Federal Reserve System ; Capital assets pricing model

Edward J. Green

Jose A. Lopez

Zhenyu Wang

English

Research Papers in Economics

Chicago Fed Letter
ESSAYS ON ISSUES THE FEDERAL RESERVE BANK JULY 2001
OF CHICAGO NUMBER 167
The Federal Reserve’s
imputed cost of equity
capital: A survey
by Edward J. Green, Jose A. Lopez, and
Zhenyu Wang
The U.S. Federal Reserve System pro-
vides services to depository financial
institutions through the twelve Feder-
al Reserve Banks. U.S. federal legisla-
tion, contained in the Monetary
Control Act of 1980, requires the Fed-
eral Reserve Banks to price their ser-
vices at a level that fully recovers their
costs. The act specifically requires im-
putation of various costs that the Fed-
eral Reserve Banks do not actually
pay, but that they would pay if they
were commercial enterprises. Promi-
nent among these imputed costs is a
cost of capital, that is, a proxy for the
cost of the debt and equity liabilities
that a commercial enterprise would
have to issue in order to finance its
assets. The Federal Reserve has com-
plied with the act by adopting an im-
putation formula for the overall cost
of capital that combines separate im-
putations of costs of debt and equity.
This Chicago Fed Letter provides a sur-
vey of the economic and statistical is-
sues in imputing a cost of equity
capital to the Reserve Banks and sug-
gests a revised approach for doing so.1
Shortly after the Monetary Control
Act was passed, the Federal Reserve
formulated a Private Sector Adjust-
ment Factor (PSAF) to quantify the
costs that must be imputed to comply
with the act. Currently, the Federal
Reserve is considering possible revi-
sion of the PSAF. The goal is to adopt
an imputation formula that will:
1. Provide a conceptually sound basis
for economically efficient pricing;
2. Be consistent with actual Reserve
Bank financial information;
3. Be consistent with economy-wide
practice, and particularly with private-
sector practice, in accounting and
applied financial economics; and
4. Be intelligible and justifiable to
the public, and replicable from in-
formation that can be obtained by
the public.
The cost of equity capital used in the
current implementation of the PSAF
is estimated from a comparable ac-
counting earnings (CAE) method.
For each holding company (HC) in
the specified peer group (currently,
the largest 50 HCs by asset size), the
estimate is calculated as the return on
equity (ROE), defined as ROE = (Net
income)/(Book value of equity). The in-
dividual ROE estimates are averaged to
determine the average HC peer group
ROE for a given year. For example, if
the values of ROE for firms in the peer
group were currently distributed uni-
formly between 15% and 25%, then
the average ROE adopted for purpos-
es of the PSAF would be 20%. A fur-
ther complication is that, in order to
smooth year-to-year fluctuations, the
CAE estimate actually used in the PSAF
for a given year is the average over the
previous five years of these firm-aver-
age ROE measures.
The CAE method has been criticized
for being “backward looking” since
past earnings may not be a good fore-
cast of expected earnings due to
cyclical changes in the economic en-
vironment. As a firm makes its way
through the business cycle, its earn-
ings may rise above or fall below the
trend line that might more accurately
reflect sustainable economic earnings.
A high ROE in the past does not nec-
essarily imply that a firm’s future
ROE will remain high. A declining
ROE might be evidence that the firm’s
new investments have offered a lower
ROE than its past investments. The
best forecast of future ROE in this
case may be lower than the most re-
cent ROE.
Therefore, one focus of efforts to
meet the criteria for a revised PSAF is
to take account of the scientific view
that financial asset prices reflect mar-
ket participants’ assessments of future
stochastic revenue streams has received
strengthened statistical corroboration
and general public acceptance. Quan-
titative models that reflect this view,
rather than the backward-looking as-
sessment implicit in the CAE method,
have come into widespread use in in-
vestment banking and also for regula-
tory rate-setting in utility industries.
We suggest an imputation formula
that would average the estimated costs
of equity capital from two such mod-
els, discounted cash flow (DCF) mod-
el and a capital asset pricing model
(CAPM), together with the estimates
from the CAE method. We show that
the proposed approach would have
provided stable and sensible estimates
of the cost of equity capital for the
PSAF over the past 18 years.
The theoretical foundation of corpo-
rate valuation is the DCF model, in
which the stock price equals the dis-
counted value of all expected future
dividends. It is difficult to project ex-
pected dividends for all future periods.
To simplify the problem, financial
economists often assume that divi-
dends grow at a constant rate, which
they estimate from accounting state-
ments. They assume that reinvest-
ment of retained earnings generates
the same return as the current ROE.
The assumption of a constant dividend
growth may lead financial analysts to
unreasonable estimates of the costpercent, estimated cost of equity capital
Note: The Treasury bill rate is aligned with the PSAF year as defined
in the text.
Source: Data provided by I/B/E/S International Inc.
1. Equity cost of capital estimates
1981 ’83 ’85 ’87 ’89 ’91 ’93 ’95 ’97
2
8
14
20
DCF
CAPM
CAE
One-year
T-Bill
Combined
of capital. However, the DCF model
with multi-stage growth gives an eco-
nomically meaningful and statistical-
ly robust estimate. We therefore
recommend the implementation of
the DCF model with multi-stage divi-
dend growth rates for the cost of eq-
uity capital used in the PSAF.
A widely accepted financial model
for estimating the cost of equity capi-
tal is the CAPM. In this model, the
cost of equity capital (or the expected
return) is determined by the system-
atic risk affecting the firm.
How much faith can we place in the
CAPM model? First, few people quar-
rel with the idea that equity investors
require some extra return for taking
on risk. Second, equity investors do
appear to be concerned principally
with those risks that they cannot
eliminate through portfolio diversifi-
cation. The CAPM captures these
risks in a simple way, which is why fi-
nance professionals find it to be the
most convenient tool with which to
grip the slippery notion of equity
risk. Given that the CAPM is readily
accepted in the private sector, we rec-
ommend that it be incorporated into
the estimation of the cost of equity
capital for the PSAF.
Although clearly related, the three
methods for calculating the HC equi-
ty cost of capital are based on differ-
ent assumptions, models, information
sets, and data sources. The question
of which method is “correct” or “most
correct” is difficult to answer directly.
We know that all models are simplifi-
cations of reality and hence misspeci-
fied, i.e., their results cannot be a
perfect measure of reality. In certain
cases, the accuracy of competing
models can be compared with ob-
servable outcomes, such as reported
HC earnings or macroeconomic an-
nouncements. However, since equity
cost of capital cannot be directly ob-
served, we cannot make clear quality
judgements among our three pro-
posed methods.
Recommendation
In light of this, we propose to calcu-
late a simple measure of HC equity
cost of capital that incorporates the
three measures. Since one measure
may contain some information not
included in the others, it might be
disadvantageous to ignore any one
of them. The practice of combining
different economic forecasts is quite
common in the academic and practi-
tioner literature; it is generally seen
as a relatively costless way of combin-
ing overlapping information sets on
an ex-post basis. We propose to com-
bine our three measures within a
given PSAF year using a simple
average; that is, ROE = [ROE(cae) +
ROE(dcf) = ROE(capm)]/3. We choose
equal weights because we do not
have a strong prior opinion about
which model provides more accurate
estimates.
The combined measure has a mean
value of 13.3% and a standard devia-
tion of 1.34%. As expected, the aver-
aging of the three ROE measures
smooths this measure over time and
creates a series with less variation than
the three individual series (see figure
1). Individual differences between the
combined and the individual mea-
sures range between +5% and –5%
over this historical period; however,
the average differences are less than
2% and cannot be said to be statisti-
cally different from zero. Note also
that the deviations between the DCF
and CAPM measures from the one-
year risk-free rate (measured by the
interest rate on a Treasury bill) are
not as large as for the CAE measure
due to their greater
sensitivity to general
market and economic
conditions. This prop-
erty is obviously passed
on to the combined
ROE measure through
the averaging.
Our analysis assumes
that calculation of the
Reserve Banks’ cost of
capital would contin-
ue to be based on the
largest 50 HCs. This
choice was made, and
will likely continue to
be made, despite the
knowledge that the
services provided by Federal Reserve
Banks are only a segment of the lines
of business in which these HCs en-
gage. Some of these lines of business
(such as lending to firms in particu-
larly volatile segments of the econo-
my) intuitively seem riskier than the
financial services that the Federal Re-
serve Banks provide. Moreover, there
are differences among the HCs in
the mix of activities in which they en-
gage. These observations raise three
related conceptual issues that we dis-
