Estimation of Multiperiod Expected Rates of Return When Investment Relatives Are Lognormally Distributed

Abstract

This article extends Blume's (1974) work on the estimation of multiperiod expected rates of return to the interesting case in which investment relatives are lognormally distributed. We derive the minimum variance unbiased estimator for the expected multiperiod investment relative and its variance. We also develop five other estimators, including an approximate minimum mean squared error estimator. Two empirical studies are made, one based on portfolios of New York Stock Exchange stocks and the other on an index mutual fund.

KEY WORDS:

• Minimum variance unbiased estimator
• Lognormally distributed returns
• Mean squared error