CAPM CAPM T-M H-M Randolph Cohen Joshua Coval Lubos Pastor 2002 1 2 57 40 70% 3 4 q 2004 2003
2
1. 2004 122 CAPM - Fama-French Carhart Sharpe CAPM Without Benchmark MeasureT-M H-M 3
2. 4
2002 Randolph Cohen Joshua Coval Lubos Pastor M m=1,,m N n=1,,n w m,n m n δ m mn n M δ = v δ 1 m= 1 m, n m v mn, w = 2 mn, M m= 1 w mn, δ * m N = wm, nδ n 3 n= 1 1 3 δ * m δ m Cohen δ n δ m Cohen 5
Jensen s alpha 13 $ * N m wmn, δ n n= 1 δ = 4 n M δ = v $ δ m 5 $ δ m m= 1 m, n m Jensen s alpha 45 $ δ m $* δ m $ δ m Cohen h n M n h M wmn, = = w m= 1 n N M n= 1 m= 1 mn, M w m 1 mn, = 6 M W N*Mw m,n V N*Mv m,n $ δ { $ δ m} M m = 1 M*1 δ { δ n} N n = 1 N*1 $* δ $ δ * m = 1 { m} M $ * M*1 δ =W δ,δ =V $ δ 4 $ δ* = Z$ δ 7 Z=W V m 6
$ * M m z $ m, jδ j j= 1 δ = 8 z m, j Z m, j. 26 N N 1 z = w v = w w 1 9 m, j mn, jn, mn, jn, n= 1 M n= 1 hn Cohen $* δ m 1 jz m, j m j mj m j 9 1/h n Z z i, j = z j, i 9 Cohen 1 M * $ 1 M M $ 1 M $ M 1 M δ $ i = zi, jδ j = δ j zi, j= j M M M M 1 δ (10) i= 1 i= 1 j= 1 j= 1 i= 1 j= Cohen Cohen Cohen 1 1 1 z = w w = w w = w M M N N M N, = m, j mn, jn, mn, jn, mn j= 1 j= 1 n= 1 Mhn n= 1 Mhn j= 1 n= 1 7 1
Cohen Cohen M N r n = α + e n=1, N 11 n n 8
α n en αn N 2 σ N(0, σ ) α n 2 (0, α ) e e n e n α γ m α s mn, = α n un u n γ m 1-γ m n m 12 γ m γ m γ m γ m = qg+ (1 q) gm m=1,,m 13 g g γ q m m q 12 γ m σ e α n Bayes Rule α n m n E = γ s 14 mn, m mn, n V = σ + σ + γ ( s σα ) s γ 15 2 2 2 2 2 2 mn, e a m mn, mn, m Sharp Ratio m n w V E, 16 1 mn, mn. mn 9
0 m δ m = w α 17 ' m α α N 1 2 δ ' δ m = wr m 18 r r N 1 δ * m * m m n δ = Z δ 19 Z m 7 Z m 3 19 δ δ δ *i m 19δ δ * m δ * i * m Zmδ ZmZ = = δ 20 population version δ * * δ = δ 21 Z m µ* δ 10
10000 M 10 50 100 300 N 10 50 100 q 0 0.4 0.8 σ α = 0.1 σ = 0.2 e δ δ δ * δ *i δ * γ 1 γ 10000 γ 1 δ * δ γ M=10 q 1 300 50 q=0 γ 0.8951 0.7194 δ *i γ δ * δ δ * γ δ * 11
1 q q=0 M=100 N=10 δ * 0.4238 N=100 δ * 0.9681 1 M * δ δ *i δ q=0 q=0.4 q=0.8 δ * δ δ * δ *i δ N=10 δ * δ δ * δ *i δ δ * δ 10 0.3508 0.3897 0.3949 0.6985 0.7144 0.2289 0.2362 0.2303 0.4854 0.4680 0.0854 0.0794 0.0725 0.1988 0.1796 50 0.3519 0.4184 0.4332 0.7048 0.7433 0.2309 0.2565 0.2617 0.4954 0.5019 0.0909 0.0886 0.0829 0.2013 0.1855 100 0.3531 0.4238 0.4403 0.7084 0.7499 0.2349 0.2639 0.2716 0.4941 