cuss below.
Three conceptual issues
The first conceptual issue regarding
the HC sample is that the cost of a
firm’s equity capital should depend
on the firm’s lines of business and on
its debt–equity ratio. A firm engaged
in more risky activities (or, more pre-
cisely, in activities having risks with
higher correlation to the overall risk
in the economy) should have a high-
er cost of capital. There is some indi-
rect, but perhaps suggestive, evidence
that the Federal Reserve Banks’ busi-
ness activities may be less risky, on
the whole, than some business lines
of the largest HCs. Notably, the Fed-
eral Deposit Insurance Corporation
has a formula for a risk-weighted cap-
ital/asset ratio. According to this for-
mula, the collective risk-weighted
capital/asset ratio of the Federal Re-
serve Banks would currently be 30.8%.
This ratio is substantially above the
average ratio in the HC sample.Michael H. Moskow, President; William C. Hunter,
Senior Vice President and Director of Research;  Douglas
Evanoff, Vice President, financial studies; Charles
Evans, Vice President, macroeconomic policy research;
Daniel Sullivan, Vice President, microeconomic policy
research;  William Testa, Vice President, regional
programs and Economics Editor; Helen O’D. Koshy,
Editor; Kathryn Moran, Associate Editor.
Chicago Fed Letter is published monthly by the
Research Department of the Federal Reserve
Bank of Chicago.  The views expressed are the
authors’ and are not necessarily those of the
Federal Reserve Bank of Chicago or the Federal
Reserve System. Articles may be reprinted if the
source is credited and the Research Department is
provided with copies of the reprints.
Chicago Fed Letter is available without charge from
the Public Information Center, Federal Reserve
Bank of Chicago, P.O. Box 834, Chicago, Illinois
60690-0834, tel. 312-322-5111 or fax 312-322-5515.
Chicago Fed Letter  and other Bank publications are
available on the World Wide Web at http://
www.chicagofed.org.
ISSN 0895-0164
A firm with a higher debt–equity ra-
tio should have a higher cost of equity
capital, other things being equal, be-
cause there is risk to equity holders
in the requirement to make a larger,
fixed payment to bondholders regard-
less of the random profit level of the
firm. The imputed debt–equity ratio
of the Federal Reserve Banks might
not equal the average ratio for the
HCs, if the imputed ratio were to be
based on regulatory requirements
rather than directly on the HC sam-
ple average. Such a difference would
also lead to different conclusions on
the imputed equity cost of capital of
the Federal Reserve Banks.
The second conceptual issue is how
to weight the 50 HCs in the peer
group sample in defining their aver-
age cost of equity capital. Currently,
the PSAF is calculated using an equal-
ly weighted average of the HCs’ costs
of equity capital according to the CAE
method. An obvious alternative would
be to take a value-weighted average,
i.e., multiply each HC’s cost of equity
capital by its stock market valuation,
and then divide the sum of these
weighted costs by the total market
valuation of the entire sample. Other
alternatives, such as weighting the
HCs according to the ratio between
their balances due to other banks
and their total assets could conceiv-
ably be adopted.
Equal weighting was originally adopt-
ed to mitigate defects of measurement
in the CAE method. Those grounds
do not apply with much force to the
DCF and CAPM methods. In fact, val-
ue-weighted averaging is the stan-
dard procedure in studies using these
methods. If an average of several esti-
mates of equity cost of capital were to
be adopted for the PSAF, there would
not be any serious problem with using
equal weighting to compute a CAE
estimate, where that weighting scheme
does some good, while using value
weighting to compute DCF and CAPM
estimates if value weighting would be
preferable on other grounds. We rec-
ommend such a mixed procedure.
A final issue worthy of attention is that
the equity cost of capital estimated
via the CAPM method for some of
the very largest HCs increased sub-
stantially in the mid-1990s due to in-
creases in their sensitivity to market
risk. Those increases might be sus-
pected to be results of measurement
error, and of course equal weighting
would help to minimize them. How-
ever, an estimate of equity capital
costs will be more credible if it is
based on a weighting scheme that
has been chosen ex ante on grounds
of conceptual appropriateness, rath-
er than on one that has been chosen
with a view toward minimizing the
influence of data that has already
been observed.  The recommenda-
tion to average several measurements
of equity costs of capital is based on
the idea that each method will be sub-
ject to some error, and that averag-
ing across methods will diminish its
