Ebook Equity Market Volatility and Expected Risk Premium
Standard asset pricing theory, e.g., the capital asset pricing model (CAPM), predicts that investors demand an ex ante risk premium for bearing the systematic risk that they cannot diversify away. The market portfolio in the equity market is the most diversified portfolio; as such, its conditional variance represents one of the most commonly used measures of market systematic risk. A positive relation between the expected return and variance of the market portfolio is intuitively appealing and Ghysels, Santa-Clara, and Valkanov (2005) argue that it is the “first fundamental law of finance.”
The empirical evidence on this relation, however, has been mixed. Some authors, including Pindyck (1984), French, Schwert, and Stambaugh (1987), and Ghysels, Santa-Clara, and Valkanov (2005), find that, consistent with CAPM, the conditional excess stock market return is positively related to the conditional stock market variance. Many others, including Campbell (1987), Glosten, Jagannathan, and Runkle (1993), Whitelaw (1994), Lettau and Ludvigson (2003), and Brandt and Kang (2004), document a significantly negative risk-return tradeoff in the data.
One important reason for the conflicting results could be that the expected return is unobservable. The early studies had to use either realized stock returns or instrumental variables as proxies for it. Such practice, albeit usually out of necessity, has its limitations. For example, as pointed out by Elton (1999), realized returns are a poor measure of expected returns. Similarly, Campbell (1987), among others, finds that the results are sensitive to the choice of instrumental variables.
In this paper we reexamine the intertemporal risk-return tradeoff by using a direct measure of the expected return, as developed by Campello, Chen, and Zhang (2005, CCZ hereafter). Such a measure makes use of the intuition that, because debt and equity are financial claims written on the same corporation productions, they must share the same systematic risk that affects firm fundamentals. The yield spread—the difference between the corporate bond yield and the Treasury bond yield—incorporates both the fair compensation for default risk and the ex ante risk premium. It is well known in the default risk literature that the fair compensation for default risk is only a relatively small portion of the yield spread (e.g., Jones, Mason, and Rosenfeld (1984) and Huang and Huang (2003)). Therefore, even though the fair default risk compensation needs to be estimated using past information, the yield spread adjusted by this estimate retains largely the forward-looking property of the ex ante risk premium. CCZ provide an analytical formula that links the ex ante equity risk premium to the yield spread after adjusting for the estimated fair compensation for default risk and for the tax effects. We follow CCZ to construct the ex ante equity risk premium. This risk premium not only is forward looking, but also does not rely critically on the choice of instrumental variables.
We then turn to estimate the conditional volatility of the market portfolio. Following Campbell (1987), French, Schwert, and Stambaugh (1987), and Whitelaw (1994), we estimate conditional variance using the instrumental variables approach. In particular, as in Merton (1980) and Andersen, Bollerslev, Diebold, and Labys (2003), we construct monthly realized stock market variance (RV) using daily data and use lagged RV as a proxy for the conditional variance. To be robust, we also use more elaborate measures by projecting RV on its own lags and some financial variables, including the options-implied S&P100 volatility; however, our main results are not sensitive to these alternative measures of the conditional stock market variance.
We find strong support for a positive risk-return relation in the stock market using the ex ante aggregate equity premium (EP). For example, the lagged realized stock market variance is found to be positively and significantly related to EP. This relation remains significantly positive even after we include the lagged EP in the regression to correct for the autocorrelation in the dependent variable. Moreover, the realized stock variance exhibits significant influence on EP in the formal Granger causality test.
EP is also significantly correlated with commonly used predictors of stock market returns, including the dividend yield, the default premium, and the term premium (e.g., Fama and French (1989)), the stochastically detrended risk-free rate (e.g., Campbell, Lo, and MacKinlay (1997)), and idiosyncratic stock volatility (e.g., Goyal and Santa-Clara (2003)). However, realized stock market variance remains significantly positive after we control for these variables. Importantly, except for idiosyncratic volatility, these variables become insignificant after controlling for the lagged EP. These results suggest that the stock market volatility is a significant determinant of the ex ante equity premium.
The result of a positive relation between the conditional stock market return and variance is not sensitive to a number of additional robustness checks. We reach qualitatively the same conclusions when (1) the conditional stock market variance is estimated using different instrumental variables; (2) the ex ante equity premium is either value- or equal-weighted; (3) the ex ante equity premium is constructed using different datasets; and (4) we use either monthly or quarterly data.
Merton (1973) points out that, in addition to the stock market variance, a hedging demand for time-varying investment opportunities is also an important determinant of the expected stock market risk premium. Scruggs (1998) and Guo and Whitelaw (2005) show the importance of controlling for the hedging demand in the investigation of the risk-return tradeoff. Given that both studies find that the omission of the hedging demand generates a downward bias in the estimate of the risk-return relation, controlling for it is unlikely to affect our results in any qualitative manner. More important, as mentioned above, the positive relation between the conditional stock market variance and the ex ante equity premium remains significant after we control for commonly used predictors of stock returns, which are potential proxies for investment opportunities.
Our approach is closely related to that of a concurrent paper by Pastor, Sinha, and Swaminathan (2005), who use analyst forecast data to construct the ex ante equity premium and uncover a positive risk-return relation in stock markets of G7 countries. These two papers are in general complementary to each other. Our risk premium measures have the unique characteristic that they are backed out from market-traded financial securities. This difference might help explain why, unlike Pastor, Sinha, and Swaminathan, our results are robust to the weighting schemes used in the construction of the ex ante equity premium. Graham and Harvey (2005) also obtain direct measures of the equity risk premium from surveying chief financial officers of U.S. corporations for a relatively short sample period.
The remainder of the paper is organized as follows. Section I describes the construction of the ex ante risk premium. Section II provides data summary. Section III explores whether the ex ante risk premium predicts (realized) stock market returns. Section IV constructs the conditional variance. Section V studies the relation between the ex ante risk premium and the conditional variance and provides robustness checks. Section VI concludes.
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