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452 14. Gestion de Portefeuilles multimoments et équilibre de marché assessment and optimization. We have shown that these risk measures, which contain centered moments (and cumulants with some restriction) as particular examples, generalize them significantly. We have presented a generalization of previous generalizations of the efficient frontiers and of the CAPM based on these risk measures in the cases of homogeneous and heterogeneous agents. We have then proposed a simple but powerful specific von Mises representation of multivariate distribution of returns that allowed us to obtain new analytical results on and empirical tests of a general framework for a portfolio theory of non-Gaussian risks with non-linear correlations. Quantitative tests have been presented on a basket of seventeen stocks among the largest capitalization on the NYSE. This work opens several novel interesting avenues for research. One consists in extending the Gaussian copula assumption, for instance by using the maximum-entropy principle with non-extensive Tsallis entropies, known to be the correct mathematical information-theoretical representation of power laws. A second line of research would be to extend the present framework to encompass simultaneously different time scales τ in the spirit of (Muzy et al. 2001) in the case of a cascade model of volatilities. 28
A Description of the data set We have considered a set of seventeen assets traded on the New York Stock Exchange: Applied Material, Coca-Cola, EMC, Exxon-Mobil, General Electric, General Motors, Hewlett Packard, IBM, Intel, MCI WorldCom, Medtronic, Merck, Pfizer, Procter & Gambel, SBC Communication, Texas Instrument, Wall Mart. These assets have been choosen since they are among the largest capitalizations of the NYSE at the time of writing. The dataset comes from the Center for Research in Security Prices (CRSP) database and covers the time interval from the end of January 1995 to the end of December 2000, which represents exactly 1500 trading days. The main statistical features of the compagnies composing the dataset are presented in the table 5. Note the high kurtosis of each distribution of returns as well as the large values of the observed minimum and maximum returns compared with the standard deviations, that clearly underlines the non-Gaussian behavior of these assets. 29 453
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UNIVERSITE DE NICE-SOPHIA ANTIPOLIS
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4 Table des matières 2.2.2 Bulles
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6 Table des matières 7.3.2 Tests n
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8 Table des matières 12.1.1 Distri
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10 Table des matières Références
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12 m’ont souvent été d’un gra
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14 Introduction pour espérer se co
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16 Introduction les distributions e
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18 Introduction
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Chapitre 1 Faits stylisés des rent
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1.1. Rappel des faits stylisés 23
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1.1. Rappel des faits stylisés 25
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1.2. De la difficulté de représen
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1.3. Modélisation des propriétés
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Chapitre 2 Modèles phénoménologi
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2.1. Bulles rationnelles multi-dime
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2.2. Des bulles rationnelles aux kr
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Chapitre 3 Distributions exponentie
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Empirical Distributions of Log-Retu
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concerning tail fatness can be form
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To fit our two data sets, section 4
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properties, stressing the problems
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Another problem lies in the determi
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In order to obtain a process with S
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and Sornette (1999) for instance. W
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1. The Pareto distribution: 79 Fu(x
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empirical analog FN(x), estimated f
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have been chosen to converge to 1 a
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5 Comparison of the descriptive pow
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ased on the fact that the quantity
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tail (positive or negative) of the
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Equation (46) depends on c only and
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B Minimum Anderson-Darling Estimato
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C Local exponent In this Appendix,
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D Testing non-nested hypotheses wit
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where α = (c ∗ ,d ∗ ). It can
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where E0[·] denotes the expectatio
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References Andersen, J.V. and D. So
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Gouriéroux C. and A. Monfort, 1994
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Rubinstein, M., 1973, The fundament
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(a) Independent Data Stretched-Expo
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(a) Dow Jones Positive Tail Negativ
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Nasdaq Dow Jones Pos. Tail Neg. Tai
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Dow Jones positive tail Dow Jones n
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Variation coefficient Variation coe
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Mean excess function Mean excess fu
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Hill‘s estimate b u Hill‘s esti
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Wilks statistic (doubled log−like
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Tail 1−F(x) and parameter b Tail
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1.4 1.2 1 0.8 0.6 0.4 0.2 0 1 2 3 4
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Chapitre 4 Relaxation de la volatil
