The Legacy Debt Associated with Past Social Security Transfers

by Dean R. Leimer
Social Security Bulletin, Vol. 76 No. 3, 2016

Text desciption for Appendix Chart A-1.
Portfolio efficiency frontiers with and without a wages-and-salaries PAYGO asset based on annual real rates of return to six broad financial asset classes, 1930–2009

This scatterplot shows the following (standard deviation, mean rate of return) coordinates for six financial asset types (1930–2009) and the PAYGO asset (aggregate wages-and-salaries tax base).

Annual real rates of return for six broad financial asset classes and the PAYGO asset (aggregate wages-and-salaries tax base), 1930–2009
Asset class Standard deviation (rounded) Mean rate of return (rounded)
Large-company stock 0.20 0.08
Small-company stock 0.32 0.14
Long-term corporate bond 0.10 0.03
Long-term government bond 0.11 0.03
Intermediate-term government bond 0.07 0.02
U.S. Treasury bill 0.04 0.01
PAYGO asset (aggregate wages-and-salaries tax base) 0.06 0.03
SOURCE: Author's calculations.
NOTE: The mean-variance analysis is constrained to exclude negative asset shares.

Two line plots overlay the scatterplot: one line shows the efficiency frontier with the PAYGO asset and the other line shows the efficiency frontier without the PAYGO asset. The efficiency frontier with the PAYGO asset starts at standard deviation 0.0297 and mean rate of return 0.0142. The efficiency frontier without the PAYGO asset starts at standard deviation 0.0383 and mean rate of return 0.0079. Both lines show increases in the mean rate of return as standard deviations increase. The mean rate of return for the efficiency frontier with the PAYGO asset is higher than that of the efficiency frontier without the PAYGO asset at all standard deviations lower than 0.20. The efficiency frontiers converge at standard deviations higher than 0.20.

Text description for Appendix Chart A-2.
Asset shares on the portfolio efficiency frontier with a wages-and-salaries PAYGO asset and six broad financial asset classes based on annual real rates of return, 1930–2009

This line chart illustrates asset shares across an x-axis range of standard deviations between 0.0297 and 0.3190.

The large-company stock share starts at 0.0001 at standard deviation 0.0306, increases to 0.0080 at standard deviation 0.0474, then decreases to zero at standard deviation 0.0555. The share at all other standard deviations is zero.

The small-company stock share increases from 0.0062 at standard deviation 0.0297 to 1.000 at standard deviation 0.3190.

The long-term corporate bond share starts at 0.0005 at standard deviation 0.0709, increases to 0.0925 at standard deviation 0.0808, then decreases to zero at standard deviation 0.1249. The share at all other standard deviations is zero.

The long-term government bond share starts at 0.0007 at standard deviation 0.0812 and increases to 0.1449 at standard deviation 0.0971. The share remains 0.1449 through standard deviation 0.1249, then decreases to zero at standard deviation 0.3010. The share at all other standard deviations is zero.

The intermediate-term government bond share starts at 0.0039 at standard deviation 0.0306, increases to 0.3684 at standard deviation 0.0474, then decreases to zero at standard deviation 0.0971. The share at all other standard deviations is zero.

The U.S. Treasury bill share decreases from 0.6694 at standard deviation 0.0297 to zero at standard deviation 0.0475. The share at all other standard deviations is zero.

The PAYGO asset (aggregate wages-and-salaries tax base) share increases from 0.3245 at standard deviation 0.0297 to 0.5555 at standard deviation 0.0474. The share fluctuates narrowly between 0.5375 and 0.5490 at standard deviations from 0.0474 to 0.0903, then decreases to zero at standard deviation 0.3190.