Optimal Asset Allocation Strategy for Defined-Contribution Pension Plans with Different Power Utility Functions

The relationship between the optimal asset allocation and the functional form of power utility is investigated for defined-contribution (DC) pension plans. The horizon dependence of optimal pension portfolios is determined by the argument of the power utility function. The optimal composition of pension portfolios is horizon independent when terminal utility is a power function of wealth-to-wage ratio, and deterministically horizon dependent when terminal utility is a function of terminal wealth or replacement ratio (the pension-to-final wage ratio). The optimal portfolios all contain a speculative component to satisfy the risk appetite of DC plan members, which is dominated by bonds under usual market assumptions. The optimal compositions of financial wealth on hand (the sum of pension portfolio and the short-sold wage replicating portfolio) are stochas- tically horizon dependent when wages are fully hedgeable and stochastic. The optimal pension portfolios also have a preference free component to hedge wage risk, when terminal utility is a function of wealth-to-wage ratio or replacement ratio. A state variable dependent component in optimal pension portfolios exists when terminal utility is a function of terminal wealth or replacement ratio, but it disappears when terminal utility is a function of terminal wealth-to-wage ratio and the risk premium is constant.