On The Relationship Between Expected Returns and Implied Volatility of Interest Rate-Dependent Securities

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 lto 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.