ow through various parameters
like equipment characteristics, economic life of the asset, taxes or residual value risk. Leasing
companies have also skills in …nance, credit, equipment acquisition and dealing. All things
considered, they facilitate the transactions between equipment suppliers and equipment users29 .
25
26
Capital heterogeneity would explain di¤erent choices of leasing by di¤erent degrees of irreversibility.
Schmitt and Stuyck (2002) analyzed defaulting leasing contracts issued from 1976 to 2000 in 6 countries and
originated from 12 major European companies and found that the recovery rate of defaulting leasing contracts
are comparable to senior secured bonds.
27
The estimation of the probability density function of losses and the standard portfolio credit value at risk
(VAR) measures in the leasing industry reveals a relatively low risk activity. See also Pirotte and Vaessen (2008).
28
See Fishbein, McGarry and Dillon (2000).
29
Among the numerous contributions related to the advantages of leasing, we could also mention Kichler and
Haiss (2009), showing the support of leasing in economic growth of central and Eastern Europe, as well as the
xxvi
For Leasing companies, the risk of loss on sales at the end of the contract term, as well as
the pricing, are critically impacted by the forecasted resale price of the asset.
In the thesis, we study a crucial challenge for the lessor : the residual value risk.
The three key parameters of a leasing contract are the original equipment price, the lease
period and the residual value. They drive the competitiveness and, at the same time, a risk
on the asset. The lessor has to set the end of contract market value of the equipment and the
residual value is a forecasted value of the asset. The three parameters mainly de…ne the level of
depreciation (which can be seen as the variance between the original equipment price and the
residual value all along the lease period) and the rental amount paid by the lessee to use the
equipment. The depreciation part of the lease payment (usually the larger component) can be
calculated by the total amount of depreciation divided by the number of periods30 . Additionally,
several features are included in the payments made by the lessee during the contract ; depreciation of the asset interests on the lessor investment, servicing charges (including operational
costs, insurance, counseling, repairs) and taxes. Figure A illustrates the mechanism involved in
the calculation of the lease payments31 .
thesis of Brage and Eckerstom (2009), comparing the incentives to lease in Sweden and Japan.
30
For instance, in an automotive lease contract with an original equipment price of $ 12000, a residual value
of $ 7200 and a lease period equal to 24 months, the monthly payment of the depreciation (excluding interest
rate and taxes) should be $ 200 per month ( 1200024 7000 ).
31
For simpli…cation purpose, we did not mention another key element : the end of term options. At the end
of the contract, there are options allowed to the lessee. Lease period can be extended ; lease can be renewed ;
the equipment can be bought or returned.
xxvii
Figure A : Depreciation in a leasing contract
Price - Residual Value
LeaseRental = ( Original Equipment
) + interestrates + taxes + servicing charges.
Lease Period
As a result, when the residual value increases, the variance with the original equipment
cost decreases, as well as the rental amount. A high residual value creates, for the lessee, an
opportunity to pay a lower amount for the usage of the equipment and therefore, for the lessor,
better competitiveness.
What makes the success of a leasing company can lead to di¢ culties when market conditions
change. The lessor faces the risk to not being able to recover su¢ cient capital value from the
resale of the asset, the residual value risk. As illustrated by Figure B, the fair market value
curve implies a gain on sale, or a loss on sale, depending on the level of residual value.
xxviii
Figure B : Fair Market Value of an Asset
So the lessor faces a dilemma ; the lower the residual value, the lesser the risk of loss on
sale, but the lower the residual value, the higher the rental payment and the worse the competitiveness. Conversely the higher the residual value risk, the better the competitiveness.
We bring an academic perspective to the practice of residual value risk management.
In a leasing company, the Asset Management department is in charge of the residual value
risk and forecasts how much the equipment will be worth at the end of the contract. For the last
seven years, I have been working in General Electric Capital Finance, one of the biggest leasing
companies in the world32 , on residual value analysis. Thanks to my European position, I meet
asset analysts across various countries and I have had some insight from the US, New Zealand,
Australia and Japan. I experienced a common situation for professionals in various areas : asset
teams reproduce operational processes, created by predecessors, and improved through trial
and error33 . There is a transmission of know-how, by applying minimum theory. As a matter of
32
33
Commercial Finance’s assets total was over $230 billion in 2008.
For instance the situation is similar in the …nancial derivatives industry. “Option hedging, pricing, and
trading (. . . ) is a rich craft with traders learning from traders (or traders copying other traders) and tricks
developing under evolution pressures, in a bottom-up manner.” Haug and Taleb (2009).
xxix
fact, few academic literature34 and few developed models are dedicated to residual value risk.
For instance, although the volumes involved are similar (Figure C)35 , structured …nance and
its vast growth attracted much more academic research than leasing.
Figure C : Volume of equipment leased in the world
Nevertheless, asset analysts did not wait for theory and academics to estimate residual
values. They have to propose a price in order to set a contract. Analysts are in a position of
practice with limited theory36 . As a general purpose, we aim to contribute to the rare literature
in the area, and accordingly to bring theory to the practice. The aim of any theory is to model
phenomena so that we can better understand and exploit them. The academic view adds a
theoretical control on tools and assumptions used by the specialists. Furthermore, it provides
an overview free of bias created by the inner position of the asset analyst.
A residual value analysis involves several elements including the characteristics of the equipment, the mix of the portfolio, and the depreciation curve. Consequently, we can bene…t from
diverse kinds of literature already in use in others area, like hedonic or macroeconomic models.
34
The rare contributions are listed in the second chapter.
Sources : White Clark Global rapport de leasing, World Leasing Yearbook 2009, SIFMA.
36
An explanation of the few academic studies could be that the leasing business is in the middle of …nance
35
and engineering. Equipment …nancing involves di¤erent areas of expertise : …nance and the industrial sectors
where it operates.
xxx
The empirical parts of the thesis focus on automotive leasing contracts. By and large, automotive constitutes a huge market providing numerous information. The high level of residual
value of cars at the end of the contract, by comparison with other types of equipment, increases
the probability of losses and represents a critical challenge for leasing companies.
Two kinds of auto lease contracts can be de…ned : short-term auto lease contracts include
cars (or trucks) rented to private or professional clients for a relatively short period of time
in order to meet their occasional transport needs ; in contrast, long-term auto lease covers
contracts for businesses outsourcing their vehicle ‡eet needs to a leasing company. In addition
to the necessary cars (or trucks) the leasing company usually provides various related services,
like maintenance, fuel management, and insurance. The thesis primarily focuses on long-term
auto leasing.
The thesis is divided into three chapters. In the …rst chapter, we discuss the valuation and
the depreciation of an asset : a car. In the second chapter, we propose a new way to hedge
residual value risk. In the third chapter, we study the relation between the new and the used
markets.
In the …rst chapter, we apply the Hedonic methodology to European auto lease portfolios,
in order to estimate the resale price distribution. The Hedonic approach estimates the price
of a good through the valuation of its attributes. Following a discussion on Hedonic prices,
we propose an operational model for the automobile resale market. The model is applied to
four European countries (France, Germany, Spain and Great Britain), and distributions are
calculated on two vehicle versions (Audi A4 and Ford Focus) allowing a comparison of market
depreciation patterns and residual value risks.
The second chapter proposes a model to hedge residual value risk using the Gaussian
copula methodology. After discussing residual value risk and credit risk models, a new derivative
product is introduced and analyzed ; the Collateralized Residual Value (CRV). The model
is applied to a European auto lease portfolio of Operating Lease contracts pertaining to a
major company. Our results indicate that the …nancial product is easy to customize, and to
implement through the contract characteristics and the level of correlation between the assets
of the portfolio. The second chapter is intended for people within the leasing industry interested
by an innovative …nancial product, as well as people from the …nancial market concerned by
xxxi
leasing risk opportunities.
Asset Management teams have to take into consideration macroeconomic factors impacting
the asset resale prices in the used market. The last chapter analyzes a crucial element of
the problem. The new cars of today are used cars of tomorrow and a competition is assumed
between new and used markets. There are numerous, pre-conceived ideas and academic theories
regarding the interactions between primary and secondary markets. We propose to go further
through a macroeconomic analysis of the French, the British and the US car markets. The
di¤erent concepts are listed and statistically evaluated. What are the interactions between the
new and the second-hand car markets ? Can we use the interactions to estimate the car prices
of tomorrow ? Our results indicate that the relations appear limited for France and the UK,
whereas the US market faces a Scitovscky mechanism. Furthermore, they illustrate that the
interrelations are not strong enough to fully explain and forecast market patterns.
xxxii
Chapitre 1
The European used-car market at a
glance
Hedonic resale price valuation in automotive leasing industry1
1
This chapter has been published in Economics Bulletin : Prado Sylvain M. (2009) The European used-car
market at a glance : Hedonic resale price valuation in automotive leasing industry. Economics Bulletin, Vol. 29
No.3 pp. 2086-2099.
1
2
CHAPITRE 1. THE EUROPEAN USED-CAR MARKET AT A GLANCE
1.1
Introduction
In the auto lease industry, a large part of the rent paid by the customer during a life contract
is the di¤erence between the list price and the residual value. The leasing company makes or
losses money depending on whether it accurately predicts the value of the asset at the end of
the contract (fair market value). If residual values are forecasted to be higher than what the
asset is actually worth at lease-end, then there will be a loss. At the opposite, if residual values
are forecasted to be lower, then there will be a gain on resale. The estimated resale price of
the car at the end of the contract term appears as a key component for the pricing, the risk of
losses and the reserve calculation2 .
Akerlof (1970) explained why used car valuation is so much lower than new car valuation.
The automotive resale market is a¤ected by something called the ’lemon e¤ect’. A used car has
the probability to be of a good quality or a bad one (i.e. lemon), and the uncertainty about
quality implies a price adjustment3 . The Akerlof theory helps to understand the large variance
of prices between new and used markets, but it does not propose a methodology to calculate
car depreciation.
Another way of looking at it is the Hedonic approach. The Hedonic theory provides solutions and estimates price-quality relation through a detailed calculation. A Hedonic model has
been originally proposed by Waugh (1928) on vegetable products and by Court (1939) in the
automobile industry. Hedonic models have been applied to a lot of commodities (mainly real
estate and automobile but also fruits or vine4 ). The automobile market itself has had di¤erent
applications (quality corrected price index5 , demand for fuel e¢ ciency, valuation of environmen-
2
This article is part of a general study on resale market hedging (Prado, 2008). We aim to estimate the
distribution of the resale price in order to include the depreciation behavior in a derivative product.
3
In the resale market, there is an asymetry of information ; the car owner has a better knowlegde of the
probability of bad lemons. If Second hand vehicles were valued like as new vehicles, then it would attract lemons
(lemons’sellers would have the opportunity to sale their vehicles and buy a new one on the new vehicle market)
and it would create an arbitraging opportunity. Akerlof used the automotive market as a best illustration and
extended his idea to other markets (the cost of deshonesty...).
4
Combris, Lecoq and Visser (1997).
5
Cowling and Cubbin (1972) and Van Dalen and Bode (2004).
1.1. INTRODUCTION
3
tal and safety demand6 , test of the Akerlof e¤ect7 , behavior of the automobile market through
price quality and competition8 ...). The main point underlying this paper is to apply the Hedonic methodology to estimate the resale price distribution of cars in a leasing perspective. The
…rst chapter is intended for people within the leasing industry intersted by residual value risk
management, as well as academics concerned by a comparison of European markets.
We propose a methodology for operational applications to estimate the distribution of resale
price. To this end, we apply a Hedonic model (a method of estimating value through constituent
characteristics of the asset) on historical information from a major leasing company9 . Further
to this, we estimate a value according to vehicle characteristics and country singularities. Resale
price distributions of two vehicles (Ford focus C-max, Audi A4) are calculated in various European markets (France, Germany, Spain and Great Britain). The chapter is organized as follows.
Section 2 discusses the Hedonic theory underlying our model. In section 3 some meaningful
characteristics of the model are exposed. Section 4 presents our approach. Section 5 estimates
the distributions and analyzes the results, …nally. Section 6 concludes.
6
Atkinson and Halvorsen (1990).
Couton, Gardes, and Thepaut (1995).
8
Cowling and Cubbin (1971) and Cubbin (1975).
9
In Europe, statistics on resale prices are not as abundant as in …nancial markets and leasing companies
7
often have to use internal data to forecast the market value. External information is usually not available on
line, costly and time consuming to collect. Morevover, there is a non homogeneous information and format by
country. Therefore we use the internal resale information (GE resale data warehouse).
4
1.2
The Hedonic theory underlies our model
The section discusses the Hedonic model approach, identi…cation issues and automotive
assets speci…cities.
1.2.1
Goods attributes constitute the Hedonic theory.
To explain consumer behavior, Lancaster (1966) assumes that consumers get utility from
goods attributes10 . Assuming that a car is the only good involved in the activity consumption
of driving, it produces a …xed vector of attributes and the level of activity is a scalar associated
with the vector (the relationship could be linear). The driver chooses a combination to maximize
his utility function according to the characteristics of the goods under a constraint budget.
Inspired by Lancaster (1966), Pickering et al(1973) added an empirical perspective to the
approach by conducting a survey in the UK. Following their results, they de…ned …ve groups of
commodities (utilities, luxuries, leisure goods, central heating and automotive) and identi…ed
eleven characteristics as signi…cant discriminators between groups. The principal attributes
desired by car buyers were comfort, durability, economical, manoeuvrability, performance safety
and style. They acknowledged that products and attributes may change groups through time
because of product life cycle, di¤erent tastes between consumers, the growth of the market
penetration (i.e. luxuries becoming utilities), complementarity or substitutability of goods11 .
They also …gured out that it could be relevant sometime to disaggregate a group (i.e. cars by
makes).
The Hedonic model assumes that goods are valued for their utility-bearing attributes or
characteristics. In 1974, Rosen12 developed the framework of Hedonic models. The theory describes cars by n measurable characteristics (oil consumption, car size, power, technology...) and
a vector Z(= z1 ; z2 ; :::; zn ) with zi measuring the amount of the ith characteristics. The exis10
Similar attributes or characteristics could be shared by di¤erent goods. Usually goods have several charac-
teristics, and a combination of goods may have attributes di¤erent to goods used separately.
11
We could also add the technology obsolescence to the list.
12
See Appendix A1.
1.2. THE HEDONIC THEORY UNDERLIES OUR MODEL
5
tence of product di¤erentiation implies that a wide variety of alternative packages, completely
described by numerical value of z, are available. Buyers and sellers locate in a spatial equilibrium. On one side, the consumption decision is made by a maximization of utility. On the
other side, the production decision is made by minimizing factor costs subject to a joint production function constraint relating to the number of units and factors of production. A price
p(z) = p(z1 ; z2 ; :::; zn ) is de…ned at each point on the plane. Both consumers and producers
are guided by prices through packages of characteristics bought and sold. Observations of p(z)
represent a joint envelope of a family of value functions and another family of o¤er functions.
At equilibrium, buyer and seller are perfectly matched when their demand and o¤er functions
meet at eye level.
The approach consists in estimating the following model :
P i(z) = F i(zi ; :::; zn ; y1 ) (demand)
P i(z) = Gi(zi ; :::; zn ; y2 ) (supply)
P i(z) is the implicit market price for attribute zi , y1 and y2 are vector of exogenous demand
shift variables and a vector of exogenous supply shift variables, respectively. At equilibrium,
market quantity demanded for products with characteristics z, (Qd (zi )) is equal to market
quantity supplied with those attributes (Qs (zi )). A P (z) function has to be found to make this
equality possible. Unfortunately, di¤erential equations for setting (Qd (zi )) = (Qs (zi )) are not
linear in most cases and closed solution are not always possible.
1.2.2
An identi…cation problem appears in Hedonic models.
There are identi…cation problems in the Rosen model : if p(z) is non linear, it may not be
possible to …nd closed solutions. A lot of conditions must be imposed and partial di¤erential
equations must be solved when there is more than one characteristic. Rosen believed that the
form of the Hedonic function is an empirical matter and developed an empirical methodology to
estimate demand and supply parameters (if no explicit solution for the Hedonic price function
is available). Rosen solved the "garden variety identi…cation problem" by simultaneous identi-
6
…cation methods like 2SLS : p(z) is estimated by regressing all observed di¤erentiated product
prices p on all their characteristics, z, using the best adaptable function. The estimated prices
are then included in the complete formula as endogenous variables. Later, Brown and Rosen
(1982) showed that this technique is not always possible (it still requires prior restriction on
functional form)13 .
But Bartik (1987) argued that the econometric problem of estimating Hedonic demand
parameters is not a standard identi…cation problem caused by demand-supply interactions :
because a consumer decision cannot a¤ect an Hedonic function, it does not a¤ect the supplier.
He pointed out another identi…cation problem : the Hedonic price function is not linear and the
consumer can endogenously choose both quantities and marginal prices. Formulated through a
characteristic bid equation14 it highlights the impact of consumer traits.
Let
@p
(Zi )
@zj
be the estimated Hedonic marginal price of characteristics zj = Wij , where Zi
denotes a vector of observed characteristics of the product and Wij a consumer marginal bid
for zj :
@p
(Zi )
@zj
= b0 + b1 Zi +b2 Xi +bD0i +eij .
Xi is consumer expenditure on commodities others than Z. D0i is a vector of observed
demander traits a¤ecting the marginal bid. eij is a disturbance term.
It becomes
@p
(Zi )
@zj
= b0 + b1 Zi +b2 Xi +bD0i + Dui +rij .
Dui is an unobserved taste component form. rij is a random component and rij + Dui = eij .
Therefore Zi and Xi are correlated with unobserved tastes in the residual, leading to biased
results (equivalent to di¤erent population of consumers).
In Bartik’s article, the identi…cation problem is caused by the endogeneity of both prices
and quantities when households face a nonlinear budget constraint (the distribution of income
13
Ekeland, Heckman and Nesheim (2004) reconsidered the identi…cation and estimation of the hedonic model. They show that most of empirical studies are based on arbitrary linearisation. Two
new estimations procedures are proposed : a non parametric transformation method and instrumental
variables in a general nonlinear setting.
14
See Appendix A1.
1.2. THE HEDONIC THEORY UNDERLIES OUR MODEL
7
follows no simple law through its range making it di¢ cult to specify the problem entirely). An
instrumental variable solution is suggested and applied (household example with addition of
budget constraint). The implicit market price is estimated by regressing all observed di¤erentiated product prices p on all their characteristics by group of modality of Dui
15
. We follow on
the Bartik critic in our analysis and propose a solution to manage the unobserved taste issue
in Section 3.
1.2.3
Used cars are durable commodities.
Berndt (1983) provided general frameworks on Hedonic prices for durable goods. Assuming
that the asset price of the nth capital good of vintage
at time t is equal to the present value
of its future services, we have :
s=T
n
P
qn;t; =
s=0
s
1
1+r
Vn;t+s;
+s
where Tn is the life time of the asset, r the interest rate, Vn;t; the value of the asset at
time of the ‡ow of services of the nth capital good of vintage . Berndt demonstrated that the
Hedonic price equation can be expressed in terms of service prices in a single equation16 .
This concept has been used originally in the second-hand automobile market analysis by
Akerman (1973), who produced one of the …rst study on the rapid used car falling prices. The
price of an automobile is evaluated as the discounted present value of its remaining services. The
Akerman model included a Hedonic price, a repair cost, a service function and an expected gain
on resale estimation. Akerman used a single equation and a regression to estimate the Hedonic
price17 . Ho¤er and Pratt (1990), inspired by Akerman approach (the price of a resold vehicle
as an implicit rental cost of holding a s year old automobile, including also automotive price
less market price of interest) proposed a simpler model. A single equation, where depreciation
declines with age at constant exponential rate, includes technological obsolescence, di¤erential
repair record and fuel e¢ ciency as shift variables. The depreciated value (s; t) of an s-year old
machine in year t is
15
Bartick made an adjustment by group of cities.
See Appendix A2.
17
See Appendix A3.
16
8
ln( (s; t)) = A
b1 s + b2 tech + b3 maint + b4 EP A:
tech = 0 if the vehicle is not discontinued. maint = 1 if the maintenance expenses are
greater than average and EP A is a fuel e¢ ciency indicator.
All along the referenced studies, methodology moved from a remaining service approach to
a Hedonic model including essentially the vehicle characteristics (physical or not). We acknowledge the "remaining service approach", however we believe that vehicle characteristics contain
most of the information. As a consequence, we adjust the resale price from in‡ation and we set
a statistical model mainly through variables related to the vehicle characteristics.
1.3
Some characteristics of the model are discussed.
The model construction brings comments and discussions : The used market is (i)demand
oriented and (ii)correlated with fuel price ; (iii)Multicollinearity is a critical issue in Hedonic
calculation ; (iv)We have to choose a functional form, and (v)Heteroscedasticity impacts the
model speci…cation.
1.3.1
Coe¢ cients interpretation depends on used market substitution to new market.
Berndt (1983) pointed out an argument against the Rosen identi…cation problem for the used
market : under speci…c conditions, equation parameters can be directly interpreted as re‡ecting
demand (rather than cost or supply) and there is no identi…cation problem. If the supply curves
of products are perfectly inelastic, then the market demand and supply curves would intersect
at di¤erent levels of each combination of characteristics. The structure combination would be
determined by the demand. The di¤erence of price level among products could be interpreted
unambiguously as providing implicit measures of consumers’ evaluation of the characteristic
combinations. So coe¢ cients of the equation are well identi…ed, as well as estimates of the
demand function parameters. Because the total quantities are …xed (assuming that there is
1.3. SOME CHARACTERISTICS OF THE MODEL ARE DISCUSSED.
9
a non signi…cant link with new market), the equation only re‡ects demand in the used car
market.
Hartman (1987) results validate that an application to the resale market avoids the identi…cation problem. If the supply of the attributes embodied into used cars is almost perfectly
inelastic, he states that simultaneity should not pose a problem in recovering Hedonic demand
and supply parameters in new product market. If the simultaneity is important, di¤erent assumptions about quantity of each make and model sold should generate di¤erent parameter
estimates. Therefore the only question is : are the parameters statistically and economically
signi…cant ? In his analysis, the resale value calculation was very robust to alternative sales assumptions. Hartman applied a single equation model18 to estimate the e¤ect of product recalls
on resale prices and …rm valuation.
Two main conclusions can be stated : All referenced automotive studies use single equation
techniques, and remarketing professionals usually believe in a substitution relation for young
resale automotive market only which is a situation where demand and supply characteristics
are quite similar. Therefore we apply a single equation and we exclude short term duration (less
than 12 months age) vehicles.
1.3.2
Others products interact with price.
De…ning a framework on the demand analysis, Berndt (1983) discussed the input pricedependent quality adjustment case : the quality of a good (i.e. fuel e¢ ciency) is dependent on
the quantity (or price) of another good (i.e fuel price). Berndt states that we could test the
dependent19 (or independent) price hypothesis using classical testing procedures (i.e. economical
and statistical signi…cance of fuel price on auto price). Fuel price has a signi…cant part in the
total cost of automobile usage, and then monthly fuel price constitutes our model.
18
19
See Appendix A4.
See Appendix A5.
10
1.3.3
Multicollinearity is a main issue in Hedonic models.
The econometrician walks between the two following risks while he selects the relevant variables for an Hedonic estimation : correlated explanatory variables and trickle down hypothesis.
In the automotive area, physical characteristics are often correlated (i.e. four wheels correlated to fuel capacities). According to the Gauss Markov theorem, OLS has the smallest variance.
However, if explanatory variables are correlated, then small change in the data produces wrong
sign, implausible magnitude and wide swings in parameter estimates
20
. As a consequence, pa-
rameter correlations present a major issue for forecast applications. The simplest solution is
to exclude variables at risk (i.e all variables related to the engine power, number of cylinders,
kilowatt, fuel consumption, fuel capacity...) in the case of non economical signi…cance21 .
Triplett (1969) highlights another problem. Because a small amount of variables is able
to explain most of the variance (i.e. the weight of the vehicle correlated with engine power
and price), there are some risk of biases in the Hedonic model and a substantial number of
innovations are missed throughout this ’trickle down’hypothesis.
Therefore, the selected parameters of our model cover four axes of depreciation e¤ects :
the level of usage, the original equipment cost, the market interactions and the pure physical
characteristics of the vehicle.
1.3.4
Which functional form ?
Rosen (1974) states that the functional form is an empirical matter. In the same logic,
Grilitch and Otha (1976) choose a semilogarithmic form for their regression because ’it provided
a good …t of the data’. Most of the literature suggests the log form, others studies apply the
20
But it also produces instability of coe¢ cient and higher standard errors, R2 quite high, coe¢ cient with high
standard error and low signi…cance levels (even if signi…cant). See Greene (2003) chapter 4 p57.
21
An advanced solution is the ridge regression estimator or principal component methodology. The problem
is that we lost visibility on coe¢ cients meaning.
1.3. SOME CHARACTERISTICS OF THE MODEL ARE DISCUSSED.
11
log-log form22 , and the Box Cox test23 has also been used to compare several functional forms.
The Hedonic functional form problem constitutes a great discussion but it is not the main
purpose of the chapter.
We followed the Grilitch and Otha position (1976) (’a good …t of the data’) and empirical
results lead us to the linear form of Cowling and Cubbin (1972). Their linear model includes
multiple physical variables like horse power and length and to allow approximation to a non
linear form, square transformation, cubic transformation and log transformation were applied
to exogenous variables. Interactions terms were also included.
1.3.5
Unobserved tastes create heteroscedasticity.
