17. Using CAMP [LO4] A stock has a beta of 1.35 and an expected return of 16 per

Question

17. Using CAMP [LO4] A stock has a beta of 1.35 and an expected return of 16 percent. A risk free asset currently earns 4.8 percent. a. What is the expected return on a porfolio that is equally invested in the two assets? b. If a portfolio of the two assets has a beta of .95 what are the portfolio weights? c. If a portfolio of the two assets has an expected return of 8 percent, what is its beta? d. If a portfolio of the two assets has a beta of 2.70, what are the portfolio weights? How do you interpret the weights for the assets in this case? Explain

Explanation / Answer

a. What is the expected return on a porfolio that is equally invested in the two assets? 10.4+ 1.0% Again we have a special case where the portfolio is equally weighted, so we can sum the returns of each asset and divide by the number of assets. The expected return of the portfolio is: E(Rp) = (.16 + .048)/2 = .1040 or 10.40% =============== b. If a portfolio of the two assets has a beta of .95 what are the portfolio weights? the portfolio weights that result in a portfolio with a b of 0.95. We know the b of the risk-free asset is zero. We also know the weight of the risk-free asset is one minus the weight of the stock since the portfolio weights must sum to one, or 100 percent. So: bp = 0.95 = wS(1.35) + (1 – wS)(0) 0.95 = 1.35wS + 0 – 0wS wS = 0.95/1.35 wS = .7037 And, the weight of the risk-free asset is: wRf = 1 – .7037 = .2963 70.37+ 1.0% ; 23.63+ 1.0% ================= c. If a portfolio of the two assets has an expected return of 8 percent, what is its beta? 0.386+ 1.0% the portfolio weights that result in a portfolio with an expected return of 8 percent. We also know the weight of the risk-free asset is one minus the weight of the stock since the portfolio weights must sum to one, or 100 percent. So: E(Rp) = .08 = .16wS + .048(1 – wS) .08 = .16wS + .048 – .048wS wS = .2857 So, the b of the portfolio will be: bp = .2857(1.35) + (1 – .2857)(0) = 0.386 d. If a portfolio of the two assets has a beta of 2.70, what are the portfolio weights? How do you interpret the weights for the assets in this case? Explain 200+ 1.0% -100+ 1.0% for the ß of the portfolio as we did in part b, we find: ßp = 2.70 = wS(1.35) + (1 – wS)(0) wS = 2.70/1.35 = 2 wRf = 1 – 2 = –1 The portfolio is invested 200% in the stock and –100% in the risk-free asset. This represents borrowing at the risk-free rate to buy more of the stock.

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