An Unbiased Estimator of the N-Period Relative

Abstract

Define Rt as the ratio of the value of an asset at the end of the tthperiod to its value at the end of the previous period. Rt is then a one-period relative equal to unity plus the interest rate. Assume that Rt is an independent, normally distributed random variable with mean μ and nonzero variance σ2. Rt is then observed aswhere the disturbance term ∈t t is independently and normally distributed with mean zero and variance σ2. To assess the long-term expected rate of return of the asset, it is desirable to estimate its expected increment in value of the one-period relative raised to the Nth power, i.e., μN.