The effect upon future Social Security benefits resulting from the introduction of individual accounts depends on both the potential risks and returns of private equities, yet the historical evidence about the determinants of stock market risks and returns is mixed. In particular, correlations between equity returns and market fundamentals (such as the dividend-price ratio) are weak at annual frequencies, which has led some to conclude that a random returns (fixed mean and variance) model is the preferred specification for simulating the future path of equity returns. Although choosing between the random returns model and models based on market fundamentals does equally well for explaining variation of equity returns in the short run, the distinction is important when projecting equity returns over longer periods, as shown here in the context of a Monte Carlo simulation of Social Security reform. If equity returns are even weakly correlated with market fundamentals then (1) the expected future average return may be a function of the starting values for market fundamentals, and (2) the overall range of cumulative outcomes is narrower than the random returns model suggests.
How would introducing individual accounts affect outcomes for future Social security beneficiaries? Individual accounts with investment in corporate equities could raise expected benefits, but the welfare cost of increased risk could offset those gains (Congressional Budget Office (CBO), 2003; Feldstein and Rangulova, 2001; MaCurdy and Shoven, 2001). When attempting to quantify the trade-off between risk and return in a policy simulation context, one key modeling decision is how the probability distribution of future equity returns should be tied to underlying economic fundamentals. In particular, a mean-reverting process, which ties equity returns to the underlying growth of capital income, can lead to policy conclusions that differ significantly from a textbook random-returns specification in which the probability distribution of annual returns is fixed.
The distinction between mean-reverting and random equity returns models plays an important role in behavioral finance. At stake is whether the textbook model of efficient markets is a better description of historical outcomes than a model in which investors seem to overreact to changes in market fundamentals, which makes future equity returns predictable (for example, see the general discussion in Malkiel  and Shiller ). The empirical evidence on mean reversion is still debatable; although Poterba and Summers (1988) found evidence of mean reversion at long horizons, those results were qualified as being very period-specific by Kim, Nelson, and Startz (1991).
This article does not attempt to resolve whether any specific version of a mean reversion process is able to explain equity prices over time. The approach here is to use alternative specifications for equity returns that (statistically) are all defensible representations of how equity returns evolve over time. The direct results of the Monte Carlo simulations for equity returns are expected values and variability of outcomes from stock market investments generally. However, the goal here is much more specific. The policy question being addressed is how replacing a fraction of traditional Social security benefits with individual accounts would affect benefit outcomes. That answer is somewhat dependent on one's views about the process generating equity returns over time.
From the perspective of this article, the choice between random returns and mean reversion in equity prices matters for two reasons. First, the starting values of financial valuation ratios will affect average equity returns if market fundamentals play a role, because starting with an overvalued stock market implies below-average future returns whereas the market is in transition to its long-run equilibrium (Campbell and Shiller, 1998; Diamond, 1999). …