It is well-known that standard structural models of default predict counterfactually low credit spreads for corporate debt, especially for investment grade bonds of short maturity. Early work includes Jones, Mason and Rosenfeld (1984), who find that the Merton (1974) model generates yield spreads that fall far below empirical observation for investment grade firms.
Although subsequent work (e.g., Eom, Helwege and Huang (2004)) has found that various structural models can generate very diverse predictions for credit spreads, Huang and Huang (HH 2003) demonstrate that once these various models are calibrated to be consistent with historical default and recovery rates, they all produce very similar credit spreads that fall well below historical averages. For example, HH report that the theoretical average 4-year (Baa Treasury) spread is approximately 32 basis points (bp) and relatively stable across models. This contrasts sharply with their reported historical average (Baa-Treasury) spread of 158 bp. Similarly, HH find that the theoretical average 4-year Aaa-Treasury spread is about 1 bp, well below their reported historical average of 55 bp.
Over the past few years, stock market indices around the world have experienced a period of strong growth compared to the long-run average. Developed markets have recovered rather swiftly from the technology bubble a few years ago, and emerging markets have seen startling amounts of liquidity channeled toward their stock exchanges, driving up stock prices. Selected markets have experienced major corrections, partly related to economic crises. Some of these corrections were temporary, others more pronounced.
A popular asset allocation strategy for managing equity risk during the accumulation phase of a defined contribution (DC) pension plan is deterministic lifestyling. At the beginning of the plan, the contributions are invested entirely in equities. Then on a predetermined date prior to retirement (e.g., ten years), the assets are switched gradually into bonds at a rate equal to the inverse of the length of the switchover period (e.g., 10% per year). By the date of retirement, all the assets are held in bonds, which are then sold to purchase a life annuity that provides the pension. The aim of the strategy is to reduce the impact on the pension of a catastrophic fall in the stock market just before the plan member retires. Although deterministic lifestyling is a simple strategy to explain to plan members and to implement, there is no evidence that it is optimal in the sense of maximising the plan member’s expected terminal utility.
The purpose of this paper is to find the optimal dynamic asset allocation strategy for a defined contribution pension plan, taking into account the stochastic features of the plan member’s lifetime salary progression as well as the stochastic properties of the assets held in his accumulating pension fund. Of particular importance is the fact that salary risk (the fluctuation in the plan member’s earnings in response to economic shocks) is not fully hedgeable using existing financial assets. To illustrate, wage-indexed bonds could be used to hedge productivity and inflation shocks, but such bonds are not widely traded. The paper builds on Blake, Cairns & Dowd (2001) which developed a pension plan accumulation programme designed to deliver a pension in retirement that is closely related to the salary (and hence standard of living) that the plan member received prior to retirement. We call the optimal dynamic asset allocation strategy stochastic lifestyling and we compare it against various static and deterministic lifestyle strategies in order to calculate the cost of adopting suboptimal strategies. Despite the apparent increase in complexity in comparison with deterministic lifestyling, stochastic lifestyling is still a relatively easy strategy to implement in practice.
