T1 Tm 7. You are given the following information: The covariance matrix of the r

Question

T1 Tm 7. You are given the following information: The covariance matrix of the rate of return on stock 1, stock 2, and the market portfolio is: T2 0.160 0.020 0.064 0.020 0.090 0.032 Tm 0.064 0.032 4. r = 0.12 and r,= 0.04. 0.040 Consider forming a portfolio p that has 75% invested in asset 1 and 25% invested in asset 2. a. What is the variance of portfolio p? b. What are the betas of 1, 2, and p relative to the market, Bim, B2m, and Bpm, respectively? c. What are the Rº values in regressions of the return on 1, 2, and p on the market portfolio? (Here you can define R' = systematic risk / total risk) d. According to CAPM, what are the expected returns on asset 1, asset 2, and portfolio p?

Explanation / Answer

a)

Var (P) = 0.752*0.16 + 0.252*0.09 + 2*0.75*0.25*0.02 = 0.103125 = 10.3125%

b)

Beta = Covar(Stock,market) / Var(market)

B1 = 0.064 / 0.04 = 1.6

B2 = 0.032 / 0.04 = 0.8

Portfolio Beta = 0.75*1.6 + 0.25*0.8 = 1.4

c)

R2 = Corelation2 = (Beta* SDm / SDi)2

R12 = (1.6*SQRT(0.04) / SQRT(0.16) )2 = 0.64

R22 = (0.8*SQRT(0.04) / SQRT(0.09) )2 = 0.2844

R22 = (1.4*SQRT(0.04) / SQRT(0.103125) )2 = 0.760242

d)

R = Rf + Beta*(Rm - Rf)

R1 = 0.04 + 1.6*(0.12 - 0.04) = 0.168 = 16.8%

R1 = 0.04 + 0.8*(0.12 - 0.04) = 0.104 = 10.4%

R1 = 0.04 + 1.4*(0.12 - 0.04) = 0.152 = 15.2%

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