Pricing Personal Account Pricing Personal Account Guarantees: A Simplified Guarantees: A Simplified

ApproachApproach

October 21, 2006October 21, 2006

Andrew Biggs, SSAAndrew Biggs, SSA

Clark Burdick, SSAClark Burdick, SSA

Kent Smetters, Wharton SchoolKent Smetters, Wharton School

OverviewOverview

Many personal account plans include Many personal account plans include guarantees against market risk, but few guarantees against market risk, but few guarantees are priced using market guarantees are priced using market techniquestechniques

Some market approaches are ungainly Some market approaches are ungainly when applied to personal accountswhen applied to personal accounts

We propose a simple change to current We propose a simple change to current “expected cost” models to calculate “expected cost” models to calculate market prices for guaranteesmarket prices for guarantees

BackgroundBackground

Social Security faces long-term financing Social Security faces long-term financing shortfall that will require tax increases or shortfall that will require tax increases or benefit reductionsbenefit reductions

One rationale for personal accounts is that One rationale for personal accounts is that higher expected returns will reduce impact higher expected returns will reduce impact of lower traditional benefitsof lower traditional benefits

But higher returns come with higher risk; But higher returns come with higher risk; some retirees could do worse by choosing some retirees could do worse by choosing an accountan account

GuaranteesGuarantees

Several reform plans contain provisions Several reform plans contain provisions protecting account holders against low protecting account holders against low investment returnsinvestment returns

Account holders effectively receive the Account holders effectively receive the greater of their account-based benefit or greater of their account-based benefit or current law scheduled benefitcurrent law scheduled benefit

Protection against risk for workers is Protection against risk for workers is contingent liability for governmentcontingent liability for government

How are guarantee costs estimated?How are guarantee costs estimated?

Costs generally estimated on an “expected Costs generally estimated on an “expected cost” basiscost” basis

Using assumptions regarding mean and Using assumptions regarding mean and variation in returns, SSA OACT calculates variation in returns, SSA OACT calculates the most likely cost for the guaranteethe most likely cost for the guarantee

Discussion focuses on these expected Discussion focuses on these expected costs as component of overall package costs as component of overall package costcost

But this ignores the cost of riskBut this ignores the cost of risk

Example: If account earns more than average Example: If account earns more than average return, excess returns are “clawed back.” If return, excess returns are “clawed back.” If account earns less than average, it is topped up.account earns less than average, it is topped up.

Expected cost: Expected cost: zerozero. Above-average returns . Above-average returns finance guarantee to below-average returnsfinance guarantee to below-average returns

Market cost: Market cost: highhigh. Equivalent to simultaneous . Equivalent to simultaneous purchase of put option and sale of call option. Put purchase of put option and sale of call option. Put is significantly more expensive than call, so net is significantly more expensive than call, so net cost of guarantee is high.cost of guarantee is high.

Do market prices for guarantees Do market prices for guarantees apply to government?apply to government?

Some argue that market prices shouldn’t Some argue that market prices shouldn’t apply to governmentapply to government Markets too small to provide Social Security Markets too small to provide Social Security

guaranteesguarantees Governments have abilities markets lackGovernments have abilities markets lack

In most cases, the market price is the best In most cases, the market price is the best estimate of the total cost of the liabilityestimate of the total cost of the liability

Alternate approachesAlternate approaches

Black-Scholes or Lattice methodsBlack-Scholes or Lattice methods Each will produce the correct answer, but Each will produce the correct answer, but

implementation is difficultimplementation is difficult Reason: Rather than a single purchase, Reason: Rather than a single purchase,

personal accounts imply multiple purchases personal accounts imply multiple purchases that must sum to a set amount at retirementthat must sum to a set amount at retirement

Alternate approachAlternate approach1.1. Generate multiple random return paths based upon the Generate multiple random return paths based upon the

risk-freerisk-free rate of return and the standard deviation on the rate of return and the standard deviation on the riskyrisky asset asset

2.2. Calculate the payoff (if any) from the guaranteeCalculate the payoff (if any) from the guarantee3.3. Calculate the mean of the sample payoffs to get an Calculate the mean of the sample payoffs to get an

estimate of the expected payoff in a risk-neutral worldestimate of the expected payoff in a risk-neutral world4.4. Discount the expected payoff at the risk-free rate to get Discount the expected payoff at the risk-free rate to get

an estimate of the value of the guaranteean estimate of the value of the guarantee

