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5 AR(3) What Will Happen When Stock Price Close to the Limit? ---Evidence From the Shanghai Stock Exchange Guotai Jun'an Securities Research Institute (No.2008, Chunfeng Road, Shenzhen 518002, China) ABSTRACT: This paper investigates the influence of the price limit to the return of stock price by using 5 minutes data in the Shanghai Stock Exchange. To see what will happen when stock price is close to the limit, we use two methods in our empirical research: a regression analysis of AR(3) model and a transfer probability analysis. The results of the two methods are same that there is a cooling off effect in Shanghai Stock Market due to the price limit. The stock price of next 5 minute is more possible downward when the current price is close to the upside limit and is more possible upward when the current price is close to the downside limit. The cooling off effect is asymmetrical with a stronger rebound near the downside limit and can not be treated as a result of the reversal effect existed in the intra-day return of stock price. KEYWORDS: price limit cooling off effect reversal effect regression analysis transfer probability analysis - 2 -
1.4 1.1 4 1.2 6 1.3 7 2. 7 2.1 AR-GARCH 7 2.2 8 2.3 / 9 3. 9 3.1 10 3.2 AR 14 4. 21 22-3 -
1 1.1 1987 9.11 ( ) (Circuit Breaker) Harris. L.(1998) Circuit Breakers (Price Limit) (Trading Halt) (Position Limits) (Margin requirements) Joan Evans and James M. Mahoney(1997) Harris. L.(1998) Collars 1996 12 16 1-4 -
1 ( ) 7 10 10 15 30 30 40 (*http://www.tse.or.jp/ english/cash/stock/sttrading.html) * ( (2001) ) Fama 1989 (Fama(1989)) (Kim. K. A., and S. G. Rhee (1997)Woo Suk Choi, Sang Bin Lee (2000)Jie-Haun Lee, Robin K. Chou (2001)) Joan Evans and James M. Mahoney(1997) ( ) ( ) ( )Jimmy J. Yang and Yong H. Kim(2001) - 5 -
IPO( ) IPO Kim. K. A., and Richard J. Sweeney (2000) (2001) (2001), 1.2 price stabilization effect Lee, S.B. and K.J. Kim(1995) cooling off effect Ma, Rao, and Sears (1989) volatility spillover effect delayed price discovery effect ceiling effect Jeff Chung, Li Gan (2000) trading interference effect Kim. K. A., and S. G. Rhee (1997) Woo Suk Choi, Sang Bin Lee (2000a) (2001) Magnet Effect - 6 -
Fama(1989) Daewhan Cho, Jerrey Russell, George C. Tiao and Ruey Tsay (2001) Woo Suk Choi, Sang Bin Lee(2000b) 1.3 2. 2.1 AR-GARCH Daewhan Cho, Jerrey Russell, George C. Tiao and Ruey Tsay (2001) AR-GARCH CRTT CRTT 1998 1 3 1999 3 20 5 345 19 AR(3)-GARCH(2,2) 1, 3% D ( ceiling) t = (1) 0, 1, 3% D ( floor) t = (2) 0, AR(3) - 7 -
RET t = c0 + c1rett 1 + c2rett 2 + c3rett 3 + 1D ceiling) t 1 + λ2d( floor) t 1 λ ( + ε (3) t RET t t (5 )λ ε D(ceiling) t-1 RET t 1 D(floor) t-1 RET t 2 GARCH(2,2) ( D( ceiling) t 1 + D( floor t 1 ) λ DLIM t 2 2 ht = α 0 + α1ht 1 + α 2ht 2 + β1ε t 1 + β 2ε t 2 + λ3 ) + 4 ht t DLIM ( ) CRTT S&P500 1999-2000 ( 1) 2.2 2001 1 2 2001 6 29 A 5 5 ( ) ( ) ( ) (4) - 8 -
