Chapter 7

Chapter 7

Capital Asset Pricing and Arbitrage Pricing

Theory

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

Capital Asset Pricing Model (CAPM)

• 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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

Assumptions

•

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

Assumptions (cont.)

•

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

Resulting Equilibrium Conditions

• 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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

• Risk premium on the market

• Risk premium on an individual security

Resulting Equilibrium Conditions (cont.)

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

E(r)E(r)

E(rE(rMM))

rrff

MMCMLCML

mm

Capital Market Line

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

M = Market portfoliorf = Risk free rate

E(rM) - rf = Market risk premium

E(rM) - rf = Market price of risk

= Slope of the CAPM

Slope and Market Risk Premium

MM

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

Expected Return and Risk on Individual Securities

• The risk premium on individual securities is a function of

• Individual security’s risk premium is a function of

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

E(r)E(r)

E(rE(rMM))

rrff

SMLSML

MMßßßß = 1.0= 1.0

Security Market Line

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

SML Relationships

= [COV(ri,rm)] / m

2

Slope SML = E(rm) - rf

= market risk premium

SML = rf + [E(rm) - rf]

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

Sample Calculations for SML

E(rm) - rf = .08 rf = .03

x = 1.25

E(rx) =

y = .6

e(ry) =

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

E(r)E(r)

RRxx=13%=13%

SMLSML

mm

ßß

ßß1.01.0

RRmm=11%=11%RRyy=7.8%=7.8%

3%3%

xxßß1.251.25

yyßß.6.6

.08.08

Graph of Sample Calculations

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

E(r)E(r)

15%15%

SMLSML

ßß1.01.0

RRmm=11%=11%

rrff=3%=3%

1.251.25

Disequilibrium Example

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

Disequilibrium Example

• Suppose a security with a of 1.25 is offering expected return of 15%

• According to SML, it should be • : offering too high of a

rate of return for its level of risk

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

Security Characteristic Line

ExcessExcess Returns (i) Returns (i)

SCLSCL

..

..

........

.. ..

.. ....

.. ....

.. ..

.. ....

......

.. ..

.. ....

.. ....

.. ..

.. ....

.. ....

.. ..

..

.. ...... .... .... ..

ExcessExcess returns returnson market indexon market index

RRii = = ii + ß + ßiiRRmm + e + eii

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

Using the Text Example p. 231, Table 7.5

Jan.Jan.Feb.Feb.....DecDecMeanMeanStd DevStd Dev

5.415.41-3.44-3.44

..

..2.432.43-.60-.604.974.97

7.247.24.93.93

..

..3.903.901.751.753.323.32

ExcessExcessMkt. Ret.Mkt. Ret.

ExcessExcessGM Ret.GM Ret.

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.

Estimated coefficientEstimated coefficientStd error of estimateStd error of estimateVariance of residuals = 12.601Variance of residuals = 12.601Std dev of residuals = 3.550Std dev of residuals = 3.550R-SQR = R-SQR =

ßß

(1.547)(1.547)

(0.309)(0.309)

rrGMGM - r - rf f = + ß(r= + ß(rmm - r - rff))

Regression Results: