[2], [3] Bremer [3] Fortune % Overreaction hypothesis Benou [2] 1 20% [9] 1 [10] 1 [1], [4], [5], [6], [7], [8] [1] [8] [6] [2], [3] stylized f

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1 1,a) 2,3 3, , An Analysis on the Reversal Mechanism for Large Stock Price Declines Using Artificial Markets Isao Yagi 1,a) Takanobu Mizuta 2,3 Kiyoshi Izumi 3,4 Received: January 26, 2012, Accepted: July 2, 2012 Abstract: Fundamentals deterioration of firms due to their scandals or disasters causes the decline in their stock prices. We know empirically that stock prices rebound after they fall largely. In this paper, this trend is called the reversal phenomenon. There are some preceding researches on the issue, however, little has been explained about the market mechanism such as a market pricing mechanism in the reversal of large stock price declines. We reproduced the reversal phenomenon in the artificial market with the degree of variation of expected prices and Itayose system which is one of the stock pricing mechanisms and a kind of double auction, not with the overreaction hypothesis. On the other hand, the reversal phenomenon does not always occur in the artificial market with Zaraba system which is a kind of continuous double auction. Keywords: artificial market, reversal phenomenon, overreaction hypothesis, stock pricing mechanism 1 Department of Information and Computer Sciences, Kanagawa Institute and Technology, Atsugi, Kanagawa , Japan 2 SPARX Asset Management Co., Ltd., Shinagawa, Tokyo , Japan 3 School of Engineering, The University of Tokyo, Bunkyo, Tokyo , Japan 4 JST PRESTO, JST, Chiyoda, Tokyo , Japan 1. Reversal phenomenon a) [email protected] c 2012 Information Processing Society of Japan 2388

2 [2], [3] Bremer [3] Fortune % Overreaction hypothesis Benou [2] 1 20% [9] 1 [10] 1 [1], [4], [5], [6], [7], [8] [1] [8] [6] [2], [3] stylized facts [11] stylized facts [13] [12], [13] c 2012 Information Processing Society of Japan 2389

3 * (1) (2) (3) (1) : (2) : (3) = 45 : 45 : ,000, *2 t P t 1,000 P t P t 1000 (0.1P t 1000 ) 2 P ( ) 2 i t P i,t (1+ɛ i,t )P t (α(1+ɛ i,t )P t ) P t ɛ i,t i t *3 α i α =0.1 t Q i,t 1 t q i,t 1 t 1 P t 1 t t *1 t =(t (t 1) )/(t 1) *2 *3 W i,t 1 W i,t 1 = Q i,t 1 + P t 1 q i,t 1 (1) (1) q i,t q i,t = (1 + ɛ i,t)p t P t 1 a(α(1 + ɛ i,t )P t ) 2 [8] a > 0 i q i,t t q i,t q i,t 1 > 0 i P i,t q i,t q i,t 1 S max q i,t 1 t q i,t q i,t 1 < 0 i P i,t q i,t 1 q i,t q i,t 1 S min q i,t 1 t q i,t = q i,t 1 i i t n i,t MA t,ni,t = 1 n i,t n i,t j=1 P t j ΔMA t,ni,t = MA t,ni,t MA t 1,ni,t i ΔMA t,ni,t > 0 (1 + α t )P t 1 qi,t T ΔMA t,ni,t < 0 (1 + α t )P t 1 q T i,t ΔMA t,ni,t =0 ΔMA t,ni,t > 0 (1 + α t )P t 1 q T i,t ΔMA t,ni,t < 0 (1 + α t )P t 1 qi,t T ΔMA t,ni,t =0 n i,t 1 n i,t 25 α t P t 1 (0.1P t 1 ) 2 qi,t T <qi,t T S max q i,t 1 q T i,t c 2012 Information Processing Society of Japan 2390

4 <q T i,t q i,t 1 S min 0 <q T i,t q i,t i 1/3 i (1 + α t )P t 1 qi,t N qn i,t <qi,t N S max q i,t 1 (1 + α t )P t 1 q N i,t q N i,t <q N i,t q i,t 1 S min 0 <q N i,t q i,t [12], [13] i t 1 t R i,t = W i,t /W i,t 1 N N =5 R i,t = 1 N N j=1 R i,t (j 1) N L % p i = i ɛ i,t N H % 1 i i N ɛ i,n = 1 N N j=0 ɛ i,t j ɛ i,t+1 N L N H 20 N H % 5% R i,t N L % i p i = i n i,t N H % i i n i,t n i,t+1 N H % 5% n i,t+1 1 n i,t t c 2012 Information Processing Society of Japan 2391

5 Fig. 1 1 The special case of supply and demand curve * D(p) p S(p) p 1 (a) p d, p d p d <p d p s p s p s <p s D(p d )=q D(p d )=q S(p s )=q S(p s )=q p d <p s, p s <p d (p s + p d )/2 q 1 (b) D(p d )=q D(p d )=q S(p s )=q S(p s )=q p d <p d p s <p s p d = p s p d q q 1 (b) q , ,000 D(351) D(347) , *4 t =(t (t 1) )/(t 1) 2 1 Fig. 2 Price transitions at period 1,000 when theoretical prices decline at all once under condition 1. 1 Table 1 Transitions before or after theoretical prices decline. 1,000 1,001 1, ,000 S(243) S(248) ,000 60% 3 [12], [13] ,000 c 2012 Information Processing Society of Japan 2392

