Analysis of Simple Investment Strategies Assuming Lognormal Returns

Abstract

This paper analyses the properties of two popular portfolio strategies. They are the Buy and Hold strategy and the Discretely Rebalanced strategy. It is assumed that the underlying stocks have a multivariate lognormal distribution. The distribution of the sum of correlated lognormals plays a central role in our analysis. We derive expressions for the moments of the terminal portfolio distribution under both strategies. In the case of a Discretely Rebalanced portfolio, we analyze how the risk profile of the strategy depends on the number of assets and the rebalancing frequency. We derive the limiting distribution of the strategy as the number of assets increases and also when the frequency of rebalancing increases.

Keywords: Buy and Hold portfolios, Rebalanced portfolios, Lognormal distribution, Sums of lognormals, Moments of lognormals

JEL Classification: C10, G10