تعامل پویا میان نوسانات و بازده در بازار سهام ایالات متحده با استفاده از شبیه ساز های خود راه انداز قوی

One of the most important stylized facts in finance is that stock index returns are inversely related to volatility. The theoretical rationale behind the proposition is still controversial. The causal relationship between returns and volatility is investigated in the US stock market over the period 2004–2009 using daily data. We apply a bootstrap test with leveraged adjustments that is robust to non-normality and ARCH. We find that the volatility causes returns negatively and returns cause volatility positively. The policy implications of our findings are discussed in the main text.

The underlying link between the return on a financial asset and its variance or volatility as a proxy for risk is of fundamental importance for valuing financial assets, for identifying optimal hedging strategies and for evaluating regulatory proposals on monitoring the impact of international capital flows. Therefore, the theoretical asset pricing models (e.g., Sharpe, 1964 and Merton, 1973) are based on the interaction between returns and risk. However, it is still controversial whether such a relationship is positive or negative, i.e., a fully acceptable economic clarification for the effect has not yet been offered (Bouchaud et al., 2001 and Bollerslev and Zhou, 2006). Although most asset pricing models highlight a positive link between stock portfolio's expected returns and volatility (Baillie and DeGennarro, 1990) under the assumption of investor risk aversion, it is a long tradition in empirical finance to model stock return volatility as negatively correlated with stock returns (Cox and Ross, 1976 and Whitelaw, 2000). The first effort to provide an economic justification for the negative return correlation relies on a corporate finance argument. Black (1976) and Christie (1982) argue that a positive stock return enhances the market value of the firm's equity, which in turn reduces its financial leverage ratio.1 The diminished leverage gear will result in a lower volatility of stock returns. The empirical observations do not support this leverage hypothesis, however, for the two reasons that follow: (i) it is inconsistent with the observed asymmetry of the effects of volatility on stock returns in bull and bear markets (Figlewski and Wang, 2000) and (ii) it predicts a significant relationship of the volatility-return nexus on individual stock rather than on stock market indices, although Bouchaud et al. (2001) do not provide empirical evidence to support this prediction. However, the leverage effect implies that the causality runs from stock return to volatility. That is, the leverage effect is only one possibility to explain a return-driven negative correlation. Another potential explanation for a negative correlation between returns and volatility is that bad news might have different consequences for future uncertainty than good news (Glosten et al., 1993 and Chen and Ghysels, 2007). For example, a decrease in price could result in more extensive portfolio adjustment of risk-averse agents than price increases. Bouchaud et al. (2001) claim that the return-driven relationship originates from a retarded effect, i.e., the scale for price updates is not a function of the current price level but of a moving average of previous prices which implies that present returns lead subsequent volatility returns. On the other hand, the hypothesis of a volatility-driven negative correlation (known as feedback effect in the literature) relies on the assumption that volatility is related to systematic risk and is therefore relevant for pricing (French et al., 1987 and Campbell and Hentschel, 1992). If new information causes an unanticipated increase in volatility, this will also lead to an increase in risk-adjusted discount rates and stock prices will decrease under the condition that cash flow expectations are not affected. The return-driven and volatility-driven effects might have interactions. That is, an initial price change could create a volatility movement which in turn amplifies the price change with yet another impulse on volatility (Bekaert and Wu, 2000). In efficient financial markets, the actors will anticipate these reactions, therefore, the steps will occur almost simultaneously and this makes it difficult to identify the different stages of the process. Generally speaking, most empirical finance literature found an insignificant and unstable relationship between returns and conditional variance in international stock markets (Turner et al., 1989 and Glosten et al., 1993). Some studies report a positive relationship between stock market returns and conditional variance of these returns (French et al., 1987, Campbell and Hentschel, 1992, Scruggs, 1998, Ghysels et al., 2005 and Brailsford et al., 2006), others a negative relationship (Campbell, 1987 and Nelson, 1991). In the case of return-driven as well as volatility-driven effects, the results of most empirical studies also are mixed. Bollerslev et al. (1988), Giot (2005), Dufour et al. (2006), and Masset and Wallmeier (2008) support a return-driven relationship while Bekaert and Wu (2000) and Dennis et al. (2006) reveal evidence of volatility-driven effect. Our main contribution is to go beyond a correlation analysis by studying causality directions. To the best of our knowledge, this is the first study which applies bootstrap causality tests to the interaction of index returns and volatility. The method we apply is robust to non-normality and ARCH effects. These properties are frequently common elements of financial data in which standard methods perform poorly. The rest of the paper is organized as follows. Section 2 presents data and the underlying model. Section 3 presents the estimated empirical results. The last section provides conclusions and policy implications.

The main objective of the current paper is to identify causality between returns and volatility for the US stock market using a bootstrap test that is robust to non-normality and ARCH. Based on the causality test results, we conclude that there is bi-directional causality between the variables. Volatility causes returns negatively and returns cause volatility positively. The bidirectional causality implies that the return-driven and volatility-driven effects might well coexist. That is, an initial price change could induce a volatility movement which in turn amplifies the price change with yet another impulse on volatility. In efficient financial markets, the actors will anticipate these reactions. Therefore, the steps will evolve almost simultaneously and this makes it difficult to identify the different stages of the process. The results of this study may have interesting value for policymakers, financial institutions and investors whose investment achievement depends on the ability to forecast volatility movements and the related expected returns and accordingly construct their equity portfolios based on these predictions. Under the proposition of investor risk aversion, our end results confirm that stock return volatility is negatively correlated with stock returns. This provides some support for the hypothesis of a volatility-driven negative relationship in the literature, and it is in line with the findings of other authors. The relationship between the return of financial assets and its volatility plays a vital role in portfolio selection, asset pricing, value at risk (VaR) calculation, Black–Scholes option pricing, and dynamic hedging strategies. Indeed, in all of these financial techniques and strategies, time-varying volatility should play a vital role. In particular, our results should be useful to both institutional and retail investors, whose investment achievement depends on the ability to forecast volatility movements and the related expected returns in these markets and, accordingly, to construct their equity portfolios based on these predictions. Regarding return-volatility driven hypothesis, a number of researchers have suggested that the positive relation between returns and volatility can be explained by viewing a firm's stock as an option on the assets of the firm. Since an option's price rises when the underlying asset volatility rises, one might think that a stock price should rise when the volatility of the value of the firm (and therefore the volatility of the value of the stock) rises. This finding is in line with the results in Duffee (1995) who shows that stock returns are positively related to contemporaneous levels of return volatility. The second potential alternative explanation for our results is Pástor and Veronesi (2003) effect of uncertainty about the growth rate of future profits on firm values. According to Pástor and Veronesi, the positive relation between returns and changes in uncertainty, can be due to the convex relation between future firm values and future growth rates.