Assignment1 Solution

# Assignment1 Solution - Assignment 1 Solution. 1. Because...

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Assignment 1 Solution . 1. Because the Capital Asset Pricing Model holds, both securities must lie on the Security Market Line (SML). Given the betas and expected returns on the two stocks, solve for the slope of the SML. Slope of SML = [E(r MP ) – E(r PSD )] / ( β MP - β PSD ) where E(r MP ) = the expected return on Murck Pharmaceutical E ( r PSD ) = the expected return on Pizer Drug Corp β MP = the beta of Murck Pharmaceutical β PSD = the beta of Pizer Drug Corp Slope of SML = [E(r MP ) – E(r PSD )] / ( β MP - β PSD ) = (0.30 – 0.19) / (1.4 – 0.7) = 0.1571 A security with a beta of 0.7 has an expected return of 0.19. As you move along the SML from a beta of 0.7 to a beta of 1, beta increases by 0.3 (= 1 – 0.7). Since the slope of the security market line is 0.1571, as beta increases by 0.3, expected return increases by 0.0471 (= 0.3 * 0.1571). Therefore, the expected return on a security with a beta of one equals 23.71% (= 0.19 + 0.0471). Since the market portfolio has a beta of one, the expected return on the market portfolio is 23.71%. According to the Capital Asset Pricing Model: E(r) = r f + β [E(r m ) – r f ] where E(r) = the expected return on the security r f = the risk-free rate β = the security’s beta E ( r m ) = the expected return on the market portfolio Since Murck Pharmaceutical has a beta of 1.4 and an expected return of 0.30, we know that: 0.30 = r f + 1.4(0.2371 – r f ) r f = 0.07985 The risk-free rate is 7.985%. 2. a. The equation for the Security Market Line is: E(r) = r f + β (EMRP)

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Since the risk-free rate equals 4.9% and the expected market risk premium is 9.4%, the CAPM implies: E(r) = 0.049 + β (0.094) b. First, calculate the beta of Durham Company’s stock. β = Covariance(R Durham , R Market ) / ( σ Market ) 2 = 0.0635 / 0.04326 = 1.468 Use the Capital Asset Pricing Model to determine the required return on Durham’s stock. According to the Capital Asset Pricing Model: E(r) = r f + β (EMRP) where E(r) = the expected return r f = the risk-free rate β = the stock’s beta EMRP = the expected market risk premium In this problem: r f = 0.049 β = 1.468 EMRP = 0.094 E(r) = r f + β (EMRP) = 0.049 + 1.468(0.094) = 0.1870 The required return on Durham’s stock is 18.69%. 3 . Real GNP was higher than anticipated. Since returns are positively related to the level of GNP, returns should rise based on this factor. Inflation was less than the amount anticipated. Since returns for Lewis-Strident are negatively correlated to the level of inflation, returns should rise based on this factor. Interest Rates are lower than anticipated. Since returns are negatively related to interest rates, the lower than expected rate is good news. Returns should rise due to interest rates. The President’s death is bad news. Although the president was expected to retire, his retirement would not be effective for six months. During that period he would still contribute to the firm. His untimely death means that those contributions would not be made. Since he was generally considered an asset to the firm, his death will cause returns to fall.
The poor research results are also bad news. Since Lewis-Striden must continue to test the drug, it will not go into production as early as expected. The delay will affect expected future earnings, and thus it will dampen returns now.

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## This note was uploaded on 01/17/2011 for the course MATH 372 taught by Professor 372 during the Spring '08 term at Waterloo.

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Assignment1 Solution - Assignment 1 Solution. 1. Because...

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