The Impact of Time Horizon on the Effect of Diversification

Although investors are often advised to diversify their investment portfolios as well as to consider rebalancing them periodically, research has shown that they often ignore this advice. We try to determine if this behavior is rational by analyzing a risk-averse investor who chooses between buy-and-hold portfolios comprised of assets with dynamic uncertain returns. The assets in the portfolio evolve according to multiplicative random walks, distinguishing them from the traditional one-shot or additive models.Solving for the optimal choice, we find an interaction between diversification and the time horizon an investor is facing. This interaction results in conditions for which an optimal portfolio in one time horizon becomes suboptimal in a longer (or shorter) horizon. Moreover, we find that rebalancing may be suboptimal if the portfolio is diversified enough. Such effects are a consequence of the non-ergodicity of the value of assets that follow multiplicative dynamics.Thus we are able to provide a rational explanation for observed behavior of investors and subjects in lab experiments who choose to not diversify their portfolios or do not rebalance as often as the standard theory would prescribe