Discussion Paper Series A No.425 2002 2
186-8603 iwaisako@ier.hit-u.ac.jp 14 1 24 autocorrelataion cross-autocorrelataion Lo/MacKinlay [1988, 1990] 1990 12 13 (A) 12370027 13
1 1980 Lo/MacKinlay [1988] mean-reversion Fama/French [1988] Poterba/Summers [1988] Kim/Nelson/Startz [1991] Richardson/Stock [1989] Lo/MacKinlay [1988, 1990, 1999] cross-autocorrelation 1988 Lo/MacKinlay [1988] Center for Research in Securities Prices CRSP NYSE-AMEX variance ratio test (1) CRSP (2) (3) ; (4) 1990 Lo/MacKinlay [1990] (2)-(4) CRSP Lo/MacKinlay [1988, 1990] Lo/MacKinlay CRSP Dow-Jones S&P500 1
CRSP Dow-Jones S&P500 225 TOPIX CRSP Dow-Jones S&P500 Lo/MacKinlay [1988] 1 Chang/McQueen/Pinger [1999] PACAP Lo/MacKinlay (1988, 1990) PACAP 6 CRSP 3 Lo/MacKinlay [1988, 1990] 1990 4 1 Badrinath/Kale/Noe [1995], Boudoh/Richardson/Whitelaw [1994], Brennan/Jegadeesh/Saminathan [1993], Conrad/Kaul/Nimalendran [1991], Jegadeesh/Titman [1995], Mech [1995] 2
2 TOPIX TOPIX QUICK 1986 1 1 2001 8 15 Lo/MacKinlay [1988, 1990] 1986 1 2001 8 2 798 1 ARCH [ 1 ] 3 3.1 2 Ljung-Box Q TOPIX Q 3
[ 2 ] CRSP 3 4 2 CRSP 1993 1986 93 94 2001 8 225 TOPIX 8.8% 5% TOPIX 10% Q 5 2 4
truncated nonsynchronous trading 3.2 cross-autocorrelations 3 4 Υ(k) Υ(0) 3 Υ(1) R 4t 1 R 1t 14.0% R 1t 1 R 4t 0.2% 4 Υ(k) Υ (k) k [ 3 ] 5
1993 3 R 3t 3 R 2t, R 2t 3 R 3t Υ(3) Υ (3) [ 5 ] TOPIX r t = α + β 1 y t 1 + β 2 r t 1 u t 1 + ɛ t (1) if r t 0 u t =1 otherwise u t =0 β 2 3.1 2 TOPIX 2 truncated AR(1) (1) 6 (A) AR(1) TOPIX 6
[ 6 ] (B) β 2 β 2 5% 5% β 1 1 2 1994 TOPIX β 2 1990 4 7
Lo and MacKinlay [1990c] contrarian Lo and MacKinlay [1990] Campbell, Lo, and MacKinlay [1997, 3 ] nonsynchronous trading 2 1990 2 / / / [1998] 10 8
/ / / [1998] Badrinath, S. G., J. R. Kale, and T. H. Noe [1995], Of Shepherds, Sheep, and the Cross-autocorrelations in Equity Returns, Review of Financial Studies 8, pp.401-30. Boudoukh, J., M. P. Richardson, and R. F. Whitelaw [1994], A Tale of Three Schools: Insights on Autocorrelations of Short-Horizon Stock Returns Review of Financial Studies 7, pp.539-73. Brennan, M. J., N. Jegadeesh, and B. Swaminathan [1993], Investment Analysis and the Adjustment of Stock Prices to Common Information, Review of Financial Studies 6, pp.799-824. Campbell, J. Y., A. W. Lo, and A. C. MacKinlay [1997], The Econometrics of Financial Markets, Princeton University Press. Chang, E. C., G. R. McQueen, and J. M. Pinegar [1999], Cross- Autocorrelation in Asian Stock Markets, Pacific-Basin Finance Journal 7, pp.471-93. Fama, E. F. and K. R. French [1988], Permanent and Temporary Components of Stock Prices, Journal of Political Economy 96, pp.246-73. Jegadeesh, N. and