FRBSF Economic Letter
2006-06; April 7, 2006
What Is the Federal Reserve Banks' Imputed Cost of Equity Capital?
The Federal Reserve System is an important participant in the
nation's payments system, which is the infrastructure used for
transmitting and settling payments between individuals, firms,
and government entities. For example, as reported in the Federal
Reserve System's 2004 annual report, the twelve Federal Reserve
Banks processed about 16 billion checks, or about 45%, of the
37 billion checks written in 2003. In addition, the Federal Reserve
provides fully electronic payments services, such as automated
clearing house services. Since the Federal Reserve is required
to charge fees for these services, they are known collectively
as "priced services." Private sector firms, including
some large banking organizations, also provide certain of these
priced services, such as check processing.
To promote efficiency and competition in the national payments
system for these priced services, Congress passed the Monetary
Control Act (MCA) of 1980, which requires the Federal Reserve
Banks to set fees that, over the long run, recover all the
direct and indirect costs of providing those services. In addition,
the MCA requires that those fees recover imputed costs, such
as taxes and a cost of capital, that would be incurred if the
services were provided by a private firm. These imputed costs
are known collectively within the Federal Reserve System as
the
private sector adjustment factor (PSAF).
The methodology underlying the computation of the PSAF is reviewed
periodically to ensure that it is appropriate and relevant
in light of Reserve Banks' price services activities as well
as
current accounting standards, finance theory, and regulatory
and business practices. Such a review was conducted and changes
implemented in 2005 starting with the 2006 PSAF calculations;
see Board of Governors (2005). In this Economic Letter, we
focus specifically on the current decision to set the Reserve
Banks'
imputed cost of equity equal to that of the overall stock
market. Our research shows that while many other methods exist
for
calculating this cost of equity measure, the choice made
by the Federal Reserve
is quite reasonable.
Previous methodology
A firm's cost of capital is the weighted average of its cost
of raising debt financing and the cost of issuing equity
to shareholders. However, recent reviews of the PSAF
methodology have focused
only on how to calculate the cost of equity capital.
The previous
methodology for calculating the Federal Reserve Banks'
imputed cost of equity capital was a simple average of
three different
estimation methods; see Green et al. (2003) for more
details. All three estimation methods assumed that the relevant
peer group of firms for the Reserve Banks' priced services
business
consisted
of large, publicly traded bank holding companies (BHCs).
These firms historically have been active participants
in the payments
system, for example, through the retail deposit and checking
accounts they commonly provide.
The first method, known as the comparable accounting
earnings (CAE) method assumes that a firm's cost of
equity capital
(COE) is the ratio of the net income generated by its
assets to the
book value of its equity. In essence, this ratio gauges
the value generated by the firm's equity and sets that
ratio
as the COE
at which the firm could fund itself in the equity markets.
An important shortcoming of the CAE method is that
it relies on
purely historical accounting data, which makes it "backward
looking" relative to methods based on market prices.
The second method is known as the discounted cashflow
(DCF) method, which is based on the insight that today's
stock
price equals
the present discounted value of a firm's expected future
dividends. Forecasts of near-term dividends and long-term
dividend growth
rates are commonly generated by equity analysts and
were used in generating this measure. For the PSAF
calculations,
these
COE measures were calculated for the peer group BHCs
and then weighted according to their market capitalization
to generate
the sample's COE.
The third method is derived from the well-known capital
asset pricing model (CAPM) commonly used for analyzing
stock returns.
This method is forward-looking since it is based on
stock market prices, which incorporate equity investors'
expectations
of
firms' future earnings. The intuition behind this method
is that a firm's
COE should equal the sum of the return that it provides
relative to a diversified stock portfolio, such as
the entire stock
market, and the risk-free rate of return, usually the
Treasury rate.
For this method, a stock portfolio consisting of the
peer group BHCs' stocks weighted according to their
market capitalizations
at the end of a year is constructed. This portfolio's
historical correlation with the overall stock market,
commonly known
as
the portfolio's beta parameter, is estimated. The peer
group's COE is then calculated as the sum of the risk-free
Treasury
rate plus the product of the portfolio beta and the
overall stock
market's historical equity premium (i.e., the market
return minus the risk-free Treasury rate).
The question of which method is "correct" for the
purposes of the Federal Reserve's payments services is difficult,
if not
impossible, to answer definitively. All of these approaches
are models that simplify reality and hence are incomplete in
some
way. In certain cases, the accuracy of competing models
can be gauged with respect to observable outcomes. However, since
the
cost of equity capital for the Federal Reserve's payments
services cannot be directly observed, clear quality judgements
among the
three methods were not possible. In light of this difficulty,
Green et al. (2003) included all of the measures in
their proposed COE calculation by taking a simple average of
the three, which
is a common practice in the academic and practitioner
literature on combining multiple possible responses.
Current methodology
The PSAF review process conducted in 2005 examined
several elements of the methodology and reached
two key conclusions
that were
adopted into the methodology starting with the
2006 calculations. First, it was decided to use only the
CAPM model in the
COE calculations, as this model is the one most
widely used in
financial practice;
see Graham and Harvey (2001) for a survey.
Second, it was decided that it had become too challenging
to choose an appropriate peer group for estimating
the beta parameter
needed for the CAPM estimates, because BHCs have
expanded into businesses less related to payments
services.
