Expected Return
Capital Asset Pricing
Model (CAPM)
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What should be ABC’s share
price?
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ABC’s share price
ABC Inc. is expected to pay a liquidating (i.e.,
terminal) dividend of $112 per share one year
from today.
The required risk premium for the stock is
7%.
The risk free rate of return is 5%
The Expected Return
Significance of the expected return:
The required return helps determine asset
values.
A fundamental question in finance: How do
we determine the expected return of an
asset?
Based on risk?
How do we measure the risk?
What is the appropriate expected return for a
given level of risk?
These questions are addressed by asset
pricing models.
Price = ?
Capital Budgeting
„
Determining the expected (or required) rate of
return is necessary for evaluating projects
„ forecast cash flows
„ discount cash flows at the required rate of
return
„ calculate the NPV of the project
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Systematic Risk
Total Risk
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The total risk of an individual stock has two
components
___________________
___________________
ƒ For instance,
ƒ There could be a war
ƒ There could be an economic recession
ƒ There could be a foreign economic crisis
ƒ These are all examples of risk faced by the
entire market, and are part of our economic
system.
ƒ This is called systematic risk. It cannot be
eliminated.
Unsystematic Risk
ƒ For instance,
ƒ A firm might go bankrupt
ƒ A firm might get sued
ƒ A firm in a particular industry might be the
Systematic and Unsystematic
Risk
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target of new regulations
ƒ These are all examples of firm-specific risk,
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also called unsystematic risk.
ƒ Holding a well-diversified portfolio eliminates
Unsystematic risk of individual assets can be
eliminated by holding a diversified portfolio,
such as the market portfolio. This risk does
not add to the total risk of the portfolio, and
therefore should not be compensated
The systematic risk of individual assets
cannot be eliminated, and therefore should
be appropriate risk measure.
firm-specific risk.
Which is the Appropriate
Measure of Risk?
ƒ Standard deviation of an asset's rate of return
is a useful measure of its stand-alone risk
ƒ It is not an appropriate measure of the asset's
risk when it is part of a portfolio.
ƒ Because investors care about the return
and risk of their entire portfolios, and not
the return and risk of individual asset per
se.
CAPM
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Risk premium on the market depends on the
average risk aversion of all market
participants
Risk premium on an individual security is a
function of its covariance with the market
portfolio
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Risk Premium of the Market
Portfolio
y = (E ( rM ) − r f ) A σ M2
Measuring Systematic Risk
♦ Our measure of systematic risk is called beta,
and is defined as the covariance between the
return of a stock and the return on the market
portfolio, divided by the variance of the return
on the market portfolio:
y = 1 ⇒ E ( rM ) − r f = A σ M2
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The risk premium of the market portfolio is
proportional to the average risk aversion
across all investors and the risk of the market
portfolio, which is measured by the variance
of the market returns.
βi =
The Capital Asset Pricing
Model
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In equilibrium, the market price of the risk
should be equal between individual risky
asset and the market portfolio.
E (ri ) − r f
Cov (ri , rm )
=
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The expected return on any asset can be
written as:
E(R i ) − R f = β i ⋅ (E(R m ) − R f )
Var (rM )
excess return or risk premium
Cov (R i , R m )
where β i =
2
Cov (ri , rm )
(E (rM ) − rf )
Var (rM )
Intuition
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The Capital Asset Pricing
Model
E (rM ) − r f
⇒ E (ri ) − r f =
Intuition
Marginal utility in good states and bad states
High beta Æ high risk Æ high expected return
Æ low price
Cov (Ri , Rm )
Var (Rm )
σm
An Example
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The expected market return is 12%. The risk
free rate is 6%. What is the expected return of
a stock with a beta of 0.8?
E(R)=___________________________
What is the expected return of a stock with a
beta of 1? What is the expected return of a
stock with a beta of 0? (no calculation
needed)
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CAPM
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All investors will hold the same portfolio for
risky assets – market portfolio.
Market portfolio contains all securities and the
proportion of each security is its market value
as a percentage of total market value.
How to Estimate Beta
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We estimate beta using Ordinary Least
Squares regression of the CAPM equation,
where returns are expressed in excess return
form:
Ri = R f + β i RM − R f + ei
(R − R ) = β (R
i
f
i
M
(
− R f ) + ei
)
Y = βX + ei
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How to Estimate Beta
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where ei is an error term which reflects firmspecific risk not being captured by beta.
Data Analysis
Compute the excess returns of the stock
Compute the excess returns of the market
porfolio (proxied by S&P 500 Index)
Regress excess returns of the stock on the
excess returns of the S&P 500 index
The regression coefficient on the S&P 500
index excess returns is the beta of the stock
Regression
Regression
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Regression
Regression
Linear Regression
Security Characteristic line
Excess Return on Asset
Characteristic Line
Distance from the line to the
points are the error terms.
Stock Returns
Beta for the firm is the
slope of this line.
Jensen Alpha for the firm
is the intercept of this line.
Excess Return on Market
Market Returns
The Security Market Line
Security Market Line
Expected Return
Underpriced Securities
Implications for Active
Portfolio Strategy
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Alpha is the difference between the average
stock return and the CAPM expected return
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Invest in stocks that are underpriced, or have
positive alpha, which is determined from the
asset pricing model, such as the CAPM.
- alpha
E(Market Return)
B
A
Overpriced Securities
Risk-free Return
+ alpha
Beta of the Market = 1.00
Beta
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Multi-factor Asset Pricing
Models
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The Capital asset pricing model (CAPM)
stipulates that there is only one risk factor,
that is, the return on the market portfolio.
So the cross-sectional variations in expected
returns should be explained by assets’ beta.
„ High beta Î high expected return
„ Low beta Î low expected return
Multi-factor Asset Pricing
Models
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Macroeconomic-based risk factor models
„ Based on fundamental risks such as
inflation, interest rates and industrial
production
Characteristic-based risk factor models
„ The premise is that returns on stocks with
certain characteristics are proxies for
fundamental risks
Macroeconomic Models
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Burmeister, Roll, and Ross (1994)
„ Confidence risk
„ Time horizon risk
„ Inflation risk
„ Business cycle risk
„ Market timing risk
Multi-factor Asset Pricing
Models
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In practice, CAPM does not perform well
„ One-factor model is too restrictive
„ Poor proxy for market portfolio
An alternative approach is to use a multifactor model (analogy, E.g., predicting a
person’s weight)
„ What are the factors that affect expected
returns?
Macroeconomic Models
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Chen, Roll, and Ross (1986)
„ Market return
„ Monthly growth rate in industrial production
„ Change in inflation
„ Difference between expected and actual
inflation
„ Unanticipated change in credit spread
„ Unanticipated change in term spread
Characteristic-based Models
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Fama and French (1993) three-factor model
„ Market return
„ SMB, the return to a portfolio of small cap
stocks less the return to a portfolio of large
cap stocks
„ HML, the return to a portfolio of stocks with
high book-to-market ratios less the return
to a portfolio of low book-to-market stocks
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Fama-French Three-factor
Model
BARRA
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CAPM :
Ri − R f = α + bi (Rm − R f ) + ei
Fama − French
Ri − R f = α + bi (Rm − R f ) + s i SMB + hi HML + ei
BARRA characteristic-based risk factors (13)
„ volatility, momentum, size, size
nonlinearity, trading activity, growth,
earnings yield, value, earnings variability,
leverage, currency sensitivity, dividend
yield, nonestimation indicator
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