Estimation of Term Premiums from Average Yield Differentials in the Term Structure of Interest Rates

Abstract

The fact that long term interest rates have been higher on average than short rates in the twentieth century has often been interpreted in the term structure literature as evidence of the existence of positive or term premiums. The purpose of this paper is to point out that an average differential between long and short rates does not necessarily represent a differential between returns realized by holders of long versus short term bonds. In particular, it is shown that if short term rates are positively autocorrelated, interest rate differentials overstate differentials in realized rates of return. We conclude that liquidity or term premiums properly estimated from the Durand yield curve data are not consistent with the liquidity preference theory. LONG TERM INTEREST RATES have been higher on average than short term rates during the twentieth century. The average differential over the period 1900-1958 between long term interest rates and spot one year rates in the Durand yield curve data increases monotonically with term to about half a percentage point at forty years. The interpretation given to these differentials in the term structure literature is that they are the additional rate of return earned on average by capital invested in long term bonds. The purpose of this paper is to point out that an average differential between long and short term interest rates does not necessarily represent a differential between realized rates of return. This is because the realized increment to capital invested in a sequence of short term bonds depends on the ex post product of uncertain future spot rates. The expected value of this ex post product will in general differ from the product of expected future spot rates. We show that if short term rates are positively autocorrelated, the interest rate differentials overstate differentials in realized rates of return. We shall refer to differentials in realized rates of return as term premiums. The proper interpretation of interest rate differentials is important to the assessment of the evidence for various theories of the term structure. The liquidity preference theory of J. R. Hicks [4, pp. 144-147] predicts that a term premium will be earned by capital invested in long term bonds because their holders require compensation for risk of capital fluctuation. Forward interest rates will exceed one period spot rates on average by the amount of premium which rises monotonically with horizon. The positive and monotonic average differentials between forward and spot one year rates in the Durand data have been