George G. Pennacchi

English

Research Papers in Economics

This PDF is a selection from a published volume from the National Bureau of Economic 
Research
Volume Title:  Social Security Policy in a Changing Environment 
Volume Author/Editor: Jeffrey Brown, Jeffrey Liebman and David A. Wise, editors
Volume Publisher: University of Chicago Press
Volume ISBN: 978-0-226-07648-5
Volume URL: http://www.nber.org/books/brow08-1
Conference Date: October 19-22, 2006
Publication Date: June 2009
Chapter Title: Comment on "Pricing Personal Account Benefit Guarantees: A Simplified 
Approach"    
Chapter Author: George G. Pennacchi
Chapter URL: http://www.nber.org/chapters/c4542
Chapter pages in book: (249 - 254)Social Security Administration. 2006. 2006 annual report of the Board of Trustees of
the Federal Old-Age and Survivors Insurance and Disability Insurance trust funds.
Washington, DC: GPO.
Comment George G. Pennacchi
This chapter by Andrew Biggs, Clark Burdick, and Kent Smetters makes
two simple but very important points. First, if one has a model that can
compute the expected cost of a personal retirement account (PRA) guar-
antee, then with a couple of changes in parameter values, the model can
also compute the market cost of the guarantee. Second, knowledge of the
guarantee’s market cost is critical for determining sensible policy.
I agree wholeheartedly with these two results. In these comments, I will
oﬀer more intuition for the chapter’s ﬁndings and add arguments for why
policy should be guided by market costs and not expected costs. I will close
with some suggestions for improving estimates of the market cost of PRA
guarantees.
Biggs, Burdick, and Smetters construct a simple model that is calibrated
to roughly replicate the Social Security Administration Oﬃce of the Chief
Actuary’s (OACT) expected cost of the Ryan-Sununu PRA guarantee. For
a PRA invested 65 percent in stocks and 35 percent in bonds and assum-
ing the expected real returns on stocks and bonds are 6.5 percent and 3.5
percent, respectively, they calculate that the guarantee’s expected cost in
2050 equals 11.3 percent of total Social Security Old-Age and Survivors
Insurance (OASI) costs. The expected cost in 2050 of the same guarantee
computed by OACT’s model is 13.3 percent of total OASI costs.
Having shown that their model is comparable to that of the OACT, they
consider what would be the market cost of the same Ryan-Sununu guar-
antee, rather than its expected cost. Their computation of market cost is
based on standard asset pricing methodology that accounts for the sys-
tematic (priced) risks inherent in stock and bond returns. Speciﬁcally, they
take the identical model that was used to compute the expected cost of a
PRA guarantee and alter two parameter inputs. Rather than setting the
expected real returns on stocks and bonds equal to their physical (actual)
values of 6.5 percent and 3.5 percent, respectively, they set them equal to
their risk-neutral values, which for both is assumed to equal a risk-free real
Pricing Personal Account Beneﬁt Guarantees: A Simpliﬁed Approach 249
George G. Pennacchi is a professor of ﬁnance at the University of Illinois.
This research was supported by the U.S. Social Security Administration (SSA) through
grant #10-P-98363-1-03 to the National Bureau of Economic Research (NBER) as part of the
SSA Retirement Research Consortium. The ﬁndings and conclusions expressed are solely
those of the author and do not represent the views of the SSA, any agency of the federal gov-
ernment, or of the NBER.250 Andrew Biggs, Clark Burdick, and Kent Smetters
return of 2.9 percent.1 With this simple change, they ﬁnd that the PRA
guarantee’s market cost in 2050 equals 28.2 percent of total OASI costs.
Intuitively, it is not surprising that the market cost of this long-dated
guarantee is almost two and one-half times its expected cost. The guaran-
tor bears undiversiﬁable or systematic risk because equity losses (and to a
lesser extent bond losses) over a long horizon would tend to occur follow-
ing several years of economic recession. This is precisely the scenario when
the guarantor would least prefer to fund claims on PRA losses. A market
cost for the guarantee that exceeds its expected cost reﬂects the market
compensation for this systematic risk.
Because the systematic risk of a PRA guarantee derives from the sys-
tematic risk premiums of the stocks and bonds in the PRA portfolio, a
mathematically equivalent way of adjusting for this risk is to simulate sce-
narios of stock and bond returns using their risk-neutral expected returns,
not their physical expected returns. Speciﬁcally, the correct market cost
is found by simulating all security returns assuming that their expected
return equals that of a short-maturity, risk-free, real return, such as the
yield on a short-maturity Treasury Inﬂation-Protected Security (TIPS).
This lowers the simulated returns of the PRA portfolio because they grow,
on average, at the 2.9 percent risk-free rate rather than the portfolio’s 5.45
percent physical rate. Hence, more of these randomly simulated risk-
neutral PRA returns result in a claim on the guarantor, thereby increasing
the guarantee’s cost.
The preceding description points to an advantage of valuing guarantees
based on their market, rather than expected, costs. Estimates of market
