Stock Returns Under Alternative Volatility and Distributional Assumptions: The Case for India

Abstract

This paper has attempted studying the twin issues of asymmetry/leverage effect and excess kurtosis prevalent in Indias stock returns under alternative volatility specifications as well as conditional distributional assumptions. This study has been carried out using daily-level data, based on Indias premier stock index, BSESENSEX, covering Indias post-liberalisation period from January 1996 to December 2010. Apart from lag returns, three other variables viz., call money rate, nominal exchange rate and daily dummies have been used as explanatory variables for specifying the conditional mean. Three alternative models of volatility representing the phenomenon of leverage effect in returns viz., EGARCH, TGARCH and asymmetric PARCH along with standard GARCH have been considered for this study. As regards the assumption on conditional distribution for the innovations, apart from the Gaussian distribution, two alternative conditional distributions viz., standardized Students distribution and standardized GED for capturing the leptokurtic property of the return distribution have been considered. Further, comparisons across these models have been done using forecast evaluation criteria suitable for both in-sample and out-of-sample forecasts. The results indicate that the asymmetric PARCH volatility specification performs the best in terms of both in-sample and out-of-sample forecasts. Also, the assumption of normality for the conditional distribution is not quite statistically tenable against the standardized GED and standardized Students distribution for all the volatility models considered.

Keywords

• Leverage Effect, Excess Kurtosis, Volatility Specification, Conditional Distribution, Out-Of-Sample Forecasts.

References

1. Abdalla, I.S.A. and V. Murinde (1997). Exchange Rate and Stock Price Interactions in Emerging Financial Markets: Evidence on India, Korea, Pakistan and the Philippines. Applied Financial Economics, 7, 25-35.
2. Andrews, D.W.K. (1993). Tests for Parameter Instability and Structural Change with Unknown Change Point. Econometrica, 59 (3), 817-858.
3. Bachelier, L. (1964) [1900]. Theory of Speculation. In The Random Character of Stock Market Price, ed. P. Cootner. Cambridge: MIT Press, 17-78.
4. Batra, A. (2004). Stock Return Volatility Pattern in India, Working paper No. 12, http://www.icrier.org/pdf/wp124.pdf (accessed March 24, 2013).
5. Black, F. (1976). Studies of Stock Price Volatility Changes. In Proceedings of the 1976 Meeting of the Business and Economics Statistics Section. American Statistical Association, 177-181.
6. Bollerslev, T. (1986). Generalised Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 31, 307-327.
7. Bollerslev, T. (1987). A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return. Review of Economics and Statistics, 69, 542-547.
8. Bollerslev, T., R.F. Engle and D.B. Nelson (1994). ARCH Models In Handbook of Econometrics vol. 4, ed. R. Engle and D. McFadden. Amsterdam: Elsevier Science Publishers.

9. Christie A. (1982). The Stochastic Behaviour of Common Stock Variances – Value, Leverage and Interest Rate Effects. Journal of Financial Economics, 10, 407-432.
10. Ding Z., C.W.J Granger and R.F. Engle (1993). A long memory property of stockmarket returns and a new model. Journal of Empirical Finance, 1, 83-106.
11. Engle, R.F. (1982). Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of U.K. Inflation. Econometrica, 50, 987-1008.
12. Engle, R.F. and V.K. Ng (1993). Measuring and Testing the Impact of News on Volatility. Journal of Finance, 48, 1749-1778.
13. Goudzari, H. and C.S. Ramanarayanan.(2011). Modeling Asymmetric Volatility in the Indian Stock Market. International Journal of Business and Management, 6 (3), 221-231.
14. Glosten, L., R. Jagannathan and D. Runkle (1993). Relationship between the Expected Value and the Volatility of the Nominal Excess Return on Stocks. Journal of Finance, 48, 1779-1801.
15. Granger C.W.J., B.N. Huang and C.W. Yang (2000). A Bivariate Causality between Stock Prices and Exchange Rate: Evidence from Recent Asian Flu. Quarterly Review of Economics and Finance, 40, 337-354.
16. Hansen, B. E. (1997). Approximate Asymptotic P-values for Structural-Change Tests. Journal of Business and Economic Statistics, 15 (1), 60-67.
17. Herwartz, H. (2004). Conditional Heteroscedasticity. In Applied Time Series Econometrics, ed. H. Lutkepohl and M. Kratzig. Cambridge: Cambridge University Press, 197-220.
18. Kon, S.J. (1984). Models of Stock Returns – A Comparison. Journal of Finance, 39, 147-165.
19. MacKinnon, J.G. (1996). Numerical Distribution Functions for Unit Root and Cointegration Tests. Journal of Applied Econometrics, 11, 601-618.
20. Makridakis, S. (1993). Accuracy Measures: Theoretical and Practical Concerns. International Journal of Forecasting, 9, 527-529.
21. Makridakis, S., C. Chatfield, M. Hibon, M. Lawrence, T. Mills,, K. Ord and L.F. Simmons (1993). The M2-Competition: A Real-time Judgmentally based Forecasting Study. International Journal of Forecasting, 9, 5-22.
22. Makridakis, S. and M. Hibon (2000). The M3-Competition: Results, Conclusions and implications. International Journal of Forecasting, 16, 451-476.
23. Mandelbrot, B. (1963). The Variation of Certain Speculative Prices. Journal of Business, 36, 394–419.
24. Mills, T.C. (1995). Modelling Skewness and Kurtosis in London Stock Exchange FT-SE Index Return Distributions. The Statistician, 44, 323-332.
25. Musilek, P. (1997). Changes in Macroeconomic Variables and the Stock Market. Finance A Uver, 47, 150-162.
26. Nelson, D.B. (1991). Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica, 59, 347-370.
27. Newey, W.K. and D.G. Steigerwald (1997). Asymptotic Bias for Quasi-maximum Likelihood Estimators in Conditional Heteroskedasticity Models. Econometrica, 65, 587-599.
28. Peiró, A. (1999). Skewness in Financial Returns. Journal of Banking and Finance, 6, 847- 862.
29. Phillips, P.C.B. and P. Perron (1988). Testing for Unit Roots in Time Series Regression. Biometrika, 75, 335-46.
30. Said, S.E. and D.A. Dickey (1984). Testing for Unit Roots in Autoregressive Moving- Average Models with Unknown Order. Biometrika, 71, 599-607.
31. Sarkar, N. and D. Mukhopadhyay (2005). Testing Predictability and Nonlinear Dependence in the Indian Stock Market. Emerging Markets Finance and Trade, 41 (6), 7-44.
32. Schwert GW. (1989). Why does stock market volatility change over time? Journal of Finance, 44, 1115–53.
33. Taylor, S. (1986). Modeling Financial Time Series. New York: John Wiley & So.
34. Taylor, J.W. (2004). Volatility Forecasting with Smooth Transition Exponential Smoothing. International Journal of Forecasting, 20, 273-286.
35. Tucker, A.L. (1992). A Reexamination of Finite and Infinite-Variance Distributions as Models of Daily Stock Returns. Journal of Business and Economic Statistics, 10, 73-81.
36. Zakoian, J.M. (1994). Threshold Heteroskedastic Functions. Journal of Economic Dynamics and Control, 18, 931-955.