Therefore, the
Federal Reserve chose not to select a group of
BHCs as peers but instead to compare itself to
all publicly
traded
firms.
This choice was implemented assuming that the
beta for the Reserve
Banks' priced services is simply one—that is,
identical to the broad stock market return. The
reasons given
for this assumption
are that it is simple to understand, administer,
and monitor, while it provides reasonable results
from
a comparative
and historical
perspective.
Alternative estimation methodologies At first glance, it might seem questionable to
assume that the Federal Reserve Banks' beta
is simply equal
to the
broad stock
market return. For example, by collecting
enough additional information, it might be possible
to measure the beta
more precisely. Indeed,
academic researchers have suggested a variety
of approaches that attempt to take advantage
of such
additional information.
Barnes
and Lopez (2006) explore this issue by examining
the impact of several of these methods on
the Federal Reserve
Banks'
COE estimates,
three of which are highlighted here.
In the first alternative, the authors examined
several peer groups, from the broadest
BHC peer group previously
used
(namely, the
top 50 publicly traded BHCs sorted by total
deposits) to a narrow set of four BHCs
that specialize
in payments services
(although
not exactly the same services as the Reserve
Banks). Using simple regression analyses,
the authors found
that crafting
smaller
and potentially more focused BHC peer groups
did not generate beta and COE estimates
that were significantly
different
from
the broadest peer group. Hence, incorporating
this additional peer group information
does not enhance
the COE estimates.
The second alternative incorporated additional
BHC information directly into the CAPM
model, specifically the revenues
generated by their payments services
as a share of
total BHC revenues.
Payments revenues are not a clearly defined
accounting category, so the authors used
the definitions
proposed by Radecki (1999)
as well as by Rice and Stanton (2003).
These definitions focused on service
charges on
deposit accounts
(such as overdraft fees),
interest forgone by customers for access
to payments accounts, and credit card
revenues related to
payments (such as annual
fees). In theory, COE estimates for the
Reserve Banks' priced services business
might be
refined
by incorporating
such
information into the CAPM estimation.
However, the results suggested that
the estimated beta and COE estimates
were not materially different from those ignoring
payments
revenues.
Again, additional, potentially
useful information was found empirically
not to be useful for this application.
The third alternative incorporated the
peer group's leverage ratio into the
beta and
COE estimates.
The leverage ratio
for the peer group BHCs was defined
as the book value ratio of
total debt (excluding deposits) to
total equity. Finance theory argues
that beta estimates should reflect
leverage, because the stock prices of more leveraged
firms should
be more sensitive
to
overall market fluctuations. In their
empirical work, the authors found
that accounting for leverage again
did not generate COE estimates that were
statistically different
from those
that ignored
this information.
In summary, Barnes and Lopez (2006)
showed empirically that many potential
refinements
of the standard
CAPM estimation method
for COE estimates do not add value
for the PSAF calculations. They found
that
a standard
implementation
of the
benchmark CAPM model using a large
BHC peer group provides a
reasonable COE
estimate, which is needed to impute
costs and set prices for the Reserve
Banks'
payments business. Since the
average beta
calculated in this way over the years
1981 to 2003
is 1.06, setting the relevant CAPM
beta to one seems to
be a reasonable
choice.
Conclusion
The academic literature clearly shows
that estimating a firm's cost
of equity capital
is a difficult
theoretical and empirical
challenge. However, such estimates
are required for a number
of operational processes and
decisions by firms. The case of interest
here is the Federal
Reserve
Banks'
need for
an imputed
COE estimate for their priced
services business to meet the requirements
of the Monetary
Control Act.
Recent
research suggests that the
Federal Reserve's decision to
set the COE estimate equal to that
of the overall
equity
market
(that is, to set
their beta
equal
to one) is a reasonable and simple
solution to this challenging problem. Michelle L. Barnes
Senior Economist, FRB Boston
Jose A. Lopez
Senior Economist, FRBSF
References
Barnes, M.L., and J.A. Lopez. 2006. "Alternative Measures
of the Federal Reserve Banks' Cost of Equity Capital." Journal
of Banking and Finance, forthcoming.
Board of Governors of the Federal Reserve System. 2005. "Board
Announces Modifications to Methodology used to Calculate
the Private Sector Adjustment Factor." Press
release, October 12.
Graham, J.R., and C.R. Harvey. 2001. "The Theory and
Practice of Corporate Finance: Evidence from the Field." Journal
of Financial Economics 60, pp. 187-243.
Green, E.J., J.A. Lopez, and Z. Wang. 2003. "Formulating
the Imputed Cost of Equity Capital for Priced Services
at Federal Reserve Banks." FRB New York Economic
Policy Review 9, pp. 55-81.
Radecki, L. 1999. "Banks' Payments-Driven Revenues." FRB
New York Economic Policy Review 4(2), pp. 53-70.
Rice, T., and K. Stanton. 2003. "Estimating the Volume
of Payments-Driven Revenues." FRB Chicago Working
paper #S&R-2003-1C.
Opinions expressed in this newsletter
do not necessarily reflect the views of the management
of the Federal Reserve Bank of San Francisco or of the
Board of Governors of the Federal Reserve System. Comments?
Questions? Contact
us via e-mail or write us at:
Research Department
Federal Reserve Bank of San Francisco
P.O. Box 7702
San Francisco, CA 94120
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