As previously mentioned in Bartik’s critics24 , because the choice for the studied commodities
quality and other commodities is correlated with unobserved tastes in the residuals, then an
heteroscedasticity issue appears. If residuals from the economic relation do not have constant
variance, the model is not biased but the variance increases. Bartik states that any variable
that exogenously shifts the budget constraint of the buyer will be an appropriate instrument :
the budget constraint shift is correlated with the buyer choice of car attributes and the choice
of other products yet uncorrelated with unobserved tastes.
We follow Bartik’s approach including the index of industrial production25 as a proxy of
the economic situation of the buyer (we propose a temporal budget constraint shifter). Because
most of buyers are professionals impacted by a market seasonality, we include a seasonality
variable on a quarterly basis. Finally, in order to manage unobserved characteristics (i.e. brand
name perception and reputation...), we also insert a manufacturer e¤ect
26
.
22
See Hogarty (1975).
See Atkinson and Halvorsen (1990), Van Dalen and Bode (2004).
24
See Section 1.2.2.
25
Excluding energy and construction.
26
We do not work with a model car type level, because our goal is to apply a methodology ‡exible enough
23
to include new cars and non exhaustive data. Moreover, our model does not include the life cycle of vehicles
(’honey moon’e¤ect for new models...) because of the di¢ culty to collect and to standardize the information. In
the list of unobserved characteristics, there is also the remarketing performance. The value could be impacted
by the remarketing team in charge of the resale process. Finally, we do not include macroeconomic impacts
12
1.4
We use the Hedonic model to estimate the distribution of resale price.
We apply the straightforward regression approach of Otha and Grilitch (1976). Removing the
impact of uncertain variables and using the classical OLS properties, resale price distributions
are calculated.
1.4.1
Ohta and Griliches have an empirical approach.
Regarding theoretical issues (including the one discussed in Sections 2 and 3), Ohta and
Griliches state that Hedonic model usage ’has an air of "measurement without theory", but
one should remember the limited aspirations of the Hedonic approach and not confuse it with
attempts to provide a complete structural explanation of the events in a particular market’27 .
They exposed a strong empirical criterion for hypothesis testing28 . They included a make e¤ect
as a proxy of unmeasured characteristics. A real e¤ect linked to unmeasured physical characteristics and a putative one (linked to prestige, service availability...) constitute the make
e¤ect.
In their model, the price of model k of make i and age s at time t is
P
Pk;i;t;s = f ct(Mi ; Pt ; Ds ; e
aij xkivj
)
with Mi the e¤ect of the ith make, Pt the pure Hedonic price index at time t, Ds the e¤ect of
age s (depreciation). aij are parameters re‡ecting the imputed price of physical characteristic
(which need a proper analysis). Therefore unobserved e¤ects mentioned above constitute the random variable
of the statistical model.
27
Ohta and Griliches (1976) p326.
28
"The rejection or acceptance of an hypothesis should depend on the researcher’s interests and his loss
function"(p 339). Grilitch and Otha put in perspective the statistical and economic signi…cance. Instead of
following a formal Fisher test, they use the di¤erence in the standard errors of the unconstrained and constrained
regressions as a relevant measure of the price-explanatory power of a particular model. They do not reject null
hypothesis if di¤erences between the standard errors of the unconstrained and constrained regressions are less
than or equal to 0:01.
1.4. WE USE THE HEDONIC MODEL TO ESTIMATE THE DISTRIBUTION OF RESALE PRICE.13
j at time t. xkivj is the level of the physical characteristic j embodied in model k of make i and
vintage v (v = t
s).
They applied their models on new and used cars and tested di¤erent hypotheses29 (i.e
geometric depreciation held separately from makers). Otha and Grilitch approach is now a
standard. As a consequence, Yerger (1995) used this method to discuss an article written by
Ho¤er and Pratt (1990) which was inspired by Akerman approach30 .
Following these authors, our approach is mainly empirical. We select the model structure
that best …ts to reality and choose exogenous variables with a statistical and economic signi…cance.
1.4.2
Statistical models are slightly di¤erent by country.
Our analysis includes four countries (France, Germany, Spain, Great Britain) and we de…ne
a model for each of them31 . The real resale price is explained by a …rst group of variables
indicating the level of usage : age and mileage are in logarithm due to the well known non
linearity property of car depreciation. An indicator of usage intensity, the mileage per month,
is also included and signi…cant. The second group of variables is related to the list price. A
cubicle variable of list price is added (high initial price increase devaluation). The make e¤ect
is introduced through a dummy variable of manufacturer multiplied by the list price. Variables
bringing market information contitute the third group : the diesel pump price, the industrial
production index and the quarter sale date. The last group includes pure physical characteristics
that are slightly di¤erent from a country to another (average fuel consumption, body type,
number of seats, engine power, number of cylinders, automatic transmission, number of doors).
29
Their results on the US market are worth to mention : no gains to move to performance variables (so we can
only use the vehicle characteristics) ; geometric depreciation is an adequate approximation but it is not constant
accross time and manufacturers ; New and used car market can be analysed jointly. Unfortunately, because of
the rise of fuel cost (1973) they aknowledged that their analysis was already obsolete.
30
See Appendix A6.
31
See models details in Appendix B.
14
1.4.3
We estimate the distribution of resale price.
We wish to calculate the distribution of y0 (the resale price) for a regressor vector x0 (group
of variables explaining the resale price). The usual regression formula is y0 = a0
b0 x0 . X and
y0 denote the full data matrices. b0 is the coe¢ cient vector.
We assume32 that y0 follows a normal distribution33 equal to
N (xT0 b0 + e; s2 [1 + xT0 (X T X) 1 x0 ]).
The con…dence interval is calculated with
xT0 b0
1.4.4
t=2(n
p 1)
p
M SE[1 + xT0 (X T X) 1 x0 ]1=2 :
An adjustment removes uncertain variables e¤ects.
All the exogenous variable values are known with certainty34 , except the fuel pump price
and the production distribution index. We aim to remove the product interaction e¤ect (Dp)
and the temporal budget constraint (Ip) in order to focus on the vehicle valuation. Assuming
that the diesel price and the production price follow a normal distribution, we calculate the
mean and the variance from 2004 to 2008 and we estimate a risk neutral distribution of the
resale price.
The unconditional resale price distribution of xT0 be0 can be solved as
N[
1
R 1
R
m(x0 =Dp; Ip) g(Dp) j(Ip) dDp dIp;
1 1
32
1
R 1
R
n(x0 =Dp; Ip) g(Dp) j(Ip) dDp dIp]
1 1
Data are composed of subgroups by models, age, mileage and physical vehicle characteristics. Normality
hypothesis test are possible on subgroups with a signi…cant amount of data. For models with same age and
mileage, H0 is not rejected. The test of normality on the two analyzed vehicles (Ford focus and the Audi A4)
is not rejected.
33
See Appendix A7.
34
We limit our analysis to …xed contract with no purchase option and no rewrite, therefore age, mileage and
sale dates are known with certainty.
1.5. WE APPLY THE METHODOLOGY TO FOUR EUROPEAN COUNTRIES.
15
Where m() = xT0 b0 + e
and n() = s2 [1 + xT0 (X T X) 1 x0 ].
g() and j() are the probability density of the fuel pump price and the production distribution
index.
The integrals are calculated with numerical integration.
1.5
We apply the methodology to four European countries.
Models by country, regression results and graphical illustrations, through two vehicle versions, provide an insight of European markets.
1.5.1
Models are created according to the information usually available in the leasing industry.
In order to quantify the Hedonic price, we apply the model to four European markets
(France, Germany, Spain, and Great Britain35 ) using internal sales data from January 1st 2004
to December 31st 2008 of a major leasing company. Statistics are based on random samples of
cars sold in various channels (auction, dealers, private sellers, etc). Vehicle age samples range
from 1 to 10 years, and have mileage ranging from 1,000 to 400,000 km. As expected for leasing
companies resale statistics, a concentration of vehicles with high mileage and short age spans
(concentration on 24, 36 and 48 months of age with a mileage between 80000 km and 120000
km) constitutes a large part of our sample. All monetary values (sales prices, diesel prices) are
adjusted according to the in‡ation. We aim to create a tool allowing a leasing company to catch
35
Great Britain has a sterling pound currency and very limited cross bordering sales with others european
countries because of the right hand side weel of the car. Therefore, GB statistics add an original perspective of
european markets analysis.
16
all the available Hedonic information of the car activity from it’s historical sales. According to
the company position in markets, the amount of data is signi…cantly di¤erent by country but
su¢ cient for calculation (Fr : 112,875 units, Ger : 7,398 units, Sp : 14,674 units ; Gb : 33,506
units). Contrary to some referenced studies applying the Hedonic model to the car market,
we do not limit our analysis to a segment or version of cars. As a consequence, the explained
variance (R2 ) is slightly lower (and even more to applied studies on the much more stable new
car market). To estimate the manufacturer e¤ect, statistics include several manufacturer names
(Fr : 9, Ger : 4, Sp : 6, Gb : 8) by country.
1.5.2
The regression provides a Hedonic price assessment of the
European markets.
All variables have a signi…cant economic value36 . The explained variances of the OLS regressions are between 0.75 and 0.8. Characteristics adding quality to the car (engine power,
number of seats, etc) as well as the industrial production index (as a proxy of budget variation)
have a positive sign. According to the Hedonic theory, the price of fuel is an additional cost
of the driving activity and has therefore a negative e¤ect. The variables of age, mileage and
usage intensity (mileage per month) reduce the resale price, there are parameters correlated to
obsolescence and wear. A slight seasonal e¤ect exists in all markets. The well known and better
valuations of German manufactured cars (positive make e¤ect) are veri…ed in all countries.
1.5.3
The analysis on Ford focus and Audi A4 give additional informations.
France, Germany and Spain share the same currency (Euro) and results estimate the resale
price distribution of a vehicle, according to the amount of information available from historical
sales. The samples of the four countries have two manufacturers in common : Audi and Ford.
We choose the characteristics of the Ford Focus (C-max 1800 TDCI 115 Ghia 5P) and Audi
36
See models results in Appendix C. An indicator of automatic transmission was tested and statistically
signi…cant for France. Because the coe¢ cient sign was negative, we removed it.
1.5. WE APPLY THE METHODOLOGY TO FOUR EUROPEAN COUNTRIES.
17
A4 (1.9 Tdi 130 Pack 4P) as a basis to compare the four markets. The information provided
by the model could be summarized by two elements. On one hand, a higher valuation of car at
the end of the contract reveals better opportunities for leasing business. On the other hand, a
higher volatility implies uncertainty on the resale price, and therefore a higher risk of loss on
sale.
Bucket results : A …rst analysis approach37 on the bucket of a 36 month age group, and
90000 kilometers emphasizes three points. First, the Audi A4 has a better valuation than the
Ford Focus in every country. As mentioned previously, German cars bene…t from a ’positive
make e¤ect’; they are objects of prestige and share a reputation of good quality cars. Secondly,
the high level of standard deviation in all markets reveals a huge volatility. Acknowledging that
the second hand market is not as liquid as a …nancial market, it illustrates that a car, as an
asset in a balance sheet of a company, constitutes a signi…cant risk. Thirdly, in Germany, cars
get a better valuation. A high resale price constitutes a good element for a leasing business ;
however the German market also has a higher standard deviation, and therefore a higher risk
of loss on sales.
Graphical results : The graphics of distribution through age and mileage give an additional perspective of the depreciation38 . The variance is not economically di¤erent when we modify
age and mileage parameters (whatever the currency, the age and the mileage, the standard deviation does not exceed two Euros). Age and Mileage do not increase the volatility. Regarding
average depreciation, German vehicles are highly correlated with mileage, but Spanish cars are
not. Surprisingly, the graphical analysis of age impact on vehicles, reveals that British cars
are heavily impacted by the level of usage (kilometer per month variable coe¢ cient) and as a
consequence, 12 month age vehicles have a resale price equivalent to 24 age month vehicles.
The last two points indicate that Hedonic valuations are signi…cantly di¤erent by country. European markets are not homogeneous, and residual value distributions are always singular. On
a business perspective, leasing contracts would be impacted by country speci…cities.
37
38
See Appendix D.
See Appendix E.
18
1.6
Conclusion and extensions
The Hedonic theory has been widely used for the automotive market analysis. We discuss
and propose an application to second-hand vehicles in the leasing industry, where the residual
value is a critical parameter (residual value risk). The model is based on attributes in order to
estimate the resale price distribution. A product interaction e¤ect (fuel price), and a temporal
budget shifter (industrial production index) are also included. The methodology applied to four
European countries provides a perspective of the automotive resale markets. Focusing on the
pattern of depreciation of two vehicles (Ford Focus and Audi A4), the approach illustrates the
di¤erent levels of probability of losses according to the resale information available by a leasing
company. The approach also allows the comparison of market opportunities, through pricing
analysis and risk. Our study can be extended in several ways. The leasing industry includes all
types of equipment and the application of the Hedonic valuation would be ‡exible enough to
be extended to assets other than automotive. Moreover, our analysis could also be extended
to contracts with a purchase option or a rewrite option on age and mileage (i.e. customers can
choose to extend or interrupt their contract(s)). Two other elements in the area of residual
value risk should be included to complete the analysis : the vehicle life cycle impact and the
macroeconomic impact (the general market depreciation). The macroeconomic element would
need a more thorough study.
1.7. APPENDIX
1.7
1.7.1
19
Appendix
Appendix A : Methodological aspects.
A 1 : In Rosen Hedonic framework, we can de…ne the marginal price on a characteristic
level. For any vector of observed characteristics Z (of the car), the Hedonic marginal price
for a characteristic z (i.e. fuel consumption) is an estimate of both the marginal bid for z
of the household purchasing Z and the marginal o¤er for z of the …rm producing z. Linear
version of these marginal bid and marginal o¤er function are de…ned through two equations :
Estimated Hedonic marginal price of characteristics
p
(Zi )
zj
= Wij consumer marginal bid for
zj = B0 + B1 Zi (vector of observed characteristics of the product) +B2 Xt (consumer expenditure on commodities others than Z) +B2 D0i (vector of observed demander traits a¤ecting the
marginal bid) +eij .
p
(Zi )
zj
= Gij …rm marginal o¤er price for zj = Ao + A1 Zt + A2 S0i (vector
of observed supplier traits a¤ecting the marginal o¤er) +uij :uij and eij are disturbance terms.
A 2 : Berndt de…nes general framework on durables commodities in term of service price.
He demonstrates that in the case of the input price-dependant quality adjustment ("variable
repackaging hypothesis") the Hedonic price equation can be expressed in term of service price
as :
ln un;t; = lnpn;t + ln h0n (zn1 ; zn2 ; :::; Znk ; pn 1 ) + lnDn; :
With un;t; the resulting asset price, lnpn;t is the quality adjusted "base" price index of the
nth capital good at time t, Dn; is a depreciation index varying only with the age of the asset.
hn is the quality aggregation function that link the quality bn to the physical characteristics zn .
b0n = hn 0(zn1 ; zn2 ; :::; znk )
Tn
P
s=0
1 s
( 1+r
) dn;s : dn;s is the deterioration of the service over time. The
intercept is the quality adjusted service price.
A 3 : Akerman model estimates used car value.The price of an Automobile of a given age, K, can be expressed as the discounted present value of its remaining services :
20
P (K) =
RD
K
S(X)e
r(X K)
dX with K present age of car, D age of scrappage, X age, r discount
rate(assumed constant), S(X) value of services provided by a car of age X, P (K) price of a
car of age K.
An Hedonic price, repair cost, service function and expected gain on resale estimation are
components of the model. Akerman use a single equation and a regression to estimate the
Hedonic price :
logA(v; m) = C + E(v; m) + C(v; M ) + W (v; M ) + L(v; M ) + H(v; M )
With A(v; m)=new car list price including federal tax and handling and transportation
charges. E(v; m)=1 if car has height cylinders. C(v; M )=1 if compact. W (v; M ), L(v; M ) and
H(v; M ) are weight, length and horse power. v is model year and m is the model.
A 4 : Hartman Equation inspired by Grilitch and Otha equation :
LogP kit = Bo + B1 M Ki + B2 M Dk + B3 AGEs + B4 jAkij + B5j Rjk
P kit is the resale price in period t for a car of make i and model k.
MKi and M Dk are dummy variables indication Make and model. Age is the age of the car
in t. Akij is the level of attribute j embodied in model k and make i. Rjk summarize the car
recalls history indicating cumulative recalls of type j for model k.
A 5 : Berndt de…nes a general framework on commodities.
X(= x1 ; x2 ; :::xn ) a vector of commodity, B(= b1 ; b2 ; :::; bn )a vector of qualities for each
commodity, Z(= z1 ; z2 ; :::; zi ; zn ) a vector of physical characteristics for each commodity and
P (= p1 ; p2 ; :::; pn ) a vector of price for each commodity. Moreover we have an utility function
u = F (x; b) and Bn = Hn (Z).
As a result, we have xn = f (u; x1 ; x2 ; :::; xn 1 ; bn )
For a new quality level from bn0 to bn1 under the assumption of a log-log form ;
1.7. APPENDIX
21
In the case called the "simple packaging hypothesis" (or input price-independant quality
adjustment), bn is only dependant of zi , we have a quality function bi = hi (zi ) ;
xn must be equalized at the margin :
pn0
pn0
=
pn1
pn1
= pn
where pn is a base price constant re‡ecting the price of the standardized unit.
Through a log transformation of 1), then lnpn1 = lnpn0 + lnhn1 (zn1 ) and an assumption of
k
P
bnk ln zn1;k :
log-log form of the quality conversion function lnhn1 (zn ) =
k=1
lnpn1 = lnpn +
k
P
bnk ln zn1;k where bnk are the coe¢ cient on the k th characteristics of the
k=1
nth commodity.
Using this framework we are now able to calculate a price according to the physical characteristics of a commodity.
In the case called the "variable packaging hypothesis" (or input price-dependant quality
adjustment), for instance if bn is dependant of xn 1 as well ; bn = hn (xn
1; zn )
:
lnpn (bn ) = lnp0n + lnhn (pn 1 ; zn )
Using this formula, in an empirical analysis, we could test the simple versus the variable
repackaging hypothesis using classical hypothesis testing procedures. (i.e. fuel price on auto
price).
A 6 : Yerger(1995) applied Grilitch and Otha method to discuss an article written by Ho¤er
and Pratt which was inspired by Akerman approach.
For a model i and at trend variable, time t ((t = 1; :::; 12), the price P it is
LogP it =
0
+
1
t+ j
2 jCAT j
+ k
3 kAik
+
4 T ECH
+
5 RECOM
+
6 AV
OID
with CAT j as a variable of the category of vehicle (subcompact, midsize....) and Aik as a
22
vector summarizing the level of attribute k in model i. If the vehicle is not discontinued then
tech = 0. If the vehicle have been recommended to buy then RECOM = 1. If recommend
to avoid to buy by ’consumer reports’magazine evaluation then AV OID = 1. By his model,
Yerger tested and approved the market e¢ ciency in Automotive market.
A 7 : Ordinary Least Square allows prediction interval calculation39 .
The Ordinary Least Square Method estimate a and b by minimizing the sum of squared
nP
n
P
error SSE =
(yi yei )2 = (yi a bxi )2 = e2
i=1
i=1
An unbiased estimate s2 of e2 is given by mean squared error :
s2 =
SSE
n p
=
1
nP
n p
i=1
(yi
ae
be Xi )2 = M SE. ae and be denote the linear least squares
estimators for a and b. n is the size of the sample and p the number of parameters.
Distribution and interval calculation :
Let x0 = (1; x1 ; x2 ; x3 ; :::; xp ) ; b0 = (a; b1 ; b2 ; b3 ; :::; bp ) and be0 = (ae ; be1 ; be2 ; :::; bep )
Y j(X = x0) = xT0 b0 + e0 :e0 is the random error corresponding to the new estimation Y and
e0 ~N (0;
2
):
We use xT0 be0 to estimate xT0 b0 + e0 :
The distribution of xT0 be0 is N (xT0 b0 + e; s2 [1 + xT0 (X T X) 1 x0 ]) and the interval is xT0 be0
p
t=2(n p 1) M SE[1 + xT0 (X T X) 1 x0 ]1=2
1.7.2
Appendix B : Regression equations and notations
Resaleprice = f ct1 (age; mileage; mileagepermonth) + f ct2 (make
listprice; listprice) +
f ct3 (pump_price; industrial_production_index; sale_date)+f ct4 (car_physical_attributes):
39
Green (1992) Econometric analysis. 5 th edition. p 111.
1.7. APPENDIX
23
France :
P =
7
0+
QT Rl +
1
8
logAge+
2
logDis +
Kpm +
Diesl_p+
9
AvgF uel1+
logAge+
2
logDis +
3
10
M Kj Lp +
4j
Seat+
11k
Lp2 +
5
Bodyk +
Kwt+
12
Indx_pdrt+
6
EngnCap
13
Germany :
P =
7
0+
QT Rl +
1
Diesl_p+
8
Kpm +
3
AvgF uel1+
9
10
M Kj Lp +
4j
Seat+
11k
5
Bodyk +
Lp2 +
12
6
Kwt+
Indx_pdrt+
14
F uelCap
Spain :
P =
QT Rl +
0+ 1
8
logAge+
Diesl_p+
9
2
logDis+
AvgF uel1+
Kpm+
3
11k
M Kj Lp+
4j
Bodyk +
12
Kwt+
5
13
Lp2 +
6
Indx_pdrt+
EngnCap+
15
7
Door_5
Great Britain :
P =
0+
7 QT Rl +
1
8
logAge+
2
Diesl_p +
logDis+
9
3
Kpm+
AvgF uel1 +
11k
4j
M Kj Lp+
Bodyk +
13
5
Lp2 + 6 Indx_pdrt+
EngnCap +
16
AutoT
P is the real resale price.
Age is number of month between the registration and the sale date.
Dis is the distance travelled, including any distance done on an odometer that has been
changed.
Kpm is the distance travelled per month.
Lp2 is the cubic of the real least price (including option price).
M Kj are dummy variables indicating make multiplied by Lp. ( France : Audi,Bmw, Citroen,
Ford, Mercedes, Opel, Peugeot, Renault, Volkswagen. Germany : Audi,Bmw, Ford, Volkswagen.Spain : Audi, Ford, Opel,
24
Peugeot, Renault.Seat. UK : Audi, Bmw, Ford, Toyota,Vauxhall, Volkswagen.)
AvgF uel1 contains average fuel consumption …gures as given by the manufacturer (urban
and road). It is a company decision as to which statistical …gure goes into this attribute.
Seat is the number of seat.
Bodyk are dummy variable indicating the body type (France :berline, monospace. Germany :
Kompact, Spain :estate, berline UK : estate car, or saloon (sedan))
Kwt is the power of the engine expressed in kilowatt given by the manufacturer.
Indx_pdrt is the Industrial production by monthly index (adjusted by working days).
QT Rl are dummy variables indicating the quarter.
Diesl_p is the diesel pump price, euro per liter all taxes included.
EngnCap is the actual number of ccs the engine has.
F uelCap is the capacity of the fuel tank or tanks, in litres as …tted as standard on the
vehicle type.
AutoT is equal to 1 if the vehicle has a form of automatic transmission …tted as standard
or not.
Door_5 is equal to 1 if the vehicle has 5 doors.
1.7. APPENDIX
1.7.3
Appendix C : Regression results
France Results
Germany Results
25
26
Spain Results
Great Britain Results
1.7. APPENDIX
1.7.4
Appendix D : Pivot Point results
Bucket 30 months and 90,000 kilometers
27
28
1.7.5
Appendix E : Graphical analysis :
Ford Focus age impact :
France
Germany
1.7. APPENDIX
29
Spain
Great Britain
30
Ford Focus mileage impact :
France
Germany
1.7. APPENDIX
31
Spain
Great Britain
32
Audi A4 age impact :
France
Germany
1.7. APPENDIX
33
Spain
Great Britain
34
Audi A4 mileage impact :
France
Germany
1.7. APPENDIX
35
Spain
Great Britain
36
Chapitre 2
Hedging residual value risk using
derivatives
37
38
CHAPITRE 2. HEDGING RESIDUAL VALUE RISK USING DERIVATIVES
2.1
Introduction
A lease is a contract in which one party transfers the use of an asset to another party for a
speci…c period of time. Leasing equipment is an important means of …nancing, and consequently
represents a signi…cant part in many …nancial institutional portfolios. In 2006, leasing represented more than one-sixth of the world’s annual equipment …nancing requirement 1 . The value of
the entire Global leasing market was estimated to be more than $633 billion 2 . Academic results
suggest that "leasing allows small …rms to …nance their growth, and/or survival while for large
…rms, leasing appears to be a …nancial instrument used by sophisticated …nancial managers to
minimize the after-tax cost of their capital3 ".
In the leasing industry, residual values are the forecasted prices of equipment in the second
hand market. A large part of the rent paid by the customer during a life contract is the di¤erence
between the list price and the residual value. The leasing company makes money or losses money
depending on whether it accurately predicts the value of the asset at the end of the contract
(fair market value). If residual values are forecasted to be higher than what the asset is actually
worth at lease-end, then there will be a loss. At the opposite, if residual values are forecasted
to be lower, then there will be a gain on resale.
In the European auto lease market, most leases are closed-end leases : leasing companies
assume the residual value risk. In 2001, car resale’s price fell dramatically. As a result, US
leasing companies su¤ered large losses, and some even dropped out of the business4 . Although,
residual value risk is a key element in the leasing industry, there is very few literature on the
subject. The few studies were developed in three main areas : operational purpose5 aiming
1
Percentage market penetrations are highly signi…cant in United states (27.7%), Germany (23.6%), and Spain
(29.1%).
