ABSTRACTApplication of the geometric mean to holding‐period returns is discussed from a statistical theory standpoint. The population geometric mean is considered a parameter of the probability distribution of returns its relationship to moments of the distribution is discussed. The sample geometric mean and its relation to sample moments is assessed through its sampling distribution it is viewed as an estimator of the population geometric mean. For application to long‐term investment where a geometric mean is maximized, the distributional properties of the geometric mean should be used. The terms statistic, approximation, and parameter are differentia