statistique, théorie et gestion de portefeuille - Docs at ISFA

More documents

Recommendations

Info

332 9. Mesure de la dépendance extrême entre deux actifs financiers Negative Tail Positive Tail q = 1% q = 2.5% q = 5% q = 1% q = 2.5% q = 5% Asset ε Asset ε Asset ε Asset ε Asset ε Asset ε Abbott Labs 3.59 3.60 3.35 3.62 3.22 3.39 5.14 4.60 4.16 3.76 3.77 3.07 American Home Products Corp. 3.03 3.07 3.11 2.78 2.73 2.49∗ 4.01 3.47 3.28 3.02 2.87 2.79 Boeing Co. 3.39 3.97 3.23 3.53 3.02 3.21 4.86 3.65 3.45 3.16 3.13 3.23 Bristol-Myers Squibb Co. 3.21 3.15 2.90 3.41 2.80 3.16 2.98 3.74 3.35 3.12 3.20 2.75 Chevron Corp. 4.13 4.48 3.99 3.91 3.30 3.45 5.16 4.53 3.88 3.81 3.01 3.06 Du Pont (E.I.) de Nemours & Co. 3.99 3.49 3.76 3.23 3.02 3.04 5.36 4.33 4.31 3.35 3.44 2.76 Disney (Walt) Co. 2.83 3.24 2.76 2.97 2.85 2.83 3.97 3.70 3.68 3.33 3.15 2.87 General Motors Corp. 4.44 4.79 3.88 4.27∗ 3.44 3.56 5.76 5.32 4.45 3.86 3.43 3.22 Hewlett-Packard Co. 3.73 3.45 3.52 3.12 3.00 2.73 4.31 3.40 3.47 3.29 3.24 2.99 Coca-Cola Co. 3.01 3.76 3.14 3.48 2.99 2.86 4.06 3.47 3.45 3.16 3.37 2.87 Minnesota Mining & MFG Co. 3.52 3.38 3.21 3.39 2.88 3.04 3.76 3.46 3.95 3.22 3.10 2.76 Philip Morris Cos Inc. 3.58 3.34 3.33 3.12 2.68 2.53∗ 3.42 3.16 3.70 3.07 2.85 2.81 Pepsico Inc. 4.14 4.46 3.39 3.60 2.99 3.27 4.00 3.87 3.61 3.34 3.44 3.31 Procter & Gamble Co. 2.65 2.46 3.29 3.19 3.19 2.87 4.35 3.90 3.48 3.20 3.14 2.91 Pharmacia Corp. 2.96 3.20 3.09 2.79 2.80 2.70 4.12 4.70 3.44 3.50 3.31 2.89 Schering-Plough Corp. 4.22 5.20∗ 3.29 3.68 3.11 3.05 3.23 3.51 3.45 3.08 3.06 2.87 Texaco Inc. 3.09 3.20 3.10 3.15 2.88 2.84 3.65 3.36 3.20 3.04 2.86 2.70 Texas Instruments Inc. 3.49 3.53 3.35 3.31 2.89 2.99 4.00 3.42 3.36 3.30 2.97 3.06 United Technologies Corp 4.21 3.98 3.82 3.46 3.34 3.18 5.39 4.50 4.00 3.80 3.51 3.26 Walgreen Co. 4.06 4.35 3.81 4.04 3.20 3.40 4.60 5.12 3.79 3.54 3.20 3.07 33 Standart & Poor’s 500 3.16 - 3.17 - 3.16 - 4.00 - 3.65 - 3.19 - Table 4: This table gives the estimated value of the tail index for the twenty considered assets, the Standard & Poor’s 500 index and the residues ε obtained by regressing each asset on the Standard & Poor’s 500 index, for both the negative and the positive tails, during the time interval from January 1980 to December 2000. The tail indexes are estimed by Hill’s estimator at the quantile 1%, 2.5% and 5% which are the optimal quantiles given by the Hall (1990) and Danielsson and de Vries (1997)’s algorithms. The values decorrated with stars represent the tail indexes whose value cannot be considered equal to the Standard & Poor’s 500 index’s tail index at the 95% confidence level.
