Asset Return Distributions and the Investment Horizon

Abstract

The optimal investment decision rule and asset equilibrium prices depend on the assumed distribution of rates of return. And empirical distributions vary with the assumed time interval (investment horizon). The authors test the goodness of fit of 11 theoretical distributions including the normal distribution, fat-tailed distributions, and skewed distributions for investment horizons ranging from one day to four years. The normal distribution performs poorly, and never provides the best fit for any time interval. In the 330 goodness of fit tests reported, at least one distribution of the 11 always fits the data better than the normal distribution. As the logistic distribution fits the data best for investment horizons of up to one year, analysis focuses on this distribution and its implications for equilibrium asset prices.