Chapter 7

Capital Asset Pricing and Arbitrage Pricing

Theory

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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

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Assumptions

•

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Assumptions (cont.)

•

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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

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• Risk premium on the market

• Risk premium on an individual security

Resulting Equilibrium Conditions (cont.)

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E(r)E(r)

E(rE(rMM))

rrff

MMCMLCML

mm

Capital Market Line

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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

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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

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E(r)E(r)

E(rE(rMM))

rrff

SMLSML

MMßßßß = 1.0= 1.0

Security Market Line

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SML Relationships

= [COV(ri,rm)] / m

2

Slope SML = E(rm) - rf

= market risk premium

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

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Sample Calculations for SML

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

x = 1.25

E(rx) =

y = .6

e(ry) =

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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

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E(r)E(r)

15%15%

SMLSML

ßß1.01.0

RRmm=11%=11%

rrff=3%=3%

1.251.25

Disequilibrium Example

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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

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Security Characteristic Line

ExcessExcess Returns (i) Returns (i)

SCLSCL

..

..

........

.. ..

.. ....

.. ....

.. ..

.. ....

......

.. ..

.. ....

.. ....

.. ..

.. ....

.. ....

.. ..

..

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

ExcessExcess returns returnson market indexon market index

RRii = = ii + ß + ßiiRRmm + e + eii

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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.

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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: