# Practice problem with Answers_other part_ - CAPM Question...

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Unformatted text preview: CAPM Question Consider an economy in two periods, t=0 and t=1. At t=0, the market index is trading at a value of \$100. At t=1, the index either rises to \$130 in case of a boom (with probability 1/2), or falls to \$90 in case of a recession (with probability 1/2). A large utility company ABC is in this economy, and its stock price at t=0 is \$20. At t=1, the stock price either rises to \$22 if the economy is in a boom time, or falls to \$19 if the economy is in a recession. Neither the index nor the ABC stock pays dividends during this time, and the risk-free rate is R f = 2%. 1. What are the expected value and the variance of the return on the market index? What are the expected value and the variance of the return on ABC stock? E [ R M ] = 1 2 (0 . 3) + 1 2 (- . 1) = 0 . 1 (10%) V ar [ R M ] = 1 2 (0 . 3- . 1) 2 + 1 2 (- . 1- . 1) 2 = 1 2 (0 . 04) + 1 2 (0 . 04) = 0 . 04 E [ R ABC ] = 1 2 (0 . 1) + 1 2 (- . 05) = 0 . 025 (2.5%) V ar [ R ABC ] = 1 2 (0 . 1- . 025) 2 + 1 2 (- . 05- . 025) 2 = 1 2 (0 . 005625) + 1 2 (0 . 005625) = 0 . 005625 2. What is the covariance between the index return and the return on ABC stock? What is the market β of the ABC stock? Return on Market index Return on ABC stock Boom (prob 0.5) 0.3 0.1 Recession (prob 0.5)-0.1-0.05 Cov ( R M, R ABC ) = E [ R M R ABC ]- E [ R M ] E [ R ABC ] = 1 2 (0 . 3)(0 . 1) + 1 2 (- . 1)(- . 05)- (0 . 1)(0 . 025) = 1 2 (0 . 03) + 1 2 (0 . 005)- . 0025 = 0 . 0175- . 0025 = 0 . 015 β ABC = Cov ( R M, R ABC ) V ar ( R M ) = . 015 . 04 = 0 . 375 3. Assuming that CAPM holds, compute the expected return of ABC stock predicted by CAPM. Is it the same as the expected return calculated in (a)? If not, which one is higher? CAPM prediction: E [ R ABC ] = R f + β ABC ( E [ R M ]- R f ) = 0 . 02 + 0 . 375(0 . 1- . 02) = 0 . 05 The expected return on ABC stock predicted by CAPM is 0.05 (5%) and this is greater than the actual expected return (2.5%). 1 4. Is this fact that ABC has a different expected return than CAPM prediction consistent with what you’ve learned in the course? Yes. This is an example of the size effect. Note that ABC is a large utility company with a large market capitalization. According to the empirical facts we learned in the course, the large stocks tend to have lower expected excess returns than the small stocks and this difference in the expected excess returns is not fully explained by the difference in β ’s, i.e., by CAPM....
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## This note was uploaded on 01/25/2010 for the course ECON 136 taught by Professor Szeidl during the Fall '08 term at Berkeley.

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Practice problem with Answers_other part_ - CAPM Question...

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