bodie Chapter 4

Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition

Chapter 7The Capital The Capital Asset Pricing Asset Pricing ModelModel

Chapter Summary

Objective: To present the basic version of the model and its applicability.

Assumptions Resulting Equilibrium Conditions The Security Market Line (SML)

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

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

Summary Reminder

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)

Individual investors are price takers Single-period investment horizon Investments are limited to traded

financial assets No taxes, and transaction costs

Assumptions

Information is costless and available to all investors

Investors are rational mean-variance optimizers

There are homogeneous expectations

Assumptions (cont’d)

Summary Reminder

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

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)

Capital Market LineE(r)

M = The market portfoliorf = Risk free rate

E(rM) - rf = Market risk premium

= Slope of the CML

Slope and Market Risk Premium

fM r)r(E

Summary Reminder

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

Security Market LineE(r)

ß = 1.0

= 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

SML Relationships

GE Example

Covariance of GE return with the market portfolio:

Therefore, the reward-to-risk ratio for investments in GE would be:

( , ) , ( , )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

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:

( )Market risk premiumMarket variance

fGE rrErrCovrrE

GE Example The risk premium for GE:

Restating, we obtain:

MGEfGE rrErrCOVrrE 2

fMGEfGE rrErrE

Expected Return-Beta Relationship

CAPM holds for the overall portfolio because:

This also holds for the market portfolio:

( ) ( ) andP k kk

E r w E r

( ) ( )M f M M fE r r E r r

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

Graph of Sample Calculations

Rx=13%

Rm=11%Ry=7.8%

1.25yß

Disequilibrium ExampleE(r)

15%SML

Rm=11%

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

Figure 9.2 The Security Market Line

Figure 9.3 The SML and a Positive-Alpha Stock

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

bodie Chapter 4

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