The Relationship between Stock Returns and Volatility in the Seventeen Largest International Stock Markets: A Semi-Parametric Approach

ABSTRACT

We empirically investigate the relationship between expected stock returns and volatility in the twelve EMU countries as well as five major out of EMU international stock markets. The sample period starts from De-cember 1992 until December 2007 i.e. up to the recent financial crisis. Empirical results in the literature are mixed with regard to the sign and significance of the mean – variance tradeoff. Based on parametric GARCH in mean models we find a weak relationship between expected returns and volatility for most of the markets. However, using a flexible semi-parametric specification for the conditional variance, we unravel significant evidence of a negative relationship in almost all markets. Furthermore, we investigate a related issue, the asymmetric reaction of volatility to positive and negative shocks in stock returns confirming a negative asymmetry in almost all markets.

We empirically investigate the relationship between expected stock returns and volatility in the twelve EMU countries as well as five major out of EMU international stock markets. The sample period starts from De-cember 1992 until December 2007 i.e. up to the recent financial crisis. Empirical results in the literature are mixed with regard to the sign and significance of the mean – variance tradeoff. Based on parametric GARCH in mean models we find a weak relationship between expected returns and volatility for most of the markets. However, using a flexible semi-parametric specification for the conditional variance, we unravel significant evidence of a negative relationship in almost all markets. Furthermore, we investigate a related issue, the asymmetric reaction of volatility to positive and negative shocks in stock returns confirming a negative asymmetry in almost all markets.

KEYWORDS

Risk-Return Tradeoff, International Stock Markets, Semi-Parametric Specification of Conditional Variance

Risk-Return Tradeoff, International Stock Markets, Semi-Parametric Specification of Conditional Variance

Cite this paper

nullD. Dimitriou and T. Simos, "The Relationship between Stock Returns and Volatility in the Seventeen Largest International Stock Markets: A Semi-Parametric Approach,"*Modern Economy*, Vol. 2 No. 1, 2011, pp. 1-8. doi: 10.4236/me.2011.21001.

nullD. Dimitriou and T. Simos, "The Relationship between Stock Returns and Volatility in the Seventeen Largest International Stock Markets: A Semi-Parametric Approach,"

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[30] C. F. Lee, G. Chen and O. Rui, “Stock Returns and Volatility on China’s Stock Markets,” Jour-nal of Financial Research, Vol. 24, No. 4, 2001, pp. 523-543.

[31] L. R. Glosten, R. Jagannathan and D. E. Runkle, “On the Relation between the Expected Value and Volatility of Nominal Excess Return on Stocks,” Journal of Finance, Vol. 48, No. 5, 1993, pp. 1629-1658. doi:10.2307/2329067

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[33] Q. Li, J. Yang, C. Hsiao and Y. –J. Chang, “The Relationship between Stock Returns and Volatility in International Stock Markets,” Journal of Empirical Finance, Vol. 12, No. 5, December 2005, pp. 650-665. doi:10.1016/j.jempfin.2005.03.001

[34] P. Theodossiou and D. Lee, “Relationship between Volatility and Ex-pected Returns Across International Stock Markets,” Journal of Business Finance and Accounting, Vol. 22, No. 2, March 1995, pp. 289-300. doi:10.1111/j.1468-5957.1995.tb00685.x

[1] W. F. Sharpe, “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Market Risk,” Journal of Finance, Vol. 19, No. 3, September 1964, pp. 425-442. doi:10.2307/2977928

[2] J. Linter, “The Valuation of Risky Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets,” Review of Eco-nomics and Statistics, Vol. 47, No. 1, February 1965, pp. 13-37. doi:10.2307/1924119

[3] J. Mossin, “Equilibrium in a Capital Asset Market,” Eco- nometrica, Vol. 34, No. 4, October 1966, pp. 768-783. doi:10.2307/1910098

[4] R. C. Merton, “An Intertem-poral Capital Asset Pricing Model,” Econometrica, Vol. 41, No. 5, September 1973, pp. 867-887. doi:10.2307/1913811

[5] R. C. Merton, “On Estimating the Expected Return on the Market: An Exploratory In-vestigation,” Journal of Financial Economics, Vol. 8, No. 4, 1980, pp. 323-361. doi:10.1016/0304-405X(80)90007-0

[6] R. T. Baillie and R. P. DeGennaro, “Stock Returns and Volatility,” Journa1 of Financia1 and Quantitative Ana- 1ysis, Vol. 5, No. 2, June 1990, pp. 203-214.

[7] F. B1ack, “Studies of Stock Price Volatility Changes,” Proceedings of the 1976 Meeting of Business and Economics Statistics Sec-tion of the American Statistical Association, Vol. 27, 1976, pp. 399-418.

[8] J. Cox and S. Ross, “The Valuation of Options for Alternative Stochastic Process,” Journa1 of Financia1 Economics, Vol. 3, No.1-2, 1976, pp. 145-166.

[9] G. Bakaert and G. Wu, “Asymmetric Volatility and Risk In Equity Markets,” Review of Finan-cial Studies, Vol. 13, No. 1, 2000, pp. 1-42. doi:10.1093/rfs/13.1.1

[10] R. Whitelaw, “Stock Market Risk and Return: An Empirical Equilibrium Approach,” Review of Financial Studies, Vol. 13, No. 3, 2000, pp. 521-547. doi:10.1093/rfs/13.3.521

[11] R. Pindyck, “Risk, Infla-tion and the Stock Market,” American Economic Review, Vol. 74, 1984, pp. 335-351.

