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488 14. Gestion de Portefeuilles multimoments et équilibre de marché C 4 65 60 55 50 45 40 35 30 25 20 Fourth Cumulant for CHF / UKP 15 0 0.1 0.2 0.3 0.4 0.5 w CHF 0.6 0.7 0.8 0.9 1 Figure 19: Fourth cumulant for a portfolio made of a fraction wCHF of Swiss Franc and 1−wCHF of British Pound. The thick solid line represents the empirical cumulant while the dotted line represents the theoretical cumulant under the symmetric assumption. The dashed line shows the theoretical cumulant when the slight asymmetry of the assets has been taken into account. This cumulant has been evaluated for the time interval from Jan. 1971 to Oct. 1998. 64
Return μ 0.12 0.11 0.1 0.09 0.08 0.07 Efficient Frontier forIBM−HWP 1 1.2 1.4 1.6 min C /C , n={1,2,3} 2n 2n 1.8 2 2.2 Figure 20: Efficient frontier for a portfolio composed of two stocks: IBM and Hewlett-Packard. The dashed line represents the efficient frontier with respect to the second cumulant, i.e., the standard Markovitz efficient frontier, the dash-dotted line represents the efficient frontier with respect to the fourth cumulant and the solid line is the efficient frontier with respect to the sixth cumulant. The data set used covers the time interval from Jan. 1977 to Dec 2000. 65 489
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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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3.2 Typical recurrence time of larg
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and finally w ∗ i = χ−1 i j
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where the ˆwi’s are solution of
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Choosing x > y > Aɛ, and applying
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Expanding fi(xi) around x ∗ i yie
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for all h ∈ AC. Thus, integrating
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B Asymptotic distribution of the su
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This yields × h+ Sc−2 − 2 dh
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References Acerbi, A. and D. Tasche
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Malevergne, Y. and D. Sornette, 200
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ln(T/T 0 ) T Figure 2: Logarithm
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Chapitre 14 Gestion de Portefeuille
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Multi-Moments Method for Portfolio
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choosen risk measure. Section 5 pre
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The variance of the return X of an
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This property is verified for all c
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µn=α of order n = 2, 4, 6 and 8.
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these two assets or portfolios. The
Page 437 and 438: Due to the homogeneity property of
Page 439 and 440: invested in the risky fund depends
Page 441 and 442: C. Then, if g1(X1), · · · , gn(X
Page 443 and 444: Differentiating with respect to x1,
Page 445 and 446: 7.2 Transformation of the modified
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Page 449 and 450: 8.3 Non-symmetric assets In the cas
Page 451 and 452: y the variance will then increase).
Page 453 and 454: A Description of the data set We ha
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 )
Page 471 and 472: μ (daily return) x 10−3 2.5 2 1.
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
Page 483 and 484: 10 0 10 −1 10 0 10 −1 10 −1 1
Page 485 and 486: 10 0 10 −1 10 0 10 −1 10 −1 1
Page 487: κ 22 20 18 16 14 12 10 8 6 4 2 Exc
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
Page 503 and 504: Bibliographie ACERBI, C. (2002) :
Page 505 and 506: Bibliographie 505 BOUCHAUD, J. P. E
Page 507 and 508: Bibliographie 507 DE FINETTI, B. (1
Page 509 and 510: Bibliographie 509 GRANGER, C. W. ET
Page 511 and 512: Bibliographie 511 LILLO, F. ET R. N
Page 513 and 514: Bibliographie 513 PATTON, A. (2001)
Page 515: Bibliographie 515 SUSMEL, R. (1996)
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