Optimal asset allocation strategy for defined-contribution pension plans with different exponential utility functions

This study considers the asset allocation strategies for members of definedcontribution pension plans with exponential utility when there are three types of assets, cash, bonds and stocks. The portfolio problem is to maximize the expected utility which is a function of the terminal wealth-to-riskless asset ratio, the terminal wealth-to-wage ratio or the pension-to-wage ratio (replacement ratio) in the presence of three risk sources, interest risk, asset risk and non-hedgeable wage risk. Closed form solutions are found for the asset allocation problem, and the optimal portfolio compositions are horizon dependent. When the terminal utility is a function of the terminal wealth-to-riskless asset ratio, the investment in the two risky asset classes has two components; one with horizon- and wealth-dependent asset proportions for a speculative role, and another a wealth- and horizon-dependent component which hedges financial market risks. When the terminal utility is a function of the wealth-to-wage ratio, the investment in the two risky asset classes has two components: one with constant asset proportions to minimize the variance of wealth differential and the other with horizon- and wealth-dependent asset proportions for a speculative role. When the terminal utility is a function of the replacement ratio, there is also a third, wealth- and horizon-dependent component, which hedges financial market risks. The plan members will short-sell the riskless asset to have the optimal proportions of the two risky assets in most scenarios.