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4) Portfolio Expected Return. You have $10,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 14 percent and Stock Y with an expected return of 11 percent. If your goal is to create a portfolio with an expected return of 12.4 percent, how much money will you invest in Stock X? In Stock Y? 7) Calculating Returns and Standard Deviations. Based on the following information, calculate the expected return and standard deviation for the two stocks. Rate of Return if state Occurs State of Economy Recession Normal Boom Probability of state economy .15 .55 .30 Stock A Stock B .02 .10 .15 -.30 .18 .31 17) Using CAPM. A stock has a beta of 1.15 and an expected return of 10.4 percent. A risk-free asset currently earns 3.8 percent. a. What is the expected return on a portfolio that is equally invested in the two assets? b. If a portfolio of the two assets has a beta of .7, what are the portfolio weights? c. If a portfolio of the two assets has an expected return of 9 percent, what is its beta? d. If a portfolio of the two assets has a beta of 2.3, what are the portfolio weights? How do you interpret the weights for the two assets in this case? Explain. 29) Suppose you observe the following situation: State of Economy Recession Normal Boom Probability of state .10 .65 .25 Stock A -.12 .09 .35 Stock B -.05 .10 .21 a. Calculate the expected return on each stock. b. Assuming the capital asset pricing model holds and stock A's beta is greater than stock B's beta by .25, what is the expected market risk premium? FINANCE 1 Finance [Insert Name] [Institutional Affiliation] FINANCE 2 4) Portfolio Expected Return. You have $10,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 14 percent and Stock Y with an expected return of 11 percent. If your goal is to create a portfolio with an expected return of 12.4 percent, how much money will you invest in Stock X? In Stock Y? 0.14x + 0.11(10,000 - x) = 1,240 0.14x + 1,100 - 0.011x = 1,240 0.03x = 1400 x = $4,666.67 y = 10,000 - 4,666.67 y = $5,333.33 7) Calculating Returns and Standard Deviations. Based on the following information, calculate the expected return and standard deviation for the two stocks. Rate of Return if state Occurs State of Economy Recession Normal Boom Probability of state economy .15 .55 .30 Stock A = .15(.02) + .55(.10) + .30(.15) Stock A = 10.3% Stock A Stock B .02 .10 .15 -.30 .18 .31 FINANCE Stock B = .15(-.30) + .55(.18) + .30(.31) Stock B = 14.7% Standard deviation: Stock A = .15(.02 - .103) ^2 + .55(.10 - .103) ^2 + .30(.15 - .103)^2 Stock A = 0.001701 Stock A = (0.001701) ^1/2 Stock A = 0.04124318125 Stock A = 4.12% Stock B = .15(-.30) + .55(.18) + .30(.31) Stock B = 0.038541 Stock B = (0.038541) ^1/2 Stock B = 0.196318 Stock B = 19.63% 17) Using CAPM. A stock has a beta of 1.15 and an expected return of 10.4 percent. A risk-free asset currently earns 3.8 percent. a. What is the expected return on a portfolio that is equally invested in the two assets? 3 FINANCE 4 ER=0.5(10.4%) +0.5(3.8%) ER=7.1% b. If a portfolio of the two assets has a beta of .7, what are the portfolio weights? The beta for risk free asset is 0% while the beta of the other is 1.15; the weight of the other is computed by taking 0.7 then divide by 1.5 resulting to 61% The risk free asset =100%-61%=39% The other asset =100%-39%=61% c. If a portfolio of the two assets has an expected return of 9 percent, what is its beta? Beta =5.2/6.6=0.906 d. If a portfolio of the two assets has a beta of 2.3, what are the portfolio weights? How do you interpret the weights for the two assets in this case? Explain. It is known that the beta value for a risk free asset is zero while that of the other asset is 1.15. The computation of the other asset is done by dividing 2.3 by 1.15 which results to 200%. Therefore, the weight of risk free asset is 200% awhile the weight of the