Optimal Pension Asset Allocation Strategy when Terminal Utility is a Function of Replacement Ratio

This paper considers the optimal asset allocation problem for defined-contribution pension plan members whose terminal utility is a function of replacement ratio, i.e. the pension-to-final wage ratio. When three asset types are available for investment, the optimal portfolio composition, which is horizon dependent, includes investment in both riskless and risky assets. The investment in risky assets has three components to hedge wage risk, to speculate on risk premiums and to hedge for financial market risk respectively. When the terminal utility is a power function, closed form solution is derived for the cases where there is no further contribution from wage incomes or there is no nonhedgeable wage risk. The horizon dependence of optimal pension portfolio is deterministic under assumptions of constant equity risk premium, constant interest rate volatility and constant stock return volatility. The short-sale of wage replicating portfolio also contributes to the horizon dependence of pension plan financial wealth (the sum of pension portfolio and the short-sold wage replicating portfolio), and the effect is stochastic due to the stochastic interest rate and stock return. Therefore, the optimal asset allocation strategy in terms of financial wealth is “stochastic lifestyling”. For the cases where wage incomes cannot be hedged due to non-hedgeable wage risk, optimal asset proportions can be solved numerically by Monte Carlo simulation. The proportions invested in stocks and especially bonds are higher in early stages than those when wage replicating portfolio is used, hence more short-sale of cash assets. The optimal asset allocation derived by numerical simulation is also horizon dependent.