2
According to the White Clarke Global Leasing report (2008), "Globally, the industry continued to growth
robustly, with the top 50 countries increasing volume by 8.8%" between 2005-2006. The Percentage of the world
market volume was respectively 41.1% and 38% for Europe and North America.
3
See Lasfer and Levis (1998).
4
See Gordon (2001) for a description of the 2001 Leasing industry crisis.
5
Jost and Franke (2005) illustrate the use of a speci…c tool of statistical modelling to calculate residual value
through a wide range of parameters. In Lucko (2003) and Lucko, Anderson-cook, and Vorster (2006), residual
values are set using regression methodology. Rode, Paul, and Dean (2002) outline a framework for analysing
the uncertainty of residual value for assets, such as power generation facilities, for which few data points exists.
2.1. INTRODUCTION
39
to set the most accurate residual value ; Basel 2 requirements6 calculation of reserves. Studies
evaluate Basel 2 accuracy, and reserve calculation in relation to speci…c credit risk in the leasing
industry, and Leasing Contract Valuation7 ; in the valuation analysis, the residual value risk
is included through an American option. It allows a comparison of leasing (…nancial lease and
operating lease) v.s. purchase decision. Unfortunately, it does not aim to hedge the speci…c
Residual value risk, let-alone the correlation issue in a portfolio of equipment.
A lack of development on …nancial products hedging residual value risk lead my research
to credit risk. The recent important contributions in …nance modelling and in new …nancial
products were in credit derivatives. This implies a change in credit management involving
banks and other …nancial institutions. A credit derivative is a contract between two parties
that allows the use of a derivative instrument to transfer credit risk from one party to another.
The risk seller has to pay a fee to the risk buyer who will take the risk. Over the last ten years,
the credit derivative market has faced a substantial increase. A lot of credit risk models have
been developed, therefore increasing investor interest8 .
In 2000, Li‘s Gaussian copula model 9 facilitated a dramatic success of this derivative sector.
He proposed a fairly easy, and intuitive model depicting the payment default of a company like
the survival probability of a human life10 . It was also a new tool to evaluate the ongoing
issue of credit risk ; i.e. correlation. For instance, in a basket of loans there is an individual
risk component. Each loan has a risk to default its payment. The systemic risk is the other
component. An economic downturn could also impact the whole portfolio, and the systemic
risk implies correlation.
6
Schmit produced several articles on Credit risk in leasing industry to analyse Basel 2 requirements accuracy.
See Schmit (2003), Schmit (2004), Irotte, Schmit, and Vaessen (2004), Laurent and Schmit (2007).
7
T. Copeland and J. Weston (1982) apply an American put with a decreasing exercise price and S.E Miller
(1995) includes an American Call Option in a net present value formula to estimate the internal rate of return
of the deal. S.R Grenadier (1995), focusing on the real estate arena, adds a residual value insurance that is
equivalent to a put option on the underlying asset in the pricing of a variety of leasing contracts.
8
“At the risky end of …nance”The economist (April 21st 2007) gives an up to date on the credit derivatives
market : “According to the Bank for International Settlements, the nominal amount of credit-default swaps had
reached $20 trillion by June last year. With volumes almost doubling every year since 2000, some reckon the
CDS market will soon be worth more than $30 trillion”.
9
See Li (2000).
10
In “Gaussian copula and credit derivatives”the Wall Street Journal (September 12, 2005) tells the story of
David Li discovery and his impact on …nancial markets.
40
Collateralized Debt Obligation (CDO) turns the correlation problem into a solution. It is
a credit derivative created from a portfolio of debt instruments11 . The risk seller transfers
the risk implying that the risk buyer takes the risk. Of course, the risk seller has to pay
a fee to the risk buyer. The CDO became a successful product by allowing the credit risk
division among di¤erent tranches. Synthetic CDOs12 , in particular, were booming, improving
liquidity, and allowing corporate bonds to be sliced and diced on the basis of risk. Investors
were able to choose di¤erent levels of risk and returns13 . The growth was so huge that it had a
global macroeconomic impact, decreasing the risk of default impact, in‡ating asset prices and
narrowing credit spreads14 . Prior to summer 2007, there was up to 30% of banking investment
pro…t.
From that time, all products have slumped suddenly in value due to fraud, and low quality
loan underwriting. The "credit crunch" allowed identi…cation of several weaknesses in the industry of loan securitization. Severing the link between borrowers and risk takers, it promoted
a lack of accountability. In addition, market protagonists contributed to a credit bubble15 . Investors did not fully understand the products and had an over reliance on ratings provided by
specialized agencies. Moreover, some securities were poorly structured. Thereby, on a cleared
market with more incentives, some experts are hoping for a recovery. Fortunately, securitization
is not con…ned to consumer or corporate loans.
Residual value risk and credit risk have a clear analogy, constituting of units that are more
or less risky. A lease portfolio is similar to a loan portfolio, both could be divided into systematic
and idiosyncratic risks. Losses occur when certain events happen, and again, the correlation
risk has a huge impact. Hedging a portfolio of leasing equipment using derivative securities is
11
Collateralized debt obligations divide the credit risk among di¤erent tranches : First senior tranches (rated
AAA), second mezzanine tranches (AA to BB), and …nally equity tranches (unrated). Losses are applied in
reverse order of seniority. Therefore junior tranches o¤er higher coupons to compensate for the added risk.
12
Synthetic CDOs do not own cash assets like bonds or loans. Using credit default swaps (a derivatives
instrument), synthetic CDOs gain credit exposure to a portfolio of …xed income assets without owning those
assets.
13
See Hull (2005).
14
« La multiplication des émissions de CDO semble avoir contribué au resserrement prononcé de spreads
intervenu au cours de ces deux dernières années sur l’ensemble des marchés de crédit » . Cousseran and Rahmouni
(2006). See also “At the risky end of …nance” The economist (April 21st 2007).
15
“Fear and loathing, and a hint of hope” The economist (February 14th 2008).
2.1. INTRODUCTION
41
attractive, and the idea to use some of the signi…cant developments in Credit risk modelling is
attractive as well.
Therefore the aim of this chapter is to transfer a model from the credit risk to the residual
risk. The one factor model is presented and modi…ed. This modi…cation allows the creation
of a new product, the Collateralized Residual Value. Pykhtin and Dev (2003), …rst applied
the one factor model to auto lease. They calculated the economic loss associated to residual
risk, leading to an estimate on economic capital. The model was constructed and modi…ed for
…nancial lease with the option to buy out (the lessee has a purchase option at the end of the
contract). Moreover, loss distribution was calculated for a …ne grained portfolio (speci…c to
large portfolio without signi…cant individual exposure), as a result, the model was only driven
by the systematic factor.
Our study is somewhat di¤erent, as we aim to hedge residual risk using a derivative …nancial
product. This second chapter is intended for people within the leasing industry interested by
an innovative …nancial product, as well as people from the …nancial market concerned by
leasing risk opportunities. More speci…cally, we aim to hedge risk for a classical European
contract. The product should cover operating lease contracts on a de…ned number of units and
de…ned characteristics equipment parameters. We complete this theoretical development by an
empirical analysis in which we confront this new derivative with market reality. The rest of the
chapter is organized as follows : Sections 2 and 3 provide some backgrounds on residual value
risk and CDO pricing ; Section 4 describes the model and the …nancial product ; Section 5 is
devoted to the empirical analysis and Section 6 concludes.
42
2.2
Leasing
The initial idea of leasing is that it is the use of equipment in a business which produces
bene…ts, not the ownership. One characteristic of ownership in leasing contract is the residual
value risk that generates competitiveness or losses.
2.2.1
Main characteristics
As previously mentioned, a lease16 is a contract between two parties where a party (the
lessor) provides equipment for usage on a speci…c period of time to another party (the lessee)
for speci…ed payment. Three parties are involved in the process : equipment suppliers, lessors
and lessees. The lessor is the party that grants the use of the asset to the lessee. The lessee is
the party that obtains the use of the asset from the lessor. The lessor purchases the equipment
to the supplier. All along the contract, the lessor has the legal ownership of the asset. To use
the asset, the lessee makes periodic payments to the lessor at an agreed rate of interest.
There are two families of lease contracts. An operating lease can be considered as a typical
rental allowing the lessee to use an asset without owning it. A …nancial lease aims to transfer
all risks and rewards of ownership to the lessee.
A lease is de…ned as a …nancial lease if it contains one of the following elements :
- The ownership of the asset is transferred to the lessee by the end of the lease term.
- The lessee has an end of contract option to buy the asset lower than the fair market value.
- Whether the asset is transferred or not, the lease period is for a majority of the asset
useful life.
- Because of the specialized nature of the asset, the lessee only can use the equipment
16
Leasing de…nitions and legislations are quite di¤erent from a country to another. As we do not wish to focus
on a speci…c legislation, de…nitions are made on an international common perspective.
2.2. LEASING
43
without major modi…cation.
Otherwise, it is an operating lease17 .
A lease is a …nancial instrument for the procurement of equipment. Recovery rate on a lease
is higher than on a standard loan. But why do enterprises lease ? Regarding large …rms, leasing
minimizes the after tax cost of their capital. For small asset base companies, leasing increases
access to equipment …nance. The inherent value of the purchased asset acts as collateral. The
lessor is the owner of the equipment, and then is secured by the collateral. Another attractiveness is the leasing companies expertise. Leasing companies are not only intermediaries. Their
expertise is a real added value in the leasing process. They have knowledge of the asset. They
select the appropriate equipment based on the ability of the asset to contribute to cash ‡ow
(through various parameters like equipment characteristics, economic life of the asset, taxes or
residual value risk). Leasing companies have also skills in …nance, credit, equipment acquisition
and dealing. All things considered, they facilitate the ‡ow between equipment suppliers and
equipment users.
On lessor side, there are several key elements :
- Asset leased : Used by the lessee for business purpose, it could be any kind of equipment
(i.e. printers, trucks...)
- Asset list price : The lessor is usually able to negotiate rebates and the lessee could be
part of the acquisition process.
- Lease period : It is a pre requisite agreement between the parties. According to the contract,
it could be ‡exible.
- End of term options : At the end of the contract, there are options allowed to the lessee ;
Lease period can be extended, lease can be renewed, equipment can be bought or returned.
17
In the next sections, we propose a model to hedge residual value risk on an operating lease that is the most
common contract in Europe for Auto Lease. The model can be extended and modi…ed for a …nancial lease (see
Pykhtin and Dev (2003)).
44
- Residual value : The lessor forecasts the market value of the asset at the end of the contract.
- Depreciation : It might be seen as the variance between the List price and the Residual
value all along the lease period.
- Lease payment : As illustrated by Figure 1, several features are included in payments made
by the lessee during the contract : depreciation of the asset (usually the larger component),
interests on the lessor investment, servicing charges (including operation cost, insurances, counselling, repairs...).
Figure 1 : Lease rental calculation
2.2.2
Residual value risk versus competitiveness
The residual value risk corresponds to the fact that the lessor faces the risk to not being
able to recover su¢ cient capital value from the resale or disposal of the asset. As illustrated by
Figure 2, the fair market value curve implies a gain on sale or a loss on sale depending on the
2.2. LEASING
45
level of the residual value.
Figure 2 : Depreciation curve
Therefore the lessor faces a dilemma : The higher the residual value, the higher the risk of
loss on sale. But the higher the residual value, the higher the rental payment. At the same time,
the higher the rental payment, the worse the competitiveness. Conversely the higher the residual
value risk, the better the competitiveness. Figure 3 displays the mechanism of competitiveness
and sales results at the end of the contract.
46
Figure 3 : Dynamical bene…ts
In others words, the lessor has to set a residual value to minimizing residual value risk
and maximizing competitiveness. A solution would be the use of a …nancial product. Hedging
residual value risk could be done through a security derivative. Security de…nition includes
…nancial security (bond, stock) but also capital market securities (mortgage, long-term bonds).
It is an investment instrument which o¤ers evidence of debt or equity. A security derivative is
a …nancial security whose value is derived in part from the value and characteristics of another
security, the underlying asset18 . It would allow the lessor to transfer the risk to a fourth party
(i.e. insurance company, …nancial market...).
18
Securitization is the process of aggregating similar securities that can be transferred or delivered to another
party.
2.3. MODEL PRE REQUISITES
2.3
47
Model pre requisites
Because it allows to create a link of two survival functions, Gaussian Copula is a key element
in our analysis. CDO pricing, default modeling, and the one factor model are also inherent to
the …nancial product presented in Section 4.
2.3.1
CDO are a subclass of ABS
Asset Backed Securities are securities backed by a pool of assets. ABS include various
subclasses ( Commercial Mortgage Backed Securities (CMBS) or credit card ABS...), depending
on the underlying asset class. Obligations are usually underlying Collateral Debt Obligations
(CDO). The basic idea of CDO is to pool corporate bonds and selling o¤ pieces of the pool.
A synthetic CDO replaces pool’s bonds by speci…c credit derivatives, Credit Default Swaps
(CDS).
All in all, CDS are triggered by a credit event. A credit event increases the likelihood that
the rating of a bond decreases. Consequently, a credit event increases the risk that a bond
issuer will default, by failing to repay principal and interest in a timely manner. The events
triggering a credit derivative are de…ned in a bilateral swap con…rmation. It is a document that
refers to an agreement between the two swap counterparts. There are several standard credit
events that could be referred to in credit derivative transactions : Bankruptcy, Failure to Pay,
Restructuring, Repudiation, Moratorium.
By selling a CDS, an investor can take exposure to an individual credit. He is receiving
periodic payment from his client. At the same time, however, he has to pay contigent payment
when default occurs. The client, conversely, can hedge individual credit by buying a CDS. He
provides periodic payment to the client and receives contingent when default occurs.
48
2.3.2
Default, default, default....
Default modeling is about the expected default payment of an obligor in a bank credit portfolio. The obligor (or debtor) is an individual or company that owes debt to another individual
or company (the creditor). The obligor borrows or issues bonds.
The following framework de…nes our model. The model is underlaid by a probability space.
This probability space is constituted of three parts. F, a
into a sample space called
Algebra, is the information available
. Elements of F are the measurable events of the model. Events
of default are measurable. For instance, the event that an obligor survives or defaults is a
measurable event. The last element is Pr, a probability measure. Pr(default) is the probability
of default. Finally, to summarize, the probability space ( ; F; Pr) is underlying our model.
In survival analysis, T is a random variable denoting the time of default and t are other
di¤erent times. If T > t, then the obligor defaults. The survival function, usually denoted S is
de…ned as S(t) = Pr(T > t). This function must be non increasing : S(t + 1)
S(t).
We can now de…ne the complement of the survival function. Usually denoted F , it is a
lifetime distribution function : F (t) = P r(T
S(t). From this concept a default
t) = 1
rate per unit time can be calculated, the event density. Usually denoted f , it is the derivative
f (t) =
d
F (t).
dt
All of this allows the de…nition of an advanced function, the hazard function. The hazard
function, usually denoted , is the event rate at time t conditional until time t or later. It is
R1
0 (t)dt
(t)dt
given by (t)dt = Pr(t T < t + dt j T > t) = fS(t)
= SS(t)
( (t) 0 and 0 (t)dt = 1
with no continuous or monotonic constraints).
A cumulative hazard function is (t) =
Because (t) =
S 0 (t)
,
S(t)
then
d
dt
(t) =
Rt
0
S 0 (t)
S(t)
(u)du.
and (t) =
log S(t).
Several distributions can be used in duration modeling (usually de…ned on R+ ), the most
t
common one being the exponential distribution (S(t) = e ).
2.3.3
49
Basic elements on Copulas
Why do we use copula ? In a portfolio, credit risks are non independent. Copulas are a
convenient approach to specify a joint distribution of survival times. Using a copula function,
we are able to link the survival function of an obligor to the survival function of another obligor
in a portfolio .
In our model, we use copula on a three dimensional perspective. For simpli…cation purpose, we will focus on the bivariate distribution function and the two dimensional copula. The
following results, however, can be extended to the multivariate case (see Nelsen (2006) and
Vershuere (2006)).
For a "rigorous" copula de…nition, we …rst have to de…ne the unit square and the concept
of subcopula.
– The unit square I2 is the product I
I where I = [0; 1].
– A two dimensional subcopula is a function C 0 de…ned through the four following properties :
1_ DomC0 = S1
S2 (with S1 and S2 are subsets of I containing 0 and 1).
19
2_ C0 is grounded .
3_ C0 is 2-increasing (for every x1
x2 and y1
y2 , H(x1 ; y1 )
H(x2 ; y2 )).
4_ For every u in S1 and every v in S2 , C0(u; 1) = u and C0(1; v) = v.
We are now able to de…ne a two dimensional copula : It is a two dimensional subcopula C
whose domain is I2 .
Figure 4 gives an intuitive notion of a two dimensional copula. The graph of a two dimensional copula is a continuous surface within the unit cube I 3 .
19
A function H from S1
S2 is grounded if H(x; a2 ) = 0 = H(a1 ; y) for all (x; y) in S1
being the last elements of S1 and S2 .
S2 with a1 and a2
50
Figure 4 : Two dimensional copula
Two others elements are fundamental in our analysis ; the joint bivariate distribution function and the Sklar Theorem.
A joint bivariate distribution function is a function H with domain R2 such that H is
2-increasing :
H(x; 1) = H( 1; y) = 0, and H(+1; +1) = 1. The joint bivariate distribution func-
tion is a key element of the Sklar Theorem : Let H be a joint distribution function with margins
F and G. Then there exists a copula C, such that for all x; y in R, H(x; y) = C(F (x); G(y)):
Furthermore, if F and G are continuous, the copula C is unique. Otherwise C is uniquely determined on RanF
RanG. Conversely, if C is a copula and F and G are distribution functions,
then H is a joint distribution function with margins F and G:
We can now include random variables. Let X and Y be random variables with distribution
functions F and G, and joint distribution function H. Then there exists a copula C with
H(x; y) = C(F (x); G(y)). If F and G are continuous, C is unique. Otherwise, C is uniquely
determined on RanF
51
RanG.
In a few words, a copula function is a function that links univariate marginal to their full
multivariate distribution : C(u; v) = Pr(u
V ). Therefore, using a copula function, we
U; v
are able to link the survival function of a credit risk to the survival function of another credit
risk in a portfolio.
2.3.4
Speci…c pre requisites, the Gaussian copula
In the model presented in this chapter, we use the Gaussian copula. Let
normal distribution function with correlation coe¢ cient
(0
be the bivariate
1). The bivariate normal is
a member of the family of elliptically contoured distributions.
The density function of
is
(x; y) =
2
(
p1
2
1
e
1
2(1
2 ) (x
2 +y 2
2 xy))
.
The densities for such distributions have contours that are concentric ellipses with constant
eccentricity.
1
is the inverse of a normal distribution function.
1
Finally the Gaussian copula is C(u; v) = (
1
(u);
(v); ).
Consequently, variables are jointly elliptically distributed and we can set
using a linear
correlation as a measure of dependence : Let X and Y follow, respectively, the distribution F
and G. They jointly follow the distribution function H. Then the linear correlation
for X and
Y is de…ned, using u = F (x) and v = G(y) as
= (X; Y ) = p
1p
V ar(X) V ar(Y )
R1R1
0
0
[C(u; v)
uv]dF
1
(u)dG 1 (v).
Another property of the bivariate normal distribution is radially symmetry. A bivariate
normal distribution with parameters
(
x,
y ).
It means that H(
x
+ x;
y
2
x,
2
y
and
+ y) = H(
x
x;
x,
y,
is radially symmetric about the point
y
y).
Using copula, we are able to work on survival function. Indeed, for a pair of random variable
with joint distribution function H(H(x; y) = P [X < x; Y < y]), the joint survival function
52
copula is given by H(x; y) = P [X > x; Y > y] = 1
H(x; y) = 1
F (x)
G(y) + H(x; y) =
H(x; y). The relationship is
1 + F (x) + G(y) + C(1
F (x); 1
G(y)).
In the next section, we assume that the correlation of default is driven by a common factor
through a Gaussian copula.
2.3.5
The initial one factor model is used for CDO pricing
To resume the model in one sentence, a …rm defaults when its “asset value-like”stochastic
process X, falls below a barrier. X is commonly identi…ed as the amount of assets and X
the barrier as the amount of liabilities. The …rm defaults when the amount of assets is below
the amount of liabilities. The idea was …rst introduced by Merton (1974). He transferred an
option pricing model to the credit risk market. Then he applied the Black and Scholes model to
credit risk. We present an alternative model using copula. Value added is in copula ‡exibility to
dependent variables and copula ability to provide scale invariant measure of association between
random variables. The intuitive aspect of this model contributed to the growth of credit risk
market.
The model described below is the famous standard Gaussian copula developed by Li (2000)
and exposed20 by Gibson(2004).
In a reference portfolio of i = 1; :::N credits, for each obligor, default payment occurs when
xi (reference credit normalized asset value) falls below xi (the threshold).
x i = ai M +
q
(1
a2i )Zi
(2.1)
xi has three main components : M , Zi , and ai .
M is the common factors a¤ecting all the credits, the systematic risk. Zi is the factor a¤ec20
See also Meneguzzo and Vecchiato (2004) for an empirical study of credit derivatives within the copula
framework. Cherubini, Luciano, and Vecchiato (2004) give an overview of copula applications in Finance.
53
ting only credit i. ai is the correlation parameter (0 6 ai 6 1) and de…nes default dependency
between companies in the economy. The correlation of asset values between credits i and j is
equal to ai aj . The random variables are assumed to be independently distributed. Therefore
unconditionally on the systematic risk, default payments are correlated but conditionally there
are independent.
M , Zi , and xi are zero-mean, unit variance random variables with distribution functions
G(0; 1), Hi (0; 1), and Fi (0; 1). qi (t) is a risk neutral probability that credit i defaults before t.
The default threshold xi is equal to Fi-1 (qi (t)).
When does a default happen ?
A default happens when xi falls below xi .
But xi falls below xi if F (xi ) < qi (t) , xi < Fi-1 (qi (t)) , ai M +
and …nally Zi <
F
1 (q
pi (t)) 2 ai M
p
1
a2i Zi < F
1
(qi (t))
1 ai
Conditional on the value of the factor M , the probability of default is therefore
qi (t=M ) = H
1
(
F
1
(qi (t)) ai M
p
)
1 a2i
(2.2)
For any number of defaults in a portfolio of N obligors, we have to estimate the probability
of default on time t and conditional on the common factor M .
Therefore, we set the number of default distribution using a binomial function21 .
P N (l; t=M ) =
l
qi (t=M )
N
(2.3)
Once we have the conditional default distribution, we estimate the distribution according
the distribution of M .
21
The number of default distribution is usually computed through a recursion method (Andersen, Sidenius
and Basu (2003) or Hull and White (2004)). In the case of homogeneous credits and for simpli…cation purpose,
a binomial function is simpler and lead to similar results.
54
The unconditional default distribution P N (l; t) can be calculated as
N
P (l; t) =
Z
1
P N (l; t=M )g(M )dM:
(2.4)
1
In a CDO, the investor is responsible for the interval of loss [L; H]. The expected loss of a
CDO is de…ned on [L; H]. We de…ne the loss for any default as A(1
R) with A the notional
amount of credit and R the recovery rate.
The expected loss is
ELi =
N
X
P N (l; Ti ) max(min(lA (1
R); H)
L; 0)
(2.5)
l=0
with T i, i = 1; :::; n the periodic payment.
Now, how to price a CDO ?
A CDO contract speci…es two potential cash ‡ow streams : a Contingent leg and Fee leg.
– On the contingent leg side, the protection seller makes one payment only if the reference
credit defaults. The amount of a contigent payment is the notional amount multiplied by
(1
R).
The contigent leg is
contigent =
n
X
Di (ELi
ELi 1 )
(2.6)
i=1
with Di the risk free discount factor for payment date i (e
rt
, with r the risk free rate). The
risk free discount factor is usually derived from the risk free interest rate.
– On the …xed leg side, the buyer of protection makes a series of …xed, periodic payments
of CDO premium until the maturity, or until the reference credit defaults.
2.4. A MODIFIED MODEL : THE LEASING MODEL
55
The expected present value of the Fee leg is
F ee = s
n
X
Di
i
[(H
L)
ELi )]
(2.7)
i=1
i
is the accrual factor for payment date i and s is the spread per annum paid to the tranche
investor (
i
Ti
Ti 1 ).
The value of the CDO contract to the tranche investor at any given point of time is the
di¤erence between the present value of the contigent leg and the present value of the …xed leg.
It is the di¤erence between the protection the buyer expects to pay, and the amount he expects
to receive.
– The Mark To Market value of the tranche, from the perspective of the tranche investor is
M T M = F ee
Contigent
(2.8)
At inception the mark to market is equal to 0, therefore the spread is
s= P
n
Contigent
Di
i
[(H
L)
(2.9)
ELi )]
i=1
2.4
A modi…ed model : The leasing model
From equipment leasing speci…cities and the one factor model, we create a residual value
risk model. A new product called Collateralized Residual Value (CRV) is adjusted through the
leasing contract parameters.
56
2.4.1
There is a similarity between credit risk and residual value
risk. But there are also dissimilarities and speci…cally in Auto
Lease.
The main idea of the leasing model is that a portfolio of leased equipment is comparable to
a portfolio of credit. A portfolio with losses on resales is equivalent to a portfolio of credit with
companies defaulting.
