Required rate of return
• When valuing assets and firms, we need to use discount rates
that reflect the riskiness of the cash flows.
What is risk?
• In finance, it refers to the likelihood that we will receive a
return on an investment that is different from the return that
we expect to make
• Measured based on standard deviations of actual returns on
an investment from its expected return.
Two types of risk
• Equity risk – arises in investments where there are no
promised cash flows, but there are expected cash flows
• Default risk – arises in investments with promised cash flows
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Equity risk
– Best measured by looking at the variance of actual returns
around the expected returns. The greater the variance, the
greater the risk.
– Can be broken down into
• Firm-specific risk
– Also called idiosyncratic risk, asset-specific risk, diversifiable risk
– Risk that affects one or a few investments
– Can be diversified away so that investors are not rewarded for bearing this
risk
• Market risk
– Also called systematic risk
– Risk that affects many investments
– Cannot be diversified away so that investors expect to be rewarded for
bearing this risk. So how do we know how much “reward” to expect?
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Expected return models
The models described below attempt to relate equity risk to expected return.
Note that from the firm’s perspective, this expected return represents the
cost of equity.
Capital Asset Pricing Model (CAPM)
– All the market risk is captured in one beta measured relative to a market
portfolio, which, in theory should include all traded assets held in proportion
to their market value. The expected return on an asset can be written as
E  Ri   R f  i  E  Rm   R f 
Arbitrage Pricing Model (APM)
– Allows for multiple unspecified sources of marketwide risk. The expected
return on an asset can be written as
E  R   R f  1  E  R1   R f    2  E  R2   R f  
  K  E  RK   R f 
– where the subscripts 1 to K represent different sources (factors) of market risk.
The number of factors, the factor betas, and the factor risk premiums can all
be estimated using factor analysis.
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Multifactor Models
– Unlike the APM, multifactor models do attempt to identify the market factors
that drive market risk. For example, Chen, Roll and Ross (1986) identified
industrial production, changes in default premium, shifts in the term
structure, unanticipated inflation, and changes in the real rate of return to be
highly correlated with the factors that come out of factor analysis.
– However, the economic factors in the model can change over time, as will the
risk premium associated with each one. Using the wrong factor or missing a
significant factor can lead to inferior estimates of expected return.
Other models
– Some models (e.g. Fama and French, 1992) look for firm characteristics such
as size, that have been correlated with high returns in the past and use these
to measure market risk.
– The Fama-French (1993) three-factor model specify risk factors, in addition to
market risk, that explain the return on stocks
Ri  R f    1  Rm  R f    2 SMB   3 HML  
Where SMB is the excess returns on small stocks from big stocks and HML is
the excess returns on stocks witsh high book-to-market ratios over stocks with
low book-to-market ratios.
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More on the CAPM
– The CAPM is still the model for equity risk that is used in real-world
applications.
– To use the CAPM, we need three inputs
• The riskless asset
– For an asset to be riskless, it must be default-free and there must be no
reinvestment risk. Zero-coupon bonds (e.g. US Treasury STRIPS) meet this
criteria.
– The maturity of the riskless asset has to match the time period over which
you are projecting cash flows. Thus, yields on longer term treasury bonds
would be more appropriate than yields on treasury bills.
– When estimating cash flows in another currency, you have to use the risk-free
rate in that currency.
• The risk premium
– There are different ways to measure the risk premium. Some of them are: 1)
using historical risk premiums to estimate future risk premiums; 2) using
regression analysis to link current market variables, such as the aggregate
dividend-to-price ratio, to project the expected market risk premium; 3) using
DCF valuation, along with estimates of return on investment and growth, to
reverse engineer the market’s cost of capital
– The risk premium will be estimated for us by the portfolio managers
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• Beta
– There are three approaches to estimating beta: 1) accounting
approach, 2) using historical market betas, 3) using fundamental
betas. The accounting approach is almost never used in practice.
– Historical market betas
–
–
–
The conventional approach for estimating the beta of an investment
is a regression of returns on the investment against returns on a
market index such as: Ri  a  bRm , where the coefficient estimate
for b corresponds to the beta for the stock.
