Optimal Asset Allocation Strategy for Defined-contribution Pension Plans with Power Utility

Optimal asset allocation strategies of defined-contribution pension plans for members whose terminal utility is a power function of wealth-to-wage ratio is investigated in this paper. The portfolio problem is to maximize the expected terminal utility in the presence of three risk sources, interest risk, asset risk and wage risk. A closed form solution is found for the asset allocation problem and the optimal portfolio composition is horizon independent when there is no non-hedgeable wage risk or there is no further contribution from wage incomes. When future contributions from wage income are hedged by short-selling a wage replicating portfolio, the optimal composition of financial wealth on hand (i.e. pension portfolio wealth + short-sold wage replicating portfolio) is horizon-dependent. The optimal asset allocation strategy is equivalent to invest in two mutual funds, one of which is to hedge wage risk and the other a speculative fund to satisfy the risk appetite of the plan member.