– As in a CDO, every unit into the lease portfolio, has an idiosyncratic and a systematic
risk ; asset speci…c characteristic impact is resale price (model type, obsolescence. . . ). At
the same time, resale price of other assets has a signi…cant impact (bid and ask e¤ect,
downturn on the resale price market, in‡ation etc.. . . ).
There are also dissimilarities :
– First of all, equipment units are resold only one time at the end of the contract, although
for a CDO, there is a risk of default throughout the contract. Therefore, the model
presented in the next section is set for only one period.
– Another dissimilarity (and not the least) is on correlation estimation. Di¤erence is not on
calculation but on data source.
In credit risk, they are four main data sources available :
-Default events that are obviously concrete realization of credit risk. They are rare events
and as a result there are usually few data available. Approximations and aggregation have to
be made to constitute data bases.
-Companies credit ratings : They are provided by credit agencies and re‡ect the credit risk
of a company according to experts points of views. By and large, they are made through balance
sheet and macroeconomic analysis.
-Credit spreads : They re‡ect market perception of credit risk. A large amount of data is
available. But spreads could be impacted by external elements like liquidity
57
-Equity correlation : The factor model (cf Section 3), assumes a theoretical link between
equity and credit risk. Correlations are then more easy to compute.
In residual risk, there is one main data source available : for a residual value calculation,
inputs are observations from second hand markets. Correlation estimation of residual value is
based on resale market statistics. Resale prices, asset characteristics and price index are used
to set modelization variables. A large amount of data is available.
– The last dissimilarity is on standard de…nitions. As multiple factors de…ne a resale, there
are issues to de…ne resale asset classes or homogeneity prices.
Auto lease is an extreme illustration. The high price level in the automotive second hand
market involves a high residual value level. Combined to a competitive leasing market, the level
of price leads to high risks of loss on sale.
At the same time, automotive is a singular equipment. A car is not only a tool to go
from a place to another. It is also a living place and a symbol. Automotive often re‡ects
driver’s sociological characteristics. The purchase of a vehicle is a sensitive act, even in business.
Therefore, Auto lease is a wide area to analyze. In automotive market multiple factors in‡uence
resale price. A second hand vehicle price is impacted by age (time between registration date
and resale date), mileage (number of kilometers at the end of the contract), damages (i.e.
amount and type ), product life cycle (i.e. new model...), make (i.e. Toyota, Renault...), model
(i.e. Yaris, Laguna...), version, body type (i.e. break, pick-up...), segment (i.e. small cars...) or
external color. Figure 5 gives an overview. Choices have to be made to de…ne similar assets and
prices (c.f Section 5).
58
Figure 5 : Multiple factors of automotive market
2.4.2
Homogeneous equipment type model
The initial idea is simple : we use the equipment resale value as the asset value-like xi and
the probability of resale value below residual value (xi <xi ) as the probability of default.
In a reference portfolio of i = 1; :::N units (vehicles, equipment...), for each obligor, losses
occur when xi (reference unit normalized asset value) falls below xi (reference unit normalized
residual value).
q
xi = ai M + (1
a2i )Zi
(2.10)
-The correlation of resale’s prices between units i and j is equal to ai aj .
-M is the sectorial factor a¤ecting equipment units on resale’s market and Zi is the risk of
59
loss on resales on unit i
-Xi, M , and Zi are zero-mean, unit variance random variables with distribution functions
Fi (0; 1), G(0; 1), and Hi (0; 1).The random variables are assumed to be independently distributed.
At that point, the construction is similar to the credit model, but we include residual risk.
Resale’s value can be lower than residual value. There is a risk of loss on sale.
Three new elements will have an impact on the leasing adjustment of the model.
Vi is the residual value or in other words the expected fair market value. mF M Vi is the
historical average fair market value, eF M Vi is the historical standard deviation.
mF M Vi , eF M Vi , and Vi are set on a percentage of Lp, List price by unit. As an example,
an asset bought e 10000 and leased for a Residual value of e 5000 has Vi = 50%.
Then residual risk is added : Probability of loss at the end of the contract is qi (t). qi (t) is a
variable with mean mF M Vi , variance eF M Vi , and distribution function Ei (mF M Vi ; eF M Vi )
The probability of loss depends on residual value : qi = Ei (Vi ). So default threshold xi is equal
to Fi-1 (qi ).
Conditional on the value of the sectorial factor M , the probability of default is therefore
qi (M ) = H
1
(
F
1
(q ) ai M
pi
)
1 a2i
Again, conditional probability is P N (l; M ) =
R1
can be calculated as P N (l) = 1 P N (l)g(M )dM .
l
N
(2.11)
qi (M ) and the unconditional probability
As a result the recovery rate is equal to the probability of loss. By construction the recovery
rate is R = qi. The loss on sale for any unit is (1
R)Lp. Finally, resale price becomes RLp.
Previous elements allow the creation of a …nancial product, inspired by Collateral debts
obligations :
60
The Expected loss is
EL =
N
X
P N (l) max(min(Lpl (1
R); H)
L; 0)
(2.12)
l=0
The contigent leg is
contigent =
n
X
Di (EL)
(2.13)
L)
(2.7)
i=1
The premium leg is again
F ee = s
n
X
Di
i
[(H
ELi )]
i=1
The spread is again
s= P
n
Contigent
Di
i
[(H
L)
(2.9)
ELi )]
i=1
2.4.3
Heterogeneous equipment type model : a portfolio of three different assets
The model is extended to a portfolio with non similar units. A company ‡eet is commonly
constituted of various car models. In an European leasing contract for medium size European
company, lessee usually request di¤erent categories of cars for an auto lease contract. The ‡eet
is usually divided into three groups : Executives’cars (usually high brand car), Employee cars
(medium level cars) and Small cars.
Basically the construction is similar to the homogeneous equipment type model (cf Section
4.2).
61
Three representative’s vehicles constitute the model : Ex, Em and Sm.
Now there are di¤erent types of asset residual values, number of units, List price etc....
V 1i , V 2i ,V 3i are residual values for groups 1, 2, 3,
mF M V 1i ,mF M V 2i , mF M V 3i , are fair market values historical averages,
eF M V 1i ,eF M V 2i ,eF M V 3i are historical standard deviation historical averages.
mF M V 1i , eF M V 1i , and V 1i are set on a percentage of List price. The recovery rate for
group 1 is R1 = q1i, the loss on sale for any unit is R1(1 Lp1) with Lp1 unit list price. Indeed,
resale price is R1Lp1. The principle is the same for others groups.
For each vehicle, asset value is still xi = ai M +
p
(1
a2i )Zi :
For group 1, default threshold xi is equal to Fi-1 (qi ) with q1i = Ei (V 1i ) and Ei (mF M V 1i ; eF M V 1i ).
The principle is the same for other groups.
The distribution of the number of defaults, conditional on the common factor M, is computed for each group as P N1 (u; M ) =
w
N3
u
N1
q1i (M ), P N2 (v; M ) =
v
N2
q2i (M ) , P N3 (w; M ) =
q3i (M ) with N1 ; N2 ; N3 number of units, P N1 ; P N2 ; P N3 the conditional probabilities, and
u; v; w number of defaults for group 1, 2, 3.
The probability of default is computed on the whole portfolio.
P N (u; v; w; M ) = P N1 (u; M )P N2 (v; M )P N3 (w; M )
The Expected loss is :
EL =
N
X
P N (u; v; w; M ) max(min((Lp1u (1 R1))+(Lp2u (1 R2))+(Lp3u (1 R3)); H) L; 0)
l=0
Premium leg, contigent leg and spread are calculated like in 4.2.
(2.14)
62
It is straightforward to generalize this approach to more than three vehicle types.
2.4.4
Collateralized Residual Values
We propose a …nancial product, the Collateralized Residual Value, that covers residual value
risk. We display a sensitivity analysis of the CRV to the main characteristics of the leased asset.
A CRV is a new class of ABS
The Collateralized Residual Values (CRV) is a new class of Asset Backed Securities (ABS).
The CRV is inspired by synthetic Collateralized Debt Obligations (CDO) structure. Like a
CDO, CRV can be sliced and diced, and tranches can be sold. But CRV is not about credit
risk. The purpose is to hedge residual value risk on a portfolio of leases. A credit derivatives,
obviously, is more accurate to hedge credit risk in a portfolio of contract.
Sensitivity Analysis on a CRV
What is the sensitivity of a CRV to size, residual value, and fair market variance ?
In the following sensibility analysis, all underlying reference assets are cars. The portfolio is
p
homogeneous. List price (e 15000), Fair market value (e 4500) and Correlation ( 0:3) by car
are equal. Cars are leased on a three years contract.
We value four tranches of the CRV. The …rst tranche absorbs all losses until the …rst 25%
of the portfolio, the second tranche until 50%, the third tranche until 75% and the fourth until
100%.
63
Impact of Fleet Size
Table 1 : Sensitivity to ‡eet size
Table 1 shows that the buyer of protection on a ‡eet of 600 units should be willing to pay
125,21 basis points to hedge the …rst 50% losses using a CRV. According to our results, the
spread is stable until 500 units. Then the increasing size reduces the cost of protection. An
increase in size reduces idiosyncratic e¤ects. There is a diversi…cation of risk.
64
Impact of Residual Value level
Table 2 : Sensitivity to residual value
The higher the residual value, the higher the pricing of CRV (Table 2). As illustrated in
Section 2.2, decreasing residual value reduces the risk of loss on sales.
65
Impact of Fair Market Value variance
Table 3 : Sensitivity to fair market value variance
Fair market value distribution tails depends of FMV variance (Table 3). For an higher
variance, tail are larger. As a result, the spread is an increasing function of the variance.
66
2.5
Empirical analysis
The model is applied to a six years historic resale’s portfolio. The observations, between 2000
and 2008, are from a major European leasing company (General Electric Capital Solutions). We
…rst estimate the correlation of assets to a common factor. Then fair market value parameters
and residual value are estimated.
2.5.1
Correlation to the one sector factor
According to section 4.2, we have to set the linear correlation (ai ) between the portfolio
and a sectorial factor a¤ecting equipment units on resale’s market (M ). The sectorial factor is
assessed using Eurostat Harmonized Consumer Price index (HCPI22 ). The index Purchase of
vehicles price allows comparison within European markets. Additionally, a portfolio index has
to be created. The portfolio index provides a non-biased historical trend analysis and exposes
portfolio sale price at di¤erent times.
Automotive Price Index
To set a common factor that would a¤ect the whole portfolio, several HCPIs are available ;
HCPI all items, HCPI Energy, HCPI Petroleum products, HCPI Road transport equipment.
The Index "Purchase of vehicle" (Figure 6) appears to be the most relevant. It covers purchases
of new vehicles and purchases of second-hand vehicles from other institutional sectors. It is
available by country and on European level. This index is included in the modelization as the
sectorial factor indicator (M ). Vehicle customers have to choose between resale market and new
market. As a consequence, resale market is strongly impacted by new vehicle market. Therefore,
a positive or a negative correlation of the sectorial index with the portfolio can be expected.
22
Graphics of HCPI series are reported in Appendix.
2.5. EMPIRICAL ANALYSIS
67
Figure 6 : European HCPI
Portfolio Index Creation and Computation
A large amount of parameters impacts resale price and there is a non homogeneity of
the portfolio mix from one month to another. As a consequence, average price never re‡ects
accurately portfolio sales price variance through time. Therefore a consistent price variable
is created through an index replicating a same arti…cial portfolio. The idea is to replicate a
portfolio mix to allow time series analysis.
Portfolio Index Creation The information comes from resale vehicles statistics from 01/2000
to 01/2008 including France, Germany, Italy, Portugal, Spain and Sweden. We only include normal termination sales (sales types like wrecks or litigations are excluded). Observations with
extreme and incorrect values are cleaned. High damages (95th decile by country) that would
alter resale’s price and therefore are …ltered.
Calculation is a …ve-steps process :
1. Creation of buckets for Age and Mileage (details in appendix).
68
2. Keys are created including the following components :
age=mileage=model=f iscalclass=f ueltype=country.
3. Keys with population of less than 100 units on the whole history are excluded.
(e.g.GBR=T oyota=previa=private=lightgoods=petrol=_6:33; 39month=_3:75000; 105000km
is excluded. During the last 8 years, less than 100 units in this bucket have been sold.)
4. Representative and similar samples are created all along the history using the historical
key frequency. A Random selection is processed by month through the following criteria : -1%
of units by bucket are selected (e.g. for a bucket of 200 units, then 2 units are selected), Restricted random sampling with replacement (SAS proc survey), -Priority levels : The sample
is replicated on a monthly basis according to key frequency and by order of priority ; selected
month, semester of the selected month, whole history (e.g. If data are not available in the
current month, then data are selected in the current quarter etc...).
5. A monthly resale percentage is computed from the sample. The percentage of resale
is
resaleprice
.
Listprice+OptionListprice
It allows a comparison of resale performance between vehicles with
di¤erent levels of price and option price.
The process is replicated several time to create several sample. 1000 random samples are
created by month.
69
Portfolio Index Computation and results 565 representative buckets are selected from
an initial pool of 38257 units. 97000 samples are calculated (97 periods).
Among other perspective, it provides a graph distribution by month. Results are available
by country and on European level. For instance, Figure 7 displays the simulation result for
Portugal on January 2001. The percentage of resale distribution is on a range of [49%-72%].
Figure 7 : Portugal depreciation distribution on January 2001
Estimation of the correlation between the sectorial factor and the portfolio price
Time series are seasonally adjusted using the TRAMO-SEATS methodology23 . Graphical results
by countries are displayed in Appendix.
23
TRAMO-SEATS : They consist of new versions of programs TRAMO, "Time series Regression with ARIMA
noise, Missing values and Outliers", and SEATS, "Signal Extraction in ARIMA Time Series", created by Gómez
and Maravall in 1996, of program TERROR, "TRAMO for Errors", and program TSW, a Windows version
of TRAMO-SEATS with some modi…cations and additions, developed by G. Caporello and A. Maravall at the
Banco de España.
70
Figure 8 : European HCPI and European portfolio YoY variance
Figure 8 illustrates results for Europe. The European HCPI is more stable than the European
Portfolio YoY variance value.
A Pearson’s product moment is computed on a year on year annual variance, and results
are given in table 4.
Table 4 : Pearson Product moment on year on year annual variance
As expected, results are di¤erent by country. Correlation are negative or positive with
di¤erent levels of intensity. Impacts are negative for Germany, France and Italy. If "Purchase
of vehicle" HCPI increases, then the resale portfolio performance decreases. Therefore unlike
the initial credit model, the correlation parameter could be negative ( 1 6 ai 6 1).
2.5.2
71
Fair Market Value and Residual Value setting
mF M Vi , average fair market value, eF M Vi , standard deviation and residual value (Vi ) are
parameters to include in the model.
Fair Market Value estimation is complex We assess the Fair Market value at the end of
the contract. In others words, we estimate the depreciation of the asset for the next years.
Resale percentage Mean and Variance of resale percentage are calculated from historical
statistics. For simpli…cation purpose, resale price is computed through a percentage of List
resaleprice
).
Price ( Listprice+OptionListprice
FMV subtlety To illustrate our presentation we focus on a speci…c Key : PEUGEOT 307
Tourisme Diesel _6.]33,39]month _4.]105000,145000]km _FRA.
Figure 9 : 36 months contracts / Peugeot 307 depreciation and historical average
Figure 9 shows the time series depreciation of the key. It also shows the historical average
depreciation. Since January 2004, the key average depreciation is 37.26% and the standard
deviation is 46.76%.
72
Figure 10 : 24 months contracts and 36 months contracts depreciations
Figure 10 compares the depreciation with a 24 months Key : PEUGEOT 307 Tourisme
Diesel _6.]21,27]month _4.]105000,145000]km _FRA .
Figure 11 : Peugeot 306 and Peugeot 307
Figure 11 is a graphic of Peugeot 30624 and Peugeot 307 depreciation : PEUGEOT 306
Tourisme Diesel _6.]33,39]month _4.]105000,145000]km _FRA.
Previous graphics illustrate the fact that FMV is not a constant value. There are trends and
cycles that are not straightforward to identify. Depreciation in the value of a car occurs based
24
Peugeot 306 is the previous model version of Peugeot 307.
73
on a range of factors. The factors include cars condition, kilometers traveled and brand reputation. Moreover, brand reputation contains mechanics and popularity. Consequently, di¤erent
methodologies are possible to forecast average fair market value.
Leasing industry usually works with internal modelization. Standard models have inside a
model life cycle and a segment analysis. New legislations or macroeconomic impacts also are
sometime included. Additionally, external companies (Eurotax, X-ray, Cap) provides forecasted
FMV. Forecasts are based on market data, modelization and expertise.
74
RV and FMV, a new perspective
In an operating lease contract, Residual value is de…ned as the forecasted fair market value.
It is an input in rental calculation. It also drives the risk of loss on sales at the end of the
contract. What is the impact of a CRV ?
Elements of the contract become di¤erent. Using securitization product, elements of the
contract have to be rede…ned. The fair market value still has to be forecasted. But residual
value is now a threshold. As illustrated in Figure 12, the threshold is a level of risk chosen by
the lessor and the lessee. In the model, mF M V is a forecasted average of fair market value at
the end of the contract. And eF M Vi is the estimated standard deviation of fair market value.
So the considered residual value is now an adjustment variable. Therefore the securitization
product allows several choices within di¤erent levels of risk, di¤erent levels of rents, di¤erent
market spreads, and di¤erent fair market value variances. Additionally, hedging can be made
on speci…c tranches.
Figure 12 : Sale results through fair market value and residual value level
75
For simpli…cation purpose, the threshold is set at mF M V value in the next illustration. It
means that the contract position is neither conservative or risk taking.
Six CRV
Table 5 : Pricing of six CRV
A CRV is built accordingly to leasing contract characteristic. As illustrated in Table 5 for
six CRV, inputs in pricing are population size, list price, fair market value mean, fair market
value variance and residual value. Through the selected residual value level and tranches limits,
lessor and lessee can choose a level of risk. Moreover, in case of negative correlation parameter,
CRV could go against a downturn in the sectorial market and create opportunities for risk
diversi…cation. Like standards derivatives, CRV allows insurance or hedging for the lessor and,
for the buyer taking opposite position in the …nancial market, speculation or arbitrary.
76
2.6
Conclusion
Li Gaussian copula model, initially used for credit risk, is transposed in residual value risk
of the leasing industry. The Collateralized Residual Value (CRV), a new derivative product, is
proposed. Pooling together a large portfolio of equipment that has been leased, the derivative
converts end of contract risks into an instrument that may be sold in the capital market. As a
standard derivative, it is a tool that transfers risk, and can be used for hedging or speculation.
Moreover, it allows the lessor and lessee to select their degree of exposure to residual value risk
and to improve competitiveness. As a result, the model is a contribution geared for people from
the leasing industry interested by an innovative …nancial product, as well as people from the
…nancial market concerned by leasing risk opportunities.
The present analysis could be extended in various ways. The accuracy of the correlation
parameter can be improved by a complete macroeconomic analysis, and the fair market value
parameter can also be improved. Finally, other families of copula could be tested.
2.7. APPENDIX
2.7
77
Appendix
Figure 13
Figure 14
78
Figure 15 : HCPI YoY variance
Figure 16 : HCPI YoY variance
2.7. APPENDIX
79
Figure 17 : Age and Mileage buckets
80
Chapitre 3
A Family Hitch
Econometrics of the New and the Used Car Markets
81
82
CHAPITRE 3. A FAMILY HITCH
3.1
Introduction
Apples are non-durable goods. Out of the new market, they have no value. On the contrary,
cars are durable goods. They are usually bought with the intention to be used for a limited
time and then re-sold. A car owner can choose for a duration, and then re-sell the vehicle
on a well developed secondary market. Thanks to the durability of the car, drivers can resell cars to each other, and buy new or used vehicles. Durability creates speci…c dynamics of
overlapping generations of durable goods that are not present in non-durable markets, and
brings the question of the interaction between primary and secondary markets.
We aim to identify the relationship between new and used car markets in order to forecast
car prices. For various industries the future car prices are of special interest. Indeed, among
other things, used car market prices directly a¤ect leasing companies losses and bene…ts.
The third chapter is organized as follows. Section 2 reviews the literature related to the
interdependence between primary and secondary markets, speci…cally in the automotive sector.
Section 3 presents the data and our empirical setting. In Section 4, we empirically evaluate
the interdependence between new and used cars for three major markets (France, the United
Kingdom and the U.S.). Section 5 concludes.
3.2
Academic researches in the second-hand market are
legion.
There has been a signi…cant amount of academic researches on the subject of durable goods
in the second-hand market. The literature discusses why second-hand markets exist and highlights some mechanisms of interdependence between new and used markets, especially in the
microeconomy area. It mainly focuses on three related axes of research : the Akerlof e¤ect, the
optimal durability and the time inconsistency. Some researches, like Scitovsky (1994), also exist
into a Keynesian system.
3.2. ACADEMIC RESEARCHES IN THE SECOND-HAND MARKET ARE LEGION.
3.2.1
83
Why secondary markets exist ?
Van Cayseel (1993) provides a framework : Second-hand markets are institutions dealing
with transactions of durable goods1 , and the durability constitutes their …rst condition of existence. As a second condition, the good utility needs su¢ cient volatility. For instance, an economic depreciation2 could appear if the consumer has no further need of the good or because
the maintenance cost of the car increases3 . Consequently, the second-hand market re-allocates
goods from agents extracting a low utility to agents extracting a higher one. Mixing the condition of durability and a possible variance of utility, we can state that the longer the durability,
the higher the probability for an asset to change of valuation. The longer the durability, the
higher the probability for a consumer to drop the asset, and buy another one. The secondary
market could also be a way for some users to drop goods with malfunctions and no functionality4 . But dropping ‘lemons’could only be an incentive for a minority of agents, otherwise the
secondary market would collapse.
According to Van Cayseel (1993), the possibility of simultaneity of new and used markets
constitutes the last condition, raising the question of bene…ts and constraints in the secondhand market for producers. In order to reduce the risk of competition with new products5 ,
producers would try to prevent the existence of a secondary market (i.e. by only renting their
equipment or reducing the substitutability between new and used markets). Fortunately, some
incentives to tolerate and to even support a second- hand market, additionally exist for the
producer. The …rst incentive would be the pressure created by other competitors with similar
goods. Following researches on industrial regulation and anti-trust policies, a large amount of
academic papers have studied durable goods in a monopolistic market6 . The incentive could be
a law committing the monopoly to sell his products. The existence of asymmetric information
1
2
On a broader de…nition of Van Cayseel, the key concept should be not used goods but resales.
We are focusing on second-hand markets for automobiles. Most of the time there is a depreciation of the
good over time. However, in some markets like art or …nancial product, the secondary market has a higher
valuation than the primary market. Speci…c cars (luxury ones) could also gain value after some years because
of collectors interests.
3
Regarding maintenance, the second hand market could be a way to reallocate used goods with high maintenance cost to users who have a better maintenance technology or skills.
4
It brings the problem of adverse selection discussed in the next section.
5
The problem of Time Inconsistency is discussed in section 2.2.
6
See Waldman (2003) for a large review in the microeconomy area.
84
could also restrain the opportunity of leasing, because users are less careful with goods they
do not own. Anderson and Ginsburgh (1994), through a microeconomic analysis and under
a monopolistic assumption, show a bene…cial e¤ect of secondary markets for the producers :
consumer heterogeneous tastes result in a segmented secondary market allowing producers to
establish a system of indirect price discrimination (by setting higher prices, a producer extracts
higher surplus from consumers with higher willingness to pay). In the automotive industry,
manufacturers are selling both new and used cars7 . They also rent and provide services of
maintenance in order to bene…t most of the needs related to their products (i.e. …nancing car
ownership through their …nancial branch). Manufacturers aim to collect various revenues from
all available channels.
De…ning the automotive industry as a monopoly would be a strong assumption. According to the ACEA8 in 2008, more than 15 manufacturers (through more than 43 brands) were
sharing the market in Western Europe, and none of them had more than 21 percent of the
market share. In the US, more than 15 automotive makers are competing and none of them
had more than 15 percent of market share9 . Paredes (2006) argues that cars are ‘durable experience goods’. Before buying a car, a consumer can’t evaluate all of its characteristics. As a
consequence, Paredes states that a link exists between consumer loyalty, satisfaction and retention value. The existence of consumer loyalty (and non loyalty) implies that consumers are able
to choose di¤erent manufacturers and that car markets are not monopolistic. As a conclusion,
an automotive company could only be de…ned as a monopoly during the introduction of new
vehicles (i.e. minivans in the US market10 ). Although we reject a monopolistic assumption, we
take these studies into account by focusing on the highlighted mechanisms of interdependence.
Scitovsky (1994) adopts a macroeconomic approach to explain the existence of secondary
markets. He argues that durable goods are valued by the services they provide to the consumers. Because of time and obsolescence, the amount of services included decreases. Therefore
the secondary market has two functions : …rst, it mitigates the inequalities by allowing poor
customers to buy a cheaper bundle of services to richer ones. Second, it stimulates the economy
7
8
usually through franchise dealer.
European Automobile Manufacturers’Association :
www.acea.be/index.php/news/news_detail/new_vehicle_registrations_by_manufacturer/
9
Source : CRS report for congress.
10
See Petrin (2002).
85
by facilitating the replacement of obsolete durable goods. Scitovsky’s theory explains why there
are bigger proportions of second-hand markets (i.e. clothes, household appliances) in developing
countries. But used car markets have a signi…cant size in countries with high standard of living.
Indeed, automobiles are relatively expensive and, by increasing the price span, the second-hand
market allows most of people to a¤ord a car. The empirical analysis of Clerides (1998) on the
welfare e¤ects of trade liberalization11 in 1993 (by permitting the importation of Japanese cars
in Cyprius second-hand market) con…rms Scitovsky’s opinion. Clerides concludes of signi…cant
gains that bene…ted predominantly for low-income consumers because of an increase in product
variety.
3.2.2
The Akerlof e¤ect and the car durability are linked.
The main area of research on durable goods comes from the most famous analysis on automotive second-hand market. Akerlof (1970) explained why used car valuation is so much lower
than new car valuation. The automotive resale market is a¤ected by something called the ’lemon e¤ect’. A used car has a probability to be of a good quality or a bad one (i.e. lemon), and
the uncertainty on quality implies a price adjustment. In the resale market, there is an asymmetry of information ; the car owner has a better knowledge of the probability of bad lemons. If
second-hand vehicles were valued like as new vehicles, then it would attract lemons (sellers of
lemons would have the opportunity to sale their vehicles and buy a new one on the new vehicle
market) and it would create an arbitraging opportunity. Akerlof used the automotive market
as a best illustration and extended his idea to other markets (the cost of dishonesty...).
The Akerlof’s article helps to understand why an adverse selection happens, as well as the
large variance and the trends between new and second-hand prices. But some elements of the
article have to be discussed.
First, the in‡uence of new markets misses in the analysis. Hendel and Lizzeri (1999a) built a
microeconomic model including a primary market and according to their conclusions, a su¢ cient
level of trade could reduce the adverse selection. Moreover, buying new cars and selling used
cars are complementary activities : even if they give higher valuation to their used units, owners
11
In spite of the limitation of the study focusing on a country without a national automotive industry.
86
…nd optimal to sell their good quality cars ; once their used car has been sold, owners place a
higher value on purchasing a new car. Finally, Hendel and Lizzeri argue that new market prices
could be increased thanks to the adverse selection. The …rst explanation would be that a used
good becomes a worse substitute than a new one (in case of an average quality reduction on the
used market). The second reason would be that the buyer of new goods gets an option value
and he or she can decide to keep the high quality realization of the used car.
Empirical analyses give a second perspective. Winand and George (2002) provided a large
review of empirical tests on the Akerlof e¤ect and in various markets, as well as a speci…c
analysis, in the second-hand car market of a Swiss canton. According to their conclusions,
adverse selections are not always observed or could occur under a mitigated and non widespread
form.
Car durability constitutes a third element. An increase of average durability, through the
Akerlof analysis, could have either a negative or a positive e¤ect. A better durability implies
a better quality of cars producing a lower probability of ’lemons’on the second-hand market.
On the other hand, consumers would keep their car longer and it would increase the proportion
of ’lemons’. Whatever the consequence (positive or negative for pro…ts), a manufacturer can
impact the adverse selection e¤ect through guaranteed warranties, buyback or by improving
information on the second-hand vehicles. Similarly, by the beginning of the 90’s, Peach et al.
(1996) noticed an improvement of the information availability on the US second-hand market
and an increase of car durability. At the same time, the used car market experienced an increase
of sales and a¤ordability. All in all, it suggests a positive correlation between quality, durability,
and non-adverse selection.
To conclude, the Akerlof e¤ect and the durability could explain the price trends through
the structure of the market and the inner quality of cars. The questions of quality and optimal
durability are developed in the next section.
3.2.3
87
Optimal durability and Time inconsistency are two areas of
research.
Optimal durability constitutes another main area of research in the microeconomic analysis
of durable goods. A non-competitive market might lead to a lower socially e¢ cient durability of
goods in order to constraint consumers to increase purchase frequency. Sieper and Swan (1973),
however, argue for an absence of durability distortion : monopoly market and competitive
markets will always produce at minimum cost and then consider the durability as a minor
problem. Some articles, like Hendel and Lizzeri (1999b), contest these outcomes : although used
goods create competition for new goods, a manufacturer would bene…t from a well functioning
used-goods market increasing the willingness of consumer to buy new goods easy to resale.
At the same time, the producer could slightly reduce the durability (by under investing in
durability, by directly reducing new units durability, by introducing frequent style changes and
new products...) : it alters the substitutability of new and used market and allows the …rm
to increase the price of new units. The maintenance market could also interfere. Rust (1986)
argues that, in case of a competitive maintenance market and a monopolistic new market, most
of consumers would prefer over maintained used goods.
Durability could have a positive impact on prices for both new and used market by increasing
the quality of cars and therefore the utility of the consumer. At the same time, it has a negative
impact on prices in the new market by improving the competition with the second-hand market.
In the US market, by the beginning of the nineties, Peach and al (1996) observed that cars
reliability, survival rate, and warranties durations have been rising simultaneously with car
prices. Acknowledging that durability has not been the only factor impacting the level of price,
graphical analyses show similar trends, from 1990 to 2008, of the median age and the average
sale price of new cars. But their conclusions have to be strongly quali…ed : for used cars and
light truck markets, similar trends are less visible12 . Furthermore the Consumer Prices Index
for cars (new and used), that adjust prices through obsolescence and representative constant
mixes of vehicles, has been decreasing since 1990 in the US13 .
A third large area of research on durable goods discusses the Time inconsistency. Optimal
12
13
See graphs in Appendix 2.
88
durability and the Time inconsistency problem are embedded. According to Coase (1972) a
monopolist has to manage the dilemma that the price of units sold in the future will be a¤ected
by the characteristics of the units sold today. The Time inconsistency constitutes an issue for
producers across planned obsolescence, R&D, and the introduction of new products on the
market. Waldman (1996) argues that R&D could have a negative impact on new products
because consumers expect a technological improvement in a later period. As a consequence,
a monopolist should under invest in R&D and reduce the availability of the used goods (i.e.
by reducing the durability of new unit, by repurchasing and scrapping the used units...) to
maximize his pro…t. On the other hand, Fudenberg and Tirole (1998) argue that new and used
units could become imperfect substitutes after the improvement of new goods. They conclude
that R&D could have a positive impact on new goods prices, as well as a negative impact
on second-hand cars14 . As already mentioned, microeconomic studies usually make the strong
assumption of a monopolistic market. But Schiraldi (2009) proposed a microeconomic model in
an oligopolistic car market. She concluded on a possible collusion of manufacturers to increase
prices on second-hand markets through leasing policy, warranty policy and buy-back policy in
order to increase prices on new markets. By and large, microeconomic results lead to various
conclusions, but they always bring the idea that new and used markets impact each other prices
(and volumes) on a short and a long time perspective.
3.2.4
Scitovsky’s mechanisms are part of a Keynesian framework.
Most of mentioned articles assume a neoclassical economy driven by real factors and where
money supply has no impact. Agents are optimizing their purchase and know the function
to optimize. Scitovsky (1994) adopts a Keynesian approach that includes uncertainty and the
impact of disposable incomes on the overall economy.
Scitovsky investigates the destabilizing impact of secondary markets on the overall economy.
They strengthen both recessions and recoveries. He …rst focuses on speci…c movements of prices :
14
Petrin(2002)’s empirical analysis on the impact of introduction of the minivan in the US market does
not include the second-hand market, but the study con…rms the positive impact of innovation in a competitive
market. When automotive …rms are introducing new products, they are cannibalizing each other pro…ts ignoring
the externalities they create. In the end, new products can bring large pro…ts to the innovator and substantial
gains for the consumer.
89
consumers often react to a modi…cation of their income by shifting their demand between new
markets and cheaper secondary ones. As a result, in case of a su¢ cient elasticity of goods
substitution, new and second-hand markets become interdependent. A shock or a disequilibrium
in each market impacts prices, demand and supply in the same direction. Additionally, both
markets o¤set one another. The disturbed market excess demand (or supply) becomes equal to
the other market excess supply (or demand) and prices are stabilized accordingly. Unfortunately,
prices are stabilized only for a while.
A gap between demand and supply still exist in both markets and an opposite e¤ect soon
appears because of a slow adjustment of stock in the second-hand market. In the automotive
sector, for instance, owners of used vehicles are more or less willing to hold their vehicles
according to increases and decreases of prices. The slow variation of stock has the following
consequences : the used market volume rises and reduces the level of price in the new market.
So the interdependence disrupts the equilibrium in both markets.
To summarize, following disturbance disequilibrium in one market, a short-term e¤ect of
arbitraging creates a temporary obstacle to price movement and a move on the other market on
the same direction. Then, on a second period, the second-hand market’s disequilibrium slowly
liberates constraints of an equilibrating price movement.
Scitovsky extends the discussion to the impact on the overall US economy. The e¤ect depends of the size of the used market. It depends also on the length of time the secondary market
is able to compensate the variation of the new market without impacting prices. Automobiles
are exceptional durable goods because of the size of the second-hand market, but Scitovsky
assumes that the in‡uence of stocks would be limited to two months only15 (Car owners are
rarely relinquish and dealers stocks are quite limited).
From an empirical perspective, Peach et al (1996) also conclude that used markets intensify
economic cycles. But they have another explanation : there has been a long-term shift of the US
consumer demand from new to used car markets16 . Franchised new car dealers have captured
15
According to Scitovsky, …nancial assets are the only exception. The destabilizing impact of …anacial se-
condary market would have no limit. Their sizes and shocks duration would signi…cantly impact the overall
economy.
16
There has been a shift, as mentioned in the previous section, consequently to an increase of durability and
90
much of the second-hand market growth. They are collecting most of their pro…ts from used
cars and are less aggressive bidders on the demand side of auctions. Regarding the supply side,
when demand for new cars increases, they accelerate the used car price reduction by sending
more used cars to auctions. The mechanism become reversed when the demand for new cars
decrease. At the end, car markets have more volatility. Pashigan (2001) observed that US used
car prices index has much more volatility than the new car index. The supply curves are less
elastic for used than for new cars and, as a consequence, contribute to a higher volatility.
3.2.5
There are implied mechanisms behind the academic theories.
Other mechanisms do not come from a speci…c literature and are implied in the previous
contributions. We mention them for clari…cation purposes and to facilitate their identi…cations
in the econometric analysis that will be implemented in the next section.
"The new market feeds the used market" : as a result, volume and prices of today’s used
car market might be positively correlated with volume and prices of the past new market. The
mechanism also interacts with renewals on the used and the new markets.
"Renewals" : after some years, drivers have to renew their vehicles. Concentrations of renewals create cycles on both markets. Additionally, concentrations on the new market could
create future concentrations on the used market.
"Volume e¤ect" : an increase of transaction volumes, if caused by a greater o¤er, could
have a positive impact on the prices. An increase of transaction volumes, if caused by a greater
demand, could have a negative impact on the prices.
"Price e¤ect" : a price increase could have a positive impact on the volume of transactions
by improving o¤er, or a negative impact by decreasing demand.
"Arbitration" : a driver can buy a car on the used market or on the new market. A car
bought from one market cannot be bought from another market at the same time. When most
a¤ordability of cars, as well as a higher level of available information for consumers.
3.3. THE MACROECONOMIC TIMES SERIES NEED CLARIFICATIONS.
91
of drivers choose to buy used vehicles, volumes (and prices) improve in the used market and,
as a consequence, decrease in the new market.
"Reallocation" : when prices are too high in the new market, the buyers move to the secondhand market. Consequently, used car prices increase. In other words, prices and volumes move
in the same direction in both markets on a short term perspective. Scitovsky analyzed the
reallocation mechanism by insisting on the threshold e¤ects (due to stocks) on volumes and the
lags creating constant disequilibrium.
The "Income e¤ect" : a decrease of income (or consumption or con…dence) creates a decrease of demand, a decrease of transaction volumes, and a fall of prices in both markets17 .
Alternatively, it could create a shift of consumption from the new market to the used market.
As a consequence, volumes and prices go down in the new market while they are increasing in
the used market.
3.3
The macroeconomic times series need clari…cations.
We aim to check the accuracy of the mechanisms mentioned in the previous sections using
econometric tools. The interactions of the consumer price indexes and the volume of transactions
of new and second-hand cars are analyzed in three countries. Following an interpretation of the
relations between the academic theories on durables goods and the time series behavior, we
de…ne the limit of our macro-economic perspective.
3.3.1
Three countries are compared through four time series.
We study the automotive markets of France, the United Kingdom and the United States of
America. We consider observations related to the Consumer Price Index (CPI) and the volume
of registrations (or sales) for new and used cars18 . The US volumes make the di¤erence : in
2007, used car sales volume was more than 41,4 millions for the US market. By comparison, it
17
18
According to Scitovsky (1994), the Income e¤ ect causes cycles.
See Appendix 1 for data sources.
92
was 5.3 millions and 7 millions for France and the UK. Moreover, the passenger car populations
in use for France, the UK, and the US were 30.7 millions, 30.1 millions, and 135.4 millions19 .
We aim to analyze the interdependence between primary and secondary markets on a macroeconomic perspective. The quality of the car (to account for the Akerlof e¤ect), informations
regarding demand (i.e. consumer con…dence) and o¤er (i.e. business con…dence), the level of
R&D (for the Time inconsistency), the mix of vehicles or the level of stocks constitute relevant
explanatory variables. However, we only included four time series in our analysis (prices and
volumes) because of the di¢ culty to collect standardized information and to allow a comparison
from a country to another.
The National Statistical Institutes (INSEE for France, ONS for the UK, BLS for the US)
provide the automotive Consumer Price Indexes. They re‡ect the general movement of prices on
the new and the used car markets. The statistical institutes do not communicate a precise list
of the items included in the samples used to construct the indexes. And the precise locations,
where the observations are collected, are neither provided. They communicate, however, a
general setting of their methodologies20 . The frameworks are not always similar from a country
to another, but share the same objectives. First, the CPI has to re‡ect the cost of life and to
give an overview of price variation of the general expenditure across the country. Then prices
are collected from various areas and the selected samples of cars aim to be representative of
what people buy in these areas. Second, although goods and services are changing through
time in their characteristics, the statistical institutes intend to measure the e¤ects of price
changes by keeping constant the other economic factors. The processes by which prices are
adjusted to account for changes in product quality constitute an important subject of research
and discussions in the automotive sector. The US applies the Grilitch methodology21 for the
quality adjustment of automotive observations : the Hedonic approach estimates the price of a
19
The number of new passenger car registrations in 2007 for France and UK was 2.0 millions and 2.4 millions.
New vehicles sales in US were more than 13,6 millions. The average car age is 8.1 and 6.7 years for France and
for UK. In US, the median age for automobiles is 9.2 years. See data sources in Appendix 1.
20
See Caillaud (98) for France
See www.statistics.gov.uk/articles/nojournal/CPISQR.pdf for UK.
See Reinsdorf and Triplett (2008) and also Pashigan (2001) who provides critical elements on the US CPI for
used cars.
21
See Otha and Grilitch (1976) for additional details the Hedonic methodology in the automotive area and
also Fixler et al (1999). See Prado (2009) for an application on the European used car market.
93
good through the valuation of its attributes. France and the UK apply another methodology,
the ’option costing’, that can be used when a product changes in speci…cation and when it is
possible to value separately the components that have changed.
We use the volumes of registrations (for France and the UK) and sales volumes (for the
US) as proxies of the total amount of transactions. They do not allow a distinction between
the variations of o¤ers and the variations of demands, and provide a slightly more ambiguous
information than the CPI : an increase of sales could be either the consequence of an increase
of demand, or an increase of o¤er, or a reduction of prices. The impacts of volumes on prices
are also ambiguous. An increase of the volumes could cause either a reduction or an increase of
prices. Following an improvement of the market size, for instance, the dealers could reduce their
prices in order to increase their market share or to reduce …xed costs. They could also consider
a high level of demand as an opportunity to improve their bene…ts by increasing prices.
3.3.2
How to connect the academic literature with a time series
analysis ?
We divide the economic literature, surveyed in Section 2, in three groups : the advanced
mechanisms (Table 1), the Scitovsky theory (Table 2) and, the basic mechanisms (Table 3).
Their consequences on the time series analyzed in our article are synthesized in the column
’Impact on Prices and Volumes’. The arrows ( =) () ) indicate that a parameter a¤ects or
causes another one. In order to avoid any misunderstanding, we have to mention that we do not
assume mechanical relations similar to a clockwork (or deterministic links), but we expect to
identify probable interdependence between the new and the used markets (or stochastic links).
94
Mechanisms
Descriptions
Impact on Prices and Volumes
Akerlo¤ e¤ect 1
An increase of quality or information in
Quality " or Information " =) Volumes
the Used Car Market creates an increase
in price and demand on the used mar-
Used " and/or Prices Used "
ket.
Akerlo¤ e¤ect 2
An increase of quality or information in
the Used Car Market creates an increase
in price and demand on the Used Car
Market and the New Market.
Optimal durability
An increase of durability creates a decrease of demand of new cars ; therefore, a decrease of prices in the New Car
Market as well as a decrease of o¤ers in
Quality " or Information " =) Volumes
Used " and/or Prices Used " and Volumes New " and/or Prices New "
Durability " =) Volumes New # =)
Prices New # and Volumes Used # =)
Prices Used "
the Used Car Market and an increase of
prices.
Time Inconsistency
An increase of durability creates a decrease of demand of new cars ; therefore, a decrease of prices in the New Car
Market as well as a decrease of o¤ers in
R&D " =) Volumes Used " and/or
Prices Used " and Volumes New #
and/or Prices New #
the Used Car Market and an increase of
prices.
Table 1 : Advanced Mechanisms.
Mechanisms
Descriptions
Scitovsky Theory
Interactions creating constant disequi-
Volumes New # (insu¢ cient stocks) =)
librium in the primary and secondary
markets.
Prices New " =) Volumes Used " =)
Prices Used " =) Volumes New ! =)
Prices New ! =) Volumes Used # (in-
su¢ cient stocks) =) Prices Used " =)
Volumes New " =) Prices New " and
again =) Volumes Used " =) Prices
Used ". . . .
Table 2 : Scitovsky Theory.
Mechanisms
New
market
used market
feeds
95
Descriptions
Past volumes of new sales transac-
Positive Correlation : Past New Vo-
tions correlated positively with the cur-
lumes () Current Used Volumes / Past
rent volumes of Used Sales transactions.
Past prices of New Sales transactions
New Prices () Current Used Prices
correlated positively with current prices
of Used Sales transactions
Reallocation
Prices and volumes of New sales
Positive Correlation :
transactions correlated positively with
() Used Volumes / New Prices ()
prices and volumes of Used Sales tran-
New
Volumes
Used Prices
sactions
Arbitration
A car bought in one market can’t be
bought, at the same time, in another
market.
Renewals
Used Volumes / New Prices , Used
Prices
Concentrations of renewals create cycles
Cycles of Prices and volumes :
in both markets. Concentrations in the
New Volumes " =) Current Used
new market could create future concentrations on the used market.
Price e¤ect
Negative Correlation : New Volumes ,
A price increase could have a positive
impact on the volume of transactions by
improving o¤ers/sales, or a negative im-
Past
Volumes " and Past New Prices " =)
Current Used Prices "
Prices " =) O¤er " =) Volume " or
Demand # =) Volume #
pact by decreasing demand.
Volume e¤ect
A volume increase could have a positive
impact on the prices if caused by a grea-
Volume " =) Prices # or Prices "
ter o¤er or a negative impact, if caused
by a greater demand.
Income e¤ect 1
A decrease of consumers’ income (or
business activity or con…dence) reduces
the demand for new cars and used cars
Income # =) Demand # =) Volumes #
and/or Prices #
decreasing in prices and volume in both
markets.
Income e¤ect 2
A decrease of consumers income (or business activity or con…dence) reduces
the demand for new cars and creates a
shift to the used car market It’s decreasing prices and volumes in the new mar-
Income # =) Demand New # =) Volumes New # and/or Prices New # and
Demand Used " =) Volumes Used "
and/or Prices Used "
ket and an increase in the used market
Table 3 : Basic Mechanisms.
96
As discussed in section 2.2, the new market could experience di¤erent consequences from
the Akerlo¤ e¤ect. Therefore we made a distinction between the Akerlo¤ e¤ect 1 having only
an impact on the used market and the Akerlo¤ e¤ect 2 impacting both markets. There was a
similar issue with the Income e¤ect driving both markets in the same direction or in di¤erent
ones. Another roadblock exists regarding the e¤ect of demand. As an example, for the Time
inconsistency e¤ect, an increase of demand would create either an higher volume of transactions,
or only an increase of prices, or both22 .
The Akerlo¤, the Optimal durability and the Time inconsistency e¤ects are di¢ cult to
investigate because they involve additional information (quality, durability, R&D...). They could
be invalidated, however, when series move in di¤erent directions than the ones listed in the
tables. For instance, the improvement of quality in the Akerlo¤ e¤ect would take some time to
spread across the population of cars and therefore could be identi…ed by an increasing trend
on volumes, or prices, or both. If the trends are decreasing, then the theory should be refuted.
Our attempt to translate the theoretical economic literature under an econometric analysis
highlights a critical point : the timing. In most of academics papers, except the Scitovsky
(1994)’s article, the period in which the mechanism has an e¤ect was never explicit and the
lags are not precisely de…ned. For instance, are the adjustments simultaneous in the Arbitration
e¤ect ? Or are they lagged ? Do they last for the next six months ? Do they last for a year ?
The econometrics of the next section will provide an insight on timing.
3.3.3
We work on macroeconomic time series, a limited information.
The macroeconomic perspective presents four limits : the cross border sales, the availability
of the historical observations, the usual critics on Consumer Prices Indexes, and the heterogeneity of the markets.
As a …rst concern, the cross border sales might a¤ect the national prices and transactions
of cars : the imported vehicles, for instance, could increase the competitiveness and reduce car
prices. In the European market (including France) the existence of signi…cant cross bordering
22
It is identi…ed every time there is an "and/or" in the table.
97
transactions should lead to a price convergence. Gaullier and Haller (2000), however, did not
notice mechanisms creating an automobile price convergence in European countries. They argue
that exchange rate ‡uctuations explain a large share of the price dispersion dynamics23 . Parities
between Euro-land countries were …xed in May 1998, so their study was too early to assess the
long-term e¤ects implied by the implementation of the single currency. Prado (2009), through
an Hedonic analysis on the 2005-2009 period, shows that even with the Euro implementation,
distinct national markets still constitute the European second-hand car market. Thanks to the
right wheel vehicles, we have few concerns for the UK market regarding a possible interaction,
on prices and volumes, with the other countries. As a conclusion, the impact seems limited for
France and the UK. The US car market has a size dramatically higher than the Mexican and
the Canadian markets and we also expect a limited cross bordering impact.
As a second concern, we have to keep in mind that our results might be altered by the
limited period of available observations. All in all, knowing that cars longevity can run up to
20 years, the study would hardly provide a long-term perspective. In France, the used car CPI
is available since January 1998, while, in the UK, the used car Index is available since January
1996. In the US, the BLS has published the used car index since 1952 and, in order to re‡ect the
cost of living of a representative household, light truck vehicles have only been included in the
CPI since 1998. To standardize the analyses (for the UK), for consistency purpose (for the US),
and to allow a comparison of the three countries, we selected the CPI samples from January
1998. Regarding the times series of volumes (number of registrations, number of sales), we did
not apply the same criteria for the selection of the period : we included as much information
as possible, regarding the number of registrations and sales, maximizing the opportunity to
identify a relation between prices and past volumes (i.e. correlation between used cars and
previous …ve years used cars sales). Most of the time, the volume of transactions has been
included according to the series provided by the statistical institutes and, as a result, series
of volumes are longer than CPI series24 (except for the UK used car registrations). The time
series for France, the UK and the US are presented in Appendix 3.
The relevance of the variables constitutes our third concern. Like any other statistical indi23
24
They con…rm the conclusion of Goldberg and Verboven (1998) that prices follow exchange rates closely.
France : New registrations and used car registrations since January 1987.
UK : New registrations since January 1987/ Used car registrations since January 2001.
US : New sales since January 1987/ Used car sales since January 1997.
98
cator, the Consumer Price Index has been the subject of several critics. In addition, because of
the political and economical impacts on citizen (i.e. wage negotiations), there has always been
a suspicion regarding the CPI accuracy. Two main critics show up : in the automotive area,
people complain that Hedonic adjustments over de‡ate the movement of prices and that CPI
does not re‡ect their ’feeling’of increasing prices. Greenlees and McClelland (2008) discussed
the limits of those critics. They demonstrated the limited impact of Hedonic adjustment on
CPI results25 . And a well known psychological ’loss aversion’could increase the sensibility to
increasing prices than to decreasing prices ; because the CPI cannot re‡ect the consumption of
a particular group of customers, they are de…ned as an average of the in‡ation rate. Consumers
are always members of a speci…c group and they always have the feeling that the CPI is not in
line with their speci…c consumption.
Fourth, speaking of di¤erent groups of customers, we have to clarify that, although we work
at a country level, we do not assume heterogeneity of the markets : a national car market could
be the sum of several sub markets involving very di¤erent populations of customers. A sub
market might strongly impact the whole car market through a signi…cant size or a high level of
volatility. But we aim to provide a macro-economic perspective and intra market interactions
do not constitute the subject of our study.
3.3.4
What do the series look like ?
The period of analysis has been standardized from January 1998 to June 2009. The French
market seems rather stable, whereas the UK26 and the US prices follow a negative trend and
display a high volatility27 . For the last ten years the trends of the US series look negative and
illustrate the crisis of the automotive sector in North America. All these characteristics remain
through a growth rate perspective and after a seasonal adjustment28 .
