ON THE RELATIONSHIP BETWEEN EXPECTED RETURNS AND IMPLIED VOLATILITY OF INTEREST RATE-DEPENDENT SECURITIES

In this article, the authors examine the relationship between expected excess returns and volatilities implied by options on interest rate-d ependent securities, and estimate the market price of interest rate ri sk. If the short-term riskless rate of interest follows a one-factor I to process, then the instantaneous expected excess return on any deriv ative security, whose payoff is a function only of the riskless rate a nd time, is proportional to the instantaneous standard deviation of re turns on that security. Therefore, interest rate-dependent securities with higher volatility should, on average, earn proportionally higher excess returns. The authors test this hypothesis, and also estimate th e ratio of the expected excess returns to the volatility of returns. T hey find that there is indeed a positive relationship between expected excess returns and volatility, and that interest rate risk is rewarde d in the marketplace. Implied volatility may therefore be used as a we ak market-timing signal. Additionally, the authors find that implied v olatility is approximately a linear function of duration; hence durati on is an acceptable proxy for the price volatility risk inherent in an asset.