9.2. Estimation du coefficient de dépendance de queue 333 First Centile First Quintile First Decile mean std. min. max. mean std. min. max. mean std. min. max. Abbott Labs 0.1264 0.0106 0.1039 0.1745 0.1232 0.0058 0.1039 0.1745 0.1185 0.0069 0.1039 0.1745 American Home Products Corp. 0.1181 0.0091 0.0796 0.1288 0.1349 0.0111 0.0796 0.1494 0.1401 0.0096 0.0796 0.1505 Boeing Co. 0.1116 0.0128 0.0954 0.1653 0.1090 0.0074 0.0954 0.1653 0.1066 0.0066 0.0954 0.1653 Bristol-Myers Squibb Co. 0.1927 0.0171 0.1407 0.2175 0.2220 0.0220 0.1407 0.2474 0.2180 0.0180 0.1407 0.2474 Chevron Corp. 0.1566 0.0194 0.1334 0.2368 0.1407 0.0121 0.1265 0.2368 0.1365 0.0101 0.1257 0.2368 Du Pont (E.I.) de Nemours & Co. 0.2089 0.0142 0.1785 0.2424 0.2067 0.0105 0.1785 0.2424 0.2021 0.0106 0.1785 0.2424 Disney (Walt) Co. 0.1317 0.0160 0.0930 0.1613 0.1587 0.0161 0.0930 0.1754 0.1566 0.0123 0.0930 0.1754 General Motors Corp. 0.2210 0.0149 0.2045 0.2996 0.2109 0.0096 0.1947 0.2996 0.2020 0.0120 0.1808 0.2996 Hewlett-Packard Co. 0.1455 0.0103 0.1188 0.1769 0.1615 0.0116 0.1188 0.1776 0.1603 0.0095 0.1188 0.1776 Coca-Cola Co. 0.1870 0.0259 0.1199 0.2522 0.2159 0.0204 0.1199 0.2522 0.2160 0.0164 0.1199 0.2522 Minnesota Mining & MGF Co. 0.2311 0.0254 0.1851 0.3268 0.2262 0.0126 0.1851 0.3268 0.2218 0.0115 0.1851 0.3268 Philip Morris Cos Inc. 0.1251 0.0078 0.1050 0.1526 0.1334 0.0089 0.1050 0.1526 0.1340 0.0070 0.1050 0.1526 Pepsico Inc. 0.1263 0.0111 0.1014 0.1706 0.1242 0.0071 0.1014 0.1706 0.1239 0.0057 0.1014 0.1706 Procter & Gamble Co. 0.1980 0.0325 0.1131 0.2351 0.2017 0.0153 0.1131 0.2351 0.1972 0.0131 0.1131 0.2351 Pharmacia Corp. 0.1180 0.0172 0.0596 0.1378 0.1291 0.0109 0.0596 0.1432 0.1337 0.0091 0.0596 0.1434 Schering-Plough Corp. 0.1759 0.0143 0.1320 0.2403 0.1733 0.0078 0.1320 0.2403 0.1663 0.0102 0.1320 0.2403 Texaco Inc. 0.0214 0.0017 0.0170 0.0269 0.0246 0.0023 0.0170 0.0278 0.0248 0.0018 0.0170 0.0278 Texas Instruments Inc. 0.5657 0.0687 0.3897 0.6572 0.6162 0.0438 0.3897 0.6623 0.6168 0.0368 0.3897 0.6761 United Technologies Corp 0.1300 0.0123 0.0990 0.1872 0.1254 0.0073 0.0990 0.1872 0.1192 0.0086 0.0990 0.1872 Walgreen Co. 0.0739 0.0109 0.0664 0.1185 0.0682 0.0058 0.0629 0.1185 0.0674 0.0044 0.0629 0.1185 34 Table 5: This table gives the average (mean), the standard deviation (std.), the minimum (min.) and the maximum (max.) values of the coefficient of lower tail dependence estimated over the first centile, quintile and decile during the entire time interval from July 1962 to December 2000, under the assumption that the tail of the distributions of the assets and the market are regularly varying with a index equal to three.