costs involve less subjectivity compared to estimates of expected costs.
Computing market costs requires knowledge of the real return on a short-
maturity, inﬂation-indexed bond. This real return is practically observable
and can be accurately measured from TIPS yields. In contrast, calculating
expected costs requires knowledge of the physical expected returns on each
of the securities in the PRA portfolio. Determining these expected returns
over the life of the guarantee is more subjective, largely because it is not
clear how they should be estimated. As discussed in Merton (1980), it is
quite diﬃcult to accurately estimate the expected returns on equities from
their realized (historical) returns.2 Such an exercise becomes even more
1. This implies a risk-neutral expected PRA return (before administrative costs) of 2.9 per-
cent compared to a physical expected return of (0.65   6.5%   0.35   3.5%)   5.45%. The
paper’s 2.9 percent return is based on the real return that nominal government bonds issued
to the OASDI trust funds are expected to earn. Theoretically, this real return should be set to
the real yield on a short-maturity, inﬂation-indexed government bond. Doing so may lead to
a risk-neutral real return somewhat lower than 2.9 percent and result in a 2050 market cost
slightly higher than what the paper calculates.
2. Equity variances and covariance can be estimated relatively more accurately. The accu-
racy of variance-covariance estimates improves with the frequency at which returns are sam-
pled, whereas the accuracy of expected return estimates increases with the return sample’s ob-
servation period. It may take an observation period of ﬁfty years or more to obtain an accurate
estimate of a stock’s expected return, assuming its expected return is constant over time.diﬃcult if one (realistically) assumes that expected equity returns vary over
time.
Survey evidence suggests that real expected equity returns are time vary-
ing and that the equity risk premium, deﬁned as the diﬀerence between the
expected return on equity and the short-maturity, risk-free interest rate,
has been falling. Figure 7C.1 gives the median forecasts of the real returns
on stocks, bonds, and bills, as well as the equity risk premium, from the
Survey of Professional Forecasters (SPF) for the years 1992 to 2006.3 Ex-
cept for the real return on Treasury bills, these median forecasts have
tended to decline over this ﬁfteen-year period. In particular, the median
forecast for the equity premium was 5.0 percent in 1992, peaked at 5.85
percent in 1994, and is now down to 2.75 percent. Further, the current me-
dian forecast for the real return on stocks over the next decade is 4.5 per-
cent, which is 200 basis points lower than the OACT’s assumed real return
of 6.5 percent. An implication is that the OACT’s estimate for the expected
cost of a PRA guarantee is understated.
The SPF can be used to illustrate the subjectivity in determining the eq-
uity risk premium (and equity expected returns). Figure 7C.2 plots each of
the individual forecasters’ estimates of the ten-year horizon equity pre-
mium. It is clear that there is wide cross-sectional variation in what these
Pricing Personal Account Beneﬁt Guarantees: A Simpliﬁed Approach 251
Fig. 7C.1 Survey of Professional Forecasters median 10-year forecasts
3. The Federal Reserve Bank of Philadelphia has conducted the Survey of Professional
Forecasters since 1990. It was previously carried out by the American Statistical Associa-
tion and the National Bureau of Economic Research beginning in 1968. In recent years, ap-
proximately thirty professional economic forecasters have participated in this survey. See
Croushore (1993) for details.252 Andrew Biggs, Clark Burdick, and Kent Smetters
Fig. 7C.2 Survey of Professional Forecasters’ individual equity premium forecasts
professional forecasters believe will be the average excess return on stocks
over the next decade. This suggests much potential disagreement among
reasonable individuals as to the appropriate expected return estimates to
use in calculating the expected cost of a PRA guarantee. Consequently, the
potential for political manipulation of PRA guarantees costs is greater
when they are based on expected costs rather than market costs that do not
require knowledge excess expected returns.
Another reason for valuing PRA guarantees using market, rather than
expected, costs is that policy based on expected costs can lead to large eco-
nomic distortions. All else equal, expected costs of PRA guarantees are
lower the greater is the systematic risk of the PRA portfolio. Speciﬁcally,
consider two PRA portfolios having the same real return variance, but
diﬀerent systematic risk. The market costs of a PRA guarantee would be
the same for these two portfolios, but their expected costs would diﬀer. The
portfolio with greater systematic risk, and, therefore, a greater systematic
risk premium (excess expected return), would have a lower expected cost.
Thus, policy based on expected costs produces an incentive for choosing
PRA portfolios that are highly procyclical. An implication is that the gov-
ernment would face large guarantee claims following several years of eco-
nomic recession, a time when government budget deﬁcits would already be
large. Raising taxes or further increasing the government’s debt during
