If the Correlation Between E and D Equals 15%, What Are the Weights of E and D That Form Portfolio P?

Show your work for all problems.

Question 1

1. If the correlation between E and D equals 15%, what are the weights of E and D that form portfolio P?

E(R) = wEE + wDD

11% = wE*13% + WD*8%

11% = wE*13% +8% (1-WD)

11% = 13%WE + 8% - 8% WE

3% =5%WE

WE = 60%

WD =1 -60% = 40%

WD = 40%  

1. What is the standard deviation of portfolio P?

      Correlation of Coefficient = Cov (E,D)/ σE σD

                                                   15% = Cov./(12%*7%)

                                                   Cov. = 15%*12%*7%

                                                            = 0.126

Portfolio Variance = w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cov(RA, RB)

                                    = (0.6)2*12%^2) + (0.4)2*(7%)^2+ 2*(0.6)*(0.4)*(0.126)

                                       = 6.6448

                                    σ = 2.57775

1. If the CAPM holds, what must be the risk-­‐free rate, RF?

Assume market rate = 7%

E ( ri) =  rf  + Bi E(rm - rf)  

11% = rf + 0.6667(7% -rf)

11% = rf +0.0467 – 0.6667rf

1/3rf = 0.0633

rf = 0.1899

    = 19%

Question 2.

1. What is the expected return for the market portfolio, M?

         E(R) = wED + wDE

                    = 30%*0.03 +70%*0.30

                   = 21.9

1. If the risk-­‐free bond is paying 4%, what are the betas of stock X and Y?

          E (ri) = rf + Bi E (rm - rf)  

                     0.09 = 4% +Bi (10%- 4%)

                     0.05 = 6%Bi

                  Bi (D) = 0.8

         E (ri) = rf + Bi E (rm - rf)  

                  - 0.06 = 4% +Bi (10%- 4%)

                  - 0.12 = 6%Bi

                  Bi (E) = 2.0

Question 3.

1. What rate of return would be expected for a stock with beta = 0.25?

          E (ri) = rf + Bi E (rm - rf)  

                   E (ri) = 4% +0.25 (11% - 4%)

                              = 5.75                

1. Currently priced at $55, you forecast the stock’s price to be $58.59 in two years. An annual dividend of $1 is expected at the end of each of the next two years. Given the stock’s beta, is it currently over-­‐ or under-­‐priced?

         Use CAPM to determine the firm’s required return = 4% + 0.25 × (11% − 4%)

                                                                                                           = 5.75

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