Ebook Asymmetric Stock Market Volatility and the Cyclical Behavior of Expected Returns
Why does stock market volatility vary over time? Economists have been intrigued by this issue for decades. For example, Schwert (1989a) finds that the volatility of no single macroeconomic variable could help explain low frequency movements of aggregate stock market volatility. Yet stock market volatility is related to the business cycle. Indeed, a number of empirical studies confirm Schwert’s (1989a and 1989b) further findings that the volatility of stock returns is higher in bad times than in good times (see, e.g., Brandt and Kang, 2004, and the additional evidence provided here). This paper addresses an important but still unanswered question: Why is stock market volatility asymmetric over the business cycle?
My central result is that in economies with rational expectations, return volatility is countercyclical because risk premia (i.e. the compensation investors require to invest in the stock market) change asymmetrically in response to variations in economic conditions. That risk premia are countercyclical has been a widely known empirical fact since the seminal contributions of Fama and French (1989) and Ferson and Harvey (1991). However, the main message of this paper is not a simple statement that risk premia must be countercyclical to generate countercyclical return volatility. Rather, the crucial point is that to induce countercyclical return volatility, risk premia must increase more in bad times than they decrease in good times, a new hypothesis which I support with substantial empirical evidence.
So why do asymmetric risk premia fluctuations translate into countercyclical return volatility? Consider Figure 1, in which I assume that the investors’ risk-adjusted discount rates are inversely and asymmetrically related to some variable y that tracks the state of the economy. This asymmetry implies that in good times investors do not significantly alter the discount rates used to evaluate future dividends. Consequently, price-dividend ratios do not fluctuate widely in good times. In bad times, however, the investors’ discount rates are extremely sensitive to changes in economic conditions. Therefore, variations in the price-dividend ratios become increasingly volatile as economic conditions deteriorate.
The main result of this paper is that these asymmetric movements of the price-dividend ratios occur when the asymmetry in discounting is sufficiently pronounced. Precisely, I calculate a theoretical lower bound for the asymmetric movements of the risk premia that triggers the previous asymmetric variations in the price-dividend ratios. This bound can be tight: for example, economies exist in which risk premia are countercyclical but do not satisfy this bound, and consequently induce price-dividend ratios to fluctuate more in good times than in bad.
Naturally, countercyclical return volatility may also emerge because the volatility of the state variables in the economy is inherently countercyclical. Alternatively, the conditions developed here highlight the mechanism through which countercyclical return volatility is endogenously induced by rational fluctuations of the price-dividend ratio. Moreover, empirical evidence suggests that price dividend ratios exhibit the pattern predicted in this paper. I find that over the last fifty years, price-dividend ratios movements in the US have been asymmetric over the business cycle: downward changes occurring in recessions have been far more severe than upward changes during expansions.
In the economy I study, dividend growth is independent and identically distributed, while interest rates and risk premia are driven by a state variable that is interpreted as an index of the state of the economy. This economy is rich enough to include many model examples in the literature. The distinctive feature of this article is the way I deal with interest rates and risk premia. The standard approach is to link interest rates and risk premia to markets, preferences and technology (e.g., Basak and Cuoco, 1998; Campbell and Cochrane, 1999; Jermann, 2005), or in general to make use of higher level assumptions about the exact relations among interest rates, risk premia and the primitives of the economy (e.g., Brennan, Wang, and Xia, 2004; Lettau and Wachter, 2005).
In this paper, I take an opposite approach. Rather than making assumptions on interest rates and risk premia, I look for pricing kernels that make return volatility countercyclical. It is this search process that leads to the predictions summarized in Figure 1. One additional contribution of the paper is to use these new predictions to understand when, why and how models with time-varying discount rates may predict countercyclical volatility. For example, in a seminal contribution Campbell and Cochrane (1999) find that models with external habit formation might lead to countercyclical volatility. This paper explains the rationale behind this important result. At the same time, the predictions developed here go well beyond the case of habit formation.
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