other is -100%. The portfolio represents the amount that has been borrowed through an asset that is risk free at 3.8 percent and being invested at a rate of 11.39% 29) Suppose you observe the following situation: State of Economy Recession Normal Boom Probability of state .10 .65 .25 Stock A -.12 .09 .35 Stock B -.05 .10 .21 FINANCE a. Calculate the expected return on each stock. Stock A =0.10*-0.12+0.65*0.09+0.25*0.35=0.134 or 13.4% Stock B =0.10*-0.05+0.65*0.10+0.25*0.21=0.1125 or 11.25% b. Assuming the capital asset pricing model holds and stock A's beta is greater than stock B's beta by .25, what is the expected market risk premium? The expected market risk premium = (ER for stock A-ER of stock B)/(Beta for Stock A-Beta for stock B) (0.1340-0.1125)/0.25 =0.0860 or 8.60% 5 FINANCE 1 Finance [Insert Name] [Institutional Affiliation] FINANCE 2 4) Portfolio Expected Return. You have $10,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 14 percent and Stock Y with an expected return of 11 percent. If your goal is to create a portfolio with an expected return of 12.4 percent, how much money will you invest in Stock X? In Stock Y? 0.14x + 0.11(10,000 - x) = 1,240 0.14x + 1,100 - 0.011x = 1,240 0.03x = 1400 x = $4,666.67 y = 10,000 - 4,666.67 y = $5,333.33 7) Calculating Returns and Standard Deviations. Based on the following information, calculate the expected return and standard deviation for the two stocks. Rate of Return if state Occurs State of Economy Recession Normal Boom Probability of state economy .15 .55 .30 Stock A = .15(.02) + .55(.10) + .30(.15) Stock A = 10.3% Stock A Stock B .02 .10 .15 -.30 .18 .31 FINANCE Stock B = .15(-.30) + .55(.18) + .30(.31) Stock B = 14.7% Standard deviation: Stock A = .15(.02 - .103) ^2 + .55(.10 - .103) ^2 + .30(.15 - .103)^2 Stock A = 0.001701 Stock A = (0.001701) ^1/2 Stock A = 0.04124318125 Stock A = 4.12% Stock B = .15(-.30) + .55(.18) + .30(.31) Stock B = 0.038541 Stock B = (0.038541) ^1/2 Stock B = 0.196318 Stock B = 19.63% 17) Using CAPM. A stock has a beta of 1.15 and an expected return of 10.4 percent. A risk-free asset currently earns 3.8 percent. a. What is the expected return on a portfolio that is equally invested in the two assets? 3 FINANCE 4 ER=0.5(10.4%) +0.5(3.8%) ER=7.1% b. If a portfolio of the two assets has a beta of .7, what are the portfolio weights? The beta for risk free asset is 0% while the beta of the other is 1.15; the weight of the other is computed by taking 0.7 then divide by 1.5 resulting to 61% The risk free asset =100%-61%=39% The other asset =100%-39%=61% c. If a portfolio of the two assets has an expected return of 9 percent, what is its beta? Beta =5.2/6.6=0.906 d. If a portfolio of the two assets has a beta of 2.3, what are the portfolio weights? How do you interpret the weights for the two assets in this case? Explain. It is known that the beta value for a risk free asset is zero while that of the other asset is 1.15. The computation of the other asset is done by dividing 2.3 by 1.15 which results to 200%. Therefore, the weight of risk free asset is 200% awhile the weight of the other is -100%. The portfolio represents the amount that has been borrowed through an asset that is risk free at 3.8 percent and being invested at a rate of 11.39% 29) Suppose you observe the following situation: State of Economy Recession Normal Boom Probability of state .10 .65 .25 Stock A -.12 .09 .35 Stock B -.05 .10 .21 FINANCE a. Calculate the expected return on each stock. Stock A =0.10*-0.12+0.65*0.09+0.25*0.35=0.134 or 13.4% Stock B =0.10*-0.05+0.65*0.10+0.25*0.21=0.1125 or 11.25% b. Assuming the capital asset pricing model holds and stock A's beta is greater than stock B's beta by .25, what is the expected market risk premium? The expected market risk premium = (ER for stock A-ER of stock B)/(Beta for Stock A-Beta for stock B) (0.1340-0.1125)/0.25 =0.0860 or 8.60% 5