2.3 / Jegadeesh(1990)Lehmann(1990) ( ) / (3) 1, t 1, t 2, t 3, t 4 ( 0) M ( up) t = (5) 0, 1, t 1, t 2, t 3, t 4 ( 0) M ( down) t = (6) 0, RET (3) t = c + λ M ( up) 3 0 + c RET t 1 1 t 1 + c RET + λ M ( down) 4 2 t 1 t 2 + ε + c t 3 RET t 3 + λ D( ceiling) 1 t 1 + λ D( floor) / 1 2 - M(up) t-1 RET t M(down) t-1 RET t 3 4-4 ( 0 ) 4 ( 0 ) - 2 t 1 (7) 3. 2001 1 2 2001 6 29 A 5 935 930-935 - 9 -
3.1 2 2 2 20 (%)= + (8) K -KK 00.5%1% 2 (-1,1) (0) 0 4% 0 0-6% 6% - 10 -
2 K=0 K= ± 0.5% ( ) (%) (%) -10~-9 529 0.229 0.147 0.624 0.179 0.117 0.030 0.853 0.180-9~-8 340 0.477 0.438 0.085 0.250 0.256 0.165 0.579 0.255-8~-7 664 0.485 0.387 0.128 0.068 0.197 0.149 0.654 0.057-7~-6 1640 0.457 0.407 0.135 0.064 0.162 0.123 0.715 0.060-6~-5 3298 0.414 0.428 0.159 0.012 0.130 0.122 0.748 0.017-5~-4 8499 0.416 0.411 0.174 0.014 0.107 0.097 0.797 0.017-4~-3 25562 0.412 0.396 0.192 0.022 0.082 0.065 0.853 0.021-3~-2 85713 0.405 0.381 0.214 0.017 0.061 0.047 0.892 0.014-2~-1 339988 0.382 0.358 0.261 0.012 0.036 0.027 0.937 0.009-1~0 857658 0.341 0.365 0.295-0.004 0.020 0.020 0.960 0.000 0~1 869533 0.336 0.375 0.289-0.005 0.023 0.020 0.957 0.002 1~2 290975 0.359 0.401 0.241-0.005 0.033 0.030 0.936 0.003 2~3 96036 0.374 0.430 0.196-0.009 0.045 0.044 0.911 0.003 3~4 33401 0.388 0.445 0.167-0.010 0.060 0.063 0.877 0.004 4~5 13153 0.409 0.449 0.142-0.003 0.082 0.084 0.834 0.008 5~6 6224 0.418 0.453 0.130 0.013 0.112 0.105 0.783 0.025 6~7 3307 0.408 0.474 0.119-0.018 0.111 0.139 0.750-0.004 7~8 1763 0.417 0.456 0.127 0.013 0.146 0.148 0.706 0.026 8~9 928 0.385 0.533 0.082-0.124 0.144 0.241 0.614-0.111 9~10 1125 0.218 0.257 0.525-0.128 0.037 0.129 0.834-0.133-11 -
2 ( ) K= ± 1% ( ) (%) -10~-9 529 0.062 0.000 0.938 0.184-9~-8 340 0.141 0.050 0.809 0.252-8~-7 664 0.095 0.066 0.839 0.042-7~-6 1640 0.062 0.040 0.899 0.050-6~-5 3298 0.043 0.034 0.923 0.017-5~-4 8499 0.031 0.027 0.942 0.013-4~-3 25562 0.022 0.013 0.966 0.015-3~-2 85713 0.014 0.008 0.979 0.009-2~-1 339988 0.007 0.004 0.990 0.004-1~0 857658 0.002 0.002 0.995 0.000 0~1 869533 0.003 0.002 0.995 0.001 1~2 290975 0.005 0.004 0.990 0.002 2~3 96036 0.009 0.007 0.984 0.003 3~4 33401 0.015 0.010 0.975 0.009 4~5 13153 0.024 0.016 0.959 0.014 5~6 6224 0.038 0.025 0.937 0.029 6~7 3307 0.046 0.040 0.915 0.019 7~8 1763 0.058 0.040 0.901 0.039 8~9 928 0.066 0.088 0.846-0.059 9~10 1125 0.000 0.068 0.932-0.141 2001 1 2 2001 6 29 A 5 ( ) ( ) K -KK 00.5%1% / 3-12 -
) 3 --- K=0 K= ± 0.5% K= ± 1% ( -10~-9 163 0.528 0.295 0.178 0.245 0.061 0.693 0.123 0.000 0.877-9~-8 257 0.459 0.444 0.097 0.230 0.171 0.599 0.117 0.039 0.844-8~-7 458 0.498 0.371 0.131 0.190 0.125 0.686 0.083 0.046 0.871-7~-6 1203 0.454 0.406 0.141 0.152 0.113 0.735 0.050 0.032 0.918-6~-5 2303 0.411 0.437 0.152 0.123 0.117 0.760 0.037 0.031 0.933-5~-4 5962 0.409 0.416 0.175 0.096 0.091 0.818 0.025 0.023 0.952-4~-3 18407 0.405 0.402 0.193 0.075 0.060 0.865 0.019 0.011 0.970-3~-2 62516 0.400 0.389 0.211 0.057 0.045 0.898 0.013 0.007 0.980-2~-1 246950 0.376 0.366 0.257 0.034 0.026 0.940 0.006 0.003 0.990-1~0 616794 0.339 0.370 0.291 0.019 0.019 0.961 0.002 0.002 0.995 0~1 621531 0.335 