Change from expected to riskless return shifts distribution Change from expected to riskless return shifts distribution of account balances to the left, calculates RNV of of account balances to the left, calculates RNV of guaranteeguarantee

ExampleExample

Purchase $100 in stocks, expected return Purchase $100 in stocks, expected return of 6.5% and standard deviation 20.6%of 6.5% and standard deviation 20.6%

Guarantee that in 10 years it will produce Guarantee that in 10 years it will produce $187.71 ($100 x 1.065$187.71 ($100 x 1.06510)10)

From 10,000 simulations at riskless return, From 10,000 simulations at riskless return, average shortfall of $71.97, or $53.55 PVaverage shortfall of $71.97, or $53.55 PV

Put option price through Black-Scholes Put option price through Black-Scholes equals $53.71equals $53.71

Ryan-Sununu proposalRyan-Sununu proposal

PRAs investing 10% of first $10,000 in PRAs investing 10% of first $10,000 in taxable wages, 5% of remaining taxable wages, 5% of remaining

Standard portfolio of 65% stocks (6.5% Standard portfolio of 65% stocks (6.5% real), 35% corporate bonds (3.5% real)real), 35% corporate bonds (3.5% real)

Admin cost of 25 basis pointsAdmin cost of 25 basis points At retirement, guarantee that PRA balance At retirement, guarantee that PRA balance

can purchase annuity equaling scheduled can purchase annuity equaling scheduled benefitsbenefits

A simple model for expected costsA simple model for expected costs

Stylized earners: very low, low, medium, high, Stylized earners: very low, low, medium, high, maximum wagemaximum wage

For each, calculate scheduled Social Security For each, calculate scheduled Social Security benefit; PRA balance at retirement based on benefit; PRA balance at retirement based on expectedexpected return; distribution of PRA balances return; distribution of PRA balances

Calculate average top-up cost for each worker Calculate average top-up cost for each worker typetype

Weight costs based on percentage of population Weight costs based on percentage of population with lifetime earnings closest to each typewith lifetime earnings closest to each type

Altering to estimate market pricesAltering to estimate market prices

In previous model, compound account In previous model, compound account contributions at the contributions at the risklessriskless rather than rather than expected rate of returnexpected rate of return

Calculate guarantee cost for each worker Calculate guarantee cost for each worker type, then weight to represent populationtype, then weight to represent population

Result will be estimated market price of Result will be estimated market price of guaranteeguarantee

Example: Medium Earner 2050Example: Medium Earner 2050

0 0.5 1 1.5 2

x 106

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Rela

tive F

req

uen

cy

Expected Cost

P(G>0) = 0.29 E(G|G>0) = $62,059.00 Cost = $17,854.38

Mean Std Dev Geo Mean Cal : 1.0545 0.10685 Sim: 1.0544 0.10654 1.0491

0 0.5 1 1.5 2

x 106

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

$Millions (2004 Dollars)

Rela

tive F

req

uen

cy

Market Cost

P(G>0) = 0.81 E(G|G>0) = $105,178.75 Cost = $85,152.72

Mean Std Dev Geo Mean Cal : 1.0292 0.10685 Sim: 1.0292 0.10647 1.0237

Cost of Inflation Indexed Current Law Annual Benefit Annuity Due: $288,241.30 = 13.97 x $20,636.00

Cost of Inflation Indexed Current Law Annual Benefit Annuity Due: $288,241.30 = 13.97 x $20,636.00

Summary of resultsSummary of results

Expected cost of guarantee in 2050: Expected cost of guarantee in 2050: 11.3% of total OASI benefits11.3% of total OASI benefits

Compares to 13.3% OACT expected cost Compares to 13.3% OACT expected cost projectionprojection

Market price of guarantee: 28.2 percent of Market price of guarantee: 28.2 percent of total benefitstotal benefits

Further issuesFurther issues How much do guarantee costs change when How much do guarantee costs change when

calculated with representative sample of retiree calculated with representative sample of retiree population?population?

How much does allowing portfolio choice alter How much does allowing portfolio choice alter the cost of guarantees?the cost of guarantees?

Does long-term correlation of wage growth and Does long-term correlation of wage growth and market returns reduce cost of guarantees?market returns reduce cost of guarantees?

Are market prices the most appropriate measure Are market prices the most appropriate measure for guarantees provided by the government?for guarantees provided by the government?