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Distribution of multi-period returns and criteria for multi-period portfolio selection

Adcock C. J.

Management

2002

Vol. 6, no 1

127-142

This paper is concerned with the probability distribution of the geometric mean return of an individual asset or a portfolio that is held for multiple periods. An improvement to the conventional approximation to the geometric mean is presented. The implications for portfolio selection based on expected utility maximisation are considered. Criteria for portfolio selection based on quadratic and negative exponential utility functions are developed and their properties described. The paper concludes by showing that, when returns have a multivariate normal distribution, multi-period expected utility maximisers will select a portfolio that lies on the efficient frontier.