Mean-downside risk versus mean-variance efficient asset class allocations in relation to the investment horizon

In this paper we examine the difference between a Mean-Downside Risk (MDR) based asset allocation decision and a Mean-Variance (MV) based decision. Using a vector autoregressive specification, future return series, trom 1 month up to 10 years, of several US stock and bond asset classes have been generated. A comparison of MDR-efficient frontiers to MV-frontiers shows the following. First, for investment horizons less than 1 year and allocations above the minimum downside risk point, MV-allocations do not have a significant different downside risk compared to the MDR-efficient allocation having the same mean. For longer horizons however there is a significant difference. By allocating more to bonds (instead to stocks) an investor can lower his downside risk while keeping the same mean return. The difference in downside risk is more pronounced for longer horizon. Second, for all horizons (trom 1 month up to 10 years) the minimum variance allocation is located significantly below the minimum downside risk allocation. However only for long-term horizons (more than 1 year) the difference in the mean and downside risk is significant trom a practical point of view. This implies that highly risk (variance) averse long-term investors can be much better off by investing in the minimum downside risk allocation. This can be done by shifting the allocation more to stocks. The conclusions are based on various assumptions. In order to get insight in the robustness of the aforementioned results we carried out an extensive sensitivity analysis. For short-term horizons the conclusions remained unchanged. For long-term horizons the simulations show that the availability of small stocks is crucial only for the results regarding allocations above the minimum downside risk point (the minimum variance allocation is still located below the minimum downside risk point). When leaving out small stocks trom the analysis, we find for all horizons no significant difference anymore. In the literature there is evidence of long-term mean-reverting behavior of stocks. Since our simulated