To investigate further, we construct several diagnostic plots showing the simulated retirement-wealth amounts of the maximally ascending, static 40/60 and maximally descending glide paths. These plots appear in Figure 8. They are arranged in a matrix, with all horizontal and vertical axes aligned. On the diagonal of the matrix appear labels and a histogram showing the simulated retirement wealth amounts for the labeled glide path. Each off-diagonal axis plots the two glide-path retirement-wealth simulations on the corresponding diagonal labels against each other. The upper three plots are matched on simulated outcomes—each point on the plot underwent the same history of returns under both glide paths. The lower three plots are matched on distribution quantiles, i.e., the simulated wealth amounts for each glide path are sorted before plotting. These quantile-quantile plots in the lower three axes demonstrate any differences in skewness among the plotted elements. If one distribution is more skewed, the blue path of quantiles curves away from the red diagonal rule in the direction of the more skewed sample. For example, it can be seen that the maximally descending glide path is slightly more skewed than either of the others, matching the analysis from computing the numerical sample skewness from the simulations.
The matrix of plots does show slight differences among the three cases, but given that the majority of these differences occur in extreme cases and the expected return is substantially different for these cases, it is our opinion that the differences in skewness are far outweighed by the major differences in expected return. The skewness differences shown in either the numerical or the graphical analysis here are not great enough to be of concern. Other risk measures were considered for matching as well, but none matched as consistently as standard deviation, and they all fared much worse insofar as overall differences in final wealth distribution.
Figure 8 also shows the lack of perfect correlation in terms of wealth outcome offered by the different glide paths. The upper three off-diagonal plots fan out considerably from the diagonal lines representing equality between horizontal and vertical axes. The shape of the clouds of points mean that many good outcomes under one glide path, within a particular history, would have been bad outcomes had another glide path been selected.