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Volatility Fingerprints of Large Sh
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2 Long-range memory and distinction
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Figure 2: Measuring the conditional
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the system to the accumulation of m
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Appendix C: “Conditional response
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Baillie, R.T., 1996, Long memory pr
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Chapitre 5 Approche comportementale
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5.1. Prix d’un actif et excès de
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5.2. Modèles d’opinion contre mo
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5.4. Conséquences des phénomènes
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5.5. Conclusion 157 ce qui induit u
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Chapitre 6 Comportements mimétique
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RESEARCH PAPER Q UANTITATIVE F INAN
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A Corcos et al Q UANTITATIVE F INAN
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Deuxième partie Etude des proprié
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182 7. Etude de la dépendance à l
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192 8. Tests de copule gaussienne
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194 8. Tests de copule gaussienne 1
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200 8. Tests de copule gaussienne t
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202 8. Tests de copule gaussienne T
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204 8. Tests de copule gaussienne a
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206 8. Tests de copule gaussienne c
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208 8. Tests de copule gaussienne t
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210 8. Tests de copule gaussienne (
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212 8. Tests de copule gaussienne R
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228 8. Tests de copule gaussienne f
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236 8. Tests de copule gaussienne T
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238 9. Mesure de la dépendance ext
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Chapitre 10 La mesure du risque Dan
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10.1. La théorie de l’utilité 3
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10.2. Les mesures de risque cohére
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10.3. Les mesures de fluctuations 3
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10.4. Conclusion 361 et de manière
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Chapitre 11 Portefeuilles optimaux
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11.2. Prise en compte des grands ri
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11.3. Equilibre de marché 367 s’
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11.5. Annexe 369 Collective Origin
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11.5. Annexe 371 point λ = 1. Thus
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Chapitre 12 Gestion des risques gra
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12.1. Comprendre et gérer les risq
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12.2. Minimiser l’impact des gran
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Chapitre 13 Gestion de portefeuille
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VaR-Efficient Portfolios for a Clas
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dependence: from independence to co
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given a series of return {rt}t foll
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eads cV (u1, · · · , un) = 1
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THEOREM 4 (TAIL EQUIVALENCE FOR A S
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Independent Assets Comonotonic Asse
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Page 413 and 414: B Asymptotic distribution of the su
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Page 417 and 418: References Acerbi, A. and D. Tasche
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Page 421 and 422: ln(T/T 0 ) T Figure 2: Logarithm
Page 423 and 424: Chapitre 14 Gestion de Portefeuille
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Page 431 and 432: This property is verified for all c
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Page 445 and 446: 7.2 Transformation of the modified
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Page 455 and 456: thus and finally 1 λ1 n−1 = w
Page 457 and 458: C Composition of the market portfol
Page 459 and 460: D Generalized capital asset princin
Page 461 and 462: This brings us back to the problem
Page 463 and 464: F.2 General case We now consider a
Page 465 and 466: Harvey, C.R. and A. Siddique, 2000,
Page 467 and 468: µ µ2 1/2 µ4 1/4 µ6 1/6 µ8 1/8
Page 469 and 470: Mean (10 −3 ) Variance (10 −3 )
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Page 473 and 474: w i w i 0.2 0.15 0.1 0.05 Mean−μ
Page 475 and 476: Figure 6: Schematic representation
Page 477 and 478: Empirical Cumulative Distribution 1
Page 479 and 480: Z 2 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0
Page 481 and 482: Z 2 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0
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Page 485 and 486: 10 0 10 −1 10 0 10 −1 10 −1 1
Page 487 and 488: κ 22 20 18 16 14 12 10 8 6 4 2 Exc
Page 489 and 490: Return μ 0.12 0.11 0.1 0.09 0.08 0
Page 491 and 492: Conclusions et Perspectives L’obj
Page 493 and 494: Conclusion 493 en univers gaussien
Page 495 and 496: Annexe A Evaluation de la conduite
Page 497 and 498: A.2. Eléments de contexte 497 bora
Page 499 and 500: A.4. Compétences acquises et ensei
Page 501 and 502: A.5. Conclusion 501 de la recherche
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Bibliographie ACERBI, C. (2002) :
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Bibliographie 505 BOUCHAUD, J. P. E
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Bibliographie 507 DE FINETTI, B. (1
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Bibliographie 509 GRANGER, C. W. ET
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Bibliographie 511 LILLO, F. ET R. N
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Bibliographie 513 PATTON, A. (2001)
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Bibliographie 515 SUSMEL, R. (1996)
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