Statistical properties on the returns of stock prices in International Markets

1. Statistical properties on the returns of stock prices in International Markets 오갑진*, 김승환*, 엄철준** * National Research Lab - Nonlinear and Complex Systems Lab. Brain Research Center Department of Physics, POSTECH Pohang, Korea 790-784 e-mail : gq478051@postech.ac.kr WWW : http://www-ncsl.postech.ac.kr ** Department of Healthcare Management, Catholic University of Pusan Busan, Korea 609-757 e-mail : shunter@cup.ac.kr WWW : http://shunter.cup.ac.kr

2. Contents 1. Introduction 2. IED Model 3. Empirical & Simulation Result

3. Introduction (a) Black monday (b) (c) Previous notions on the stock price Random Walks Theory Louis Bachelier "The Theory of Speculation" (1900) EMH(Efficient Market Hypothesis) By Eugene Fama “Efficient Capital market(1970, JOF) ” 1970

4. Introduction Stylized facts in financial market • Gain/loss of asymmetry • Intermittency • Volatility clustering • Leverage effect • Correlation between volume • and volatility • 6. Heavy tails • 7. Slow decay of autocorrelation • in absolute returns

5. Introduction Modify concept notions on the stock price • Three forms of the efficient market hypothesis (By Eugene Fama 1970) • The “Weak” form • : all past market prices fully reflected in securities prices. In other words, technical analysis is • of no use • 2. The “Semi-strong” form • : all publicly available information is fully reflected in securities prices. In other words, fundamental analysis is of no use • 3. The “Strong” form • : all information is fully reflected in securities prices. In other words, even insider information is of no use • 1. ARCH, GARCH… Models (Volatility Prediction methods) • - ARCH (R.E, Engle 1982) (Tails index, Volatility Clustering) • - GARCH (Bollerslev 1986) (Tails index, Volatility Clustering) • - FIGARCH (Bollerslev 1996) (Long memory effects) • ….. • 2. Models based on Internal and external dynamics

6. Introduction the difference between emerging and mature markets

7. CONCEPT : Market Responses for the Information Over-reaction Under-reaction ‘a’ -> Higher : Emerging Market ‘a’ -> Lower : Mature Market A degree of Market Adjusting A degree of Shock = N + ‘ a ’ A degree of Empirical EMH Theoretical EMH Mature Market A degree of Shock = N A degree of Delay = M A degree of Shock = N A degree of Delay = 0 Emerging Market Event A degree of Shock : “ Sufficiently / Magnitude ” A degree of Delay : “ Instantaneously / Time ”

8. Gabaix,H.E. Stanley. Nature, vol 432, 267 (2003) P. Gopikrishnan, H.E. Stanley . PRE. Vol 60. PP. 5305 Matia. ,H.E. Stanley. Europhys. Lett. 66, 909-914 Heavy Tails Volatility correlation

9. Models based on Internal and external dynamics Property of the markets # of event or shock Random Process If , Otherwise , 0 Emerging Market  Low threshold Mature Market  High threshold

10. FINANCIAL DATA (low frequency Market Indices (low Frequency) 8 Market Indices (low frequency) 01 S&P500 / USA 1950.01.03~2005.06.06 02 NASDAQ / USA 1984.10.11~2005.06.06 03 HangSeng / Hong Kong 1986.12.31~2005.06.06 04 Nikkei225 / Japan 1984.01.04~2005.06.06 05 DAX / Germany 1990.11.26~2005.06.06 06 CAC40 / France 1990.03.01~2005.06.06 07 FTSE100 / UK 1984.04.01~2005.06.06 08 KOSPI / Korea 1980.01.04~2005.06.06 Individual companys 2 individual Companys 01 S&P500 / USA (400) 1993.01.03~2005.06.06 02 KOSPI / Korea (485) 1993.1031~2003.12.31 # Data Resource : Yahoo/Finance Market Indices (high Frequency] 3 Market Indices (high frequency) Starting Date for Analysis 1991. 01. 01. ~ 01 S&P500 / USA (5min) 1995 ~ 2005 02 KOSPI / Korea 1995 ~ 2002 Ending Date for Analysis ~ 2005. 05. 31. 03 KOSDAQ / Korea 1997 ~2004

11. Result

12. International Market indices (Low Frequency) Distribution Time correlation

13. Time correlation and distribution of stock indices (high frequency] Kosdaq buble Kospi IMF Kosdaq Volume S&P500 index kospi index distribution distribution distribution Time Correlatioin

14. Simulation results Tail = 5 Tail = 4 Tail = 2 emerging Mature H(absolute) - H

15. CONCEPT : Market Responses for the Information Over-reaction Under-reaction ‘a’ -> Higher : Emerging Market ‘a’ -> Lower : Maturely Market A degree of Market Adjusting A degree of Shock = N + ‘ a ’ A degree of Empirical EMH Theoretical EMH Mature Market A degree of Shock = N A degree of Delay = M A degree of Shock = N A degree of Delay = 0 Emerging Market Event A degree of Shock : “ Sufficiently / Magnitude ” A degree of Delay : “ Instantaneously / Time ”

16. Simulation results Tail = 5 Tail = 4 Tail = 2 emerging Mature H(abs) - H

17. Summary 1 The emerging and mature markets have different features in terms of the time correlation and the distribution of stock indices 2 The empirical results suggest that there exists a long-range dependence in emerging market indices that are time-varying. 3 The IED models can explain both emerging and mature markets with two control parameters, external shocks and memory.

18. Kospi (1993~2003) & Snp500 (1993~2005) H_absolute =0.5739 H_absolute =0.0657 H_absolute =0.0672 H_absolute =0.7126 H = 0.4950 H = 0.0397 H = 0.0358 H = 0.4897 H_absolute– H = 0.0830 H_absolute – H = 0.0672 H_absolute – H = 0.0684 H_absolute– H = 0.2229 Mean Standard deviation Standard deviation Mean H =0.0170 H =0.00013 H_absolute =0.025 H_absolute =0.00012 Standard deviation Standard deviation