0.5044 0.0931 0.0924 0.0880 0.2058 0.1906 300 0.3482 0.4230 0.4404 0.7056 0.7491 0.2322 0.2647 0.2756 0.4953 0.5088 0.0920 0.0924 0.0885 0.2038 0.1903 N=50 10 0.7089 0.8213 0.8410 0.9169 0.9292 0.5192 0.5829 0.5902 0.7878 0.7838 0.2259 0.2095 0.1876 0.4127 0.3665 50 0.7172 0.8844 0.8950 0.9214 0.9450 0.5276 0.6941 0.7356 0.7947 0.8231 0.2315 0.2323 0.2125 0.4202 0.3689 100 0.7211 0.8910 0.8993 0.9221 0.9464 0.5253 0.7152 0.7615 0.7958 0.8303 0.2298 0.2400 0.2236 0.4233 0.3765 300 0.7194 0.8951 0.9019 0.9231 0.9477 0.5270 0.7323 0.7765 0.7961 0.8347 0.2327 0.2505 0.2381 0.4256 0.3806 N=100 10 0.8402 0.9299 0.9422 0.9567 0.9633 0.6643 0.7460 0.7638 0.8758 0.8771 0.3134 0.2999 0.2759 0.5365 0.4949 50 0.8472 0.9654 0.9685 0.9588 0.9725 0.6747 0.8616 0.8905 0.8815 0.9069 0.3248 0.3415 0.3214 0.5476 0.5003 100 0.8510 0.9681 0.9698 0.9590 0.9732 0.6742 0.8797 0.9030 0.8812 0.9111 0.3243 0.3590 0.3458 0.5491 0.5073 300 0.8473 0.9671 0.9681 0.9592 0.9738 0.6772 0.8920 0.9099 0.8816 0.9143 0.3268 0.3811 0.3760 0.5511 0.5152 1 12
2003 2004 5 2003 6 30 2003 9 30 2003 12 31 2004 3 31 2004 6 30 2 3 2 2002 65 36 4 Cohen Jensen s alpha Jensen s alpha Jensen s alpha β Jensen s alpha 13
5 1 13 2003 6 2004 6 1 3 2003 6 30 2002 6 30 2003 6 30 2003 2003 6 30 2003 9 30 2003 7 31 2002 7 31 2003 7 31 2003 2003 7 31 2003 10 31 6 $* δ m $* δ m 7 Speraman Spearman 14
2 $ δ $ * δ 15
12 12 10 10 8 8 6 6 4 4 2 2 0-5 0 5 10 15 1 0 0 1 2 3 4 5 6 7 8 9 2 12 12 10 10 8 8 6 6 4 4 2 2 0-20 -15-10 -5 0 5 10 15 20 3 0-9 -8-7 -6-5 -4-3 -2-1 0 1 2 3 4 5 6 7 4 14 12 10 8 6 4 2 14 12 10 8 6 4 2 0-14 -12-10 -8-6 -4-2 0 2 4 6 8 5 0-6 -5-4 -3-2 6 16
1 1 1 1 1 2 2 2 1 1 2 1 Spearman 3 4 5 4 90% 0.01 17
90% 4 5 1 57 40 70% 21 3 2 2 1 1 2 2003 9 36 2003 9 42 2003 12 50 54 1 20 2 6 4 3, 1 2 18
4 2 3 1 5 2004 4 2004 1 2003 12 7 2004 4 5 6 99% t 0.12 2003 2004 2 q 2004 2003 19
20 5 20030630 0.131 0.77 0.152 0.89 0.205 1.22 0.170 1.01 0.239 1.43 0.232 1.39 0.397*** 3.12 0.407*** 3.21 0.477*** 3.91 0.451*** 3.65 0.315** 2.39 0.261* 1.95 0.138 1.11 0.123 0.99 0.248** 2.03 0.284** 2.35 0.136 1.09 0.090 0.72 20030731 0.089 0.52 0.138 0.81 0.075 0.44 0.110 0.64 0.129 0.76 0.174 1.03 0.353*** 2.72 0.347** 2.67 0.478*** 3.92 0.476*** 3.91 0.456*** 3.68 0.433*** 