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Pricing Personal Account Guarantees: A Simplified Approach

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## Pricing Personal Account Guarantees: A Simplified Approach

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