Testing for Differences in the Tails of Stock-Market Returns

In this paper, we use a database consisting of daily stock-index returns for 20 countries to test for similarities between the left and right tail of returns as well as for cross-sectional differences. To mitigate the issue of dependency between stock returns, we estimate the distribution of extremes over subsamples of two months. We document a good fit of the model and show that the left and right tails of returns behave very similarly. Across countries, we find that extremes are located at different levels and that their dispersion varies. On the other hand, the tail index, charactering large extreme realizations is found to be constant worldwide. Our results are not due to a lack of power. We also discuss the results from an economic point of view.

[1]  B. M. Hill,et al.  A Simple General Approach to Inference About the Tail of a Distribution , 1975 .

[2]  John Y. Campbell,et al.  No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns , 1991 .

[3]  R. Adler,et al.  A practical guide to heavy tails: statistical techniques and applications , 1998 .

[4]  Adrian Pagan,et al.  Estimating the Density Tail Index for Financial Time Series , 1997, Review of Economics and Statistics.

[5]  Thomas Lux.  The Limiting Extremal Behaviour of Speculative Returns: An Analysis of Intra-Daily Data From the Frankfurt Stock Exchange , 1998 .

[6]  Alexander J. McNeil,et al.  Calculating quantile risk measures for financial return series using extreme value theory , 1998 .

[7]  C. D. Vries,et al.  The Limiting Distribution of Extremal Exchange Rate Returns , 1991 .

[8]  Jón Dańıelsson,et al.  Tail Index and Quantile Estimation with Very High Frequency Data , 1997 .

[9]  A. McNeil,et al.  The Peaks over Thresholds Method for Estimating High Quantiles of Loss Distributions , 1998 .

[10]  P. Hartmann,et al.  Asset Market Linkages in Crisis Periods , 2001, Review of Economics and Statistics.

[11]  L. Haan,et al.  Using a Bootstrap Method to Choose the Sample Fraction in Tail Index Estimation , 2000 .

[12]  L. Haan,et al.  On the Estimation of the Extreme-Value Index and Large Quantile Estimation , 1989 .

[13]  R. Huisman,et al.  Tail-Index Estimates in Small Samples , 2001 .

[14]  C. Klüppelberg,et al.  Modelling Extremal Events , 1997 .

[15]  M. R. Leadbetter,et al.  Extremes and Related Properties of Random Sequences and Processes: Springer Series in Statistics , 1983 .

[16]  A. McNeil.  Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory , 1997, ASTIN Bulletin.

[17]  Olivier V. Pictet,et al.  Hill, bootstrap and jackknife estimators for heavy tails , 1998 .

[18]  B. Gnedenko.  Sur La Distribution Limite Du Terme Maximum D'Une Serie Aleatoire , 1943 .

[19]  F. Longin,et al.  Extreme Correlation of International Equity Markets , 2000 .

[20]  Susmita Dasgupta,et al.  Return Behavior in Emerging Stock Markets , 1995 .

[21]  Marcia M. A. Schafgans,et al.  The tail index of exchange rate returns , 1990 .

[22]  K. Koedijk,et al.  Tail Estimates of East European Exchange Rates , 1992 .

[23]  A. McNeil,et al.  Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach , 2000 .

[24]  B. Sherman.  Percentiles of the $\omega_n$ Statistic , 1957 .

[25]  Sidney I. Resnick,et al.  Extremal behaviour of solutions to a stochastic difference equation with applications to arch processes , 1989 .

[26]  Dennis W. Jansen,et al.  On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective , 1989 .

[27]  Giovanni Urga,et al.  A Time Varying Parameter Model to Test for Predictability and Integration in the Stock Markets of Transition Economies , 1998 .

[28]  P. Phillips,et al.  Testing the covariance stationarity of heavy-tailed time series: An overview of the theory with applications to several financial datasets , 1994 .

[29]  F. Longin.  The Asymptotic Distribution of Extreme Stock Market Returns , 1996 .

[30]  Carmela Quintos,et al.  Structural Change Tests in Tail Behaviour and the Asian Crisis , 1999 .

[31]  Tailen Hsing,et al.  Estimating the parameters of rare events , 1991 .

[32]  Malcolm R Leadbetter,et al.  On the exceedance point process for a stationary sequence , 1988 .

[33]  Campbell R. Harvey,et al.  Emerging Equity Market Volatility , 1995 .

[34]  J. Pickands.  Statistical Inference Using Extreme Order Statistics , 1975 .

[35]  Richard L. Smith.  Maximum likelihood estimation in a class of nonregular cases , 1985 .