When returns are dependent or nonstationary over time, it is obvious that the assumed investment horizon affects portfolio composition. Even if returns are independent and stationary, however, the composition of the investor's portfolio will change in some systematic manner with the assumed holding period. An analysis of the effect changes in investment horizon have on optimal portfolio composition finds that composition changes drastically and systematically with changes in holding period. Surprisingly, the longer the horizon, the larger the proportion of "safe" assets that should be included in the portfolio.