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P1.T1.609. Capital asset pricing model (CAPM) (Topic Review)

Nicole Seaman

Director of FRM Operations
Staff member

609.1. Peter is evaluating the expected performance of two common stocks, Kintech and Zimit. He has gathered the following information:
  • The riskfree rate is 1.0%
  • The volatility of the market portfolio, σ(M), is 30.0% and its expected return, E(M), is 8.0%; i.e., its expected excess return is 7.0%.
  • With respect to Kintech (k), the correlation between Kintech and the market portfolio, ρ(k, M), is 0.70; further, Kintech has a volatility, σ(k), of 60.0% and its forecast return, E(k), is 10.0%
  • With respect to Zimit (z), the covariance between Zimit and the market portfolio, COV(z, M), is 0.0540; further, the forecast return of Zimit, E(z), is 6.0%
Based on the capital asset pricing model (CAPM) and each stock's required rate of return, are these stocks undervalue, fairly valued, or overvalued?

a. Both are undervalued
b. Both are overvalued
c. Kintech is fairly valued but Zimit is overvalued
d. Kintech is overvalued and Zimit is undervalued

609.2. John has regressed three years of monthly excess portfolio returns (n = 36) against the excess returns for a broad-based market index which represents a proxy for CAPM's theoretical market portfolio. Where R(i) is the predicted portfolio return, Rf is the risk-free rate, β(0) and β(1) are the generated regression coefficients, and e(i) is the regression residual, his single-factor regression model is given by the form: R(i) - Rf = β(0) + β(1)*[R(M) - Rf] + e(i). His regression results are given by: R(i) - Rf = 0.40% + 0.732*[R(M) - Rf].

John is asked by his manager, "Did the manager of this portfolio generate positive ex post alpha?" Which of the following answers is BEST?

a. Alpha is the regression intercept, in this case β(0) which is +0.0040; therefore, yes, the portfolio did generate positive alpha
b. Alpha is the average regression residual which has a mean value of zero; therefore, no, the portfolio did not generate positive alpha
c. Alpha is the slope coefficient, in this case β(1) which is +0.732; therefore, yes, the portfolio did generate positive alpha but this +0.732 is actually "beta disguised as alpha"
d. Alpha is the difference between the average portfolio return and the average market return; because we are not given these average return values, we do not have enough information to determine alpha

609.3. Which of the following statements is TRUE about the capital asset pricing model (CAPM)?

a. CAPM implies that expected return increases with higher volatility
b. Portfolio beta is equal to the value-weighted average beta of its components
c. CAPM is premised on a relaxed set of real-world assumptions, as a model it is rather easily tested, and it has generally passed these empirical tests
d. Because volatilities must be positive, CAPM beta must be positive and therefore a portfolio's expected excess return (excess = net of the risk free rate) must be positive

Answers here: