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Transcript of Chapter 7
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-1Slide 7-1
Chapter 7
The Capital The Capital Asset Pricing Asset Pricing ModelModel
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-2Slide 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) Black’s Zero Beta Model CAPM and Liquidity
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-3Slide 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 7-4Slide 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 7-5Slide 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) Black’s Zero Beta Model CAPM and Liquidity
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-6Slide 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 7-7Slide 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 7-8Slide 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 7-9Slide 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) Black’s Zero Beta Model CAPM and Liquidity
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-10Slide 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 7-11Slide 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 7-12Slide 7-12
Capital Market Line
E(r)
E(rM)
rf
MCML
m
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-13Slide 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 7-14Slide 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) Black’s Zero Beta Model CAPM and Liquidity
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-15Slide 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 7-16Slide 7-16
Security Market Line
E(r)
E(rM)
rf
SML
M
ßß = 1.0
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-17Slide 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 7-18Slide 7-18
E(rm) - rf = .08 rf = .03
a) x = 1.25
E(rx) = .03 + 1.25(.08) = .13 or 13%
by = .6
E(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 7-19Slide 7-19
Graph of Sample Calculations
E(r)
Rx=13%
SML
m
ß
ß1.0
Rm=11%
Ry=7.8%
3%
xß
1.25
yß.6
.08
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-20Slide 7-20
Disequilibrium Example
E(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 7-21Slide 7-21
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 7-22Slide 7-22
Summary Reminder
Objective: To present the basic version of the model and its applicability.
Assumptions Resulting Equilibrium Conditions The Security Market Line (SML) Black’s Zero Beta Model CAPM and Liquidity
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-23Slide 7-23
Black’s Zero Beta Model
Absence of a risk-free asset Combinations of portfolios on the
efficient frontier are efficient All frontier portfolios have companion
portfolios that are uncorrelated Returns on individual assets can be
expressed as linear combinations of efficient portfolios
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-24Slide 7-24
Black’s Zero Beta Model Formulation
)r,r(Cov
)r,r(Cov)r,r(Cov)r(E)r(E)r(E)r(E
QP2P
QPPiQPQi
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-25Slide 7-25
Efficient Portfolios and Zero Companions
Q
P
Z(Q)Z(P)
E[rz (Q)]
E[rz (P)]
E(r)
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-26Slide 7-26
Zero Beta Market Model
2M
Mi)M(ZM)M(Zi
)r,r(Cov)r(E)r(E)r(E)r(E
CAPM with E(rz (M)) replacing rf
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-27Slide 7-27
Summary Reminder
Objective: To present the basic version of the model and its applicability.
Assumptions Resulting Equilibrium Conditions The Security Market Line (SML) Black’s Zero Beta Model CAPM and Liquidity
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-28Slide 7-28
CAPM & Liquidity
Liquidity – cost or ease with which an asset can be sold
Illiquidity Premium Research supports a premium for
illiquidity Amihud and Mendelson
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-29Slide 7-29
CAPM with a Liquidity Premium
)c(fr)r(Er)r(E ifiifi
f (ci) = liquidity premium for security i
f (ci) increases at a decreasing rate