The Market Value of Accrued Social Security Benefits

John Geanakoplos, Stephen Zeldes

NBER Retirement Research Center Paper No. NB 07-18
Issued in December 2007

One measure of the health of the Social Security system is the difference between the market value of the trust fund and the present value of benefits accrued to date. How should present values be computed for this calculation in light of future uncertainties? The Office of the Chief Actuary estimates the present value of expected benefits. We think it is important to use market value. Since claims on accrued benefits are not currently traded in financial markets, we cannot directly observe market value. We therefore use a model to estimate what the market value would be if these claims were traded.

One key issue in this valuation is how to adjust for risk. The traditional actuarial approach is to ignore risk and compute expected value. If benefits are risky and this risk is “priced” by the market, then the actuarial estimates will differ from market value. Effectively, market valuation uses a discount rate that incorporates a risk premium.

The exact adjustment for risk requires a careful examination of t he stream of future benefits. The U.S. Social Security system is “wage-indexed”, i.e. future benefits depend directly on the realization of the future economy-wide average wage index. We assume that there is a positive long-run correlation between average labor earnings and the stock market. We then use derivative pricing methods standard in the finance literature to compute the market price of individual claims on future benefits, which depend on age and on the macro state variables. Finally, we aggregate the market value of benefits across all cohorts to arrive at an overall value of accrued benefits.

We find that the difference between market valuation and “actuarial” valuation is large, especially when valuing the benefit s of younger cohorts. Over all, the market value of accrued benefits is only 3/4 of that implied by the actuarial approach. Ignoring retirees (for whom the valuations are t he same), market value is only 2/3 as large as that implied by the actuarial approach.

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