The authors aim to demonstrate the importance of taking into account “mean reversion” in asset prices and show that this type of modeling leads to a high share of equities in pension funds’ asset allocations.
First, the authors will study the long-run statistical characteristics of selected financial assets during the 1895-2011 period. Such an analysis corroborates the fact that, for long holding periods, equities exhibit lower risk than other asset classes. Moreover, they will provide empirical evidence that stock market returns are negatively skewed in the short term and show that this negative skewness vanishes over longer time horizons. Both these characteristics favor the use of a semi-parametric methodology.
This empirical study led to two major findings. First, the authors noticed that the distribution of stock returns is negatively skewed over short time horizons. Second, they observed that the fat-tailed shape of the returns distribution disappears for time periods longer than five years. Finally, they demonstrated that stock returns exhibit “mean-reversion”. Consequently, the optimization program should not only take into account the non-Gaussian nature of returns in the short run but also incorporate the speed at which volatility “mean reverts” to its long-run mean.
To simulate portfolio allocation, the authors used a Cornish–Fisher Value-at-Risk criterion with the advantage of providing an allocation that is independent of the saver’s preferences parameters. A backtesting analysis including a calculation of replacement rates shows a clear dominance of the “non-Gaussian” strategy because the retirement outcomes under such a strategy would be positively affected.
