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

This paper considers the asset allocation strategies for members of defined-contribution pension plans with exponential utility when there are three types of asset, cash, bonds and stocks. The portfolio problem is to maximize the expected utility of terminal wealth that uses the plan member’s final wage as a numeraire, in the presence of three risk sources, interest risk, asset risk and wage risk. The use of a stochastic numeraire makes usual riskless cash assets risky. A closed form solution is found for the asset allocation problem when a portfolio replicates exactly the wage process exists, which is the true riskless asset. The optimal portfolio composition is horizon dependent, while the investments in the three asset classes have constant wealth-to-wage ratios. The paper discusses the implication of using wage as numeraire and assuming exponential utility function in portfolio and pension investment strategy studies.