such a scenario would be especially painful to current and future taxpay-
ers. This incentive to amplify the magnitude of business cycles is avoided
by use of market costs.4
Related to how a PRA guarantee should be valued is the issue of how it
should be funded. Suppose that a premium that covered the cost of a PRA’s
guarantee was deducted from the account balance. Then based on the pre-
vious logic, setting premiums equal to the expected cost of the guarantee
would induce individuals to choose a portfolio with excessive systematic
risk. This moral hazard incentive is avoided by setting the premium equal
4. Other government guarantee programs that charge premiums equal to expected costs
may also be subject to moral hazard that results in excessive systematic risk. Pennacchi (2006)
describes how this distortion arises when bank deposit insurance premiums are based on ex-
pected, rather than market, costs.to the guarantee’s market cost. However, while a policy of market cost pre-
miums avoids distortions, it may be politically problematic. Charging a
premium above the guarantee’s expected cost means that the government
guarantor would proﬁt, on average, even though this proﬁt reﬂects fair
compensation to taxpayers for their exposure to systematic risk. To the ﬁ-
nancially unsophisticated, it might appear that the government is over-
charging for PRA guarantees.
A potential solution is to avoid explicit premiums but constrain PRA in-
vestment allocations along the lines proposed in Feldstein (2005). This in-
volves investing a portion of the PRA portfolio in assets that pay risk-free
real returns (TIPS) until the portfolio’s guaranteed return is obtained. Un-
der this portfolio restriction, the PRA guarantee is implicitly funded by the
PRA holder who relinquishes the potential up-side returns that would be
available from a riskier PRA portfolio.
I conclude by suggesting some extensions to the chapter’s simulation
model that might ﬁne-tune the estimates of the market cost of a PRA guar-
antee.5 In addition to stochastic security returns, I believe a model should
recognize at least two other sources of uncertainty aﬀecting PRA guaran-
tees. One is the stochastic nature of wage contributions to a worker’s PRA.
A satisfactory simulation model should include risk-neutral processes for
workers’ real wages, where these wage processes might diﬀer depending on
a worker’s age and industry.
Another potentially important source of uncertainty is the term struc-
ture of real interest rates. Figure 7C.3shows that TIPS yields have changed
Pricing Personal Account Beneﬁt Guarantees: A Simpliﬁed Approach 253
5. These extensions are detailed in Pennacchi (1999) where they are incorporated into a
model for valuing a Chilean PRA guarantee.
Fig. 7C.3 Term structures of TIPS yieldsconsiderably over the past few years. Randomness in real interest rates
aﬀects guarantee costs in at least two ways. First, they cause variation in
the risk-neutral expected returns on PRA securities, adding more ran-
domness to a worker’s PRA balance at retirement. Second, the real inter-
est rate that a worker faces at retirement aﬀects the level of annuity pay-
ments that can be purchased with his or her balance. If a PRA guarantee is
truly a guarantee of minimum annual retirement beneﬁts, rather than
simply a ﬁnal account balance guarantee, then the guarantee’s cost de-
pends on the term structure of real interest rates at the worker’s retirement
date.
A risk-neutral process for real interest rates based on the Vasicek (1977)
model can be combined with risk-neutral processes for security returns
and real wages. This can be done while assuming a general correlation
structure between these processes. Personal retirement account guarantee
costs are computed using Monte Carlo simulations of these processes for
diﬀerent worker cohorts.
References
Croushore, Dean. 1993. Introducing: The Survey of Professional Forecasters.
Business Review, Federal Reserve Bank of Philadelphia Business Review (No-
vember/December):3–13.
Feldstein, Martin. 2005. Reducing the risk of investment-based Social Security re-
form. NBER Working Paper no. 11084. Cambridge, MA: National Bureau of
Economic Research.
Merton, Robert. 1980. On estimating the expected return on the market: An ex-
ploratory investigation. Journal of Financial Economics 8:323–61.
Pennacchi, George. 1999. The value of guarantees on pension fund returns. Jour-
nal of Risk and Insurance 66:219–37.
———. 2006. Deposit insurance, bank regulation, and ﬁnancial system risks. Jour-
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Vasicek, Oldrich. 1977. An equilibrium characterization of the term structure.
Journal of Financial Economics 5:177–88.
254 Andrew Biggs, Clark Burdick, and Kent Smetters

An equilibrium characterization of the term structure.

Deposit insurance, bank regulation, and ﬁnancial system risks.

Introducing: The Survey of Professional Forecasters. Business Review, Federal Reserve Bank of Philadelphia Business Review (November/December):3–13.

On estimating the expected return on the market: An exploratory investigation.

Reducing the risk of investment-based Social Security reform.

The value of guarantees on pension fund returns.

Social Security Policy in a Changing Environment

Social Security Policy in a Changing Environment

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