رابطه بین بازده سهام و نوسانات در بازارهای بین المللی سهام

This study examines the relationship between expected stock returns and volatility in the 12 largest international stock markets during January 1980 to December 2001. Consistent with most previous studies, we find a positive but insignificant relationship during the sample period for the majority of the markets based on parametric EGARCH-M models. However, using a flexible semiparametric specification of conditional variance, we find evidence of a significant negative relationship between expected returns and volatility in 6 out of the 12 markets. The results lend some support to the recent claim [Bekaert, G., Wu, G., 2000. Asymmetric volatility and risk in equity markets. Review of Financial Studies 13, 1–42; Whitelaw, R., 2000. Stock market risk and return: an empirical equilibrium approach. Review of Financial Studies 13, 521–547] that stock market returns are negatively correlated with stock market volatility.

The relationship between the return on an asset and its variance (or volatility) as a proxy for risk has been an important topic in financial research. The theoretical asset-pricing models (e.g., Sharpe, 1964, Linter, 1965, Mossin, 1966, Merton, 1973 and Merton, 1980) typically link the return (or the price change) of an asset to its own return variance, or to the covariance between its return and the return on the market portfolio. However, whether such a relationship is positive or negative has been controversial. As summarized in Baillie and DeGennarro (1990), most asset-pricing models (e.g., Sharpe, 1964, Linter, 1965, Mossin, 1966 and Merton, 1973) postulate a positive relationship between a stock portfolio's expected returns and volatility. On the other hand, there is also a long tradition in finance that models stock return volatility as negatively correlated with stock returns (Black, 1976, Cox and Ross, 1976, Bekaert and Wu, 2000 and Whitelaw, 2000). For example, Bekaert and Wu (2000, p. 1) recently claim that “it appears that volatility in equity markets is asymmetric: returns and conditional volatility are negatively correlated.” Although their paper is critically motivated by such a claim, the empirical evidence for such a negative relationship between expected returns and volatility is mixed in the US stock markets and has not yet been reported in international stock markets other than the US. In this context, our study substantially complements Bekaert and Wu (2000). Furthermore, Glosten et al. (1993) and Nelson (1991) argue that across time there is no theoretical agreement about the relationship between returns and volatility within a given period of time and that either a positive or a negative relationship between current stock returns and current volatility is possible. Numerous empirical studies have been conducted to investigate the relationship between stock market returns and volatility. The findings of early studies are mixed (e.g., Pindyck, 1984 and Poterba and Summers, 1986). As pointed out by Bollerslev et al. (1992, pp. 17–18), inference from early studies may not be reliable because variance modeling in these studies does not make efficient use of the data. More recent studies have typically used (G)ARCH-in-Mean models (Engle et al., 1987) to allow for time-varying behavior of volatility. Surprisingly, most find an insignificant relationship between returns and conditional variance (as defined by the parametric GARCH process) in international stock markets. Although French et al. (1987) document a significant positive relationship between US stock market returns and the conditional variance of these returns, Baillie and DeGennarro (1990) report that such a positive relationship is weak and almost nonexistent in the US stock market. Similarly, Theodossiou and Lee (1995) and Lee et al. (2001) also find a positive but insignificant relationship between stock market returns and the conditional variance in many other international stock markets. In contrast, Nelson (1991) documents a negative but insignificant relationship between expected returns and the conditional variance of the US stock market. Glosten et al. (1993) show evidence that such a negative relationship is significant in the US market. Obviously, the empirical findings remain inconclusive. The finding of an insignificant relationship appears puzzling. Though a significant impact of volatility on the stock prices can take place only if shocks to volatility persist over a long period of time (Poterba and Summers, 1986), it is well documented that stock market volatility is persistent. Hence, many of the previous studies, e.g., Baillie and DeGennarro (1990), Theodossiou and Lee (1995), and Choudhry (1996), challenge the appropriateness of using the conditional variance (as modeled by a parametric GARCH process) to proxy for risk and attribute the finding of the weak relationship to the lack of a proper measure of risk. In view of the above mixed results, this study uses a flexible semiparametric specification of conditional variance to examine the relationship between expected returns and volatility in 12 major stock markets. The use of a flexible functional form for conditional variance is appealing because estimation of a parametric GARCH-M model is sensitive to model misspecification. Consistent estimation in the (G)ARCH-M model requires that the full model be correctly specified (Bollerslev et al., 1992, p. 14). Indeed, the problem that inferences drawn on the basis of GARCH-M models may be highly susceptible to model misspecification is well known to applied researchers. For example, Jones et al. (1998) choose not to estimate a GARCH-M model to measure a possible change in the risk premium, simply due to the concern that a potential misspecification problem may contaminate the estimation of conditional variance parameters. Nelson (1991, p.347) also argues that parameter restrictions imposed by GARCH models may unduly restrict the dynamics of the conditional variance process. In contrast, a semiparametric specification of the conditional variance allows flexible functional forms, and therefore can lead to more reliable estimation and inference. In this paper, we propose a semiparametric test for testing the null hypothesis of zero GARCH-M effect. The simulation results show that the proposed test has good finite sample performance compared with a parametric test based on EGARCH specification. We then apply the proposed test to the empirical data of 12 largest international stock markets and show some evidence that a significant negative relationship between (current) stock market returns and (current) market volatility prevails in most major stock markets, which has not yet been reported in the literature. The rest of this paper is organized as follows. Section 2 discusses the empirical methodology, Section 3 first presents a small-scale Monte Carlo simulations to examine the finite sample performance of the proposed semiparametric test for GARCH-M effect, and then reports the empirical findings, and finally, Section 4 concludes the paper.

