Robustness To Changes In The Return Distribution Assumptions
We first investigate changes in assumptions that motivate different choices of glide paths. First, we present two other return distribution scenarios. These are admittedly contrived, but demonstrate the sensitivity of glide-path wealth to outperformance of an asset class early or late in the savings period. These return distribution assumptions are different from the base case only in the expected return of the equity asset. The first variation is a decreasing expected equity return, linearly from 8 to 2 percent annualized return over the investment period. The second case is a reversal of the first, with expected stock returns increasing linearly from 2 to 8 percent over the savings period.
The performance charts for these two cases are shown in Figures 4 and 5. The increasing returns scenario favors an ascending glide path, whereas the descending returns scenario favors a descending one. This is completely consistent with the intuition that the investor wants exposure to better performance when it is likelier to happen.
Clearly, different trends over the investment period support different glide-path choices. The optimal glide path is quite sensitive to subtle variations in return assumptions and investment changes over time. Perhaps these examples are not inconsistent with the realities of many potential TDF investors. Along with the evidence in Figure 2, we find these modifications to the base simulation provide a persuasive case that choosing a particular glide path amounts to a bet on the relative performance of the constituent assets over time.