6 3 1 1,000 Fig. 3 A quantity of orders at period 1,000 when theoretical 6 1 1,001 Fig. 6 A supply and demand curve at period 1,001 when theoretical 4 1 1,000 Fig. 4 A supply and demand curve at period 1,000 when theoretical 5 1 1,001 Fig. 5 A quantity of orders at period 1,001 when theoretical 1, , , q i, i 44 1,001 *5 (103) 1, ,001 1, *5 2.3 c 2012 Information Processing Society of Japan 2393

7 2 Table 2 Rebound rates and averages of return rate volatilities when the theoretical price declines at all once ,002 Fig. 7 A quantity of orders at period 1,002 when theoretical Fig. 9 Price transitions at period 1,000 when theoretical prices decline at all once under condition ,002 Fig. 8 A supply and demand curve at period 1,002 when theoretical 8 1,002 (142) 2 = ( 1,002 1,001 ) /( 1,000 1,001 ) ,001 1, c 2012 Information Processing Society of Japan 2394

8 10 3 Fig. 10 Price transitions at period 1,000 when theoretical prices decline at all once under condition ,001 1, ,000 1,001 1,002 3 Fig. 11 Price transitions when theoretical prices decline every 1 period from period 1,000 to period 1, ,000 1,010 1,020 3 Fig. 12 Price transitions when theoretical prices decline every 10 period from period 1,000 to period 1, ,000 20% ,000 1,100 1,200 3 Fig. 13 Price transitions when theoretical prices decline every 100 period from period 1,000 to period 1,200. 1, ,001 1,003 1,004 c 2012 Information Processing Society of Japan 2395

9 3 Table 3 Rebound rates and averages of return rate volatilities when the theoretical price declines in stages ,000 60% , Fig. 14 The case that price does not decline largely just after theoretical price declined in the market with Zaraba system. 15 Fig. 15 The case that the reversal phenomenon does not occur in the market with Zaraba system. c 2012 Information Processing Society of Japan 2396

10 * [12], [13] 5. *6 [1] Arthur, W., Holland, J., Lebaron, B., Palmer, R. and Tayler, P.: Asset pricing under endogenous expectations in an artificial stock market, The Economy as an Evolving Complex System II, pp.15 44, Addison-Wesley (1997). [2] Benou, G. and Richie, R.: The reversal of large stock price declines: The case of large firms, Journal of Economics and Finance, Vol.27, No.1, pp (2003). [3] Bremer, M. and Sweeney, R.J.: The reversal of large stock price decreases, The Journal of Finance, Vol.46, No.2, pp (1991). [4] Chen, S.-H. and Yeh, C.-H.: On the emergent properties of artificial stock markets: the efficient market hypothesis and the rational expectations hypothesis, Economic Behavior & Organization, Vol.49, No.2, pp (2002). [5] Darley, V. and Outkin, A.V.: A NASDAQ Market Simulation: Insights on a Major Market from the Science of Complex Adaptive Systems, World Scientific Pub. Co. Inc. (2007). [6] Feldman, T.: Leverage regulation: An agent-based simulation, Journal of Economics and Business, Vol.63, No.5, pp (2011). [7] ADG Vol.43, No.7, pp (2002). [8] (2003). [9] 7 pp.1 6 (2011). [10] 8 pp.1 6 (2012). c 2012 Information Processing Society of Japan 2397

[11] Palmer, R.G., Arthur, W.B., Holland, J.H., LeBaron, B. and Tayler, P.

75, No.1-3, pp.264 274 (1994). [12] Vol.26, No.1, pp.208 216 (2011). [13] Yagi, I., Mizuta, T.

: A Study on the Effectiveness of Short-selling Regulation in view of Regulation Period using

11 [11] Palmer, R.G., Arthur, W.B., Holland, J.H., LeBaron, B. and Tayler, P.: Artificial economic life: A simple model of a stockmarket, Physica D: Nonlinear Phenomena, Vol.75, No.1-3, pp (1994). [12] Vol.26, No.1, pp (2011). [13] Yagi, I., Mizuta, T. and Izumi, K.: A Study on the Effectiveness of Short-selling Regulation in view of Regulation Period using Artificial Markets, Evolutionary and Institutional Economics Review, Vol.7, No.1, pp (2010) IEEE JAFEE c 2012 Information Processing Society of Japan 2398

23_02.dvi

23_02.dvi Vol. 2 No. 2 10 21 (Mar. 2009) 1 1 1 Effect of Overconfidencial Investor to Stock Market Behaviour Ryota Inaishi, 1 Fei Zhai 1 and Eisuke Kita 1 Recently, the behavioral finance theory has been interested