Page 1:
UNIVERSITE DE NICE-SOPHIA ANTIPOLIS
Page 4 and 5:
4 Table des matières 2.2.2 Bulles
Page 6 and 7:
6 Table des matières 7.3.2 Tests n
Page 8 and 9:
8 Table des matières 12.1.1 Distri
Page 10 and 11:
10 Table des matières Références
Page 12 and 13:
12 m’ont souvent été d’un gra
Page 14 and 15:
14 Introduction pour espérer se co
Page 16 and 17:
16 Introduction les distributions e
Page 18 and 19:
18 Introduction
Page 21 and 22:
Chapitre 1 Faits stylisés des rent
Page 23 and 24:
1.1. Rappel des faits stylisés 23
Page 25 and 26:
1.1. Rappel des faits stylisés 25
Page 27 and 28:
1.2. De la difficulté de représen
Page 29 and 30:
1.3. Modélisation des propriétés
Page 31 and 32:
Chapitre 2 Modèles phénoménologi
Page 33 and 34:
2.1. Bulles rationnelles multi-dime
Page 35 and 36:
Page 37 and 38:
Page 39 and 40:
Page 41 and 42:
Page 43 and 44:
2.2. Des bulles rationnelles aux kr
Page 45 and 46:
Page 47 and 48:
Page 49 and 50:
Page 51 and 52:
Page 53 and 54:
Page 55 and 56:
Page 57 and 58:
Page 59 and 60:
Page 61 and 62:
Page 63 and 64:
Chapitre 3 Distributions exponentie
Page 65 and 66:
Empirical Distributions of Log-Retu
Page 67 and 68:
concerning tail fatness can be form
Page 69 and 70:
To fit our two data sets, section 4
Page 71 and 72:
properties, stressing the problems
Page 73 and 74:
Another problem lies in the determi
Page 75 and 76:
In order to obtain a process with S
Page 77 and 78:
and Sornette (1999) for instance. W
Page 79 and 80:
1. The Pareto distribution: 79 Fu(x
Page 81 and 82:
empirical analog FN(x), estimated f
Page 83 and 84:
have been chosen to converge to 1 a
Page 85 and 86:
5 Comparison of the descriptive pow
Page 87 and 88:
ased on the fact that the quantity
Page 89 and 90:
tail (positive or negative) of the
Page 91 and 92:
Equation (46) depends on c only and
Page 93 and 94:
B Minimum Anderson-Darling Estimato
Page 95 and 96:
C Local exponent In this Appendix,
Page 97 and 98:
D Testing non-nested hypotheses wit
Page 99 and 100:
where α = (c ∗ ,d ∗ ). It can
Page 101 and 102:
where E0[·] denotes the expectatio
Page 103 and 104:
References Andersen, J.V. and D. So
Page 105 and 106:
Gouriéroux C. and A. Monfort, 1994
Page 107 and 108:
Rubinstein, M., 1973, The fundament
Page 109 and 110:
(a) Independent Data Stretched-Expo
Page 111 and 112:
(a) Dow Jones Positive Tail Negativ
Page 113 and 114:
Nasdaq Dow Jones Pos. Tail Neg. Tai
Page 115 and 116:
Page 117 and 118:
Page 119 and 120:
Page 121 and 122:
Dow Jones positive tail Dow Jones n
Page 123 and 124:
Variation coefficient Variation coe
Page 125 and 126:
Mean excess function Mean excess fu
Page 127 and 128:
Hill‘s estimate b u Hill‘s esti
Page 129 and 130:
Wilks statistic (doubled log−like
Page 131 and 132:
Tail 1−F(x) and parameter b Tail
Page 133 and 134:
1.4 1.2 1 0.8 0.6 0.4 0.2 0 1 2 3 4
Page 135 and 136:
Chapitre 4 Relaxation de la volatil
Page 137 and 138:
Volatility Fingerprints of Large Sh
Page 139 and 140:
2 Long-range memory and distinction
Page 141 and 142:
Figure 2: Measuring the conditional
Page 143 and 144:
the system to the accumulation of m
Page 145 and 146:
Appendix C: “Conditional response
Page 147 and 148:
Baillie, R.T., 1996, Long memory pr
Page 149 and 150:
Chapitre 5 Approche comportementale
Page 151 and 152:
5.1. Prix d’un actif et excès de
Page 153 and 154:
5.2. Modèles d’opinion contre mo
Page 155 and 156:
5.4. Conséquences des phénomènes
Page 157 and 158:
5.5. Conclusion 157 ce qui induit u
Page 159 and 160:
Chapitre 6 Comportements mimétique
Page 161 and 162:
RESEARCH PAPER Q UANTITATIVE F INAN
Page 163 and 164:
A Corcos et al Q UANTITATIVE F INAN
Page 165 and 166:
Page 167 and 168:
Page 169 and 170:
Page 171 and 172:
Page 173 and 174:
Page 175 and 176:
Page 177 and 178:
Page 179:
Deuxième partie Etude des proprié
Page 182 and 183:
182 7. Etude de la dépendance à l
