An Unbiased Estimator of the N-Period Relative

Cliff J. Huang

Journal of Financial and Quantitative Analysis, 1977, vol. 12, issue 3, 505-507

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.

Date: 1977
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