Social Security and Market Risk

Policy Reports | Social Security

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


  1. This paper's stock analysis is based on the performance of the Standard & Poor's 500 and the bond analysis is based on the Moody AAA Corporate Bond yield series after 1919 and American railroad bond yields prior to that. See the appendix for details.
  2. All data series begin in 1871, including the price index. Thus the first annual inflation rate is the 1871 to 1872 change. As a result the data series for the real rates of returns on stocks and bonds begin in 1872.
  3. Although interest on bonds would also be reinvested, because of differences in the rate of return between stocks and bonds the mixed portfolios would have to be "rebalanced" annually - with, for example, some of the stock dividends going to purchase additional bonds to keep the same percentage of dollars invested in each. Returns from a bond-only portfolio are not considered because, as shown later, even a minimum-risk portfolio would include some stocks.
  4. The rates of return for the 35-year investment periods are the internal rates of return from annual $1 investments. The annual investments are used rather than a single investment to emulate Social Security tax payments. We limit the comparison to 1906 to 2000 because the first completed 35-year holding period begins in 1872 and ends at the end of 1906.
  5. The rate of return on a mixed portfolio assumes that investors myopically rebalance their portfolio in each year to maintain the equity and bond shares.
  6. Jeremy J. Siegel, Stocks for the Long Run, 2nd ed. (New York: McGraw-Hill, 1998).
  7. Moving down the table from lower to higher stock holdings, the average returns rise but the measures of dispersion actually decline and then rise again. This is as expected from portfolio theory; namely, the portfolio with the minimum risk is some combination of stocks and bonds. Over a 35-year period, and for an investment of the sort we consider involving annual contributions, stocks would comprise 37.1 percent of the minimum risk portfolio - the portfolio with the minimum standard deviation from the mean. For shorter investment horizons the share of stocks in the minimum risk portfolio declines - down to 3.7 percent for one-year investments. The minimum risk portfolio does not represent the optimal holding of stocks and bonds for all investors, however. That optimal holding is determined by the investor's willingness to trade between higher returns and additional risk.
  8. James M. Poterba and Mark J. Warshawsky, "The Costs of Annuitizing Retirement Payouts from Individual Accounts," in J. Shoven, ed., Administrative Costs and Social Security Privatization(Chicago: University of Chicago Press, 2000).
  9. See Olivia S. Mitchell et al., "New Evidence on the Money's Worth of Individual Annuities," American Economic Review, No. 89, 1999, p. 1311.
  10. Ibid.
  11. Ibid.
  12. To keep the exercise simple, we use the same annual earnings profile for each period considered - what a person born in 1960 is expected to earn each year between the ages of 31 and 65, based on both historical data and projected earnings. The projections are based on the methodology described in Andrew J. Rettenmaier and Thomas R. Saving, The Economics of Medicare Reform (Kalamazoo, Mich.: W. E. Upjohn Institute for Employment Research, 2000).
  13. The rate of return used to calculate the annuity amount that could be purchased with the individual's retirement account balance is set to the average rate of return earned on AAA corporate bonds over the investment period. Also, we assume that the annuity provider requires an amount equal to 8 percent of the cumulative value of the annuity to cover administrative costs. We calculate the annuity amount using the unisex mortality experience of individuals born in 1960, assuming they live to the age of 65. The probability of dying at each age between 65 and 119 is used to weight the annuity payments up to the year of death. The annuity formula is in the appendix. The mortality data are from Felicitie C. Bell et al., "Life Tables for the United States Social Security Area 1900-2080," Actuarial Study No. 107, U.S. Department of Health and Human Services, Social Security Administration, Office of the Actuary, August 1992. In other words, we use the same life-cycle deposits to the accounts and the same longevity experience for each consecutive 35-year period, so that the rates of return for all the periods can be compared.
  14. See Table III.B5, in the 2000 Trustees Report.
  15. Martin Feldstein, "Social Security Reform: America's Golden Opportunity," Economist, March 13, 1999.
  16. Liqun Liu and Andrew J. Rettenmaier, "The Attractiveness of the Social Security Investment for Members of Different Racial and Education Groups," Private Enterprise Research Center, PERC Working Paper #0010, November 2000.

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