Stocks Versus Bonds: A Stochastic Dominance Approach

Abstract

We have seen in the previous chapters that even if the rates of return on uncertain assets are independent over time, the various parameters characterizing the distribution of returns are not invariant to the assumed length of the investment horizon. Moreover, these parameters do not change randomly, but rather change in some systematic way with the increase in the assumed investment horizon. Of course, these systematic changes in the various parameters have a direct effect on the optimal diversification which is appropriate for various planned investment horizons. We also have seen that the SD rules may change the prospects’ ordering even in the independent case over time, let alone in the dependent case. As generally we have in the market people investing for various investment horizons it is interesting from a theoretical as well as a practical perspective to analyze how the weights of the risky assets, which for simplicity of the discussion will be called in the rest of the chapter “stocks,” and the weights of the less risky assets which will be called “bonds,” change in the optimal portfolio as the investment horizon changes. These issues are important particularly for investments for pension which at the beginning of the saving process are generally for a relatively large number of years, and the number of saving years left decreases gradually as the saver for pension grows older, and particularly when she approaches the retirement age. Thus, the investment horizon becomes gradually shorter which may require an adjustment in the optimal portfolio, so long the optimal diversification indeed changes with the change in the investment horizon.