Social Security and Market Risk

Studies | Social Security

No. 244
Tuesday, July 31, 2001
by Liqun Liu, Andrew J. Rettenmaier, and Zijun Wang


Returns on Annuitized Personal Retirement Accounts

Figure V - Overall Rate of Return

Some of the reform proposals before Congress would require that, upon retirement, the holder of a personal retirement account convert his or her account balance into an annuity yielding a fixed monthly income for life. The balance in the personal retirement account depends on the amounts deposited, the length of time it was held and the rate of return. The annuity amount that could be purchased depends on the account balance and the annuity provider's assumptions regarding the longevity of the purchaser, administrative costs for such annuities and the rate of return the provider expects to receive by investing the initial premium. Since the riskiness of personal retirement accounts depends on the volatility of the stock and bond markets, we are particularly interested in determining the degree to which annuitization affects the variation in returns retirees could expect from personal retirement accounts.

Assumptions. Most current Social Security reform proposals would allow workers to deposit part of their tax payments to personal retirement accounts. In this way workers prepay part of their currently promised benefits. A number of reform proposals call for workers to contribute 2 percent of earnings over their work lives. In this section we estimate the rates of return on a personal retirement account if an individual had invested 2 percent of earnings for 35 years, ending any year from 1906 to 2000.12 In the 35th year the investor annuitizes the entire amount he or she has accumulated.13

Qualifications. Several qualifications are in order. First, we assume annuitization of the entire balance in the account on the day of retirement.

Table III - Summary Statistics of Internal Rates of Return on Annuitized Personal Retiremnet Account

"We analyzed ninety-five 35-year periods."

A retiree would be more likely to annuitize only part of the account at retirement and the remainder later, depending on whether the market was up or down at the time of retirement. Requiring total annuitization at retirement induces more variation in returns, while allowing flexibility regarding timing would tend to smooth out fluctuations. However, here we annuitize the entire amount at retirement for consistency with Social Security and many of the proposals that include partial privatization. Second, using the corporate bond rate of return produces the most conservative set of annuity amounts. Even the portfolio with the minimum variance would not be comprised totally of bonds, but we use the bond return in consideration of annuity providers' short planning horizons and historical reliance on bonds. Third, we use mortality and life-cycle earnings data for a person born in 1960 across all time periods to restrict the variations in the rate of return from period to period to those arising from underlying market conditions, rather than any related to increasing life spans and rising real earnings.

Rates of Return. Figure V shows the rates of return at the beginning of the retirement year for each of the ninety-five 35-year investment periods. Since an annuity is based on the amount paid in and the expected life span of the retiree, these rates of return take into account 35 years of accumulation and about 18 years of payout, on the average.

Figure VI - Expected Annuity

"Even the minimum rate of return on the all-stock portfolio exceeds the rate of return on Social Security taxes that young people can expect."

In all but five of the 95 periods, the 100 percent stock portfolio outperforms any other portfolio. Thus, even though there is more volatility with a 100 percent stock portfolio, it dominates the others' rates of return almost 95 percent of the time. Those retiring at the beginning of 1921 earn the lowest return, 2.2 percent, and those retiring at the beginning of 2001 earn the highest, 7.6 percent, with the 100 percent stock portfolio. Table III summarizes the series presented in Figure V. The average returns range from 3.0 percent when stocks are 25 percent of the portfolio to 5.1 percent when the portfolio is entirely stocks. Note that even the minimum rate of return on the 100 percent stock portfolio exceeds the rate of return on Social Security taxes of less than 2 percent that virtually all the young people entering the labor market can expect to receive.

Annuity Values. Figure VI presents the annuity values in each retirement year. The pattern is similar to the pattern of portfolio returns, but now the vertical axis measures the size of the annuities. Recall that the annuities purchased using the accumulated funds in workers' personal retirement accounts would be used to offset their scheduled Social Security benefits. Figure VI also illustrates how the size of an annuity component compares to Social Security benefits. In the figure the scheduled Social Security benefits are set to 42 percent of the workers' pre-retirement income, which is the long-run expectation for workers with average earnings levels.14 Since we used the same life-cycle earnings for each consecutive 35 year period, the line reflecting Social Security benefits is constant at $10,850. For illustrative purposes, the difference between the Social Security benefit and the lines reflecting the annuity values indicates the portion of each set of new retirees' benefits paid by taxpayers. But this difference is only for the new retirees in each year; averaging across all retirees in any given year, the variation in the amount taxpayers will have to pay is dampened significantly.

