The Effect of Investment Horizon on Equity Allocation: An Optimal Portfolio Approach

Abstract

This paper examines the effect of investment horizon on the optimal allocation to equities in order to find evidence of time diversification. By using genetic optimization, we create optimal portfolios for different time horizons. Each portfolio has an ideal equity allocation based on a value at risk (VaR) or an expected utility framework. The optimization is based on a dataset covering U.S. real return data for a number of asset classes for the years 1802–2016.
In 1969, Paul Samuelson provided mathematical proof against time diversification that was reliant on three assumptions; that investors exhibit constant relative risk aversion (CRRA), that asset returns are independently and identically distributed (IID) and that wealth is only a function of returns from financial assets. The subsequent time diversification debate has centred on these three assumptions. This paper provides input to the debate by discussing the validity of, as well as relaxing, the three assumptions. The first assumption is relaxed by introducing a VaR framework and other risk preferences than CRRA. The second and third assumption are relaxed when we find evidence of mean reversion in the equity return data and when we introduce a fixed non-financial asset, respectively.
We find solid historical evidence to support the notion that a higher allocation to equities is optimal for agents with longer investment horizons, and that the time diversification effect is present over time. The mean reversion characteristic in our dataset is sufficiently strong to show equity allocation increasing with time horizon irrespective of VaR or utility framework. The introduction of a fixed non-financial asset leads to more aggressive optimal equity allocations, with time diversification still being present.