However, regression betas will almost always be either too noisy
(i.e., large standard errors) or skewed (i.e., biased) by estimation
choices (such as the time period of estimation, the return interval
(daily, weekly, etc), and the choice of market index to use) to be
useful measures of the equity risk in a company.
Service betas (such as those obtained from Bloomberg,
Morningstar, Standard & Poor’s, etc) are estimated using the
methodology just described, and make adjustments for what they
feel are better estimates of future risk.
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– Fundamental betas (which we will also call the bottom-up
approach)
– This approach estimates betas by looking at the fundamentals of the
business. According to this approach, the beta of a firm is
determined by: 1) the type of business or businesses the firm is in, 2)
the degree of operating leverage of the firm, 3) the firm’s financial
leverage.
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Default risk
– The risk associated with investments with promised cash
flows (e.g., bonds), is default risk – i.e., that the borrower
will not be able to repay interest and principal.
– Default risk is a function of two variables: the firm’s
capacity to generate cash flows from its operations, and,
its financial obligations.
– Most models of default risk use financial ratios to measure
the cash flow coverage (magnitude of the cash flows
relative to the obligation) and control for industry effects
in order to evaluate the variability of the cash flows.
– The most widely used measure of a firm’s default risk is its
bond rating.
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Estimating the default risk and the default spread
– The cost of debt for a company is primarily determined by its
default risk, in addition to the risk-free rate (the higher the riskfree rate is, the higher is the cost of debt) and the tax advantage
associated with debt (the higher is the firm’s marginal tax rate,
the greater the tax benefits associated with debt).
– The easiest way to estimate the cost of debt is when a firm has
long-term bonds outstanding that are widely traded. We can
simply calculate the yield-to-maturity on these outstanding
bonds.
– However, most corporate bonds are not actively traded. In this
case, we can get the ratings on the bonds (e.g. AAA, etc), and
find the corresponding default spread.
– A third way is to estimate synthetic ratings using financial ratios.
– In the last two cases, we add the default spread to the risk-free
rate to arrive at an estimate of the firm’s cost of debt.
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Hybrid securities
– Preferred stock – shares some of the characteristics of
debt (the dividend is prespecified at the time of issue and
is paid out before common dividends) and some of the
characteristics of equity (the preferred dividend is not tax
deductible). (see Illustration 8.13 on p. 213 for an example)
– Convertible bond – a bond that can be converted into
equity at the option of the bondholder. We usually break
down these securities into their debt and equity
components and assign the cost of debt and equity to each
component. (see Illustration 8.14 on p. 213 for an
example)
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Estimating the cost of capital (WACC)
– Thus far we have calculated the costs of a firm’s different
sources of capital. Most firms will usually have a mix of the
different components of capital.
– To calculate the WACC, we need to weight each
component (i.e. debt, equity, etc) by its market value and
sum across the weighted components, that is,
WACC  ke we  k d wd 1  t   k p w p
– Estimating market values of debt and equity
• The market value of equity is straightforward, we multiply the
stock price by the number of shares outstanding.
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• The market value of debt is usually a little more difficult
to obtain.
– First we consider only interest-bearing debt (that is, we do not
count accounts payable and other supplier credit)
– A simple way would be to use the book value since, unlike
equity, this typically does not diverge greatly from market
value.
– Another way is to treat the entire debt on the books as one
coupon bond, with a coupon set equal to the interest
expenses on all the debt, and the maturity set equal to the
face-value weighted average maturity of the debt, and then to
value this coupon bond at the current cost of debt for the
company. (see Illustration 8.16 on p. 216)
– We also have to capitalize operating leases and count that as
debt. We do this by getting the present value of operating
lease commitments in future years (these can be found in the
footnotes to the financial statements), using the firm’s pretax
cost of debt.
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• Sources:
– Damodaran, Investment Valuation, 2nd ed.
– McKinsey & Company, Koller, Goedhardt, and Wessels, Valuation:
Measuring and managing the value of companies, 5th ed.
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