25
Although there is no European study that would corroborate these results, we also assume a limited impact
regarding the quality adjustment methodologies applied on the French and the UK Consumer Price Index.
26
For UK, they are two big variances after 1999. There has been a change in the car registrations process
after 1999. Prior to 1999, new plates were introduced in August. From 1999 onwards, there has been two plate
changes, in March and September.
27
28
Series are seasonally adjusted using X11 methodology. See graphs in Appendix 4.
3.4. THE ECONOMETRIC ANALYSIS SHOWS DIFFERENT RESULTS BY COUNTRY.99
At a glance, new car CPI are always more stable than used car CPI. Prices on the used
market are the result of demands and o¤ers, while new car prices are set by the dealers and
manufacturers according to constraints of production and maximization of pro…ts. If new car
prices become too high, the number of sales decreases because of prices rigidity on the new
market and the adjustment operates mainly by the volume of transaction29 . As a result, registration (or sale) volumes are more volatile for new cars than second-hand cars, and new car
prices are quite stable. The market readjustment through volumes explains why some economic institutions (i.e. OECD) use new car transactions as a short-term economic indicator. In
contrast, prices in the second-hand market are set through o¤er and demand. As a result, used
car prices display more volatility than new car prices.
By the beginning of 2008, the time series falled sharply. The subprime crisis, a global
economical event, appears as an opportunity to compare the reaction on the di¤erent markets
and to con…rm the previous statements. The new cars registrations (or sales for the US) are
more impacted (by a stronger drop) than the used car registrations (or sales), and used car
CPI is more impacted than new car CPI. As a …rst conclusion, it suggests that, in the case
of an Income e¤ect, the used car market has an higher probability to be impacted on a price
perspective, whereas the new market would rather be impacted on a volume perspective because
of a relative price rigidity from car manufacturers. The mechanisms mentioned as the Feeds
e¤ect, Arbitration, Prices e¤ect and Volume e¤ect might be similarly a¤ected.
All in all, new car markets in the UK and the US have been declining for the last 10 years,
while France has been a stable market.
3.4
The econometric analysis shows di¤erent results by
country.
The econometric tools identify trends, cycles and correlations through various durations
(short-term, very short-term, the whole ten years period). At the same time, we evaluate if the
29
These conclusions should be con…rmed by an analysis of the automotive production (does the manufacturers
adjust the production according to prices ?) and stocks available (how the stocks impact the markets ?).
100
outcomes are in line with the academic theories. At the end of the section, we estimate the
VAR models to investigate the relations between the markets and the possible forecasts30 .
3.4.1
The unit root tests undermine the advanced mechanisms.
As previously stated, France appears as a stable market. To check this intuition, we apply
the Augmented Dickey Fuller unit root test to the growth rate of the series. The results are
reported in Table 4 and show that the French volumes and index prices have been stationary
for the last ten years. On the contrary, the UK and the US have trends : new cars CPI in the
UK, as well as the volume of new car and used car sales in the US, have a unit root (Di¤erence
Stationnarity or DS). According to the econometric theory, it means that a macroeconomic
shock would have an impact on the trend series forever. In contrast, a trend stationnarity (TS)
has been identi…ed for the new car prices index in the US, implying that a macroeconomic
shock would have a temporary e¤ect on the prices. Finally, the used car CPI has no trend in
every country.
France
UK
US
Used cars CPI
S
New cars CPI
S
Used cars Registrations
S
New cars Registrations
S
Used cars CPI
S
New cars CPI
DS
Used cars Registrations
S
New cars Registrations
S
Used cars and light trucks CPI
S
New cars and light trucks CPI
TS
Used cars and light trucks Sales
DS
New cars and light trucks Sales
DS
Stationarity (S)
Di¤erence Stationarity (DS)
Trend Stationarity (TS)
Table 4 : Augmented Dickey Fuller Results.
30
The econometrical analysis is inspired by Chazi (2007) and Lescaroux and Mignon (2008).
The unit root test invalidates the assumption that, for the last ten years, prices and volumes
have been moving in the same direction in the UK new car market (the new car CPI follows
a DS process while the volume of used car sales was stable), and in the US new market (sale
volumes and prices follow a di¤erent trend, a TS and a DS). Turning to the economic theories,
it rejects the presence of mechanisms involving similar long-term trend on prices and volumes
(like the Akerlo¤ e¤ect, the Time inconsistency....). As an example, the decreasing trend in
the US might be explained by the Optimal durability e¤ect : the demand for vehicles decreases
because cars durability has improved. Drivers do not have to renew their vehicles as often as
in the past. An improvement of cars quality should also lead to an expansion of the secondhand market, and in the same manner, an increase of used cars prices (and volumes). But the
Optimal durability mechanism is invalidated by the stationnarity of the used car prices (and
the decrease of used car volumes).
Focusing on car prices, the estimated trends refute several mechanisms and illustrate the
absence of a long term relation between prices. The stability in France and the trends moving
in the same direction in the UK invalidate the existence of a strong Akerlo¤ e¤ect 2, or an
Optimal durability e¤ect.
Regarding the sale volumes, the trend analysis on the whole period illustrates the well known
fact that the new cars of today are the used cars of tomorrow. In France and the UK, the new
and the used car registrations share a similar stationnarity. In the US market, a cointegration
test identi…es a common long-term trend between new car and used car sales31 : for the last ten
years, the new and used US sales have been declining. These results also weaken the mechanisms
reported in Table 1. It is highly unlikely that the stability in France and the UK, as well as the
decline in the US, would be due to a global decrease of cars quality32 (according to the Akerlo¤
e¤ect, the Time inconsistency....).
31
See cointegration test details in Appendix 9. The construction of an Error Correction Model (ECM) including
the US volumes series did not provide a good adjustment. As a result, the model did not constitute a useful tool
to forecast the volumes and we did not keep it in the study. Moreover, the US market only has two identi…ed
Di¤erentiated Stationnnarity (DS) time series. As a consequence, there is no possibility of a cointegration test
and an ECM for France and the UK.
32
We can’t believe, as well, that it would be due to a decreasing quality of information available for buyers.
102
3.4.2
The correlation analysis provides a one-month period perspective.
The correlation calculation provides a …rst insight on the simultaneity of market evolutions33 .
For France, a negative correlation between new CPI and used CPI suggests an arbitrage
on prices (i.e. when prices decrease on the new market, they improve on the used market).
The signi…cant correlation between new and used registrations has a positive sign that might
be caused by an Income e¤ect on the volume of transactions. In other words, when drivers
incomes (and demand) improve, the volume of sales increases on both markets.
For the UK, there is a positive correlation between the new car registrations and the used
car prices. These results are in line with the graphical analysis : Market adjustments are made
through new volumes and used prices whereas constraints exist on new car prices and on the
volumes of used car transactions ; following an economic crisis, new sales and second-hand prices
fall sharply while new prices and second-hand volumes remain relatively stable.
For the US, a strong positive correlation exists between new and used prices (r = 0:54) as
well as a negative correlation between new and used transactions. The US market dynamics
are converse to the French ones ; it suggests an Income e¤ect on a price perspective and an
Arbitraging e¤ect on a volume perspective. These results evoke a Scitovsky’s framework : in
the new and the second-hand markets, prices move in the same direction but the variation of
bid, o¤er and stocks in both markets lead to a constant disequilibrium.
3.4.3
The Granger causality tests elaborate the assessments of the
correlation analysis.
To investigate the interdependence between new and used car markets, we …rst apply the
Granger causality test34 evaluating how much the previous six month information contained in
33
Details are given in Appendix 6. The econometrics tools are applied on the seasonally adjusted growth rates
and stationnary time series.
34
The Granger test has been set with six months lags.
a variable could improve the prediction of another variable. Results are given in Table 5.
France
Used cars CPI =) Used cars Registrations
Used cars CPI =) New cars Registrations
Used cars Registrations () New cars Registrations
UK
Used cars CPI =) New cars Registrations
New cars CPI () New cars Registrations
US
Used cars CPI () New cars CPI
New cars CPI =) Used cars Sales
New cars Sales =) New cars CPI
New cars Sales =) Used cars Sales
=) : Signi…cant Causality
() : Signi…cant causality in both directions.
Table 5 : Granger test Results.
In the French market, new and used cars registrations are interrelated : the null hypothesis, that the volume of used car registrations does not Granger cause the volume of new car
registrations, has not been rejected at the 5% signi…cante level. In addition, the volume of new
car registrations Granger causes the volume of used car registrations35 . It con…rms the Income
e¤ect mentioned in the correlation analysis. Furthermore, the Granger test indicates that the
used car CPI helps to predict used car registrations and new cars registrations : rising used car
prices improve drivers willingness to resale their cars and to buy a new one, as a result, the
number of registrations goes up.
For the UK, the used car CPI helps also to predict new cars registrations. The results
corroborate the graphical and the correlation analyses and emphasize that the adjustments on
the new market are more on volumes than on prices. Nevertheless, it seems that dealers and
manufacturers try to adjust prices and volumes according to the state of the market, because
new car registrations and new car prices also help to predict each other.
35
See the detailed Granger test results in Appendix 5.
104
The causalities are more numerous in the US market : new car prices and used car prices
help to predict each other ; new car sales and new car prices help to predict used sales ; at the
same time, the new car sales help also to forecast new car prices. The test suggests the existence
of multiple relations between new and second-hand cars and shows a strong interdependence
in the US markets by comparison to France and the UK. To be speci…c, the Scitosky’s theory,
of constant disequilibrium from one market to another, constitutes a possible explanation.
3.4.4
The Hodrick-Prescott …lter reveals economic cycles.
In order to identify long-term trends of the series, we calculate Hodrick-Prescott …ltered
series36 . The …lter produces a smoothed non-linear representation of the time series that is
more sensitive to long-term than to short-term ‡uctuations37 .
For France, the graphs show larger cycles (of 2 years) for used car prices index by comparison
to new car prices (6 months) and the volume of transactions. Similarly, second-hand price follows
a longer and more visible cycles in the UK and the US car markets. The distinct pattern of the
used car prices mitigates the validation of mechanisms involving prices and volumes moving in
harmony (Akerlo¤ e¤ect, Time inconsistency).
We evaluate the synchronizations of prices and volumes ‡uctuations. Following Fiorito and
Kollintzas (1994), we measure the degree of co-movement of the series’ cyclical components
through the correlation coe¢ cient . If the correlation between the cyclical components of two
series is positive, null or negative the series cycles are identi…ed as procyclical, acyclical, or
countercyclical. If 0:1 j j < 0:23 or 0:23 j j < 1:0 the cycles are classi…ed as weakly correlated
or strongly correlated. We also calculate (j) with j 2 f 3; 6; 9; 12; 24; 36g in order
to identify lagged correlations. We report the strong correlations38 on Table 6.
36
37
See HP …lter cycle and trend graphs in Appendix 7.
The sensitivity of the trend to short-term ‡uctuations is adjusted through a multiplier . From an Empirical
perspective the suggested is equal to 14,400 for monthly data. See Hodrick and Prescott (1997).
38
The complete results are reported in Appendix 8.
France
New Car CPI
Used Car CPI (+9, +36 months)
Used Car Registrations
New Car CPI (-12)
New Car registrations
New Car registrations
Used Car Registrations (-24)
New Car registrations (-12)
Used Car CPI
Used Car CPI (+12, +18)
Used Car CPI (-3)
Used Car CPI
New Car CPI (-36)
Used Car CPI
New Car Registrations (-36)
New Car Registrations
UK
New Car CPI
Used Car CPI (+3, +6, +9,+12)
Used Car CPI (-3, -6, -9, -12, -36)
New Car CPI
New Car CPI (-12)
New Car CPI
New Car CPI (-36)
Used Car CPI
US
New Car CPI
Used car CPI (0, +3, +9)
Used Car CPI (-9, -12)
Used Sales Volume
Used Sales Volume
New Car CPI
New Car CPI (-24)
New Car CPI
Used Sales Volume (-12, -36)
New Car CPI (-24)
Used Sales Volume
New Sales Volume
New Sales Volume (-24)
New Sales Volume
New Sales Volume (-36)
New Sales Volume
Strong Pro-cyclic Correlation
Strong Counter-cyclic Correlation
Table 6 : Cycles Correlations.
The …lter, applied to the French car prices series, allows the assumption of a Feed e¤ect :
there is a 36 month pro-cyclical movement of new prices with used prices39 . The new prices of
the past 36 months impact the second-hand prices of today. Furthermore, the …lter indicates
a critical correlation between new cars and used cars registrations40 : the cycles of new and
second-hand transactions increase and decrease simultaneously. As a result, like the correlation
39
40
= 0:34
= 0:42
106
analysis of Section 4.2, the Hodrick-Prescott …lter identi…es an Income e¤ect on a volume
perspective.
On the UK market, the …lter also con…rms the existence of a Feed e¤ect : used car prices
cycles are pro-cyclical to new car prices through lags of 3 to 12 and 36 months41 . The absence of
strong correlations on registrations cycles with other series reduces the probability of a Scitovsky
mechanism.
For the US, markets cycles are well interrelated. There are several pro-cyclical and countercyclical relations between prices and volumes. First of all, we identify a positive correlation
between new car CPI and the used car CPI. In addition, the used car CPI, with 9 months
and 12 month lags, appears countercyclical to the volume of used sales. Finally, the used sales
volumes have a cyclical relation with new car prices. These results are in line with the Scitovsky
theory.
3.4.5
Vector Autoregressive (VAR) models clarify the previous results.
A Vector Autoregressive model gives a straight perspective of the relation between prices
and volumes in both markets. We selected the best model using the Akaike and the Schwarz
criteria. The results are reported in Appendix 10 and show the usual greater interaction between
the primary and the secondary markets for the US. Let us discuss the outcomes for each country.
For France, the used car prices mainly depend on their own lagged values42 . The equation
is in line with the Hodrick Prescott results displaying that used CPI cycles are di¤erent to
other series cycles. For the new car prices equation, the model has a good …t to the data
thanks to the relevant information from the previous month new prices and the constant.
These results corroborate the graphical analysis revealing rigidity of new car prices by showing
few ‡uctuations of the new car CPI.
41
42
At the same time, new car prices with a lag of 3 to 12 and 36 months are counter-cyclical to used car prices.
Previous months of used CPI variables have a high statistical signi…cativity according to the student test.
Regarding the French volume equations, the new and the used cars registration models
have a poor adjustment to the historical observations and none of the variables are statistically
signi…cant. In other words, none of the variables from one market are relevant to model the other
market, and the VAR methodology does not identify the suggested relations of the previous
section (correlation and arbitraging). Gautier (1995) attempted to identify new car registration
cycles, which would be a characteristic of durable goods in the French market since 1945. He
concluded that registration cycles are more the result of the economic activity (with additional
volatility and sectorial events) than to the internal dynamics of car markets. It means that, in
order to forecast the registrations in France, a model including variables related to the economic
activity would be more relevant.
For the UK, the used car CPI equation shows that, in a similar way to France having distinct cycles for used car CPI, the previous months used car prices information is statistically
signi…cant. The new market variables are also crucial, but they have smaller coe¢ cients compared to used car prices lagged values. To be more speci…c, the coe¢ cients of the variables from
the new market have a positive e¤ect and therefore reinforce the conclusions of the graphical
and the correlation analyses (the new CPI coe¢ cient is less important because of the rigidity
of new car prices created by production constraints), as well as the Granger causality test (in
spite of the rigidity, dealers try to modify the prices according to the state of the economy).
Regarding the new cars CPI equation, although the adjustment is poor, two variables appear
signi…cant (the used car price index and the used car registrations). But even with a new car
CPI series positively correlated to the used car market, the weakness of the relation suggests
that any involved mechanism would be quite limited.
For the British used cars registrations equation, the model has also a poor adjustment and
registrations seem slightly and positively impacted by the used car prices : when prices go up,
dealers and privates get an opportunity and they increase the volumes of sales, but stocks are
limited and the evolution remains limited as well. Into the new cars registrations equation,
though the used cars CPI and the constant constitute the only relevant information, the model
adjustment is quite good. Again, it strengthens the previous conclusions that economic readjustments are mainly made on the new market by volume (and on the used market by price) :
when the state of the economy improves, for instance, the volume of new cars and the prices
of used cars react …rst and increase. The new car volumes are, however, limited by production
108
constraints and consequently, the constant in the equations appears highly signi…cant. The positive coe¢ cient of the new car volume variable would only allow the existence of mechanisms
with similar co-movements in both markets (Income e¤ect, Akerlo¤ e¤ect...) on a short period.
From the previous results in the US market, we know that the used CPI follows speci…c
cycles and, at the same time, was positively correlated to new car prices. Accordingly, in the
used CPI equation, the lagged used car prices and the new car CPI (with a positive sign) are
statistically signi…cant. On the contrary to France and the UK, the new CPI equation is well
…tted to the historical observations. New car prices are explained by the previous used car CPI
and the previous new CPI. They are also positively impacted by the volume of transactions of
the new market. Therefore the US car prices are connected in various ways with the new and
the used market.
The explained variance of US volume equations are not as good : R2 are equal to 20% and
47% for new and used sale equations. In the new sales equation the only important variables
are the previous new sales ; in the used sales equation the new and the used sales are signi…cant
variables. Scitovsky (1994) mentioned that the market adjustments were altered by the limited
variation of volumes. He argued that used car market volumes were limited by stocks. In
addition, we argue that new car volumes are limited by production constraints, and that the
VAR results on volumes are fully in line with his theory.
3.5
To conclude, an interdependence ?
To conclude, what kind of interdependence exists between the new and the second-hand car
markets ?
The aim of this chapter was to investigate the interdependences between the new and
the second-hand car markets in three countries : France, the UK and the US. The analysis
was limited to a ten year period ; since cars are durable goods that can be used for more
than 20 years, it might have restricted the results to interdependences shorter than a decade.
The econometric tools, however, show consistent outcomes all along the study. Results are
synthesized in Tables 7, 8, and 9.
3.5. TO CONCLUDE, AN INTERDEPENDENCE ?
Mechanisms
109
Results and Comments
Akerlo¤ e¤ect
1 /
All these mechanisms might be altered by rigidity on the new car prices
Akerlo¤ e¤ect
2 /
and constraints on the used car transaction volumes. However, we can’t
Optimal durability /
validate any of them : The main reasons are the stable prices and volumes
Time Inconsistency
in France, as well as the decrease of used car prices in UK and US.
Table 7 : General Results on Advanced Mechanisms.
Links are too weak in the French and the UK markets to allow the possibility
Scitovsky Theory
of a situation similar to the one described by Scitovsky article. In contrast,
most of the statistical analyses identi…ed multiple and signi…cant relations
between new and used cars in the US market and therefore, are in line with
the assumption of a Scitovsky mechanism.
Table 8 : General Results on Scitovsky Theory.
Mechanisms
New
market
Results and Comments
feeds
The trend analysis illustrates a feed e¤ect on a volume perspective in all
markets. For the US market, new and used car sales time series are coin-
used market
tegrated. Additionally, the Hodrick-Prescott …lter suggests that used car
prices of today are related to new car prices of yesterday.
Correlation calculations suggest an instantaneous Reallocation e¤ect, bet-
Reallocation
ween the new and the used market, on volumes in France and on prices in
the US
Correlation calculations suggest an instantaneous Arbitration e¤ect, bet-
Arbitration
ween the new and the used market, on prices in France and on volumes in
the US.
The Hodrick-Prescott …lter did not allow a clear identi…cation of a renewal
Renewals
e¤ect in any of the three countries, neither in the new or the used market.
It is may be due the limited sample (ten years) used in the study.
Price e¤ect / Volume
They are no signi…cant results for France and the UK. Regarding the US
e¤ect
market, we noticed that in line with Scitovsky theory, prices impact volumes
in both directions.
Income e¤ect 1 / In-
Although our results suggest some income e¤ects, it needs to be con…rmed
come e¤ect 2
through a proper analysis of the relations between disposables incomes and
car market volatility.
Table 9 : General Results on Basic Mecanisms.
Initially, we argue that in all countries the new market of the past is linked to the used
110
market of today, through volumes and prices. Secondly, the interrelations appear limited for
France and the UK, whereas the US market is characterized by a Scitovsky dynamics, de…ned
by constant disequilibrium and multiple interactions between primary and secondary markets.
Our contribution also highlighted that, depending of a short-term or a long-term perspective,
interactions are di¤erent. Thirdly, theories implying volumes and prices moving in the same
direction (Akerlo¤ e¤ect, Optimal durability, Time Inconsistency) are di¢ cult to con…rm. Finally, for France, the UK, and the US the connections between primary and secondary car
markets are not similar, but all markets experience a characteristic rarely mentioned in the
literature : a rigidity of both the new car prices and the used car volumes of transactions.
Another similar characteristic is that, for all countries, used car prices follow distinct cycles.
All things considered, our results illustrate that the interrelations between the new and used
car markets are not strong enough to fully explain and forecast the market patterns. The use
of macroeconomic variables related to the disposable income of buyers or the general state of
the economy might improve the forecast accuracy, and is left for future research.
3.6. APPENDIX
3.6
3.6.1
111
Appendix
Appendix 1 : Data sources
The Time series43 :
CPI FR
Www.bdm.insee.fr/bdm2/serie/A¢ chRechDirecte.do Identi…ant : 000638803 000638804
CPI UK
Www.statistics.gov.uk/statbase/tsdtimezone.asp Consumer prices indices DE78 DE79
CPI US
Www.data.bls.gov/cgi-bin/srgate Series Id : CUSR0000SS45011 CUSR0000SETA02
New Car Reg FR
Www.statistiques.developpement-durable.gouv.fr/rubrique.php3 ?id_rubrique=122
New Car Reg UK
Www.smmt.co.uk/dataservices/vehicleregistrations.cfm
New car sales US
Www.bea.gov/national/xls/gap_hist.xls
Used car Reg FR
Www.statistiques.developpement-durable.gouv.fr/rubrique.php3 ?id_rubrique=122
Used car Reg UK
Driver and Vehicle Licensing Agency Www.dvla.gov.uk/
Used car sales US
CNW Marketing Research Www.cnwmr.com/
Others Statistics :
France and UK, new registra-
ACEA Www.acea.be/index.php/collection/statistics
tions and vehicles in use
France second-hand registra-
Fichier
tions
durable.gouv.fr/rubrique.php3 ?id_rubrique=32
central
des
UK second-hand registrations
British Car Auctions Used Car Market Report Www.bca-europe.com/
US new and used average sale
National
price
Www.bts.gov/publications/national_transportation_statistics/
US car on use
National Automobile Dealers Association Www.nada.org/NR/ rdonlyres/0FE75B2C-
Transportation
automobiles
Statistics
from
Www.statistiques.developpement-
the
US
department
of
statistics.
69F0-4039-89FE-1366B5B86C97/0/NADAData08_no.pdf
US median age
Www.nada.org/NR/rdonlyres/0FE75B2C-69F0-4039-89FE-1366B5B86C97/0/ NADAData08_no.pdf
43
A special thanks to Tom Webb (Www.manheimconsulting.com/) for his support on US data.
112
3.6.2
Appendix 2 : Median Age and Average Sales price in the US
(see data source in Appendix 1)
Median Age in US market
Average Sale Price Real US $
3.6. APPENDIX
3.6.3
113
Appendix 3 : Raw data
(see data source in Appendix 1)
FR
114
UK
US (CPI data provided by the BLS are seasonally adjusted.)