S. Titman [1995], Overreaction, Delayed Reaction, and Contrarian Profits, Review of Financial Studies 8, pp.973-93. Kim, M., C. R. Nelson, and R. Startz [1991], Mean Reversion in Stock Prices? A Reappraisal of the Empirical Evidence, Review of Economic Studies 58, pp.515-28. Lo, A. W. and A. C. MacKinlay [1988], Stock Market Prices Do Not Follow Random Walks: Evidence From a Simple Specification Test, Review of Financial Studies 1, pp.41-66. and [1990], When are Contrarian Profits Due to Stock Marekt Overreaction? Review of Financial Studies 3, pp.175-208. 9
and, A Non-random Walk Down Wall Street, Princeton: Princeton University Press, 1999. Mech, T. S. [1993], Portfolio Return Autocorrelation, Journal of Financial Economics 34, pp.307-44. Poterba, J. M. and L. H. Summers [1988] Mean Reversion in Stock Prices, Journal of Financial Economics 22, pp.27-59. Richardson, M. and J. H. Stock [1989], Drawing Inferences from Statistics Based on Multiyear Asset Returns, Journal of Financial Economics 25, pp.323-48. 10
1 1986 1 1 2001 8 2 798 0.016 2.69 0.18 3.11 12.83 12.27 344 [0.04] [0.00] 0.019 2.70 0.32 3.20 13.48 13.92 515 [0.00] [0.00] 0.027 2.90 0.02 1.76 11.77 13.39 613 [0.79] [0.00] TOPIX 0.021 2.79 0.08 1.94 10.85 13.41 N/A [0.35] [0.00] 0.016 2.71 0.04 2.43 12.21 10.81 580 [0.64] [0.00] 200 8 11
2 ρ i = i Q i = i Ljung-Box Q ( ) 1% ( ) 5% ( ) 10% 3 4 (A) 1986 1 1 2001 8 2 798 ρ 1 ρ 2 ρ 3 ρ 4 Q5 Q10 2 17.1 13.4 14.0 4.2 58.1 66.2 17.1 13.6 9.4 3.0 46.0 47.7 4.4 8.3 7.4 3.9 12.7 16.2 3.0 3.3 6.0 1.5 5.8 9.8 225 0.7 9.2 3.6 2.5 7.9 10.9 TOPIX 2.1 4.2 6.1 1.9 6.0 10.8 5.1 8.0 7.2 1.4 11.7 15.3 9.5 9.7 8.9 0.5 21.6 25.5 12
2 (B) 1986 1 1 1993 407 ρ 1 ρ 2 ρ 3 ρ 4 Q5 Q10 2 27.7 18.0 13.8 4.4 53.4 62.5 21.9 15.9 7.6 2.8 34.2 42.0 9.0 14.0 5.2 3.1 15.0 25.4 1.2 6.0 7.5 0.0 3.9 12.7 225 0.3 12.0 5.0 2.3 7.2 14.8 TOPIX 2.1 7.6 7.0 0.7 4.8 15.4 9.5 11.7 5.9 1.0 12.2 24.3 14.8 13.3 7.7 0.5 19.8 31.6 (C) 1984 1 1 2001 8 2 391 ρ 1 ρ 2 ρ 3 ρ 4 Q5 Q10 2 9.0 9.6 14.0 3.8 20.0 38.0 11.6 9.7 11.1 1.6 15.4 23.1 1.8 0.6 9.8 7.0 11.5 15.3 8.9 0.9 3.5 4.2 9.3 11.2 225 7.5 0.2 4.2 8.1 7.5 10.4 TOPIX 8.2 0.6 4.9 4.4 9.5 11.5 0.4 2.3 8.4 3.3 8.2 13.0 3.5 4.7 9.9 0.7 11.0 18.7 13
3 Cross-autocorrelation matrices 1986 1 1 2001 8 2 798 R 1t = 2 R 2t = 1 R 3t = 1 R 4t = 1 Lo/MacKinlay [1988, 1990] Υ(0) = R 1t R 2t R 3t R 4t 1.000 0.869 0.808 0.635 0.869 1.000 0.927 0.726 0.808 0.927 1.000 0.851 0.635 0.726 0.851 1.000 Υ(1) = R 1t 1 R 2t 1 R 3t 1 R 4t 1 0.173 0.160 0.062 0.002 0.192 0.175 0.059 0.040 0.184 0.163 0.047 0.034 0.140 0.102 0.130 0.028 Υ(2) = R 1t 2 R 2t 2 R 3t 2 R 4t 2 0.133 0.110 0.062 0.009 0.143 0.132 0.090 0.032 0.129 0.113 0.078 0.025 0.083 0.064 0.057 0.032 Υ(3) = R 1t 3 R 2t 3 R 3t 3 R 4t 3 0.138 0.094 0.051 0.008 0.110 0.092 0.052 0.008 0.116 0.101 0.072 0.033 0.107 0.074 0.071 0.058 14
