Chapter 13
Capital Asset Pricing Theory
Learning Objectives
 Capital market line (CML)
 Capital Asset Pricing Model (CAPM)
 Beta compared to Standard Deviation
 Applying CAPM to security analysis
 Estimating Beta
 Beta - good news and bad news
Capital Asset Pricing Model (CAPM)
 Equation that quantifies security risk and defines a risk/return
relationship
 Based on the idea that investors accept a higher risk only for a
higher return
 Other assumptions are not realistic, but necessary to develop the
model
Assumptions of the CAPM
 Investors have equal information and perceptions, leading to
equal expectations
 Frictionless capital markets
No transaction costs
No taxes
Portfolios may be divided among securities in any proportion for
optimization
 Investors are rational and seek to maximize their expected utility
functions
 All investment is for the same time period
 All investors can borrow or lend at the risk-free rate
Efficient Frontier and
the Optimal Risky Portfolio
 The efficient frontier is a series of portfolios representing the
highest return for a given level of risk or the lowest risk for a given
expected return
 Any individual security will lie inside the efficient frontier, but
may be a part of portfolios on the efficient frontier
 Choosing the optimal efficient frontier depends on individual
preferences for risk and return
 Measuring risk aversion and utility curves still won’t provide an
objective portfolio choice
Developing the Capital Market Line (CML)
ERp = (X) ERp1 + (1 - X) RF
SDP = (X) SDP1
Combinations of risk-free assets and risky portfolios can be used to
create portfolios along a line connecting the apex of the efficient
frontier and the risk-free rate
The Capital Market Line (CML)
 Describes the percentage holdings in the risk free asset and the
risky diversified market portfolio, surpassing the efficient frontier
except at the point of intersection
 Utility curves may cross the CML, indicating appropriate
portfolio selections
 Borrowing-lending line is the CML, divided where it intersects
the efficient frontier (point M) with the lending line on the left and
borrowing on the right
 Portfolio separation theorem allows investors to separate the
decision of selecting the risky portfolio from the investor’s risk
preference
Market Portfolio
The Market Portfolio (point M) must be the only risky portfolio
chosen by all risk-averse investors. Because it is demanded by
all investors, it must contain all the securities and other traded
assets
Capital Asset Pricing Model
 Portfolio M’s risk = Market risk
 Security risk = total risk
 Security risk = Market risk + firm-specific risk
 Portfolio M’s risk = (Security 1’s market risk + Security 2’s
market risk + … + Security N’s market risk)
Relative Risk
 Relative risk contribution of security i
Total risk contribution of security i divided by Total risk of market
portfolio, M
 Known as beta, , it measures security risk, or volatility relative
to the market portfolio
 Beta greater than 1.0 is riskier than the market
Understanding Beta
 All security beta’s are measured relative to the market portfolio
beta, which equals 1.0
 A beta greater than 1.0 means the security contributes more than
the average risk to the well-diversified market portfolio
 The value of beta implies something about returns relative to the
market
 The index used to approximate the market portfolio can affect the
beta estimate
Risk recap
 Market risk
 Firm-specific risk
 Security’s total risk is market risk plus firm-specific risk
 Relative market risk for a security is its beta
 Security’s total risk is beta plus firm-specific risk
 Beta is the systematic or nondiversifiable risk
 Diversifiable risk is irrelevant in a well diversified portfolio
 Decisions made by total risk (standard deviations) instead of beta
ignore the systematic risk and diversifiable risk components of
total risk
Deriving the CAPM
 All risk averse investors will invest in one risky portfolio, M,
which must be the market portfolio of all traded securities
 Mmust have the same slope as the CML
 ERi = RF + Risk premium
 (ERi - RF) = Risk premium
 The left side is the reward for accepting security risk
Risk/return relationships
 Security systematic risk, beta, can be defined as a ratio to the
market return
 ERi = RF + i (ERM - RF)
 Security market line (SML) shows the risk/return relationship for
securities and a graphical representation of the CAPM
 Equation of a line is Y = a + bX
a is the y-intercept and b is the slope
 The y-intercept is the risk-free rate
 The slope is (ERM - RF)
 The equation of the SML is
ERi = RF + (ERM - RF) i
equal to equation for CAPM and similar to CML
Differences between CML and SML
 Capital market line measures risk by standard deviation, or total
risk
 Security market line measures risk by beta to find the security’s
risk contribution to portfolio M
 CML graphs only defines efficient portfolios
 SML graphs efficient and nonefficient portfolios
 CML eliminates diversifiable risk for portfolios
 SML includes all portfolios that lie on or below the CML, but
only as a part of M, and the relevant risk is the security’s
contribution to M’s risk
 Firm specific risk is irrelevant to each, but for different reasons
CAPM and Security Analysis
 Value Line provides beta estimates for stocks
 Ibbotson Associates gives an average yield spread between the
S&P 500 Index and the U. S. Treasury bill rate
 Negative beta means the security is negatively correlated to the
market and can significantly reduce portfolio risk
 With the equation:
ERi = RF + i (ERM - RF)
we can estimate the required return for a security, on an SML
graph
 Calculate the predicted return for the security based on today’s
price, a predicted price a year from today, and expected dividends
in the coming year
Predict a holding period return and compare to the SML expected
return
If a security seems likely to have a higher return than its risk level
justifies, then it is undervalued (good investment)
A lower expected return than its risk would justify suggests a
security is overvalued (not a good investment)
Estimating Beta
 A beta estimate measures the changes of a security’s return
relative to the market return
 A security characteristic line graphs the relationship between the
return on the market portfolio and a security return
 The market model uses linear regression to estimate the
relationship between the market return and the security return
Regression analysis to estimate Beta
0.2
Security Return
0.16
0.12
0.08
0.04
0
0.00
0.05
0.10
Market Return
0.15
0.20
Differences between the SML and Security
Characteristic Line
 SML graphs required return against betas of many securities
 Security Characteristic Line measures security returns against the
market portfolio’s returns
 The SML has a slope the Expected rate less the risk-free rate, and
an intercept of the risk-free rate
 The SCL is used to determine how a security return correlates to
a market index return and it can be used to estimate beta, the slope
of the SCL
 The SML is used to estimate the required return for a security
relative to its risk measured by beta
 The beta value for the SML comes from the slope estimate of the
SCL
Beta: good news/bad news
 The SCL estimates beta and the SML graphs it
 Two issues with beta
How well can we estimate beta ?
How well can we predict the future beta using past beta estimates?
 Research has shown little correlation between a security returns
and market portfolio returns
 Historical betas can be better predictors of future betas for large
portfolios than it is for individual securities
 The more securities in the portfolio, the better predictor the
portfolio beta is
 Other strategies can be more successful than strictly investing in
beta based strategies
 Some choose to ignore beta - “Beta is dead”
 Beta isn’t perfect, but risk must be measured in making
risk/return decisions
 The assumptions of the CAPM were stringent, and not
realistic and will be relaxed in the next chapter in developing
a general risk/return relationship