[12] R.J. Shiller, “Do Prices Move too Much to be Justified by Subsequent Changes in Dividends,” American Economic Review, Vol. 71, No. 3, June 1981, pp. 421-436.

[13] J. Poterba and L. Summers, “The Persistence of Volatility and Stock Market Fluctua-tions,” American Economic Review, Vol. 76, No. 5, 1986, pp. 1142-1151.

[14] K. R. French, G. W. Schwert and R. F. Stambaugh, “Expected Stock Returns and Volatility,” Journal of Financial Economics, Vol. 19, No. 1, 1987, pp. 3-30. doi:10.1016/0304-405X(87)90026-2

[15] H. A. Shawky and A. Marathe, “Expected Stock Returns and Volatility in a Two Regime Market,” The Journal of Economics and Business, Vol. 47, No. 5, December 1995, pp. 409-422. doi:10.1016/0148-6195(95)00035-6

[16] J. Y. Campbell and L. Hentschel, “No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns,” Journal of Financial Economics, Vol. 31, No. 3, 1992, pp. 281-318. doi:10.1016/0304-405X(92)90037-X

[17] E. F. Fama and W. G. Schwert, “Asset Returns and Inflation,” Jour-nal of Financial Economics, Vol. 5, No. 2, 19- 77, pp. 115-146.

[18] D. Nelson, “Conditional Heteroscedastic-ity in Asset Returns: A New Approach,” Econometrica, Vol. 59, No. 2, March 1991, pp. 347-370. doi:10.2307/2938260

[19] K. C. Chan, A. Karolyi and R. Stulz, “Global Financial Markets and the Risk Premium on US Equity,” Journal of Financial Economics, Vol. 32, No. 2, 1992, pp. 137-167. doi:10.1016/0304-405X(92)90016-Q

[20] C. R. Harvey, “Time-Varying Conditional Covariances in Tests of As-set Pricing Models,” Journal of Financial Economics, Vol. 24, No. 2, 1989, pp. 289-317. doi:10.1016/0304-405X(89)90049-4

[21] Τ. Bollers1ev, R. Y. Chou and K. F. Kroner, “ARCH Modeling in Fi-nance: A Review of the Theory and Empirical Evidence,” Journal of Econometrics, Vol. 52, No. 1-2, 1992, pp. 5-59.

[22] T. Bollerslev, R. F. Engle and D. B. Nelson, “ARCH Models,” In: R. F. Engle and D. McFadden, Eds., Handbook of Econometrics, North-Holland, Vol. 4, 1994, pp. 2959-3038.

[23] H. Ludger, “All in the Family Nest-ing Symmetric and Asymmetric GARCH Models,” Journal of Financial Economics, Vol. 39, No. 1, Sep-tember 1995, pp. 71-104. doi:10.1016/0304-405X(94)00821-H

[24] Τ. Bollerslev, “Generalized Autoregressive Conditional Heteroscedas-ticity,” Journa1 of Econometrics, Vol. 31, No. 3, 1986, pp. 307-327.

[25] R. F. Eng1e and V. K. Ng, “Measuring and Testing the Impact of News on Volatility,” Journa1 of Finance, Vol. 48, No. 5, 1993, pp. 1749-1778.

[26] L. Yang, “Direct Estimation in an Additive Model When the Components are Proportional,” Statistica Sinica, Vol. 12, No. 3, 2002, pp. 801 -821.

[27] W. Newey, “Conver-gence Rates and Asymptotic Normality for Series Esti-mators,” Journal of Econometrics, Vol. 79, No. 1, July 1997, pp. 147-168. doi:10.1016/S0304-4076(97)00011-0

[28] R. De Jong, “Convergence Rates and Asymptotic Norma1ity for Se-ries Estimators: Uniform Convergence Rates,” Jouma1 of Econometrics, Vol. 111, No 1, 2002, pp. 1-9.

[29] Τ. Choudhry, “Stock Market Volatility and the Crash of 1987: Evidence from Six Emerging Markets,” Journa1 of Intemationa1 Money and Finance, Vol. 15, No. 6, 1996, pp. 969-981.

[30] C. F. Lee, G. Chen and O. Rui, “Stock Returns and Volatility on China’s Stock Markets,” Jour-nal of Financial Research, Vol. 24, No. 4, 2001, pp. 523-543.

[31] L. R. Glosten, R. Jagannathan and D. E. Runkle, “On the Relation between the Expected Value and Volatility of Nominal Excess Return on Stocks,” Journal of Finance, Vol. 48, No. 5, 1993, pp. 1629-1658. doi:10.2307/2329067

[32] L. L. Schumaker, “Spline Functions: Basic Theory,” Wil- ey, New York, 1981.

[33] Q. Li, J. Yang, C. Hsiao and Y. –J. Chang, “The Relationship between Stock Returns and Volatility in International Stock Markets,” Journal of Empirical Finance, Vol. 12, No. 5, December 2005, pp. 650-665. doi:10.1016/j.jempfin.2005.03.001

[34] P. Theodossiou and D. Lee, “Relationship between Volatility and Ex-pected Returns Across International Stock Markets,” Journal of Business Finance and Accounting, Vol. 22, No. 2, March 1995, pp. 289-300. doi:10.1111/j.1468-5957.1995.tb00685.x