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Unformatted text preview: Previous lecture Lecture 4 – Pricing Models:
CAPM and the Beta
Dr. Quach Manh Hao Diversification and portfolio risk
Asset allocation with risky assets
Optimal risky portfolio with a riskfree
asset
Indifference curve and complete portfolio This lecture
Brief on pricing models
Capital asset pricing model (CAPM)
CAPM and the Index models
CAPM and the real world
Conclusions and practices Key assumptions
Individual
Individual investors are price takers
SingleSingleperiod investment horizon
Investments are limited to traded financial assets
No taxes nor transaction costs
Information is costless and available to all
investors
Investors are rational meanvariance optimizers
meanHomogeneous expectations 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
The model is used widely and commonly by
most analysts and cited in academia field. 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
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 71 The Efficient Frontier and the CML The Risk Premium of the Market Portfolio M
rf
E(rM)  rf
E(r =
=
= Market portfolio
Risk free rate
Market risk premium E(rM)  rf
E(r = Market price of risk = = Slope of the CAPM σM Expected returns on individual securities
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 The Security Market Line and Positive
Alpha Stock Expected returns on Individual securities:
an example
Using
Using the Dell example: E ( rM ) − rf
1 = E (rD ) − rf βD Rearranging gives us the CAPM’s expected
returnreturnbeta relationship E (rD ) = rf + β D E (rM ) − rf SML Relationships β = [COV(ri,rm)] / σm2
[COV(r
E(rm) – rf = market risk premium
E(r
SML = rf + β [E(rm)  rf]
[E(r 72 Sample Calculations for SML Graph of Sample Calculations
E(r) E(rm)  rf = .08 rf = .03
.03
β x = 1.25
1.25
E(rx) = .03 + 1.25(.08) = .13 or 13%
β y = .6
e(ry) = .03 + .6(.08) = .078 or 7.8% Estimating the Index Model SML
Rx=13%
Rm=11%
Ry=7.8% .08 3%
.6 1.0 1.25
ß y ßm ßx ß Monthly Return Statistics for Tbills,
S&P 500 and General Motors An application of the CAPM
Using historical data on Tbills, S&P 500
Tand individual securities
Regress risk premiums for individual
stocks against the risk premiums for the
S&P 500
Slope is the beta for the individual stock Cumulative Returns for
Tbills, S&P 500 and GM Stock Characteristic Line for GM 73 Security Characteristic
Line for GM: Summary Output GM Regression: What We Can Learn
GM is a cyclical stock
Required Return:
rf + β (rM − rf ) = 2.75 + 1.24 x5.5 = 9.57% Next compute betas of other firms in the
industry
Please refer to Lecture 4 – Excel file for
examples of REE and SAM Predicting Betas CAPM and the Real World The beta from the regression equation is
an estimate based on past history
Betas exhibit a statistical property The CAPM was first published by Sharpe
in the Journal of Finance in 1964
Journal
Many tests of the theory have since
followed including Roll’s critique in 1977
and the Fama and French study in 1992 – Regression toward the mean 74 ...
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This note was uploaded on 01/16/2012 for the course ECON 101 taught by Professor Tom during the Spring '11 term at FH Joanneum.
 Spring '11
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