Υ(4) = R 1t 4 R 2t 4 R 3t 4 R 4t 4 0.044 0.035 0.009 0.029 0.042 0.028 0.027 0.057 0.042 0.022 0.039 0.071 0.060 0.044 0.006 0.014 15
4 1986 1 1 2001 8 2 798 3 Υ(1) Υ (1) = R 1t 1 R 2t 1 R 3t 1 R 4t 1 0.000 0.032 0.122 0.142 0.032 0.000 0.104 0.142 0.122 0.104 0.000 0.164 0.142 0.142 0.164 0.000 Υ(2) Υ (2) = R 1t 2 R 2t 2 R 3t 2 R 4t 2 0.000 0.033 0.067 0.074 0.033 0.000 0.023 0.032 0.067 0.023 0.000 0.032 0.074 0.032 0.032 0.000 Υ(3) Υ (3) = R 1t 3 R 2t 3 R 3t 3 R 4t 3 0.000 0.016 0.064 0.099 0.016 0.000 0.049 0.067 0.064 0.049 0.000 0.038 0.099 0.067 0.038 0.000 Υ(4) Υ (4) = R 1t 4 R 2t 4 R 3t 4 R 4t 4 0.000 0.007 0.052 0.089 0.007 0.000 0.049 0.100 0.052 0.049 0.000 0.077 0.089 0.100 0.077 0.000 16
5 (A) 1986 1 1 1993 12 31 407 Υ(1) Υ (1) = R 1t 1 R 2t 1 R 3t 1 R 4t 1 0.000 0.066 0.173 0.209 0.066 0.000 0.114 0.150 0.173 0.114 0.000 0.060 0.209 0.150 0.060 0.000 Υ(2) Υ (2) = R 1t 2 R 2t 2 R 3t 2 R 4t 2 0.000 0.050 0.060 0.082 0.050 0.000 0.020 0.054 0.060 0.020 0.000 0.079 0.082 0.054 0.079 0.000 Υ(3) Υ (3) = R 1t 3 R 2t 3 R 3t 3 R 4t 3 0.000 0.011 0.069 0.090 0.011 0.000 0.052 0.053 0.069 0.052 0.000 0.026 0.090 0.053 0.026 0.000 Υ(4) Υ (4) = R 1t 4 R 2t 4 R 3t 4 R 4t 4 0.000 0.054 0.119 0.127 0.054 0.000 0.069 0.096 0.119 0.069 0.000 0.062 0.127 0.096 0.062 0.000 17
5 (B) 1994 1 1 2001 8 5 391 Υ(1) Υ (1) = R 1t 1 R 2t 1 R 3t 1 R 4t 1 0.000 0.002 0.077 0.072 0.002 0.000 0.091 0.125 0.077 0.091 0.000 0.023 0.072 0.125 0.023 0.000 Υ(2) Υ (2) = R 1t 2 R 2t 2 R 3t 2 R 4t 2 0.000 0.015 0.067 0.057 0.015 0.000 0.024 0.006 0.067 0.024 0.000 0.041 0.057 0.006 0.041 0.000 Υ(3) Υ (3) = R 1t 3 R 2t 3 R 3t 3 R 4t 3 0.000 0.025 0.068 0.115 0.025 0.000 0.048 0.082 0.068 0.048 0.000 0.051 0.115 0.082 0.051 0.000 Υ(4) Υ (4) = R 1t 4 R 2t 4 R 3t 4 R 4t 4 0.000 0.042 0.026 0.035 0.042 0.000 0.016 0.086 0.026 0.016 0.000 0.086 0.035 0.086 0.086 0.000 18
6 TOPIX r t = α + β 1 r t 1 + β 2 u t 1 r t 1 if r t 0 u t =1 otherwise u t =0 r t TOPIX (A) β 2 =0 TOPIX β 1 0.021 0.021 0.079 [S.E.] [0.046] [0.067] [0.059] R 2 0.1(%) 0.2 0.4 β 1 0.029 0.013 0.088 [S.E.] [0.046] [0.066] [0.059] R 2 0.0(%) 0.2 0.5 (B) TOPIX β 1 0.127 0.154 0.108 [S.E.] [0.069] [0.090] [0.103] β 2 0.289 0.245 0.393 [S.E.] [0.134 ] [0.178] [0.181 ] R 2 0.7(%) 0.3 1.7 19
6 TOPIX (B) β 1 0.102 0.129 0.075 [S.E.] [0.067] [0.086] [0.101] β 2 0.272 0.233 0.359 [S.E.] [0.137 ] [0.184] [0.188 ] R 2 0.7(%) 0.2 1.6 S.E. =White Heteroskedasticity-Consistent ( ) 5% ( ) 10% 20