Chapter 13: The Capital
Asset Pricing Model
Objective
•The Theory of the CAPM
•Use of CAPM in benchmarking
• Using CAPM to determine
correct rate for
discounting
1
Copyright © Prentice Hall Inc. 2000. Author: Nick Bagley, bdellaSoft, Inc.
Chapter 13 Contents
1 The Capital Asset Pricing Model in
Brief
2 Determining the Risk Premium on
the Market Portfolio
3 Beta and Risk Premiums on
Individual Securities
4 Using the CAPM in Portfolio Selection
5 Valuation & Regulating Rates of
Return
2
Introduction


CAPM is a theory about equilibrium
prices in the markets for risky
assets
It is important because it provides


a justification for the widespread
practice of passive investing called
indexing
a way to estimate expected rates of
return for use in evaluating stocks and
projects
3
CAPM Assumptions
1.
2.
Investors agree in their forecasts of
expected rates of return, standard
deviations, and correlations of the risky
securities.
Investors generally behave optimally. In
equilibrium, when investors hold their
optimal portfolios, the aggregate demand
for each security is equal to its supply.
4
Market Portfolio
Investor’s relative holdings of risky
assets is the same, thus the only
way the asset market can clear is if
those proportions are the
proportions in which they are
valued in the market place.
A portfolio that holds all assets in
proportion to their observed market
values is called the market
portfolio.
5
Market Portfolio
Suppose that the market consists of
n Assets with values S1 , S 2 ,..., S n ,
there are m investors with
A1 , A2 ,..., Am
capitals
participating
in the markets, and they all invest
in proportions 1 ,  2 ,...,  n
in the
existing assets. Then we have
6
Market Portfolio
S1 ,  , S n
Ai  1 Ai     n Ai , i  1,..., m
S j   j A1     j Am
j  1,..., n
  j ( A1    Am )

j 
Sj
A1    Am

Sj
M
, j  1,..., n
7
The Capital Market Line
20
18
16
Expected Return
14
12
10
8
6
4
2
0
0
5
10
15
20
25
30
35
Standard Deviation
8
The Capital Market Line (CML)
 m  rf
r 
 r  rf
m
 m  rf
slope 
m
9
Determining the Risk Premium on
the Market Portfolio

CAPM states that

the equilibrium risk premium on the
market portfolio is the product of


variance of the market, 2M
weighted average of the degree of risk
aversion of holders of risk, A
r  rf  A
M
2
M
10
Example: To Determine ‘A’
 r  0.14,  r  0.20, rf  0.06,
M
M
 r  rf  A
M
2
rM
 r  rf
 A
2
r
M
M
0.14  0.06
A
 2.0
2
0.20
11
Beta
The marginal contribution of the
security’s return to the standard
deviation of the market portfolio’s
return
i  i,M
 i , M  i M  i , M  i  i , M
 2 

2
M
M
M
12
CAPM Risk Premium on any Asset
According the the CAPM, in
equilibrium, the risk premium on
any asset is equal to the product of




the risk premium on the market
portfolio
 r  rf   m  rf  i   r  rf   m  rf  i
i
i
13
Market
Portfolio
Security Market Line
20%
Expected Risk Premium
15%
10%
5%
0%
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
-5%
-10%
-15%
-20%
Beta (Risk)
14
The Beta of a Portfolio

When determining the risk of a
portfolio
using standard deviation results in a
formula that is quite complex

 w1r1  w2r2 ... wn rn    wi ri 2  2 wi w j ri  r j  i , j
i j
 i 1,n
 using beta, the formula is linear









1
2
 w r  w r ... w r  w1 r  w2  r  ...  wn  r   wi  r
11
2 2
n n
1
2
n
i
i
15
Using CAPM in Portfolio Selection


Diversify your holdings of risky
assets in the proportions of the
market portfolio, and
Mix this portfolio with the risk-free
asset to achieve a desired riskreward combination.
16
CAPM and Portfolio Selection


The portfolio used as a proxy for the
market portfolio often has the same
weights as well-known stock market
indexes such as S&P’s 500
Thus the CAPM strategy in selecting
portfolio has come to be known as
indexing
17
Indexing
1.
2.
Indexing is an attractive investment
strategy because
As an empirical matter, it has
historically performed better than
most actively managed portfolios
It costs less to implement, no costs
of research, less cost of
transactions
18
CML, SML and alpha



CML provides a benchmark for measuring
the performance of the investor’s entire
portfolio
SML provides a benchmark for the
performance of different parts of the
whole portfolio
alpha: The difference between the risk
premium of a portfolio and its risk
premium according to SML
19
Positive alpha, Example
rf  6%
E[rM ]  rf  8%
 M  20%
Alpha Fund :
  0.5,   1%,   15%
20
Alpha Fund and SML
20
15
Risk Premium
10
5
0
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
-5
-10
-15
-20
Beta
21
Alpha Fund and CML
20
Expected Return
16
12
8
4
0
0
5
10
15
20
25
30
Standard Deviation
22
Valuation and Regulating Rates of
Return
 Assume
the market rate is 15%, and
the risk-free rate is 5%
A
company’s capital structure consists
of 80% equity with a beta of 1.3, and
20% dept. The price of one share of
the company?
23

Compute the beta
 company  wequity  equity  wbond  bond
 company  0.80 *1.3  0.20 * 0
 company  1.04
24
Valuation and Regulating Rates of
Return

To find the required return on the
new project, apply the CAPM
 r  rf   rm  rf 
 0.05  1.040.15  0.05
 15.4%
25
Valuation and Regulating Rates of
Return

Assume that your company has an
expected dividend of $6 next year,
and that it will grow annually at a
rate of 4% for ever, the value of a
share is
D1
6
p0 

 $52.63
r  g 0.154  0.04
26
CAPM in Practice
Empirically it is observed that CAPM
does not explain fully the structure of
expected returns on assets
27
Explanations
1.
2.
3.
CAPM does hold, but the market portfolios
used for testing it are incomplete
representations of market portfolio
Market imperfections, Like borrowing
costs are not contemplated in CAPM
Greater realism should be added to the
modeling assumptions
28
Modifications
ICAPM, Intertemporal CAPM
In this dynamic model equilibrium
risk premiums come from several
dimensions of risks, not only from
their beta
29
Alternatives
APT, Arbitrage Pricing Theory
APT gives a rationale for the expected
return-beta relation that relies on the
condition that there be no arbitrage profit
opportunities. APT and CAPM complement
each other
30