Pricing Personal Account Guarantees: A Simplified Approach

1. Pricing Personal Account Guarantees: A Simplified Approach October 21, 2006 Andrew Biggs, SSA Clark Burdick, SSA Kent Smetters, Wharton School

2. Overview • Many personal account plans include guarantees against market risk, but few guarantees are priced using market techniques • Some market approaches are ungainly when applied to personal accounts • We propose a simple change to current “expected cost” models to calculate market prices for guarantees

3. Background • Social Security faces long-term financing shortfall that will require tax increases or benefit reductions • One rationale for personal accounts is that higher expected returns will reduce impact of lower traditional benefits • But higher returns come with higher risk; some retirees could do worse by choosing an account

4. Guarantees • Several reform plans contain provisions protecting account holders against low investment returns • Account holders effectively receive the greater of their account-based benefit or current law scheduled benefit • Protection against risk for workers is contingent liability for government

5. How are guarantee costs estimated? • Costs generally estimated on an “expected cost” basis • Using assumptions regarding mean and variation in returns, SSA OACT calculates the most likely cost for the guarantee • Discussion focuses on these expected costs as component of overall package cost

6. But this ignores the cost of risk • Example: If account earns more than average return, excess returns are “clawed back.” If account earns less than average, it is topped up. • Expected cost: zero. Above-average returns finance guarantee to below-average returns • Market cost: high. Equivalent to simultaneous purchase of put option and sale of call option. Put is significantly more expensive than call, so net cost of guarantee is high.

7. Do market prices for guarantees apply to government? • Some argue that market prices shouldn’t apply to government • Markets too small to provide Social Security guarantees • Governments have abilities markets lack • In most cases, the market price is the best estimate of the total cost of the liability

8. Alternate approaches • Black-Scholes or Lattice methods • Each will produce the correct answer, but implementation is difficult • Reason: Rather than a single purchase, personal accounts imply multiple purchases that must sum to a set amount at retirement

9. Alternate approach • Generate multiple random return paths based upon the risk-free rate of return and the standard deviation on the risky asset • Calculate the payoff (if any) from the guarantee • Calculate the mean of the sample payoffs to get an estimate of the expected payoff in a risk-neutral world • Discount the expected payoff at the risk-free rate to get an estimate of the value of the guarantee Change from expected to riskless return shifts distribution of account balances to the left, calculates RNV of guarantee

10. Example • Purchase $100 in stocks, expected return of 6.5% and standard deviation 20.6% • Guarantee that in 10 years it will produce $187.71 ($100 x 1.06510) • From 10,000 simulations at riskless return, average shortfall of $71.97, or $53.55 PV • Put option price through Black-Scholes equals $53.71

11. Ryan-Sununu proposal • PRAs investing 10% of first $10,000 in taxable wages, 5% of remaining • Standard portfolio of 65% stocks (6.5% real), 35% corporate bonds (3.5% real) • Admin cost of 25 basis points • At retirement, guarantee that PRA balance can purchase annuity equaling scheduled benefits

12. A simple model for expected costs • Stylized earners: very low, low, medium, high, maximum wage • For each, calculate scheduled Social Security benefit; PRA balance at retirement based on expected return; distribution of PRA balances • Calculate average top-up cost for each worker type • Weight costs based on percentage of population with lifetime earnings closest to each type

13. Altering to estimate market prices • In previous model, compound account contributions at the riskless rather than expected rate of return • Calculate guarantee cost for each worker type, then weight to represent population • Result will be estimated market price of guarantee

14. Example: Medium Earner 2050

15. Summary of results • Expected cost of guarantee in 2050: 11.3% of total OASI benefits • Compares to 13.3% OACT expected cost projection • Market price of guarantee: 28.2 percent of total benefits

16. Further issues • How much do guarantee costs change when calculated with representative sample of retiree population? • How much does allowing portfolio choice alter the cost of guarantees? • Does long-term correlation of wage growth and market returns reduce cost of guarantees? • Are market prices the most appropriate measure for guarantees provided by the government?