3.6. APPENDIX
3.6.4
115
Appendix 4 : Growth rate and seasonally adjusted times series
FR
UK
116
US
FR
3.6. APPENDIX
117
UK
US
118
3.6.5
Appendix 5 : Granger Test
Pairwise Granger Causality Tests
Lags : 6
Null Hypothesis :
NEW_CARS_CPI does not Granger Cause USED_CARS_CPI
USED_CARS_CPI does not Granger Cause NEW_CARS_CPI
USED_CARS_VOL does not Granger Cause USED_CARS_CPI
USED_CARS_CPI does not Granger Cause USED_CARS_VOL
NEW_CARS_VOL does not Granger Cause USED_CARS_CPI
USED_CARS_CPI does not Granger Cause NEW_CARS_VOL
USED_CARS_VOL does not Granger Cause NEW_CARS_CPI
NEW_CARS_CPI does not Granger Cause USED_CARS_VOL
NEW_CARS_VOL does not Granger Cause NEW_CARS_CPI
NEW_CARS_CPI does not Granger Cause NEW_CARS_VOL
NEW_CARS_VOL does not Granger Cause USED_CARS_VOL
USED_CARS_VOL does not Granger Cause NEW_CARS_VOL
Obs
120
120
120
120
120
252
F-Statistic
1.0125
0.3615
0.5774
2.5318
0.8105
2.6519
0.8364
0.9842
1.0053
0.8752
2.1592
3.8416
Probability
0.4212
0.9017
0.7476
0.0248
0.5640
0.0194
0.5444
0.4397
0.4258
0.5158
0.0477
0.0011
F-Statistic
0.5688
0.8581
1.5144
1.7610
0.7487
3.5091
0.8961
0.4179
10.6495
0.3673
1.5057
0.7780
Probability
0.7543
0.5283
0.1859
0.1196
0.6117
0.0033
0.5027
0.8648
0.0000
0.8982
0.1888
0.5899
France
Lags : 6
Null Hypothesis :
UK
Obs
119
84
120
84
119
84
3.6. APPENDIX
Lags : 6
Null Hypothesis :
US
119
Obs
120
120
120
120
120
134
F-Statistic
3.2097
2.3908
1.6204
1.7257
0.7601
0.4233
0.3855
2.5894
2.0814
1.2774
4.2343
1.7096
Probability
0.0062
0.0331
0.1485
0.1219
0.6028
0.8621
0.8869
0.0221
0.0613
0.2738
0.0007
0.1244
120
3.6.6
Appendix 6 : Correlation Analysis
USED_CARS_CPI
NEW_CARS_CPI
USED_CARS_VOL
NEW_CARS_VOL
USED_CARS_CPI
1.00
-0.31
-0.03
0.10
NEW_CARS_CPI
-0.31
1.00
-0.13
-0.17
USED_CARS_VOL
-0.03
-0.13
1.00
0.44
NEW_CARS_VOL
0.10
-0.17
0.44
1.00
USED_CARS_CPI
NEW_CARS_CPI
USED_CARS_VOL
NEW_CARS_VOL
USED_CARS_CPI
1.00
0.16
0.05
0.35
NEW_CARS_CPI
0.16
1.00
-0.09
0.01
USED_CARS_VOL
0.05
-0.09
1.00
0.16
NEW_CARS_VOL
0.35
0.01
0.16
1.00
USED_CARS_CPI
NEW_CARS_CPI
USED_CARS_VOL
NEW_CARS_VOL
USED_CARS_CPI
1.00
0.54
-0.01
-0.01
NEW_CARS_CPI
0.54
1.00
0.02
0.04
USED_CARS_VOL
-0.01
0.02
1.00
-0.28
NEW_CARS_VOL
-0.01
0.04
-0.28
1.00
France
UK
US
3.6. APPENDIX
3.6.7
121
Appendix 7 : Hodrick-Prescott Filter, cycles and trends
France
France
France
France
122
UK
UK
UK
UK
3.6. APPENDIX
123
US
US
US
US
124
3.6.8
Appendix 8 : Hodrick-Prescott Cycles Correlations
France
NEW_CARS_CPI
USED_CARS_VOL
NEW_CARS_VOL
USED_CARS_CPI
NEW_CARS_CPI
1.000
0.082
0.058
0.087
USED_CARS_VOL
0.082
1
0.421
0.14
NEW_CARS_VOL
0.058
0.421
1
0.179
USED_CARS_CPI
0.087
0.14
0.179
1
USED_CARS_CPI(36)
0.341
0.068
0.206
-0.158
USED_CARS_CPI(24)
-0.137
-0.068
-0.005
-0.169
USED_CARS_CPI(18)
-0.107
-0.077
-0.065
-0.371
USED_CARS_CPI(12)
-0.116
-0.085
-0.223
-0.321
USED_CARS_CPI(9)
0.298
-0.078
-0.145
-0.116
USED_CARS_CPI(6)
0.215
0.128
-0.094
0.101
USED_CARS_CPI(3)
0.049
0.156
0.101
0.513
USED_CARS_CPI(-3)
-0.119
0.101
0.018
0.513
USED_CARS_CPI(-6)
-0.06
0.011
-0.013
0.101
USED_CARS_CPI(-9)
-0.012
0.066
0.04
-0.116
USED_CARS_CPI(-12)
0.008
-0.001
0.058
-0.321
USED_CARS_CPI(-18)
-0.019
-0.181
-0.107
-0.371
USED_CARS_CPI(-24)
-0.07
-0.084
0.019
-0.169
USED_CARS_CPI(-36)
0.217
0.077
-0.065
-0.158
NEW_CARS_CPI(-6)
-0.068
0.116
0.195
0.215
USED_CARS_VOL(-6)
0.041
0.152
0.085
0.128
NEW_CARS_VOL(-6)
-0.079
-0.114
0.006
-0.094
NEW_CARS_CPI(-12)
-0.392
-0.032
0.035
-0.116
USED_CARS_VOL(-12)
-0.038
-0.155
-0.012
-0.085
NEW_CARS_VOL(-12)
-0.015
-0.16
-0.447
-0.223
NEW_CARS_CPI(-24)
-0.171
0.021
-0.235
-0.137
USED_CARS_VOL(-24)
-0.026
-0.299
-0.064
-0.068
NEW_CARS_VOL(-24)
0.047
-0.102
0.045
-0.005
NEW_CARS_CPI(-36)
-0.07
-0.131
0.117
0.341
USED_CARS_VOL(-36)
0.047
-0.258
-0.18
0.068
NEW_CARS_VOL(-36)
-0.072
-0.067
-0.205
0.206
3.6. APPENDIX
125
UK
NEW_CARS_CPI
USED_CARS_VOL
NEW_CARS_VOL
USED_CARS_CPI
NEW_CARS_CPI
1
-0.192
-0.042
0.085
USED_CARS_VOL
-0.192
1
0.026
-0.132
NEW_CARS_VOL
-0.042
0.026
1
0.176
USED_CARS_CPI
0.085
-0.132
0.176
1
USED_CARS_CPI(36)
0
-0.05
-0.018
-0.158
USED_CARS_CPI(24)
0.1
-0.209
-0.005
-0.169
USED_CARS_CPI(18)
-0.043
-0.032
-0.047
-0.371
USED_CARS_CPI(12)
-0.283
0.192
-0.059
-0.321
USED_CARS_CPI(9)
-0.389
0.117
-0.053
-0.116
USED_CARS_CPI(6)
-0.447
0.052
0
0.101
USED_CARS_CPI(3)
-0.315
-0.143
0.13
0.513
USED_CARS_CPI(-3)
0.258
0.055
0.132
0.513
USED_CARS_CPI(-6)
0.339
-0.036
0.081
0.101
USED_CARS_CPI(-9)
0.347
0.071
-0.015
-0.116
USED_CARS_CPI(-12)
0.333
0.134
-0.131
-0.321
USED_CARS_CPI(-18)
0.137
0.141
-0.177
-0.371
USED_CARS_CPI(-24)
-0.208
-0.067
-0.139
-0.169
USED_CARS_CPI(-36)
0.281
-0.024
-0.144
-0.158
NEW_CARS_CPI(-6)
0.116
0.181
-0.051
-0.447
USED_CARS_VOL(-6)
-0.058
-0.007
-0.037
0.052
NEW_CARS_VOL(-6)
-0.156
0.069
0.152
0
NEW_CARS_CPI(-12)
-0.333
0.146
-0.18
-0.283
USED_CARS_VOL(-12)
0.125
-0.542
0.073
0.192
NEW_CARS_VOL(-12)
0.078
0.035
-0.183
-0.059
NEW_CARS_CPI(-24)
-0.224
-0.094
0.039
0.1
USED_CARS_VOL(-24)
0.123
-0.161
-0.179
-0.209
NEW_CARS_VOL(-24)
-0.016
-0.132
-0.16
-0.005
NEW_CARS_CPI(-36)
-0.066
-0.083
0.15
0
USED_CARS_VOL(-36)
-0.263
0.158
-0.011
-0.05
NEW_CARS_VOL(-36)
0.002
0.011
-0.051
-0.018
126
US
NEW_CARS_CPI
USED_CARS_VOL
NEW_CARS_VOL
USED_CARS_CPI
NEW_CARS_CPI
1
0.299
0.044
0.421
USED_CARS_VOL
0.299
1
-0.048
0.055
NEW_CARS_VOL
0.044
-0.048
1
0.136
USED_CARS_CPI(36)
0.097
0.139
0.196
0.19
USED_CARS_CPI(24)
-0.134
-0.164
-0.171
-0.087
USED_CARS_CPI(18)
0.016
-0.02
0.025
-0.22
USED_CARS_CPI(12)
-0.105
0.023
0.096
-0.522
USED_CARS_CPI(9)
0.146
0.054
0.068
-0.213
USED_CARS_CPI(6)
0.369
0.123
0.047
0.201
USED_CARS_CPI(3)
0.445
0.048
0.12
0.69
USED_CARS_CPI
0.421
0.055
0.136
1
USED_CARS_CPI(-3)
0.206
0.024
-0.027
0.69
USED_CARS_CPI(-6)
-0.113
-0.034
-0.127
0.201
USED_CARS_CPI(-9)
-0.176
0.034
-0.238
-0.213
USED_CARS_CPI(-12)
-0.178
0.027
-0.287
-0.522
USED_CARS_CPI(-18)
-0.051
-0.082
0.06
-0.22
USED_CARS_CPI(-24)
-0.222
-0.006
0.266
-0.087
USED_CARS_CPI(-36)
0.067
-0.15
0.104
0.19
NEW_CARS_CPI(-6)
-0.122
-0.09
-0.033
0.369
USED_CARS_VOL(-6)
-0.108
-0.037
0.038
0.123
NEW_CARS_VOL(-6)
-0.237
-0.137
0.066
0.047
NEW_CARS_CPI(-12)
-0.159
0.079
-0.169
-0.105
USED_CARS_VOL(-12)
-0.137
-0.289
0.052
0.023
NEW_CARS_VOL(-12)
0.144
-0.05
-0.407
0.096
NEW_CARS_CPI(-24)
-0.472
-0.117
0.27
-0.134
USED_CARS_VOL(-24)
-0.075
-0.174
0.113
-0.164
NEW_CARS_VOL(-24)
-0.054
0.139
-0.256
-0.171
NEW_CARS_CPI(-36)
-0.066
-0.215
0.08
0.097
USED_CARS_VOL(-36)
0.098
-0.24
-0.061
0.139
NEW_CARS_VOL(-36)
-0.105
0.035
0.245
0.196
3.6. APPENDIX
127
APPENDIX 9 : Cointegration test
us_used_sls_ = C(1) + C(2)* us_new_cars_trk_s_
Null Hypothesis : RES_US_REG has a unit root
Exogenous : None
Lag Length : 0 (Automatic based on SIC MAXLAG=13)
t-Statistic
Augmented Dickey-Fuller test statistic
-9.46
Test critical values :
Prob.*
0.00
1 prct level
-2.58
5 prct level
-1.94
10 prct level
-1.62
Variable
Coe¢ cient
Std. Error
t-Statistic
Prob.
RES_US_REG(-1)
-0.79
0.083
-9.46
0.00
R-squared
0.39
Mean dependent var
0.00
Adjusted R-squared
0.39
S.D. dependent var
0.077712394
S.E. of regression
0.06
Akaike info criterion
-2.76
Sum squared resid
0.51
Schwarz criterion
-2.74
Log likelihood
194.28
Durbin-Watson stat
2.06
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable : D(RESn_USn_REG)
Least Squares Included observations : 140 after adjustments
Sample (adjusted) : 1997M11 2009M06
128
APPENDIX 10 : Vector AutoRegressions
3.6. APPENDIX
129
In c lu d e d o b se rva tio n s : 1 2 4 a fte r a d ju stm e nts
FRANCE
S ta n d a rd e rro rs in ( ) & t-sta tistic s in [ ]
USED_CARS_CPI
U S E D _ C A R S _ C P I(-1 )
S a m p le (a d ju ste d ) :
1999M 03 2009M 06
NEW _CARS_CPI
USED _ C ARS_ VO L
NEW _ CARS_ VO L
1 .4 7 6 2
0 .0 2 3 9
0 .8 3 1 3
-0 .5 5 5 5
0 .0 7 7 9
0 .2 1 3 9
1 .6 7 4 3
2 .5 9 2 9
[ 1 8 .9 5 3 8 ]
[ 0 .1 1 1 8 9 ]
[ 0 .4 9 6 5 2 ]
[-0 .2 1 4 2 5 ]
-0 .5 1 2 5
-0 .1 1 7 4
-1 .1 9 7 7
0 .5 5 5 0
0 .0 7 8 1
0 .2 1 4 5
1 .6 7 8 7
2 .5 9 9 7
[-6 .5 6 3 0 2 ]
[-0 .5 4 7 2 9 ]
[-0 .7 1 3 4 7 ]
[ 0 .2 1 3 5 0 ]
-0 .0 4 3 6
0 .5 4 1 9
-1 .2 4 4 3
-1 .8 8 2 2
0 .0 3 2 8
0 .0 9 0 1
0 .7 0 5 0
1 .0 9 1 9
[-1 .3 2 8 4 4 ]
[ 6 .0 1 5 8 3 ]
[-1 .7 6 4 9 4 ]
[-1 .7 2 3 8 8 ]
0 .0 5 4 3
0 .1 1 4 6
0 .7 3 9 6
0 .6 6 5 0
0 .0 3 2 2
0 .0 8 8 5
0 .6 9 2 6
1 .0 7 2 6
[ 1 .6 8 6 9 5 ]
[ 1 .2 9 5 1 6 ]
[ 1 .0 6 7 9 6 ]
[ 0 .6 1 9 9 6 ]
-0 .0 0 0 2
-0 .0 2 3 1
-0 .0 2 9 7
0 .1 3 7 8
0 .0 0 4 9
0 .0 1 3 5
0 .1 0 5 5
0 .1 6 3 5
[-0 .0 4 4 3 4 ]
[-1 .7 1 2 6 0 ]
[-0 .2 8 1 2 9 ]
[ 0 .8 4 3 2 4 ]
-0 .0 0 0 1
-0 .0 1 1 2
0 .0 4 7 3
-0 .1 8 4 0
0 .0 0 5 1
0 .0 1 4 0
0 .1 0 9 8
0 .1 7 0 0
[-0 .0 2 6 8 9 ]
[-0 .8 0 1 9 5 ]
[ 0 .4 3 0 9 3 ]
[-1 .0 8 1 9 2 ]
-0 .0 0 3 0
-0 .0 0 0 4
0 .0 3 7 0
0 .0 5 1 2
0 .0 0 3 2
0 .0 0 8 8
0 .0 6 8 5
0 .1 0 6 1
[-0 .9 4 3 3 4 ]
[-0 .0 4 1 6 8 ]
[ 0 .5 3 9 3 3 ]
[ 0 .4 8 2 4 5 ]
0 .0 0 3 3
-0 .0 0 7 4
0 .0 3 6 1
0 .1 1 5 1
0 .0 0 3 2
0 .0 0 8 8
0 .0 6 8 8
0 .1 0 6 6
[ 1 .0 2 7 3 3 ]
[-0 .8 4 0 2 6 ]
[ 0 .5 2 3 8 4 ]
[ 1 .0 8 0 2 1 ]
0 .0 0 0 3
0 .0 0 4 4
0 .0 1 6 5
0 .0 1 3 2
0 .0 0 0 5
0 .0 0 1 3
0 .0 0 9 8
0 .0 1 5 2
[ 0 .6 1 6 3 9 ]
[ 3 .4 8 9 8 9 ]
[ 1 .6 8 5 8 3 ]
[ 0 .8 6 9 3 3 ]
R -sq u a re d
0 .9 6 4 4
0 .5 5 2 4
0 .0 4 8 8
0 .0 6 7 8
A d j. R -sq u a re d
0 .9 6 1 9
0 .5 2 1 2
-0 .0 1 7 3
0 .0 0 3 0
S u m sq . re sid s
0 .0 0 1 2
0 .0 0 8 7
0 .5 3 5 3
1 .2 8 3 8
A ka ike in fo rm a tio n c rite rio n
-1 9 .5 3 4 5
S chw a rz c rite rio n
-1 8 .7 1 5 8
U S E D _ C A R S _ C P I(-2 )
N E W _ C A R S _ C P I(-1 )
N E W _ C A R S _ C P I(-2 )
U S E D _ C A R S _ V O L (-1 )
U S E D _ C A R S _ V O L (-2 )
N E W _ C A R S _ V O L (-1 )
N E W _ C A R S _ V O L (-2 )
C
130
In c lu d e d o b se rva tio n s : 8 8 a fte r a d ju stm e nts
UK
USED_CARS_CPI
U S E D _ C A R S _ C P I(-1 )
2002M 03 2009M 06
D_NEW _CARS_CPI
USED _ C ARS_ VO L
NEW _ CARS_ VO L
1 .6 6 6 7
0 .1 3 1 9
-1 .1 6 6 9
2 .3 7 3 0
0 .0 8 3 7
0 .0 3 8 4
0 .8 6 6 8
1 .0 9 4 8
[ 1 9 .9 1 4 3 ]
[ 3 .4 3 7 7 8 ]
[-1 .3 4 6 2 7 ]
[ 2 .1 6 7 4 8 ]
-0 .8 0 4 0
-0 .1 3 7 7
1 .6 9 4 9
0 .0 0 2 3
0 .0 8 1 4
0 .0 3 7 3
0 .8 4 3 2
1 .0 6 5 0
[-9 .8 7 4 8 9 ]
[-3 .6 8 9 4 2 ]
[ 2 .0 1 0 1 9 ]
[ 0 .0 0 2 1 8 ]
0 .4 4 9 1
0 .0 4 3 2
0 .6 2 3 3
-3 .5 8 6 2
0 .2 3 3 1
0 .1 0 6 8
2 .4 1 3 9
3 .0 4 9 1
[ 1 .9 2 6 6 7 ]
[ 0 .4 0 4 1 4 ]
[ 0 .2 5 8 2 0 ]
[-1 .1 7 6 1 6 ]
-0 .2 3 0 9
-0 .0 6 2 0
-0 .0 7 5 3
-3 .1 4 8 4
0 .2 1 6 5
0 .0 9 9 2
2 .2 4 1 8
2 .8 3 1 7
[-1 .0 6 6 8 1 ]
[-0 .6 2 4 9 0 ]
[-0 .0 3 3 5 7 ]
[-1 .1 1 1 8 2 ]
-0 .0 1 9 5
-0 .0 0 0 2
0 .0 9 8 7
-0 .1 3 1 3
0 .0 1 0 8
0 .0 0 5 0
0 .1 1 1 9
0 .1 4 1 4
[-1 .8 0 3 6 8 ]
[-0 .0 3 8 4 2 ]
[ 0 .8 8 2 1 1 ]
[-0 .9 2 8 5 7 ]
0 .0 2 0 5
0 .0 1 3 8
0 .0 9 8 5
-0 .0 8 9 2
0 .0 1 1 0
0 .0 0 5 0
0 .1 1 3 4
0 .1 4 3 3
[ 1 .8 7 3 6 2 ]
[ 2 .7 4 1 1 6 ]
[ 0 .8 6 8 7 8 ]
[-0 .6 2 2 7 0 ]
0 .0 1 9 6
0 .0 0 4 8
0 .0 1 8 3
0 .0 5 4 6
0 .0 0 8 5
0 .0 0 3 9
0 .0 8 8 3
0 .1 1 1 6
[ 2 .2 9 9 9 1 ]
[ 1 .2 2 0 7 7 ]
[ 0 .2 0 6 8 0 ]
[ 0 .4 8 8 9 7 ]
0 .0 0 2 9
-0 .0 0 0 2
-0 .1 3 7 6
0 .1 3 6 7
0 .0 0 8 6
0 .0 0 3 9
0 .0 8 9 1
0 .1 1 2 6
[ 0 .3 3 4 0 4 ]
[-0 .0 4 0 4 1 ]
[-1 .5 4 3 9 0 ]
[ 1 .2 1 4 3 3 ]
-0 .0 0 5 3 ]
0 .0 0 0 0
0 .0 3 0 0
0 .0 7 9 8
0 .0 0 1 6
0 .0 0 0 8
0 .0 1 7 0
0 .0 2 1 5
[-3 .2 5 7 0 6 ]
[ 0 .0 0 0 3 4 ]
[ 1 .7 6 8 0 9 ]
[ 3 .7 2 1 9 3 ]
R -sq u a re d
0 .9 6 8 1
0 .2 1 4 0
0 .1 0 3 2
0 .5 9 2 6
0 .9 6 4 9
0 .1 3 4 4
0 .0 1 2 3
0 .5 5 1 4
S u m sq . re sid s
0 .0 0 3 0
0 .0 0 0 6
0 .3 2 6 0
0 .5 2 0 2
-2 0 .7 4 6 5
-1 9 .7 3 3 0
U S E D _ C A R S _ C P I(-2 )
D _ N E W _ C A R S _ C P I(-1 )
D _ N E W _ C A R S _ C P I(-2 )
U S E D _ C A R S _ V O L (-1 )
U S E D _ C A R S _ V O L (-2 )
N E W _ C A R S _ V O L (-1 )
N E W _ C A R S _ V O L (-2 )
C
3.6. APPENDIX
131
In c lu d e d o b se rva tio n s : 1 2 4 a fte r a d ju stm e nts
US
USED_CARS_CPI
U S E D _ C A R S _ C P I(-1 )
1999M 03 2009M 06
T_NEW _CARS_CPI
D _ USED _ C AR S_ VO L
D _ NEW _ C AR S_ VO L
1 .7 3 7 7
0 .1 0 2 8
0 .3 1 6 2
0 .0 3 1 4
0 .0 5 6 3
0 .0 2 9 1
0 .4 8 3 5
0 .7 1 4 7
[ 3 0 .8 6 1 1 ]
[ 3 .5 3 5 5 6 ]
[ 0 .6 5 4 0 0 ]
[ 0 .0 4 3 9 1 ]
-0 .8 1 5 7
-0 .0 9 2 7
-0 .3 8 2 5
-0 .3 1 2 3
0 .0 5 6 7
0 .0 2 9 3
0 .4 8 6 5
0 .7 1 9 2
[-1 4 .3 9 6 1 ]
[-3 .1 7 0 8 7 ]
[-0 .7 8 6 2 1 ]
[-0 .4 3 4 2 8 ]
-0 .1 0 2 9
1 .2 2 4 5
1 .7 8 3 6
1 .5 5 8 7
0 .1 5 7 0
0 .0 8 1 0
1 .3 4 7 7
1 .9 9 2 3
[-0 .6 5 5 5 3 ]
[ 1 5 .1 1 1 5 ]
[ 1 .3 2 3 3 6 ]
[ 0 .7 8 2 3 5 ]
0 .3 9 2 0
-0 .4 5 0 2
-1 .5 2 7 1
0 .4 2 9 3
0 .1 6 5 5
0 .0 8 5 4
1 .4 2 1 1
2 .1 0 0 8
[ 2 .3 6 8 7 3 ]
[-5 .2 6 8 8 6 ]
[-1 .0 7 4 5 5 ]
[ 0 .2 0 4 3 7 ]
-0 .0 0 9 0
0 .0 0 1 3
-0 .5 3 8 1
0 .0 5 6 1
0 .0 1 0 4
0 .0 0 5 4
0 .0 8 9 7
0 .1 3 2 6
[-0 .8 5 8 9 0 ]
[ 0 .2 3 6 3 0 ]
[-5 .9 9 8 5 9 ]
[ 0 .4 2 2 6 7 ]
-0 .0 1 6 2
0 .0 0 1 6
-0 .3 1 0 9
0 .0 1 7 6
0 .0 0 9 4
0 .0 0 4 9
0 .0 8 1 1
0 .1 1 9 9
[-1 .7 1 5 5 7 ]
[ 0 .3 2 9 8 1 ]
[-3 .8 3 2 5 7 ]
[ 0 .1 4 6 8 7 ]
-0 .0 0 6 7
0 .0 0 0 7
0 .2 9 2 8
-0 .4 0 8 3
0 .0 0 7 5
0 .0 0 3 8
0 .0 6 4 0
0 .0 9 4 6
[-0 .9 0 5 0 6 ]
[ 0 .1 8 3 8 8 ]
[ 4 .5 7 4 3 7 ]
[-4 .3 1 4 9 9 ]
0 .0 0 9 8
0 .0 0 7 9
0 .0 8 7 0
-0 .3 0 2 9
0 .0 0 8 0
0 .0 0 4 1
0 .0 6 8 3
0 .1 0 0 9
[ 1 .2 2 9 9 1 ]
[ 1 .9 3 3 9 0 ]
[ 1 .2 7 3 9 7 ]
[-3 .0 0 0 5 5 ]
-0 .0 0 1 0
0 .0 0 0 3
0 .0 0 1 2
-0 .0 1 0 3
0 .0 0 0 7
0 .0 0 0 3
0 .0 0 5 6
0 .0 0 8 3
[-1 .5 9 2 0 4 ]
[ 1 .0 2 8 9 3 ]
[ 0 .2 1 0 0 4 ]
[-1 .2 3 2 5 8 ]
R -sq u a re d
0 .9 8 3 2
0 .8 3 8 0
0 .4 4 0 5
0 .1 9 6 8
0 .9 8 2 0
0 .8 2 6 7
0 .4 0 1 6
0 .1 4 0 9
S u m sq . re sid s
0 .0 0 5 3
0 .0 0 1 4
0 .3 9 0 6
0 .8 5 3 5
-2 0 .4 2 7 1
-1 9 .6 0 8 3
U S E D _ C A R S _ C P I(-2 )
T _ N E W _ C A R S _ C P I(-1 )
T _ N E W _ C A R S _ C P I(-2 )
D _ U S E D _ C A R S _ V O L (-1 )
D _ U S E D _ C A R S _ V O L (-2 )
D _ N E W _ C A R S _ V O L (-1 )
D _ N E W _ C A R S _ V O L (-2 )
C
132
Conclusion Générale
Dans un contrat de leasing, le bailleur prend le risque de subir des pertes …nancières lors de
la revente de l’actif. Il exite un risque de valeur résiduelle. L’objectif général de cette thèse est
d’apporter une contribution académique à ce problème peu connu mais essentiel dans l’activité
de leasing. La thèse traite des di¤érents outils d’analyse quantitative disponibles pour les départements de gestion d’actifs et couvre trois thèmes : la valorisation des équipements par la
méthode des prix hédoniques, la couverture du risque de valeur résiduelle à l’aide de produits
…nanciers dérivés, et en…n les relations macro-économiques entre le marché du neuf et celui de
l’occasion.
