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.