Risk-free Yields, Risk Aversion, and Volatility

Abstract

The classic approach to risk analysis is rooted in the belief that risk aversion is constant, determined by constant preferences. It is becoming clear that this proposition is no longer acceptable. Risk aversion can change over short time, between sovereign countries, and on different financial and capital assets. Secondly volatility of asset prices is itself variable, and can be apprehended like the VIX volatility index which is so popular. Risk-free yields are affected by this variability in aversion and volatility, contrary to what is commonly envisioned, and contrary to what intuition suggests. This paper assumes complete markets, and simulates 14 values for the volatility, and 25 values for the coefficient of relative risk aversion (CRRA), and it measures the impact of these changes on the risk-free yield. One conclusion is that the CRRA is indeterminate, and is therefore consistent with the many different estimates in the literature. Another conclusion is that, by setting the volatility to 17.5%, roughly the average stock market volatility over a long period, there is evidence that the range of the implied risk premiums correspond to the range in the empirical literature.

Keywords

• risk aversion
• volatility
• risk-free yields
• consumption strata
• simulation