Lecture 4 - Pricing models - CAPM and the Beta

Lecture 4 Pricing - Previous lecture Lecture 4 – Pricing Models CAPM and the Beta Dr Quach Manh Hao Diversification and portfolio risk Asset

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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 risk-free 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 SingleSingle-period 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 mean-variance 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 7-1 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 returnreturn-beta 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 7-2 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 T-bills, S&P 500 and General Motors An application of the CAPM Using historical data on T-bills, 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 T-bills, S&P 500 and GM Stock Characteristic Line for GM 7-3 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 7-4 ...
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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.

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