1,a) 2,3 3,4 2012 1 26, 2012 7 2 1 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 243 0292, Japan 2 SPARX Asset Management Co., Ltd., Shinagawa, Tokyo 140 0002, Japan 3 School of Engineering, The University of Tokyo, Bunkyo, Tokyo 113 8656, Japan 4 JST PRESTO, JST, Chiyoda, Tokyo 102 0076, Japan 1. Reversal phenomenon a) iyagi2005@gmail.com c 2012 Information Processing Society of Japan 2388
[2], [3] Bremer [3] Fortune500 1 10% 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] 2 3 3.1 3.2 3.3 3.2 1 3.3 3.4 4 3 5 2. [12], [13] c 2012 Information Processing Society of Japan 2389
*1 1 100 3 (1) (2) (3) (1) : (2) : (3) = 45 : 45 : 10 0 10 1,000,000 0 2.1 3 2.1.1 *2 t P t 1,000 P t P t 1000 (0.1P t 1000 ) 2 P 0 300 (0.1 300) 2 i t P i,t (1+ɛ i,t )P t (α(1+ɛ i,t )P t ) 2 100 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 2.1.2 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 10 1 0 <qi,t T S max q i,t 1 q T i,t c 2012 Information Processing Society of Japan 2390
10 1 0 <q T i,t q i,t 1 S min 0 <q T i,t q i,t 1 2.1.3 i 1/3 i (1 + α t )P t 1 qi,t N qn i,t 10 1 0 <qi,t N S max q i,t 1 (1 + α t )P t 1 q N i,t q N i,t 10 1 0 <q N i,t q i,t 1 S min 0 <q N i,t q i,t 1 2.2 [12], [13] 2.2.1 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% 2.2.2 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+1 25 2.3 t 3.4 3. 3.2 3.3 c 2012 Information Processing Society of Japan 2391
Fig. 1 1 The special case of supply and demand curve. 3.4 3.5 *4 3.1 2.3 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 3.2.1 4 1,000 351 8 347 9 1,000 D(351) D(347) 8 17 4 1,000 243 10 248 *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 1,002 285 120 120 295 103 142 300 123 109 274 297 115 9 1,000 S(243) S(248) 10 19 4 295 295 3.2 1,000 60% 3 [12], [13] 3.2.1 3.2.2 3.2.3 3.2.1 0.1 1 2 2 1 3 8 3 4 1,000 c 2012 Information Processing Society of Japan 2392
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 1,001 297 123 287 5 120 123 1,000 295 297 287 1,001 103 6 q i,1001 0 i 44 1,001 *5 (103) 1,002 115 109 7 1,001 1,001 142 *5 2.3 c 2012 Information Processing Society of Japan 2393
2 Table 2 Rebound rates and averages of return rate volatilities when the theoretical price declines at all once. 7 1 1,002 Fig. 7 A quantity of orders at period 1,002 when theoretical 1 2 3 0.1705 0.1180 0.0744 5 5 0.0213 0.0088 0.0126 0.3735 0.3323 0.3023 9 2 Fig. 9 Price transitions at period 1,000 when theoretical prices decline at all once under condition 2. 8 1 1,002 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 ) 2 1 10 3.2.2 0.05 2 0.05 1 9 1 2 1 1,001 1,002 3.2.1 3.2.2 3.2.3 0.05 0.012 3 2 1 c 2012 Information Processing Society of Japan 2394
10 3 Fig. 10 Price transitions at period 1,000 when theoretical prices decline at all once under condition 3. 1 0.003 0.012 10 2 2 2 1,001 1,002 11 1 1 1,000 1,001 1,002 3 Fig. 11 Price transitions when theoretical prices decline every 1 period from period 1,000 to period 1,002. 12 1 10 1,000 1,010 1,020 3 Fig. 12 Price transitions when theoretical prices decline every 10 period from period 1,000 to period 1,020. 3.3 3 1 10 100 3 1,000 20% 2 3 1 3 11 12 13 1 1 10 100 3 13 1 100 1,000 1,100 1,200 3 Fig. 13 Price transitions when theoretical prices decline every 100 period from period 1,000 to period 1,200. 1,000 1 3 1,001 1,003 1,004 c 2012 Information Processing Society of Japan 2395
3 Table 3 Rebound rates and averages of return rate volatilities when the theoretical price declines in stages. 1 2 3 1 10 100 1 10 100 1 10 100 1 0.8893 0.4027 0.3941 0.7478 0.4688 0.4453 0.8145 0.1663 0.1763 2 1.7258 0.4164 0.4264 1.0142 0.3648 0.4014 1.0733 0.2496 0.1964 3 0.4969 0.4351 0.3620 0.3664 0.2749 0.2610 0.2495 0.2296 0.2196 5 5 0.0173 0.0208 0.0246 0.0095 0.0112 0.0100 0.0101 0.0109 0.0105 0.1747 0.2185 0.2112 0.1533 0.1913 0.1963 0.0675 0.1606 0.1600 10 100 3 3 3.2 3.4 1 2 2 1 1,000 60% 14 15 1,001 14 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
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[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.264 274 (1994). [12] Vol.26, No.1, pp.208 216 (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.113 132 (2010). 1995 1997 2006 2011 IEEE 2000 2002 2004 4 2010 5 2011 10 JAFEE 1993 1998 2010 2010 c 2012 Information Processing Society of Japan 2398