bodie chapter 4
DESCRIPTION
capmTRANSCRIPT
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-1
Chapter 7The Capital The Capital Asset Pricing Asset Pricing ModelModel
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-2
Chapter Summary
Objective: To present the basic version of the model and its applicability.
Assumptions Resulting Equilibrium Conditions The Security Market Line (SML)
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-3
Demand for Stocks and Equilibrium Prices
Imagine a world where all investors face the same opportunity set
Each investor computes his/her optimal (tangency) portfolio – as in Chapter 6
The demand of this investor for a particular firm’s shares comes from this tangency portfolio
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-4
Demand for Stocks and Equilibrium Prices (cont’d)
As the price of the shares falls, the demand for the shares increases
The supply of shares is vertical, fixed and independent of the share price
The CAPM shows the conditions that prevail when supply and demand are equal for all firms in investor’s opportunity set
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-5
Summary Reminder
Objective: To present the basic version of the model and its applicability.
Assumptions Resulting Equilibrium Conditions The Security Market Line (SML)
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-6
Equilibrium model that underlies all modern financial theory
Derived using principles of diversification with simplified assumptions
Markowitz, Sharpe, Lintner and Mossin are researchers credited with its development
Capital Asset Pricing Model (CAPM)
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-7
Individual investors are price takers Single-period investment horizon Investments are limited to traded
financial assets No taxes, and transaction costs
Assumptions
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-8
Information is costless and available to all investors
Investors are rational mean-variance optimizers
There are homogeneous expectations
Assumptions (cont’d)
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-9
Summary Reminder
Objective: To present the basic version of the model and its applicability.
Assumptions Resulting Equilibrium Conditions The Security Market Line (SML)
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-10
All investors will hold the same portfolio of 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
The market portfolio is on the efficient frontier and, moreover, it is the tangency portfolio
Resulting Equilibrium Conditions
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-11
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
Resulting Equilibrium Conditions (cont’d)
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-12
Capital Market LineE(r)
E(rM)
rf
MCML
m
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-13
M = The market portfoliorf = Risk free rate
E(rM) - rf = Market risk premium
= Slope of the CML
Slope and Market Risk Premium
M
fM r)r(E
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-14
Summary Reminder
Objective: To present the basic version of the model and its applicability.
Assumptions Resulting Equilibrium Conditions The Security Market Line (SML)
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-15
The risk premium on individual securities is a function of the individual security’s contribution to the risk of the market portfolio
Individual security’s risk premium is a function of the covariance of returns with the assets that make up the market portfolio
Expected Return and Risk on Individual Securities
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-16
Security Market LineE(r)
E(rM)
rf
SML
Mß
ß = 1.0
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-17
= Cov(ri,rm) / m2
Slope SML = E(rm) - rf
= market risk premium E(r)SML = rf + [E(rm) - rf]
BetaM = Cov (rM,rM) / 2
= M2 / M
2 = 1
SML Relationships
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-18
9-18
GE Example
Covariance of GE return with the market portfolio:
Therefore, the reward-to-risk ratio for investments in GE would be:
1 1
( , ) , ( , )n n
GE M GE k k k k GEk k
Cov r r Cov r w r w Cov r r
( ) ( )GE's contribution to risk premiumGE's contribution to variance ( , ) ( , )
GE GE f GE f
GE GE M GE M
w E r r E r rw Cov r r Cov r r
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-19
9-19 GE Example
Reward-to-risk ratio for investment in market portfolio:
Reward-to-risk ratios of GE and the market portfolio should be equal:
2
( )Market risk premiumMarket variance
M f
M
E r r
2, M
fM
MGE
fGE rrErrCovrrE
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-20
9-20
GE Example The risk premium for GE:
Restating, we obtain:
fMM
MGEfGE rrErrCOVrrE 2
,
fMGEfGE rrErrE
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-21
9-21
Expected Return-Beta Relationship
CAPM holds for the overall portfolio because:
This also holds for the market portfolio:
P
( ) ( ) andP k kk
k kk
E r w E r
w
( ) ( )M f M M fE r r E r r
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-22
E(rm) - rf = .08 rf = .03
a) x = 1.25
E(rx) = .03 + 1.25(.08) = .13 or 13%
by = .6E(ry) = .03 + .6(.08) = .078 or 7.8%
Sample Calculations for SML
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-23
Graph of Sample Calculations
E(r)
Rx=13%
SML
m
ß
ß1.0
Rm=11%Ry=7.8%
3%
xß
1.25yß
.6
.08
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-24
Disequilibrium ExampleE(r)
15%SML
ß1.0
Rm=11%
rf=3%
1.25
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-25
Suppose a security with a of 1.25 is offering expected return of 15%
According to SML, it should be 13% Under-priced: offering too high of a rate
of return for its level of risk
Disequilibrium Example
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-26
9-26
Figure 9.2 The Security Market Line
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-27
9-27
Figure 9.3 The SML and a Positive-Alpha Stock
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-28
9-28
The Index Model and Realized Returns
To move from expected to realized returns, use the index model in excess return form:
The index model beta coefficient is the same as the beta of the CAPM expected return-beta relationship.
i i i M iR R e