Financial Markets. Laurent Calvet. John Lewis Topic 13: Capital Asset Pricing Model (CAPM)

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1 Financial Markets Laurent Calvet John Lewis Topic 13: Capital Asset Pricing Model (CAPM) HEC MBA Financial Markets

2 Risk-Adjusted Discount Rate Method We need a theoretical model for estimating expected return on stock. Capital Asset Pricing Model posits that expected rate of return on security in equilibrium equals risk free rate plus expected market risk premium times the systematic (nondiversifiable) risk of the security.

3 Security Demand Must Equal Supply Given homogeneous expectations, all investors will demand the same efficient portfolio of risky securities. The combined portfolio of risky securities of all investors must equal the efficient portfolio. Thus, if all investors demand the efficient portfolio, and the supply of securities is the market portfolio, the demand for market portfolio must equal the supply of the market portfolio.

4 Risk and Return For every stock Total Return = expected return + unexpected return Unexpected return = systematic + unsystematic return Hence, Total Return = Expected return + Systematic return + Unsystematic return And so Total risk = Systematic risk + Unsystematic risk For a well-diversified portfolios, unsystematic risk is very small, so the portfolio risk is essentially the systematic risk

5 The Capital Market Line When the CAPM assumptions hold, an optimal portfolio is a combination of the risk-free investment and the market portfolio. When the tangent line goes through the market portfolio, it is called the capital market line (CML) The expected return and volatility of a capital market line portfolio are: E[ R ] = (1 xr ) + xer [ ] = r + xe ( [ R ] r) xcml f Mkt f Mkt f SD( R ) = xsd( R ) xcml Mkt

6 The Capital Market Line

7 The Capital Market Line

8 Determining the Risk Premium Market Risk and Beta Given an efficient market portfolio, the expected return of an investment is: E[ Ri] = ri = rf + βi( E[ RMkt] rf ) The beta is defined as: Risk premium for security i β i Volatility of i that is common with the market SD( Ri ) Corr( Ri, RMkt ) Cov( Ri, RMkt ) = = SD( R ) Var( R ) Mkt Mkt

9 Example Problem Assume the risk-free return is 5% and the market portfolio has an expected return of 12% and a standard deviation of 44%. ATP Oil and Gas has a standard deviation of 68% and a correlation with the market of What is ATP s beta with the market? Under the CAPM assumptions, what is its expected return?

10 Example Solution β i SD( Ri) Corr( Ri, RMkt) (.68)(.91) = = = SD( R ).44 Mkt 1.41 ER [ ] = r + β ( ER [ ] r) i f i Mkt f = 5% (12% 5%) = 14.87%

11 The Security Market Line There is a linear relationship between a stock s beta and its expected return (See figure on next slide). The security market line (SML) is graphed as the line through the risk-free investment and the market. According to the CAPM, if the expected return and beta for individual securities are plotted, they should all fall along the SML.

12 The Security Market Line 12-12

13 The Security Market Line (cont'd) The beta of a portfolio is the weighted average beta of the securities in the portfolio.

14 Example Problem Suppose the stock of the 3M Company (MMM) has a beta of 0.69 and the beta of Hewlett-Packard Co. (HPQ) stock is Assume the risk-free interest rate is 5% and the expected return of the market portfolio is 12%. What is the expected return of a portfolio of 40% of 3M stock and 60% Hewlett-Packard stock, according to the CAPM?

15 Example Solution β = β = (.40)(0.69) + (.60)(1.77) = x P i i i ER [ ] = r + β ( ER [ ] r) p f p Mkt f ER [ ] = 5% (12% 5%) = 14.37% p End of required material

16 Alpha To improve the performance of their portfolios, investors will compare the expected return of a security with its required return from the security market line.

17 Alpha (cont'd) The difference between a stock s expected return and its required return according to the security market line is called the stock s alpha. α = E[ R ] r = E[ R ] ( r + β ( E[ R ] r )) s s s s f s Mkt f When the market portfolio is efficient, all stocks are on the security market line and have an alpha of zero.

18 Alpha (cont'd) When the market portfolio is efficient, all stocks are on the security market line and have an alpha of zero. Investors can improve the performance of their portfolios by buying stocks with positive alphas and by selling stocks with negative alphas.

19 Deviations from the Security Market Line

20 Determining Beta Estimating Beta from Historical Returns Recall, beta is the expected percent change in the excess return of the security for a 1% change in the excess return of the market portfolio. Consider Cisco Systems stock and how it changes with the market portfolio.

21 Monthly Returns for Cisco Stock and for the S&P 500,

22 Scatterplot of Monthly Excess Returns

23 Estimating Beta from Historical Returns As the scatterplot on the previous slide shows, Cisco tends to be up when the market is up, and vice versa. We can see that a 10% change in the market s return corresponds to about a 20% change in Cisco s return. Thus, Cisco s return moves about two for one with the overall market, so Cisco s beta is about 2. Beta corresponds to the slope of the best-fitting line in the plot of the security s excess returns versus the market excess return.

24 Linear Regression The statistical technique that identifies the best-fitting line through a set of points. ( R r ) = α + β ( R r ) + ε i f i i Mkt f i α i is the intercept term of the regression. β i represents the sensitivity of the stock to market risk. ε i is the error term and represents the deviation from the best-fitting line and is zero on average.

25 Linear Regression (cont'd) Given data for r f, R i, and R Mkt, statistical packages for linear regression can estimate β i. A regression for Cisco using the monthly returns for indicates the estimated beta is The estimate of Cisco s alpha from the regression is 1.2%.

26 The Bottom Line on the CAPM The CAPM remains the predominant model used in practice to determine the equity cost of capital. Although the CAPM is not perfect, it is unlikely that a truly perfect model will be found in the foreseeable future. The imperfections of the CAPM may not be critical in the context of capital budgeting. Errors in estimating project cash flows are likely to be far more important than small discrepancies in the cost of capital.

27 Exercise You own shares of ABC, Inc. This stock has a beta of Treasury bills are returning 3.4%. The return on the market is 11.4%. What is the expected return on ABC, Inc.? [ ] = + β ( ) ER r R r f Mkt f = ( ) = 13.32%

Financial Markets 11-1

Financial Markets Laurent Calvet calvet@hec.fr John Lewis john.lewis04@imperial.ac.uk Topic 11: Measuring Financial Risk HEC MBA Financial Markets 11-1 Risk There are many types of risk in financial transactions