Note also that the accumulation phase is limited to 35 years, while the typical work life will be up to 10 years longer. With more years of investment, the annuity values would be significantly higher.

Table IV - Summary Statistics of Expected Annual Annuity Values

Table IV summarizes the series from Figure VI. For the 100 percent stock portfolio, the annuities averaged $4,681 based on 35 years of investing 2 percent of earnings. Individuals retiring in 1921 and investing in the 100 percent stock portfolio would have the smallest annuity, equal to $1,875. Those retiring at the beginning of this year would have the largest annuity, equal to $9,225.

"Workers who contributed 2 percent of earnings for 35 years to all-stock portfolios could expect a private annuity to equal 43 percent of currently promised benefits, on the average."

While the disparity between the largest and smallest annuities is large, the change from year to year is less so. Table V summarizes the percentage differences, year-to-year, in the value of the annuity that could be purchased from a personal retirement account. It shows that the largest percentage decrease in the value of an annuity purchased from a personal retirement account invested 100 percent in stocks would have been when the annuity value fell 38 percent - which occurred between 1932 and 1933. The largest percentage increase would have occurred in 1937, when the annuity value rose 40 percent.

Replacement Rate of Annuities for Social Security Benefits. Table VI shows the range of the share of Social Security benefits that could be paid for by annuities in varying portfolios of stocks and bonds. We estimate that if workers who contributed 2 percent of earnings for 35 years are in 100 percent stock portfolios prior to retirement:

Table VI - Annuities as a Share of Social Security Benefits
  • During retirement, a private annuity would be expected to equal 43 percent of currently promised Social Security benefits.
  • In the best-case scenario, the annuity would equal 85 percent of the Social Security benefit.
  • In the worst-case scenario, the annuity would equal 17 percent.

"When private annuities vary in size, who bears the risk?"

How do these potential variations in the size of the annuity affect the pension benefit the retiree actually receives? This depends on the specific reform adopted. Every serious proposal limits the downside risk to the retiree. But there are differences among them. Under one proposal, for example, the annuity would offset Social Security benefits dollar for dollar. Under this plan, the retiree would not face any risk.

Under another proposal, retirees would be guaranteed a minimum benefit equal to the current system's promises. In addition, retirees would get an extra benefit equal to 25 percent of their private annuity.

Table VII - 75 Percent of Annuity Values as a Share of Social Security Benefits

Bonuses from Annuities. A dollar-for-dollar buyout gives workers little incentive to voluntarily participate in a private account option, other than carrying with it the guarantee that they own what is in their accounts. Some, most notably economist Martin Feldstein, have suggested that workers receive a bonus related to the size of the annuity they can buy at retirement.15 Consider the average annuity of $4,681 based on the 100 percent stock investment. Retirees would receive 25 percent of this amount, or $1,170, in addition to the benefits they are now promised. This leaves 75 percent of the annuity value to defray the retirees' Social Security benefit. Table VII details the share of Social Security benefits that can be prepaid when retirees receive bonuses equal to 25 percent of their annuities' values.

"Under some proposals, the results for retirees are guaranteed."

Table VIII shows the relative size of the bonuses by portfolio. The average value of the annual bonus is $1,170 for an all-stock portfolio. So on the average total benefits are $12,020, the sum of the Social Security benefit of $10,850 and the bonus of $1,170. The maximum bonus is $2,306 and the minimum is $469. Table IX summarizes the year-to-year changes in total benefits where the total benefits are equal to the sum of Social Security benefits and the bonuses. As indicated in the table, even with bonuses, the year-to-year difference in total pension benefits for retirees with the same income would be less than 4 percent.

Table VIII - Annual Bonuses Equal to 25 Percent of Annuity ValuesTable IX - Percentage Year-to-Year Differences in Expected Total Benefits with a 25 Percent Bonus

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