Page 184 and 185:
Page 186 and 187:
Page 188 and 189:
Page 190 and 191:
Page 192 and 193:
192 8. Tests de copule gaussienne
Page 194 and 195:
194 8. Tests de copule gaussienne 1
Page 196 and 197:
Page 198 and 199:
Page 200 and 201:
200 8. Tests de copule gaussienne t
Page 202 and 203:
202 8. Tests de copule gaussienne T
Page 204 and 205:
204 8. Tests de copule gaussienne a
Page 206 and 207:
206 8. Tests de copule gaussienne c
Page 208 and 209:
208 8. Tests de copule gaussienne t
Page 210 and 211:
210 8. Tests de copule gaussienne (
Page 212 and 213:
212 8. Tests de copule gaussienne R
Page 214 and 215:
Page 216 and 217:
Page 218 and 219:
Page 220 and 221:
Page 222 and 223:
Page 224 and 225:
Page 226 and 227:
Page 228 and 229:
228 8. Tests de copule gaussienne f
Page 230 and 231:
Page 232 and 233:
Page 234 and 235:
Page 236 and 237:
236 8. Tests de copule gaussienne T
Page 238 and 239:
238 9. Mesure de la dépendance ext
Page 240 and 241:
Page 242 and 243:
Page 244 and 245:
Page 246 and 247:
Page 248 and 249:
Page 250 and 251:
Page 252 and 253:
Page 254 and 255:
Page 256 and 257:
Page 258 and 259:
Page 260 and 261:
Page 262 and 263:
Page 264 and 265:
Page 266 and 267:
Page 268 and 269:
Page 270 and 271:
Page 272 and 273:
Page 274 and 275:
Page 276 and 277:
Page 278 and 279:
Page 280 and 281:
Page 282 and 283: 282 9. Mesure de la dépendance ext
Page 345 and 346: Chapitre 10 La mesure du risque Dan
Page 347 and 348: 10.1. La théorie de l’utilité 3
Page 353 and 354: 10.2. Les mesures de risque cohére
Page 359 and 360: 10.3. Les mesures de fluctuations 3
Page 361 and 362: 10.4. Conclusion 361 et de manière
Page 363 and 364: Chapitre 11 Portefeuilles optimaux
Page 365 and 366: 11.2. Prise en compte des grands ri
Page 367 and 368: 11.3. Equilibre de marché 367 s’
Page 369 and 370: 11.5. Annexe 369 Collective Origin
Page 371 and 372: 11.5. Annexe 371 point λ = 1. Thus
Page 373 and 374: Chapitre 12 Gestion des risques gra
Page 375 and 376: 12.1. Comprendre et gérer les risq
Page 381 and 382: 12.2. Minimiser l’impact des gran
Page 383 and 384:
12.2. Minimiser l’impact des gran
Page 385 and 386:
12.2. Minimiser l’impact des gran
Page 387 and 388:
Chapitre 13 Gestion de portefeuille
Page 389 and 390:
VaR-Efficient Portfolios for a Clas
Page 391 and 392:
dependence: from independence to co
Page 393 and 394:
given a series of return {rt}t foll
Page 395 and 396:
eads cV (u1, · · · , un) = 1
Page 397 and 398:
THEOREM 4 (TAIL EQUIVALENCE FOR A S
Page 399 and 400:
Independent Assets Comonotonic Asse
Page 401 and 402:
3.2 Typical recurrence time of larg
Page 403 and 404:
and finally w ∗ i = χ−1 i j
Page 405 and 406:
where the ˆwi’s are solution of
Page 407 and 408:
Choosing x > y > Aɛ, and applying
Page 409 and 410:
Expanding fi(xi) around x ∗ i yie
Page 411 and 412:
for all h ∈ AC. Thus, integrating
Page 413 and 414:
B Asymptotic distribution of the su
Page 415 and 416:
This yields × h+ Sc−2 − 2 dh
Page 417 and 418:
References Acerbi, A. and D. Tasche
Page 419 and 420:
Malevergne, Y. and D. Sornette, 200
Page 421 and 422:
ln(T/T 0 ) T Figure 2: Logarithm
Page 423 and 424:
Chapitre 14 Gestion de Portefeuille
Page 425 and 426:
Multi-Moments Method for Portfolio
Page 427 and 428:
choosen risk measure. Section 5 pre
Page 429 and 430:
The variance of the return X of an
Page 431 and 432:
This property is verified for all c
Page 433 and 434:
µn=α of order n = 2, 4, 6 and 8.
Page 435 and 436:
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
Page 447 and 448:
In the sequel, we will first evalua
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 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
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)
show all

statistique, théorie et gestion de portefeuille - Docs at ISFA

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?