Optimal Life-Cycle Strategies in the Presence of Interest Rate and Inflation Risk

Raimond H. Maurer, Christian Schlag and Michael Z. Stamos

Abstract —The worldwide shift from public pay-as-you-go pension systems to privately funded pension schemes is accompanied by a huge increase in the households capital stock mounting to trillions of dollars worldwide which pour into defined contribution pension plans. In order to assess how these funds should be optimally invested, we derive the optimal time-dependent portfolio allocation strategy taking into account long-term stock market, term structure, and inflation risk. Our results confirm that the often advised so-called life-cycle strategy is optimal if non-financial wealth is taken into account. We also benchmark common longterm defined contribution asset allocation strategies relative to the optimum in order to the assess welfare implications for varying investment horizons and risk aversions. The outcome of utility heavily depends on whether the risk aversion of the investor is estimated appropriately. Misestimation of this parameter and hence wrong investment advice can lead to utility losses of around 60 percent in terms of certainty equivalent wealth.