Chapt.8 Capm

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Analysis of Investments and

Management of Portfolios

by Keith C. Brown & Frank K. Reilly

Ch

apter8

An Introduction to

Asset Pricing Models

Capital Market Theory: An Overview

The Capital Asset Pricing Model

Empirical Tests of the CAPM


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Capital Market Theory: An Overview

Capital market theory extends portfolio theory

and develops a model for pricing all risky

assets, while capital asset pricing model

(CAPM) will allow you to determine therequired rate of return for any risky asset


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Relationship between risk and return

The higher the Risk , The higher the required return.

SML can be used to generate risk-adjusted discount

rates to be used in Financial decisions.

Return

Return i

Risk i

SML

Risk


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Risk and Rate of Return

Portfolio Rate of Return : Average weightedreturn on the portfolio as a whole.

Standard deviation : reflection of risk inherent

in the portfolio.

It measures the extent of possible

outcomes are likely to be different from the mean

outcome


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The correlation coefficient , the covariance

Direct way to find portfolio risk by dealing with theinterrelatedness of Assets returns.

It is a number that can take values from -1 (perfect

negative relatedness) to +1( perfect positive relatedness).

*The more positively related securities in portfolio, the

less gain from diversification.


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Risk, Diversification & the Market Portfolio

Systematic Risk Only systematic risk remains in the market portfolio

Systematic risk is the variability in all risky assets

caused by macroeconomic variables

Variability in growth of money supply Interest rate volatility

Variability in factors like (1) industrial production (2)

corporate earnings (3) cash flow

Systematic risk can be measured by the standarddeviation of returns of the market portfolio and can

change over time


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Risk, Diversification & the Market Portfolio

Diversification and the Elimination ofUnsystematic Risk

The purpose of diversification is to reduce the

standard deviation of the total portfolio

This assumes that imperfect correlations existamong securities

As you add securities, you expect the average

covariance for the portfolio to decline

How many securities must you add to obtain acompletely diversified portfolio?

See Exhibit 8.3


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Exhibit 8.3


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Beta Coefficient ( Regression coefficient)

B coefficient express relationship between the returnexpected from security and that expected from the

market as whole

j =

Standard deviation Correlation of j

of return j X with the Market

Standard deviation of Market Return


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i.e = j Pjm

m

Same as j m Pjm

2m

j = j m Covariance j with Market

2m variance of Market


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Calculating Systematic Risk

The formula

2

),(

M

MiiM

M

ii

RRCovr s

sb =


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Let i=(i riM)/ M be the asset beta measuring the

relative risk with the market, the systematic risk

The CAPM indicates what should be the expectedor required rates of return on risky assets

This helps to value an asset by providing an

appropriate discount rate to use in dividend

valuation models

])[ RFRi

= Mi E(RRFR)E(R b


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The Security Market Line (SML) The SML is a graphical form of the CAPM

Exhibit 8.5 shows the relationship between the

expected or required rate of return and the

systematic risk on a risky asset The expected rate of return of a risk asset is

determined by the RFR plus a risk premium for the

individual asset

The risk premium is determined by the systematicrisk of the asset (beta) and the prevailing market

risk premium (RM-RFR)


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Exhibit 8.5


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Example:

If Market return move from 12% to 14% a security

with return of 15% and of 1.3 will move to 15%+1.3 (14%-12%) = 17.6%


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Determining the Expected Rate of Return Risk-free rate is 5% and the market return is 9%

Stock A B C D E

Beta 0.70 1.00 1.15 1.40 -0.30

Applying

E(RA) = 0.05 + 0.70 (0.09-0.05) = 0.078 = 7.8%

E(RB) = 0.05 + 1.00 (0.09-0.05) = 0.090 = 09.0%

E(RC) = 0.05 + 1.15 (0.09-0.05) = 0.096 = 09.6%

E(RD) = 0.05 + 1.40 (0.09-0.05) = 0.106 = 10.6%

E(RE) = 0.05 + -0.30 (0.09-0.05) = 0.038 = 03.8%

])[ RFRi

= Mi E(RRFR)E(R b


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Identifying Undervalued & Overvalued Assets In equilibrium, all assets and all portfolios of

assets should plot on the SML

Any security with an estimated return that plots

above the SML is underpriced

Any security with an estimated return that plots

below the SML is overpriced


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Compare the required rate of return to theestimated rate of return for a specific risky asset

using the SML over a specific investment horizon

to determine if it is an appropriate investment

Exhibit 8.8 shows A, C and E are underpriced but

B and D are over priced because

Stock Required Return Estimated Return

A 7.8% 8.0%

B 9.0% 6.2%

C 9.6% 15.15%

D 10.6% 5.15%

E 3.8% 6.0%


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Exhibit 8.8


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Empirical Tests of the CAPM

Stability of Beta

Betas for individual stocks are not stable

Portfolio betas are reasonably stable

The larger the portfolio of stocks and longer theperiod, the more stable the beta of the portfolio


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Summary

The relevant risk measure for an individualrisky asset is its systematic risk or covariance

with the market portfolio

SML is derived to show the relationship

between the required return and its systematicrisk for any risky asset

Assuming security markets are not always

completely efficient, you can identifyundervalued and overvalued securities by

comparing your estimate of the rate of return

on an investment to its required rate of return


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The Internet Investments Online

http://www.valueline.com

http://www.wsharpe.com

http://gsb.uchicago.edu/fac/eugene.fama/

http://www.moneychimp.com
http://www.valueline.com/http://www.wsharpe.com/http://gsb.uchicago.edu/fac/eugene.fama/http://www.moneychimp.com/http://www.moneychimp.com/http://gsb.uchicago.edu/fac/eugene.fama/http://www.wsharpe.com/http://www.valueline.com/

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Chapt.8 Capm