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


 In
Markets too small to provide Social Security
guarantees
Governments have abilities markets lack
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
2. Calculate the payoff (if any) from the guarantee
3. Calculate the mean of the sample payoffs to get an
estimate of the expected payoff in a risk-neutral world
4. Discount the expected payoff at the risk-free rate to get
an estimate of the value of the guarantee
1.
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
Example: Medium Earner 2050
Expected Cost
Relative Frequency
0.04
Cost of Inflation Indexed Current Law Annual Benefit Annuity Due:
$288,241.30 = 13.97 x $20,636.00
0.035
0.03
Mean
Cal : 1.0545
Sim: 1.0544
0.025
0.02
Std Dev
0.10685
0.10654
Geo Mean
1.0491
0.015
0.01
P(G>0) = 0.29
E(G|G>0) = $62,059.00
Cost = $17,854.38
0.005
0
0
0.5
1
1.5
2
x 10
6
Market Cost
Relative Frequency
0.04
Cost of Inflation Indexed Current Law Annual Benefit Annuity Due:
$288,241.30 = 13.97 x $20,636.00
0.035
0.03
Mean
Cal : 1.0292
Sim: 1.0292
0.025
0.02
Std Dev
0.10685
0.10647
Geo Mean
1.0237
0.015
0.01
P(G>0) = 0.81
E(G|G>0) = $105,178.75
Cost = $85,152.72
0.005
0
0
0.5
1
$Millions (2004 Dollars)
1.5
2
x 10
6
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?