influence. That is exactly what will
happen if a value-weighted CAPM
measure is averaged with two other
measures that do not exhibit such
marked differences between the very
largest HCs and the other HCs in the
peer group (i.e., all of the fifty larg-
est ones) on which the PSAF is
based.
To summarize, we propose a calcula-
tion of the PSAF cost of capital that
would average the result of the cur-
rent method (CAE) with those of
two methods (DCF and CAPM) that
are recommended by current theory
and practice in financial economics.
This proposal would help to achieve
four goals that the Federal Reserve
has articulated. Notably it would help
to provide a conceptually sound ba-
sis for economically efficient pricing,
and this basis would be consistent
with academic and private-sector
practice. Nevertheless some issues
remain. These issues have to do with
the inevitable situation that the Re-
serve Banks’ lines of business do not
correspond exactly to those of finan-
cial holding companies or other com-
mercial firms.
Note: Edward J. Green is a senior policy
adviser at the Federal Reserve Bank of
Chicago. Jose A. Lopez is an economist in
the Banking and Regional Studies Sec-
tion of the Federal Reserve Bank of San
Francisco. Zhenyu Wang is an associate pro-
fessor of finance and economics at the
Graduate School of Business of Columbia
University.
1This article is condensed from the au-
thors’ paper, “The Federal Reserve Banks’
imputed cost of equity capital,” issued as
Federal Reserve Bank of San Francisco,
working paper, No. 2001-01, to which
readers are referred for a detailed treat-
ment of the issues surveyed here. The
paper is also available on the Web at
www.frbsf.org/publications/economics/
papers/2001/wp01-01.pdf. Zhenyu Wang
worked on this project as a staff member
at the Federal Reserve Bank of New York
and a consultant to the Federal Reserve
Bank of Boston. The authors are grateful
to the members of the 2000 PSAF Funda-
mental Review Group, Paul Bennett, Eli
Brewer, Simon Kwan, and Hamid Mehran
for valuable comments and helpful discus-
sions. The authors thank Adam Kolasinski
and Ryan Stever for carrying out the
many calculations needed for this study
and for contributing to the technical ap-
pendix. The authors also gratefully ac-
knowledge I/B/E/S International Inc.
for providing earnings per share forecast
data, available through the Institutional
Brokers Estimate System, to Martin Hau-
gen for providing the historical PSAF
numbers, and to Eli Brewer for providing
data on mergers of bank holding compa-
nies during the sample period.1998 1999 2000 2001
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Sources: The Chicago Fed Midwest Manufactur-
ing Index (CFMMI) is a composite index of 16
industries, based on monthly hours worked and
kilowatt hours. IP represents the Federal Reserve
Board’s Industrial Production Index for the U.S.
manufacturing sector. Autos and light trucks are
measured in annualized units, using seasonal ad-
justments developed by the Board. The purchas-
ing managers’ survey data for the Midwest are
weighted averages of the seasonally adjusted pro-
duction components from the Chicago, Detroit,
and Milwaukee Purchasing Managers’ Association
surveys, with assistance from Kingsbury Interna-
tional, LTD., Comerica, and the University of
Wisconsin–Milwaukee.
Auto production was at 5.1 million units in both March and April; while light
truck production increased from 6.0 million units in March to 6.3 million
units in April. The CFMMI fell 2.2% from March to April, reaching a season-
ally adjusted level of 157.3 (1992=100). Revised data show the index was at
160.9 in March and had fallen 0.5% from February. The Federal Reserve
Board’s IP for manufacturing fell 0.3% in April after falling 0.2% in March.
The Midwest purchasing managers’ composite index for production in-
creased to 43.8% in May from 40.5% in April. The purchasing mangers’ in-
dex increased in Chicago, Milwaukee, and Detroit, with the largest increase in
Detroit. By comparison, the national purchasing managers’ survey edged
down from 42.9% to 42.7%.
Motor vehicle production (millions, seasonally adj. annual rate)
Purchasing managers’ surveys:
net % reporting production growth
May Month ago Year ago
MW 43.8 40.5 55.1
U.S. 42.7 42.9 56.3
Motor vehicle production
(millions, seasonally adj. annual rate)
Apr. Month ago Year ago
Cars 5.1 5.1 5.8
Light trucks 6.3 6.0 7.1
Cars
Light trucks
Manufacturing output indexes
(1992=100)
Apr. Month ago Year ago
CFMMI 157.3 160.9 167.0
IP 149.8 150.3 152.2
Tracking Midwest manufacturing activity

The Federal Reserve's imputed cost of equity capital: a survey

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The Federal Reserve's imputed cost of equity capital: a survey

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