3.47 0.122 0.98 0.090 0.71 0.241 1.97 0.306** 2.56 0.286** 2.37 0.235 1.92 20030831 0.171 1.01 0.205 1.22-0.092-0.54-0.045-0.26 0.051 0.30 0.128 0.76 0.370*** 2.87 0.400*** 3.15 0.275** 2.07 0.285** 2.14 0.381*** 2.97 0.418*** 3.32 0.186 1.50 0.173 1.39 0.117 0.93 0.154 1.24 0.277** 2.29 0.314** 2.63 20030930 0.242 1.58 0.229 1.49 0.197 1.27 0.236 1.54 0.242 1.58 0.258* 1.69 0.304** 2.39 0.270** 2.10 0.284** 2.22 0.273** 2.12 0.303** 2.38 0.309** 2.44 0.103 0.82 0.144 1.16 0.153 1.23 0.162 1.30 0.210* 1.71 0.162 1.30 20031031 0.308** 2.04 0.279* 1.84 0.356** 2.41 0.374** 2.55 0.292* 1.93 0.302* 2.00 0.345*** 2.75 0.346*** 2.76 0.266** 2.07 0.240* 1.85 0.304** 2.39 0.284** 2.22 0.182 1.47 0.195 1.58 0.167 1.34 0.116 0.93 0.185 1.49 0.149 1.19 20031130 0.228 1.48 0.194 1.25 0.244 1.59 0.225 1.46 0.042 0.26-0.006-0.04 0.259** 2.00 0.244* 1.88 0.196 1.49 0.122 0.92-0.002-0.01 0.016 0.12 0.296** 2.46 0.242* 1.98 0.308** 2.57 0.220 1.79 0.121 0.96 0.110 0.88 20031231 0.113 0.78 0.035 0.24-0.017-0.12-0.059-0.41 0.208* 1.68 0.008 0.06 0.070 0.56-0.015-0.12 0.221* 1.80 0.062 0.49 0.039 0.31 0.016 0.13 20040131 0.129 0.90 0.086 0.60 0.123 0.86 0.158 1.11 0.246** 2.02 0.073 0.59 0.220* 1.79 0.065 0.52 0.418*** 3.65 0.258** 2.12 0.242 1.98 0.137 1.10 20040229 0.270* 1.94 0.209 1.48 0.253* 1.81 0.174 1.22 0.308** 2.59 0.156 1.25 0.292** 2.42 0.105 0.84 0.407*** 3.54 0.124 0.99 0.335*** 2.82 0.067 0.53 20040331 0.253* 1.83 0.196 1.40 0.268* 0.95 0.134 0.95 0.223* 1.81 0.194 1.57 0.200 1.62 0.083 0.66 0.189 1.53 0.179 1.44 0.235 1.92 0.123 0.98 20040430 0.314** 2.32 0.231 1.66 0.213 1.52 0.176 1.25 0.350*** 2.96 0.227* 1.85 0.301** 2.50 0.258** 2.12 0.347*** 2.98 0.188 1.52 0.329*** 2.76 0.327*** 2.75 20040531 0.308** 2.27 0.231 1.66 0.235* 1.69 0.254* 1.84 0.319*** 2.67 0.196 1.59 0.332*** 2.80 0.283** 2.34 0.348*** 2.95 0.183 1.47 0.253** 2.08 0.336*** 2.84 20040630 0.284** 2.14 0.233* 1.73 0.290** 2.18 0.260* 1.94 0.467*** 4.19 0.270** 2.23 0.254** 2.08 0.191 1.54 0.265** 2.18 0.098 0.78 0.219 1.78 0.115 0.92 t * p [0.9,0.95] ** p [0.95,0.99] * p >0.99
1 2003 9 30 2004 9 30 2 6 2004 21
2004 9 20 2004 12 20 22
7 2004 0.37 1 2 57 40 70% 3 1 4 23
q 2004 2003 24
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