On the Relationship between Expected Returns and Implied Volatility of Interest Rate-Dependent Securities

Ehud I. Ronn and Pavan Wadha
Department of Finance, University of Texas at Austin
ERonn@utexas.edu

Abstract

In this paper, we examine the relationship between expected excess returns and volatilities implied by options on interest rate-dependent securities, and estimate the market price of interest rate risk. If the short-term riskless rate of interest follows a one-factor Ito process then the instantaneous expected excess return on any derivative security, whose payoff is a function only of the riskless rate and time, is proportional to the instantaneous standard deviation of returns on that security. Therefore, interest rate-dependent securities with higher volatility should, on average, earn proportionally higher excess returns. We test this hypothesis using price data on Coupon-STRIPS and implied volatility data from futures options on various U.S. Treasury securities and Eurodollars. We also estimate the ratio of the expected excess returns to the volatility of returns, denoted the market price of interest rate risk, using several estimation techniques. We find that there is, indeed, a positive relationship between expected excess returns and volatility, and that interest rate risk is rewarded in the marketplace. Implied volatility may therefore be used as a weak market-timing signal. Additionally, we find that implied volatility is approximately a linear function of Macaulay duration; hence duration is an acceptable proxy for the price volatility risk inherent in an asset.