0.379 0.286 0.021 0.019 0.960 0.003 0.002 0.995 1~2 209194 0.353 0.406 0.242 0.030 0.029 0.942 0.005 0.004 0.991 2~3 70430 0.370 0.430 0.200 0.040 0.040 0.920 0.008 0.007 0.985 3~4 24840 0.385 0.444 0.171 0.054 0.056 0.891 0.013 0.008 0.979 4~5 9791 0.404 0.450 0.146 0.072 0.072 0.856 0.019 0.012 0.969 5~6 4686 0.408 0.457 0.135 0.098 0.093 0.809 0.029 0.020 0.951 6~7 2496 0.389 0.489 0.122 0.087 0.128 0.785 0.034 0.034 0.932 7~8 1305 0.388 0.478 0.134 0.124 0.147 0.729 0.038 0.038 0.925 8~9 697 0.353 0.555 0.092 0.106 0.228 0.666 0.046 0.075 0.880 9~10 407 0.376 0.432 0.192 0.064 0.194 0.742 0.000 0.086 0.914 2001 1 2 2001 6 29 A 5 K -KK 00.5%1% 4 ( ) 3 / 2640336 1900390 / - 13 -
(2001)Jie-Haun Lee, Robin K. Chou (2001) 3.2 AR 2 U 1 ( ) 5 0.6 0.5 0.4 0.3 0.2 0.1 11:30 / 1:00 0 9:30 9:55 10:20 10:45 11:10 13:15 13:40 14:05 14:30 14:55 1 5 2001 1 2 2001 6 29 A 5-14 -
2 5 1998 1 3 1999 3 20 5 345 Daewhan Cho, Jerrey Russell, George C. Tiao and Ruey Tsay (2001) 6% -6% D(ceiling)D(floor)1 0 5% -5% 4 4 AR(3) ( #) 6% -6% 5% -5% t t C0 0.005 0.355 0.006 0.416 C1 0.027 1.944 0.019 1.396 C2-0.068-4.9316* -0.067-4.8357* C3-0.049-3.7127* -0.052-3.9360* 1-0.254-0.559-0.285-0.352 2 0.724 1.345 0.621 0.997 R 2 0.023 0.023 F 22.922* 24.150* # 6%-6% 128 5% -5% 232 4 3 (C2 C3) AR(3) - 15 -
1 2 (± 6% ) 1-0.2536<0 ( 6%) 2 0.7236>0 ( -6%) 1 2 t -0.55931.3454 5% 2 ( ) 1 5 R 2 F 3 4 3 Lamda2 8.00 7.00 6.00 5.00 4.00 3.00 2.00 1.00 0.00-6.00-4.00-2.00-1.000.00 2.00 4.00 6.00-2.00-3.00-4.00 Lamda1 1 --- 6% 2 --- -6% 128-16 -
12.00 10.00 8.00 6.00 t-lamda2 4.00 2.00 0.00-9.00-7.00-5.00-3.00-1.00-2.00 1.00 3.00 5.00 7.00 9.00-4.00-6.00 t-lamda1 4 t ( t ) t 5% 1.96( ) 3 128 1 2 4 1 2 t t 5% (1.96) t ( 1, 2 ) 4 ( 1, 2 ) 2 3 2 ( ) ( ) ( ) ( ) 4 t 1 2 / - 5-17 -
5 AR(3) ( / ) 6% -6% 5%-5% t t C0 0.000 0.001 0.001 0.099 C1 0.020 1.370 0.013 0.908 C2-0.074-5.231* -0.072-5.090* C3-0.054-4.006* -0.057-4.175* 1-0.278-0.630-0.303-0.438 2 0.710 1.314 0.610 0.967 3-0.018-0.213-0.013-0.132 4 0.177 2.1224* 0.168 1.925 R 2 0.024 0.025 F 17.861* 18.578* 5 1 2 - - 3 4 t - 5 6 8.00 6.00 4.00 Lamda2 2.00 0.00-6.00-4.00-2.00 0.00 2.00 4.00 6.00-2.00-4.00 Lamda1 5 --- / - 18 -
t-lamda2-10.0 0 14.00 12.00 10.00 8.00 6.00 4.00 2.00 0.00-8.00-6.00-4.00-2-2.00 0.00 2.00-4.00 4.00 6.00 8.00 10.0 0-6.00-8.00-10.00 t-lamda1 6 t --- / ( t ) 5 3 2 t 6 4 ( ) / 7 8 t Lamda4 0.8 0.6 0.4 0.2 0.0-0.5-0.4-0.3-0.2-0.1 0.0-0.2 0.1 0.2 0.3 0.4 0.5-0.4-0.6-0.8 Lamda3 7 / - 19 -
t-lamda4 8.0 6.0 4.0 2.0 0.0-4.0-3.0-2.0-1.0 0.0-2.0 1.0 2.0 3.0 4.0-4.0-6.0-8.0 t-lamda3 8 / t ( t ) 3 4 4 3 4 2 7 4 1 ( ) 8 t 6 128 ± 6% - 20 -
6 128 K=0 ) (%) ( -10~-9 156 0.519 0.301 0.180 0.360-9~-8 218 0.468 0.431 0.101 0.109-8~-7 392 0.495 0.378 0.128 0.101-7~-6 1004 0.435 0.420 0.144 0.049-6~-5 1589 0.397 0.466 0.137-0.022-5~-4 3237 0.393 0.434 0.173-0.017-4~-3 8275 0.406 0.404 0.190 0.014-3~-2 22519 0.408 0.395 0.197 0.014-2~-1 72939 0.384 0.376 0.240 0.011-1~0 137372 0.349 0.386 0.265-0.007 0~1 135570 0.348 0.392 0.260-0.006 1~2 55200 0.366 0.412 0.222-0.009 2~3 23290 0.381 0.432 0.187-0.010 3~4 10641 0.397 0.440 0.163-0.009 4~5 4586 0.422 0.441 0.137-0.004 5~6 2475 0.440 0.434 0.126 0.027 6~7 1580 0.418 0.465 0.116-0.020 7~8 859 0.387 0.484 0.129-0.040 8~9 481 0.364 0.553 0.083-0.136 9~10 302 0.404 0.411 0.185-0.124 4. 5 AR(3) (5 ) 0-21 -
