DISCUSSION PAPER PI-0818 Inter-temporal Optimization and Deterministic Lifestyle Strategy in Managing Defined- Contribution Pension Plans

Inter-temporal optimization and deterministic lifestyle asset allocation strategies for defined-contribution pension plans are investigated and compared both analytically and numerically. The pension plan is assumed to invest in two types of asset, risk free assets and equities, or bonds and equities, and the plan members‟ terminal utility a power function of pension wealth at retirement with their final wages as numeraire. The optimal asset allocation strategy using two assets is derived analytically for fully hedgeable wage incomes and compared numerically with that for non-hedgeable wage income and deterministic lifestyle strategy. The deterministic lifestyle strategy is shown to be replicable by a static allocation strategy with same expected returns and lower variances. The inter-temporal optimization strategy outperforms the lifestyle strategy in numerical simulations both when there is no further pension contribution or non-hedgeable wage risk and when the wage income is not fully hedgeable. When there are further pension contributions, the optimal proportion invested in the more risky asset is higher than that when future pension contributions are transformed into augmented wealth by short-selling a replicating portfolio to be paid by future pension contributions. With usual assumptions on market parameters, the optimal pension portfolio composition is independent of the value of non-hedgeble wage risk and the value of pension contribution rate.