Social Security Reform: Responding to the Critics

Studies | Social Security

No. 281
Wednesday, November 16, 2005
by Andrew J. Rettenmaier and Zijun Wang


Results Using Adjusted Historical Data

Table III - Simulation Results Based on the Historical Data Adjusted for Stock Return Mean

"Many argue that the performance of the U.S. stock market in the past century may not be repeated in the future."

Shiller also considered the effects on his results if the equity premium were to decline, meaning he assumed a lower estimated return for stocks. Predicting future long-term stock returns is extremely difficult. Often past experience is used as a guide to future expectations. But many argue that the performance of the U.S. stock market in the past century may not be repeated in the future. Due to demographic changes, the capital-to-labor ratio will rise and returns on domestic capital may decline, which in turn may lower long-run stock returns. Sometimes analysts use lower expected equity premiums, among other tools, to account for these effects and reduce forecasts of future stock returns. However, other factors will likely mitigate these effects. For example, the integrated global capital market will continue to be affected by the increasing demand for capital from China, India and many other developing nations in their move toward greater industrialization.

To investigate the effects of declines in equity returns, we repeat the simulation exercises from the last section using an adjusted stock return series. Specifically, we reduce all historical stock returns by a fixed amount such that the geometric average return of the adjusted series is 4.8 percent. The adjusted estimates using the 4.8 percent average return are presented in Table III and Figure II. The choice of a 4.8 average return follows Shiller. 14

With these mean-return adjustments, we assume that stock market volatility remains unchanged. We also implicitly assume that the bond market volatility and returns are unchanged from the historical levels. Thus, this exercise essentially represents a reduction in the equity premium with no associated reduction in risk. We discuss the implications of this assumption further below.

Figure II - Simulations Based on Adjusted Historical Data

Note that the results for the all bond fund remain unchanged. For the other four portfolios, which include equities, there is a small probability that the portfolio will fall below the benefit offset threshold. As expected, a comparison of Figures I and II shows the returns on portfolios with equities decline as a result of the assumed reduction in the equity premium. Remember Shiller projected an alarming frequency of outcomes falling below the break-even point, based on a static 3 percent benefit offset rate. By contrast, simulations using the realized rate of return on government bonds produces few outcomes below the benefit offset amount. For example, the lifecycle fund using Shiller’s base case allocation produced only 4 such simulations out of 91, or 4.4 percent, whereas Shiller reported 65 to 71 percent.

"Even using lower returns, the stock portfolio still outperforms the benefit offset rate."

The same holds for the other portfolios. Clearly, using a benefit offset rate based on the realized government borrowing rate eliminates much of the concern over the return on workers’ accounts falling below the benefit offset rate. In short, based on historical data, workers would have seen their personal accounts outperform the benefit offset account almost all the time.


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