/ 1. (2001) 2001 09 12 2. (2001)?-- 2001 11 10 3. Daewhan Cho, Jerrey Russell, George C. Tiao and Ruey Tsay (2001), The Magnet Effect of Price Limits: Evidence from High Frequency Data on Taiwan Stock Exchange, Working Paper, the National Central University, Taiwan, China 4. Fama, E. F., Perspectives on October 1987, or What did We learn from the Crash? Black Monday and the Future of Financial Markets. R. W. Kamphuis, Jr., R. C. Kormendi, and J. W. H. Watson eds., Chicago Illinois: Mid America Institute for Public Policy Research, Inc., (1989) 5. Harris. L.(1998), Circuit Breakers and Program Trading Limits: what Have we Learned? Working Paper of the Marshall School of Business, University of Southern California 6. JEFF CHUNG, LI GAN (2000), Empirical Estimates of Effect of Price Limits on Limit-Hitting Days, Working Paper, University of Texas at Austin 7. Jegadeesh, Narasimhan(1990), "Evidence of predictable behavior of security returns", Journal of Finance 45,881-898 8. Jie-Haun Lee, Robin K. Chou (2001), Are Price Limits Effective? A Closer Look at the Evidence from Taiwan Stock Market, Working Paper, the National Central University, Taiwan, China 9. Jimmy J. Yang and Yong H. Kim(2001), The Impact of Price Limits on Initial Public Offerings: Evidence from the Taiwan Stock Exchange, Working Paper, University of Cincinnati, Cincinnati, OH 45221, U.S.A. 10. Joan Evans and James M. Mahoney(1997), The Effects of Price Limits on Trading Volume: A Study of the Cotton Futures Market, CURRENT ISSUES IN ECONOMICS AND FINANCE, January 1997, Volume 3 Number 2 11. Kim. K. A., and Richard J. Sweeney (2000), Effects of Price Limits on Information Revelation: Theory and Evidence, Working Paper, University of Wisconsin-Milwaukee - 22 -
12. Kim. K. A., and S. G. Rhee (1997), Price Limit Performance: Evidence from the Tokyo stock Exchange, The Journal of Finance, Vol. Lll, No. 2, pp 885-901 13. Lee, S.B. and K.J. Kim(1995), The Effect of Price Limits on Stock Price Volatility: An Empirical Evidence in Korea. Journal of Business Finance and Accounting 22, 257-267 14. Lehmann, Bruce(1990), "Fades, martinggales and market efficiency", Quarterly Journal of Economics 105, 1-28 15. Ma, C.K., R.P. Rao and R.S. Sears(1989), Volatility, Price Resolution, and the Effectiveness of Price Limits. Journal of Financial Services Research 3, 165-199 16. Woo Suk Choi, Sang Bin Lee (2000a), A Transitory and Asymmetric Properties in Price Limits: Korean Evidence with Intra-day Data, Working Paper, Hanyang University, Korea 17. Woo Suk Choi, Sang Bin Lee(2000b), Price Limits and Asymmetry of Transitory Price Dynamics: Intraday Evidence from the Korea Stock Exchange, Working Paper, Hanyang University, Korea - 23 -