## Social Security Reform: Responding to the Critics

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

## Results Using Historical Data

How often will the rate of return on a worker’s PRA fail to reach the break-even point (the benefit offset amount)? Or, how frequently can workers expect a net loss?

Imagine a worker who joins the workforce in 2011 at age 21, opens a PRA and retires after working 44 years. The hypothetical worker’s earnings and contributions to a personal account are presented in Table I. Applying this earnings profile to all 91 overlapping 44-year historical periods we calculate the frequency with which the personal account returns, based on the five portfolios, accumulate less than the benefit offset. Administrative fees are assumed to be 0.3 percentage points. Table II and Figure I summarize the results for the five portfolios. 12

The upper panel of Table II identifies the frequency with which the five portfolios do not achieve the rate of return used to calculate the benefit offset (which is the realized long-term government bond rate). At the end of the contribution period, if the net value of the personal account — the account balance minus the benefit offset — is negative, then the account is designated as suffering a loss.

"Historical data shows all the investment portfolios (except the all bond fund) will have a higher return than the benefit offset account."

As can be seen in both the figure and the table, all portfolios perform better than the benefit offset in all 91 simulations with the exception of the “All Bond Fund” (50 percent in long-term government bonds and 50 percent invested at the money-market rate). A worker who held the all bond portfolio in his personal account would do worse than the benefit offset slightly more than half the time. Workers who held any of the other three portfolios would have benefited from owning a personal account because their account would be worth more than the benefit offset when they retired.

How much better would these workers have fared? The lower panel of Table II contains a summary of the net values and the associated internal rates of return for each of the five portfolios. The portfolios’ net values are equal to the difference between the total personal account accumulation minus the benefit offset. The personal account is always positive after the benefit offset — meaning it earns a return greater than the benefit offset rate — except for the all-bond portfolio. According to the table:

• Workers who invested in the “Lifecycle Fund based on Shiller,” would experience a net gain of \$15,830 to \$102,031, with an internal rate of return ranging from 1.57 percent to 4.68 percent.
• If the worker invested in the “More Aggressive Lifecycle Fund,” the account would end up with a net gain of \$50,533 in the worst scenario — the 1877-1920 contribution period — and \$248,400 in the best scenario, for the 1922-1965 contribution period; the average return is 4.7 percent after expenses.

The last two columns report the net values and internal rates of return produced by the “50/50 Fund” and the “All Stock Fund.” As shown in Figure I, the all-stock portfolio out-performed the other portfolios in almost all years. Out of 91 simulations, the all-stock portfolio fell short of the more aggressive lifecycle fund in only five cases, and all by relatively small margins.

"The all stock portfolio yields the highest return; all bond investments yield the lowest returns."

These results — using realized government bond rates to calculate the benefit offset — are a striking contrast to Shiller’s findings based on the fixed 3 percent benefit offset. Recall Shiller found that in 32 percent of the cases using his baseline lifecycle account, the personal account fell short of the benefit offset amount. By contrast, using the realized government bond return to determine the benefit offset, this same account never falls short. 13