This paper provides some evidence for the volatile, persistent and countercyclical Sharpe ratio. In the data, conditional Sharpe ratio volatility is almost 72 percent annualized with a first order autocorrelation of 0.85. The difference between trough and peak of the conditional Sharpe ratio is more than 1 annualized. I show that a model with time-varying productivity risk is more promising in matching the conditional moments of asset returns compared to a standard real business cycle model. A model with time-invariant productivity risk generates Sharpe ratio volatility that is one order of magnitude smaller than the model with time-varying productivity volatility. The time varying model also produces a positive and relatively high first order autocorrelation of the same time series, whereas the former can only generates a small and negative autocorrelation, and hence at odd with the data.
The risk-return trade-off in the market is volatile and countercyclical. Leading asset pricing models can account for the level of the unconditional Sharpe ratio, but as documented in Lettau and Ludvigson (2010) have difficulty in accounting for this feature of the data. Understanding the dynamics of the Sharpe ratio over the business cycle has potential important policy implication as pointed out by Lustig and Verdelhan (2010). Because return required for a unit of risk is higher in recession, a project must be very promising for firm to invest, and thus any stimulative policy must take into account this risk-return trade-off.
In this paper, I explore the ability of a production economy in rationalizing this risk-return trade-off relation. The model is a standard real business cycle model extended in two dimensions. First, agents have Epstein-Zin-Weil preferences, which nests the usual expected utility. The advantage of this preferences is that it allows for a separation of the intertemporal elasticity of substitution and attitude toward risk. Agents with this utility function have a preference for the timing of revelation of uncertainty, and depending on the parameters she may prefer early resolution of uncertainty or late or be indifferent. Second, productivity growth is assumed to have time-varying risk. I will show that this is important in capturing volatile conditional Sharpe ratio.
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A Model of the Volatility of the Market Price of Risk