This study examines the relationship between expected stock returns and volatility in the 12 largest international stock markets. We show that the estimated relationships between return and volatility are sensitive to the way volatilities are estimated. When parametric EGARCH-M models are estimated, we obtain results that are similar to previous findings. Ten out of 12 markets have positive but statistically insignificant relationship (with the only possible exception at the 10% ignificance level). On the other hand, using a flexible semiparametric specification of conditional variance, we show that negative relationships between returns and volatility prevail in most of these markets. Moreover, the negative relationships are significant in six markets based on the whole sample period and seven markets after the 1987 international stock market crash. Given the fact that the emiparametric specification is more robust than a parametric conditional variance specification, the result of this study lends some support to the claim that stock return volatility is negatively correlated with stock returns (Black, 1976; Cox and Ross, 1976; Bekaert and Wu, 2000). One explanation of such a negative relationship is based on leverage (Black, 1976). A drop in the value of the firm’s stock (negative return) increases financial leverage used by the firm and its debt-to-equity ratio, which makes the stock riskier and increases its volatility. Another explanation based on volatility feedback (Pindyck, 1984; French et al., 1987) suggests that if volatility is priced, an anticipated increase in volatility raises the required return on equity, leading to an immediate stock price decline (negative return). More formally, Whitelaw (2000) theoretically shows that a general equilibrium exchange economy characterized by a regime-switching consumption process generates a negative unconditional relationship between expected returns and volatility at the market level. Our results are also consistent with the empirical findings of Glosten et al. (1993) and Whitelaw (2000). However, it contradicts the prediction of a positive relation made by many asset pricing models (e.g., Sharpe, 1964; Linter, 1965; Mossin, 1966; erton, 1973) and the empirical finding of an insignificant relationship consistently reported in the previous literature (Baillie and DeGennarro, 1990; Nelson, 1991; Theodossiou and Lee, 1995; Choudhry, 1996; Lee et al., 2001). The findings of this study have some important implications. For example, as pointed out in Bekaert and Wu (2000, p. 2), the negative relationship between market volatility and expected market return immediately implies that the time-varying risk premium theory cannot be valid to explain the stock market behavior. Further investigation may be conducted on whether such a negative relationship is time-varying, as suggested in the model of Whitelaw (2000), and also prevails in emerging stock markets. It is also of interest to examine whether different explanations exist for such a negative relationship in international stock markets following the work of Bekaert and Wu (2000). For example,although both explanations based on leverage effects and volatility feedback may explain the negative (contemporaneous) relationship between stock returns and volatility, they carry different implications for causality between the returns and volatility (Bekaert and Wu, 2000). Future research may also employ the semiparametric specification of conditional variance used in this study to explore other topics concerning the relationship between mean and conditional variance, such as that between inflation rate and inflation volatility.