Les modèles statistiques de prix hédoniques ont été largement utilisés pour l’analyse du
marché automobile. Dans le premier chapitre, nous exposons la méthodologie et proposons
une application aux véhicules d’occasion dans le secteur du leasing, où la valeur résiduelle
est un paramètre critique. Le modèle exploite les caractéristiques techniques des véhicules a…n
d’estimer la distribution des prix de revente. Deux autres facteurs, pouvant in‡uencer le marché
automobile, sont inclus : le prix du carburant et l’activité économique (l’indice de production
industrielle). La méthodologie, appliquée aux marchés automobiles d’occasion dans quatre pays
européens (l’Allemagne, l’Espagne, la France et la Grande Bretagne) fournit une perspective
nouvelle. En se concentrant sur le comportement de dépréciation de deux véhicules (Ford Focus
et Audi A4), notre étude révèle les di¤érents niveaux de probabilité de pertes en utilisant les
informations de revente disponibles par les sociétés de leasing. A travers une analyse des prix et
du risque, l’approche permet également d’identi…er les opportunités de leasing sur les di¤érents
marchés.
Notre première étude peut être poursuivie de plusieurs façons. L’industrie de leasing com133
134
CONCLUSION GÉNÉRALE
prend tous les types de matériel et l’application de l’approche hédonique est su¢ samment
‡exible pour être étendue à d’autres actifs que l’automobile. En outre, notre analyse pourrait
également être étendue aux contrats avec option d’achat ou avec une option dite de ‘rewrite’sur
l’âge et le kilométrage (le client pouvant, à tout moment, choisir de prolonger ou d’interrompre
le contrat.) Deux autres éléments dans le domaine du risque de valeur résiduelle pourraient être
ajoutés pour compléter l’analyse : le cycle de vie du véhicule et la variation générale du marché.
Les facteurs macro-économiques, en particulier, appellent à une étude plus approfondie.
Dans le deuxième chapitre, le modèle des copules gaussien de Li, qui a initialement été
utilisé pour l’analyse du risque de crédit, est transposé dans le secteur du leasing pour l’étude
du risque de valeur résiduelle. Un nouveau produit dérivé est proposé, le Collateralized Residual
Value (CRV). Le produit dérivé convertit les risques de pertes à la revente d’un portefeuille de
leasing en un instrument qui peut être vendu sur les marchés …nanciers. A l’instar des produits
dérivés classiques, il constitue un outil de transfert de risque. Ainsi il peut être utilisé à des
…ns de couverture des risques ou de spéculation. En outre, il permet au bailleur et au locataire
de choisir leurs degrés d’expositions au risque de valeur résiduelle et ainsi d’améliorer leur
compétitivité. En conséquence, le modèle se présente comme un apport pour les professionnels
de l’industrie du leasing intéressés par un produit …nancier novateur, ainsi que les acteurs des
marchés …nanciers intéressés par de nouvelles possibilités d’investissement.
Notre seconde analyse peut être étendue de diverses manières. La précision des composants
du modèle pourrait être améliorée, notamment par une analyse macro-économique du paramètre
de corrélation. En…n, d’autres familles de copules pourraient être appliquées.
Dans le dernier chapitre, nous étudions les interdépendances entre les marchés de véhicules
neufs et de véhicules d’occasion dans trois pays : la France, le Royaume-Uni et les ÉtatsUnis. L’analyse porte sur une période de dix ans. Les interactions sont donc étudiées sur une
décennie, alors même que l’automobile est un bien durable avec une durée de vie qui peut aller
jusqu’à 20 ans. Pourtant, les outils économétriques montrent des résultats uniformes tout au
long de l’étude. Nous constatons que pour les trois pays étudiés, le marché du neuf et le marché
de l’occasion interagissent par les prix et les volumes. Cependant, les interrelations semblent
limitées pour la France et le Royaume-Uni, alors que le marché américain se caractérise par une
dynamique dite de ‘Scitovsky’, dé…nie par un déséquilibre constant et de multiples interactions
entre les marchés du neuf et de l’occasion. Notre étude a également révélé qu’en fonction de
135
la perspective de court ou de long terme, les comportements des marchés sont di¤érents et
que certaines théories (Akerlo¤ e¤ect, Optimal durability, Time Inconsistency) impliquant des
volumes et des prix variant dans la même direction sont di¢ ciles à con…rmer. Bien que pour
ces trois pays les relations entre les marchés automobiles du neuf et de l’occasion ne soient pas
identiques, ils partagent tout de même une spéci…cité rarement mentionnée dans la littérature :
les prix pour les voitures neuves et les volumes de transaction des voitures d’occasion subissent
des rigidités. Le fait que les prix des voitures d’occasion suivent des cycles distincts est un
autre trait commun pour tous les pays. En…n les résultats montrent que les corrélations entre
les marchés de voitures neuves et d’occasion ne sont pas su¢ samment fortes pour expliquer
pleinement les variations des marchés.
L’utilisation de variables macro-économiques liées au revenu disponible des acheteurs ainsi
que l’état général de l’économie pourraient grandement améliorer la qualité des prévisions, et
faire l’objet de futures recherches.
136
CONCLUSION GÉNÉRALE
Bibliographie
Bibliographie de l’Introduction Générale
1. An Yan (2006) Leasing and Debt Financing : Substitutes or Complements ? Journal of
Financial and Quantitative Analysis Vol. 41, no. 3.
2. Ang James and Peterson Pamela P. (1984) The Leasing Puzzle. Journal of Finance,
American Finance Association, vol. 39(4), pp. 1055-65.
3. Beattie V., Goodacre, A. and Thomson S. (2000) Operating leases and the assessment of
lease-debt substitutability. Journal of Banking and Finance 24(3) pp. 427-470.
4. Brage Viktor and Eckerström Gustaf (2009) Leasing - A Comparative Study of Swedish
and Japanese Retail Firms. University essay from Göteborgs universitet Företagsekonomiska institutionen [2009-03-12T10 :30 :41Z]
5. Branson Bruce C. (1995) An Empirical Reexamination of the Leasing Puzzle. Quarterly
Journal of Business and Economics, Vol. 34.
6. Lewis Craig M. and Schallheim James S. (1992) Are Debt and Leases Substitutes ? Journal
of Financial and quantitative Analysis, Vol 27, no.4.
7. Drakos Konstantinos and Goulas Eleftherios (2008) Irreversible investment under uncertainty : the message in Leasing Expenditures, International Journal of Monetary Economics and Finance, Vol 1, no 4 pp. 412-426.
8. Drakos Konstantinos and Goulas Eleftherios (2008) The relative importance of sector
and country factors for leasing penetration rates across European industries, Applied
Economics Letters, Vol 15, pp.1197–1200.
9. Fishbein Bette K., McGarry Lorraine S. and Dillon Patricia S. (2000) Leasing : A Step
Toward Producer Responsibility, INFORM report www.informinc.org.
137
138
BIBLIOGRAPHIE
10. Fung William and Subrahmanyam Marti (1987) Leasing and Financial Intermediation :
Comparative Tax Advantages. Ivan E. Brick, Financial Management, Vol. 16 no.1 pp.
55-59
11. Goodacre Alan (2003) Accounting reform : a review of the empirical evidence Assessing
the potential impact of lease Journal of Property Research, 20(1) pp49–66.
12. Haug Espen Gaarder and Taleb Nassim Nicholas (2009) Why We Have Never Used
the Black-Scholes-Merton Option Pricing Formula (…fth version). Available at SSRN :
http ://ssrn.com/abstract=1012075.
13. IAS documentation : http ://www.iasplus.com/standard/ias17.htm
14. Kichler E and Haiss P. (2009) Leasing and Economic Growth - Evidence for Central and
South Eastern Europe Paper submitted for presentation at the 36th Annual European
Finance Association (EFA) Meeting.
15. Krishnan Sivarama V. and Moyer Charles R. (1994) Bankruptcy Costs and the Financial
Leasing Decision Financial Management, Vol. 23, no. 2, pp. 31-42.
16. Lasfer M.A. and Levis M. (1998) The determinants of the leasing decision of small and
large companies, European Financial Management, Vol. 4 pp.159-84.
17. Lease Europe Website : http ://www.leaseurope.org/
18. Mackie-Mason Je¤rey K. (1990) Do Taxes A¤ect Corporate Financing Decisions ? The
Journal Of Finance Vol. XLV, no.5.
19. Marston F., Harris, R.S. (1988) Substitutability of leases and debt in corporate capital
structures, Journal of Accounting, Auditing and Finance, Vol. 3 pp.147-70.
20. Pirotte Hugues and Vaessen Celine (2008) Residual value risk in the leasing industry : A
European case, The European Journal of Finance, Vol 14, no.2, pp. 157–177.
21. Prado Sylvain M. (2009) The European used-car market at a glance : Hedonic resale price
valuation in Automotive leasing industry. Economics Bulletin, Vol. 29 no.3 pp. 2086-2099.
22. Schmit M. and Stuyck J. (2002) Recovery rates in the leasing industry, Working paper
presented at Leaseurope’s Annual Working Meeting, Salzburg.
23. Schimt M. (2003) Is Automotive Leasing a Risky Business ? Université Libre de Bruxelles,
Solvay Brussels School of Economics and Management, Centre Emile Bernheim (CEB)
Working Papers CEB number 03-009.RS.
139
24. Schmit M. (2004) Credit risk in the leasing industry, Journal of Banking & Finance Vol
28, no. 4, pp. 811-833.
25. Smith Cli¤ord W Jr and Wakeman Macdonald L. (1985) Determinants of Corporate
Leasing Policy. The Journal of Finance Vol. XL, no.3.
26. White Clarke Global Leasing report (2008) http ://www.whiteclarkegroup.com
140
BIBLIOGRAPHIE
Bibliographie du premier chapitre
1. Akerlof George A. (1970) The Market for "Lemons" : Quality Uncertainty and the Market
Mechanism. The Quarterly Journal of Economics, Vol. 84, No. 3 , pp. 488-500.
2. Ackerman, Susan Rose (1973) Used Cars as a Depreciating Asset. Western Economic
Journal Vol 11 pp. 463-474.
3. Atkinson Scott E. and Halvorsen Robert (1990) The Valuation of Risks to Life : Evidence
from the Market for Automobiles. The Review of Economics and Statistics, Vol. 72, No.
1 , pp. 133-136.
4. Bartik Timothy J. (Feb., 1987) The Estimation of Demand Parameters in Hedonic Price
Models. The Journal of Political Economy, Vol. 95, No. 1 , pp. 81-88.
5. Brown James N. and Rosen Harvey S. (1982) On the Estimation of Structural Hedonic
Price Models. Econometrica, Vol. 50, No. 3 , pp. 765-768.
6. Court A. (1939). Hedonic price indexes with automotive examples. In : American Statistical Association (Ed.), The dynamics of automobile demand. New York : General Motors
Corporation. pp. 99-117.
7. Couton C., Gardes F. and Thepaut Y. (1996) Hedonic Prices for Environmental and Safety
Characteristics and the Akerlo¤ E¤ect in the French Car Market. Applied Economics
Letters, Vol. 3, issue 7, pp. 435-40.
8. Combris P., Lecoq S. and Visser M. (1997) Estimation of a Hedonic Price Equation for
Bordeaux vine : Does Quality Matter ?. The Economic Journal, issue 107, (March), pp.
390-402.
9. Cowling Keith and Cubbin John (1971) Price, Quality and Advertising Competition : An
Econometric Investigation of the United Kingdom Car Market. Economica, New Series,
Vol. 38, No. 152 , pp. 378-394
10. Cowling Keith and Cubbin John (1972) Hedonic Price Indexes for United Kingdom Cars.
The Economic Journal, Vol. 82, No. 327, pp. 963-978.
11. Cubbin John (1975) Quality Change and Pricing Behaviour in the United Kingdom Car
Industry 1956-1968. Economica, New Series, Vol. 42, No. 165, pp. 43-58.
12. Dalen Jan van and Bode Ben (2004) Quality-corrected price indices : the case of the Dutch
new passenger car market, 1990-1999 Applied Economics, vol. 36, issue 11, pp 1169-1197.
141
13. Ekeland Ivar, Heckman James J. , and Nesheim Lars (2004) Identi…cation and Estimation
of Hedonic Models. Journal of Political Economy, Vol. 112, No. 1, pp. S60-S109.
14. Greene William (2003). Econometric Analysis. Prentice Hall. 6th Edition.
15. Hartman Raymond S. (1987) Product Quality and Market E¢ ciency : The E¤ect of
Product Recalls on Resale Prices and Firm Valuation. The Review of Economics and
Statistics, Vol. 69, No. 2 , pp. 367-372.
16. Ho¤er George D and Pratt Michael (1990) The E¢ ciency of Used Vehicle Markets : The
Case of Technological Obsolescence and Di¤erential Repair Records. Applied Economics,
Vol. 22, issue 9, pp. 1205-13.
17. Hogarty Thomas F. (1975) Price-Quality Relations for Automobiles : A New Approach
Applied Economics, Vol. 7, issue 1, pp. 41-51.
18. Lancaster Kelvin J. (1966). A New Approach to Consumer Theory. The Journal of Political Economy, Vol. 74, No. 2 , pp. 132-157.
19. Ohta M. and Griliches Z. (1976) Automobile prices revisited : extensions of the Hedonic
hypothesis, in N.E. Terleckyj, ed., Household Production and Consumption. New York :
National Bureau of Economic Research.
20. Pickering J. F, Harrison J. A, Isherwood B. C, Hebden J. J, Cohen, C. D.(1973) Are
Goods Goods ? Some Empirical Evidence. Applied Economics , Vol. 5 Issue 1, pp.1-18.
valuation in automotive leasing industry. Economics Bulletin, Vol. 29 No.3 pp. 2086-2099.
22. Reis H.J. and Santos Silva J.M.C. (2002) Hedonic Price Indexes for New Passenger Cars
in Portugal (1997–2001). Working paper 10-02, Banco de Portugal
23. Rosen Sherwin (1974) Hedonic Prices and Implicit Markets : Product Di¤erentiation in
Pure Competition. The Journal of Political Economy, Vol. 82, No. 1 , pp. 34-55.
24. Triplett Jack E (1969) Automobiles and Hedonic Quality Measurement. Journal of Political Economy, vol. 77, issue 3, pp. 408-17.
25. Waugh F.V. (1928) Quality Factors in‡uencing vegetables prices. Journal of farm economics, Vol10, p185-196.
26. Yerger David B (1996). Used Car Markets : Reliability Does Matter, but Do Consumer
Reports ?. Applied Economics Letters, vol. 3, issue 2, pp. 67-70.
142
BIBLIOGRAPHIE
Bibliographie du deuxième chapitre
1. Andersen L., Sidenius J., and Basu S. (2003) All your hedges in one basket. Risk, Vol 16,
pp. 67-72.
2. Bluhm C. Overbeck L., and Wagner C. (2003) An Introduction to Credit Risk Modeling.
Chapman & Hall/CRC Financial Mathematics Series.
3. Cherubini U, Luciano E, and Vecchiato W. (2004) Copula Methods in Finance. New
York : John Wiley & Sons.
4. Copeland T.E. and Weston J. (1982) A note on the evaluation of cancellable operating
leases. Financial Management, Vol 11, pp. 60-67.
5. Cousseran O. and Rahmouni I. (2006). Le marché des CDO Modalités de fonctionnement
et implications en termes de stabilité …nancière. Banque de France, Revue de la stabilité
Financière, Vol 6, pp. 47-67.
6. DEMETRA 2.1 documentation and freeware available from
circa.europa.eu/irc/dsis/eurosam/info/data/demetra.htm.
7. Gibson M.S. (2004) Understanding the risk of synthetic CDOs. Federal Reserve Board.
Finance and economic Discussion Series paper, Vol 36.
8. Gordon M.M. (2001) Retreat is sounded as those leasing residual losses mount. Ward’s
dealer Business. March 1 2001.
9. Grenadier S.R. (1995) Valuing lease contracts A real-options approach. Journal of Financial Economics, Vol 38, pp. 297-331.
10. Halladay S. D. and Amembal S. P. (1998) The Handbook of Equipment Leasing. A&H.
Vol I-II .
11. Hull J. (2005) Options, Futures, and Other Derivatives (6th ed.) Credit derivatives, Chapter 21.
12. Hull J. and A. White (2004) Valuation of a CDO and an n-th to Default CDS Without
Monte Carlo Simulation. Journal of Derivatives, Vol 12, pp. 8-23.
13. Irotte H., Schmit M., and Vaessen C. (2004) Credit risk mitigation evidence in Auto
leases : LGD and residual value risk. Working Paper.
Retrieved from www.solvay.edu/EN/Research/Bernheim/documents/wp04008.pdf
143
14. Jost A. and Franke A. (2005) Residual value analysis. Paper presented at the 23rd International Conference of the System Dynamics Society.
15. Laurent M.P. and Schmit M. (2007) An empirical approach to estimate residual value
risk and its interconnection with credit risk the case of automotive leases. Working Paper.
Retrieved from http ://a¢ 2007.u-bordeaux4.fr/Actes/178.pdf
16. Lasfert M. and Mario L. (1998) The determinants of leasing decisions of small and large
companies. European Financial Management, Vol 4.
17. Li D.X. (2000) On default correlation : a copula approach. Journal of Fixed Income, Vol
9, pp. 43-54.
18. Lucko G. (2003) Statistical Analysis and Model of Residual Value of di¤erent type of
Heavy Construction Equipment.Thesis. Virginia Polytechnic institute and state University.
19. Lucko G., Anderson-cook C., and Vorster M.C. (2006) Statistical considerations for predicting residual value of heavy equipment. Journal of construction engineering and management, Vol132, pp.723-732.
20. Meneguzzo D. and Vecchiato W. (2004) Copula sensitivity in collateralized debt obligations and basket default swaps. Journal of Futures Markets, Vol 24, No1, pp.37-70.
21. Merton, R. (1974) On the pricing of corporate debt : the risk structure of interest rates.
Journal of Finance, Vol 29, pp.449-470.
22. Miller S. E. (1995) Economics of automobile leasing : the call option value. Journal of
Consumer A¤airs, Vol 29 , pp.199-218.
23. Nelsen R. (2006) An introduction to copulas, Second Edition. New York : Springer.
24. Pykhtin M. and Dev A. (2003) Residual risk in auto leases, Risk,Vol 16, No10, pp.10-16.
25. Rode D.C., Fischbeck P. S., and Dean S.R. (2002) Residual risk and the valuation of
leases under uncertainty and limited information. Carnegie Mellon Electricity Industry
Center. CEIC. Working Paper.
Retrived from http ://wpweb2.tepper.cmu.edu/ceic/papers/ceic-02-02.asp
26. Schonbucher P. (2000). Factor models for portfolio credit risk. Department of Statistics.
Bonn University. Working Paper.
Retrived from http ://www.defaultrisk.com/pp_model_25.htm
144
BIBLIOGRAPHIE
27. Schmit M. (2004) Credit risk in leasing industry. Journal of Banking and Finance, Vol
28, pp.811-84.
28. Schmit M. (2004) Is automotive leasing a risky business ?. Finance, Vol 26, pp.35-66.
29. The economist (April 21st 2007) At the risky end of …nance.
30. The economist (February 14th 2008) Fear and loathing, and a hint of hope.
31. The Wall Street Journal (September 12, 2005) Gaussian copula and credit derivatives.
32. Vershuere B. (2006) On copula and their application to CDO pricing. University of Chicago. IL. Master thesis.
33. White E. (2008) Global Leasing Report. White Clarke Group.
145
Bibliographie du troisième chapitre
1. Akerlof George A (1970) The Market for "Lemons" : Quality Uncertainty and the Market
Mechanism. The Quarterly Journal of Economics, Vol. 84, No.3, pp. 488-500.
2. Caillaud Alain (1998) Pour comprendre l indice des Prix. Édition Insee Méthodes n
81-82.
3. Chazi Abdelaziz (2007) Is Default Risk Related to In‡ation ? Journal of Accounting.
Business & Management , Vol 14, No.0.
4. Clerides Sophronis (2008) Gains from trade in used goods : Evidence from automobiles.
Journal of International Economics, Vol 76, No.2, pp.322-336.
5. Coase Ronald. (1972) Durability and monopoly. Journal of Law and Economics, Vol 15,
pp. 143-149.
6. CRS report for congress. U.S. Automotive Industry : Policy Overview and Recent History.
http ://ncseonline.org/NLE/CRSreports/05apr/RL32883.pdf
7. Fiorito, Riccardo and Kollintzas Tryphon (1994) Stylized Facts of Business Cycles in the
G7 from a Real Business Cycles Perspective. European Economic Review , pp. 235–69.
8. Fixler Dennis, Fortuna Charles, Greenlees John, and Lane Walter(1999) The Use of Hedonic Regressions to Handle Quality Change :The Experience in the U.S. CPI. U.S. Bureau
of Labor Statistics Presented at the Fifth Meeting of the International Working Group
on Price Indices Reykjavik, Iceland 1999.
9. Fudenberg Drew and Tirole Jean (1998) Upgrades, Trade-ins, and Buybacks. Rand Journal of Economics. Vol. 29, No. 2, pp. 235-258
10. Gaulier Guillaume and Haller Séverine (2000) The Convergence of Automobile Prices in
the European Union : an Empirical Analysis for the Period 1993-1999. CEPII 2000, No
14.
11. Gautier Bernard (1995) Le marché automobile : un cycle spéci…que ? Économie et Statistique, Année 1995, Vol 282, No 1, pp. 65-90.
12. Goldberg Pinelopi K. and Verboven Frank (1998) The Evolution of Price Dispersion in
the European Car Market. NBER Working Paper No. W6818.
13. Greenlees John S and McClelland Robert B (2008) Addressing misconceptions about the
Consumer Price Index. Monthly Labor Review, Vol. 131, No 8.
146
BIBLIOGRAPHIE
14. Anderson Simon and Ginsburgh Victor A. (1994) Price discrimination via second-hand
markets. European Economic Review, Vol. 38, No 1, pp. 23-44.
15. Hendel Igal and Lizzeri Alessandro (1999a) Adverse Selection in Durable Goods Markets.
American Economic Review, Vol. 89, No 5, pp. 1097-1115.
16. Hendel Igal and Lizzeri Alessandro (1999b) Interfering with Secondary Markets. RAND
Journal of Economics, Vol. 30, No 1, pp 1-21.
17. Hodrick, Robert and Prescott, Edward (1997) Postwar U.S. Business Cycles : An Empirical Investigation. Journal of Money, Credit, and Banking Vol. 29, No 1, pp. 1-16.
18. Lescaroux François and Mignon Valerie (2008) On the In‡uence of Oil Prices on Economic
Activity and Other Macroeconomic and Financial Variables. Working Papers 2008-05,
CEPII research center .
19. Paredes Martin G. (2006) Consumer Behavior in Markets of Durable Experience Goods.
mimeo, NYU.
20. Pashigian Peter B. (2001) The used car price index : A checkup and suggested repairs,
Working paper 338, Bureau of Labor Statistics.
21. Peach Richard W. and Alvarez Karen (1996) Core CPI : Excluding Food, Energy...And
Used Cars ?. Current Issues in Economics and Finance, Vol. 2, No. 4
22. Perron Pierre (1989) The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis.
Econometrica, Vol. 57, No. 6 , pp. 1361-1401.
23. Petrin Amil (2002) Quantifying the Bene…ts of New Products : The Case of the Minivan
The Journal of Political Economy. Vol. 110, No. 4, pp. 705-729.
24. Prado Sylvain M. (2008) Hedging residual value risk using derivatives. Working Paper.
Economix.
http ://economix.u-paris10.fr/pdf/dt/2009/WP_EcoX_2009-22.pdf
valuation in automotive leasing industry. Economics Bulletin, Vol. 29 No.3 pp. 2086-2099.
26. Reinsdorf Marshall and Triplett Jack E. (January 2008) A Review of Reviews : Ninety
Years of Professional Thinking About the Consumer Price Index. NBER.
www.nber.org/chapters/c5068.pdf ?new_window=1
27. Rust John (January 1986) When Is It Optimal to Kill O¤ the Market for Used Durable
Goods ? Econometrica, Econometric Society, Vol. 54, No.1, pp. 65-86.
147
28. Schiraldi Pasquale (2006) Second-Hand Markets and Collusion by Manufacturers of Semidurable Goods. Working Papers Series WP2006-028, Boston University Department of
Economics.
29. Scitovsky Tibor (1994) Towards a Theory of Second-Hand Markets. Kyklos, Vol. 47, No.1,
pp. 33-52.
30. Sieper Edward and Swan Peter L. (1973) Monopoly and Competition in the Market for
Durable Goods. The Review of Economic Studies, Vol. 40 , pp. 333-35.
31. Summary Quality Report for Consumer Price Indices
www.statistics.gov.uk/articles/nojournal/CPISQR.pdf
32. Van Cayseele Patrick (1993) Lemons, peaches and creampu¤s : The economics of a secondhand market. Tijdschrift voor Economie en Management, Vol.38, No.1, pp.73-85.
33. Waldman Michael (1996) Planned Obsolescence and the R&D Decision. RAND Journal
of Economics, Vol. 27, No. 3, pp. 583-595.
34. Waldman Michael (2003) Durable Goods Theory for Real World Markets. Journal of
Economic Perspectives. Vol. 17 No.1, pp. 131-154.
35. Winand Emons and Sheldon George (2002) The Market for Used Cars : A New Test of
the Lemons Model. CEPR Discussion Paper No. 3360.

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