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Unformatted text preview: U NIVERSITY OF N ORTH C AROLINA A T C HAPEL H ILL K ENAN-F LAGLER B USINESS S CHOOL B USI 408: C ORPORATE F INANCE S OLUTIONS TO P RACTICE P ROBLEM SET #5: P ORTFOLIO T HEORY AND C APM P ROF . A RZU O ZOGUZ 1. Suppose that the risk-free rate is 6.3%, and the market portfolio has en expected return of 14.8%. The market portfolio has a variance of 0.0121. Portfolio Z has a correlation coefficient with the market of 0.45 and a variance of 0.0169. According to CAPM, what is the expected return on portfolio Z? According to CAPM, the expected return on portfolio Z is given by: ( ) ( ) f m Z f Z r r E r r E − + = β Recall, that the beta of an asset is given by: ( ) ( ) m m i i r r r var , cov = β We know, ( ) ( ) 0121 . var , 148 . , 063 . 2 = = = = m m m f r r E r σ . We also know the correlation coefficient of portfolio Z with the market, and the variance of portfolio Z: ( ) ( ) 0169 . var , 45 . , 2 = = = = Z Z Zm m Z r r r corr σ ρ . From the definition of correlation, we can back out the covariance of portfolio Z and the market: ( ) ( ) ( ) ( ) 532 . 0121 . 0169 . 45 . , , cov , cov , = × × = × × = ⇒ = m Z m Z m Z m Z m Z m Z r r corr r r r r r r corr σ σ σ σ ( ) ( ) % 82 . 10 1082 . 063 . 148 . 532 . 063 . = = − + = Z r E 2. Suppose you have invested $30,000 in the following four stocks: Security Amount invested Beta Stock A $5,000 0.75 Stock B $10,000 1.10 Stock C $8,000 1.36 Stock D $7,000 1.88 The risk free rate is 4%, and the expected return on the market portfolio is 15%. Based on the CAPM, what is the expected return on the above portfolio? The risk free rate is 4%, and the expected return on the market portfolio is 15%. Based on the CAPM, what is the expected return on the above portfolio? First, we need to find the weight of each stock in the portfolio: 30 7 000 , 30 $ 000 , 7 $ ; 15 4 000 , 30 $ 000 , 8 $ ; 3 1 000 , 30 $ 000 , 10 $ ; 6 1 000 , 30 $ 000 , 5 $ = = = = = = = = D C B A ω ω ω ω The beta of the portfolio is given by: ( ) ( ) ( ) ( ) 293 . 1 88 . 1 30 7 36 . 1 15 4 1 . 1 3 1 75 ....
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This document was uploaded on 11/04/2011 for the course BUSI 408 at UNC.
- Fall '08
- Corporate Finance