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7/29/2019 Chapt.8 Capm
1/22
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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8-2
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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8-8
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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The Capital Asset Pricing Model
Calculating Systematic Risk
The formula
2
),(
M
MiiM
M
ii
RRCovr s
sb =
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The Capital Asset Pricing Model
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 Capital Asset Pricing Model
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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The Capital Asset Pricing Model
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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The Capital Asset Pricing Model
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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8-18
The Capital Asset Pricing Model
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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http://www.valueline.com
http://www.wsharpe.com
http://gsb.uchicago.edu/fac/eugene.fama/
http://www.moneychimp.com
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