Project 1
Hh Ari
Lecture11and12_week6and7Oct5and102017_capm1.pptxOct 5 & 10, 2017
Lecture 11 & 12 CAPM
1 The assumptions of the capital asset pricing model (CAPM)
Single-period investment horizon
Investors are rational mean-variance optimizers
Homogeneous expectations
Individual investors are price takers
No taxes nor transaction costs
Information is costless and available to all investors
2 Market equilibrium under CAPM assumptions
Where the investor chooses along the Capital Market Line depends on her risk tolerance. The big point is that all investors have the same CML.
CAPM assumptions generate interesting results……
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3 Market equilibrium under CAPM assumptions
All investors will hold the same portfolio for risky assets – market portfolio (M). A portfolio is defined not by absolute values but by proportions of different securities in the 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 an individual security is a function of its covariance with the market, because the variance of market portfolio is the sum of individual securities’ co-variances with the market portfolio.
Beta measures the responsiveness of a security to movements in the market portfolio (i.e., systematic risk).
Market becomes the single source of systematic risk……
4 CAPM equation
Expected return version:
Actual return version:
So CAPM is a one-factor model: there is only one source of systematic risk (the fluctuation of market portfolio).
Can you tell that a portfolio’s beta is equal to the weighted average of the betas of individual securities?
What CAPM really says mathematically……
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Q
Stock A’s Beta is 1.2, risk free rate is 5% and market portfolio’s return is expected to be 10%. What is the expected return of Stock A?
Q
A share of stock sells for 50 today. It will pay a dividend of 6 at the end of the year. Its beta is1.2. T-bill rate is 6% and market expected return is 16%. What do investors expect the stock to sell for at the end of the year?
5 Abnormal return (alpha) and security market line (SML)
M
Positive α stock
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α
Asset pricing models are for finding alphas……
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Q
A. A mutual fund with beta of 0.8 has an expected rate of return of 14%. If risk free rate is 5% and you expect market return to be 15%, should you invest in this fund?
B. What passive portfolio comprised of a market-index portfolio and a money market account would have the same beta as the fund? Show that the difference between the expected rate of return on this passive portfolio and that of the fund equals the alpha from part A.
6 Estimating CAPM with Regression Using past returns of the market and the security of interest. Treasury securities are close proxies for the risk-free rate. In practice, a broad stock market index, such as the S&P 500, is used to represent the market.
( =0 when CAPM is accurate and this asset is fairly priced.)
Then how to find beta in the real world……
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