Mean–Variance, Stochastic Dominance and the Investment Horizon

Abstract

As some investors plan to invest for a relatively short investment horizon and others for a relatively long horizon, it is interesting to analyze whether the assumed length of the investment horizon affects the optimal diversification. Numerous studies are devoted to this topic. Indeed, the importance of the investment horizon and its effect on the investment strategy is well documented in the financial and economic literature. Regarding the optimal stock-bond optimal mix, it is commonly recommended that the longer the horizon the larger should be the weight of stocks in the portfolio, see for example Malkiel. Not all agree with this approach (see for example Merton and Samuelson who employ myopic CRRA preferences). Obviously, transaction costs affect the trading strategy for a given finite horizon. Jagannathan and Kocherlakota show that even with CRRA preferences if investors, due to transaction costs, are restricted to buy and hold policy, the obtained optimal portfolio is horizon dependent. Liu and Loewenstein show that with transaction costs and with CRRA preference, investors with a relatively short horizon will buy less of the risky asset and basically adhere to the buy and hold policy. Thus, it is important to analyze the effect of the assumed investment horizon on the portfolio selection under i.i.d. assumption with no transaction costs. We show that even in this framework the portfolio optimal diversification and the performance measure are affected by the assumed horizon, with the exception of portfolios constructed with the CRRA preference. Specifically, we find that the MV and SSD efficient sets and the Sharpe index are horizon dependent.