Question

Suppose that the index model for stocks A and B is estimated from excess returns with the following results:

R_A = 2.20% + 0.80R_M + e_A

R_B = -2.20% + 1.20R_M + e_B

σ_M = 24%; R-square_A = 0.16; R-square_B = 0.12

Assume you create portfolio P with investment proportions of 0.70 in A and 0.30 in B.

a. What is the standard deviation of the portfolio? (Do not round your intermediate calculations. Round your answer to 2 decimal places.)

Standard deviation %

b. What is the beta of your portfolio? (Do not round your intermediate calculations. Round your answer to 2 decimal places.)

Portfolio beta =

c. What is the firm-specific variance of your portfolio? (Do not round your intermediate calculations. Round your answer to 4 decimal places.)

Firm-specific=

d. What is the covariance between the portfolio and the market index? (Do not round your intermediate calculations. Round your answer to 3 decimal places.)

Covariance=

Answer 1

Here we first need to calculate standard deviation of both the stocks

we know

SD = Beta x SDm/ Correlation
SDA = 0.80 x 0.24 / (0.16)^.50
    = 0.48
SDB = 1.20x 0.24/ (0.12)^0.50
    = 0.8314

Covariance (A, B) = BetaA x Beta B x SDm^2
    = (0.80 x 1.20)x (0.24^2)
    = 0.055296

Correlation coefficient ( p)= COvariance / (SDA x SDB)
   = 0.055296 / (0.48 x .8314)
                        = 0.1386

Portfolio SD = (( WA x SDA)^2 + (WB x SDB)^2 + 2 x SDA x SDB x WA x WB x p)^0.50

                     =( (0.70 x 0.48)^2 + (0.30 x 0.8314)^2 + 2 x 0.48 x 0.8314 x 0.70 x 0.30 x 0.1386))^0.50

                     = (0.112896 + 0.06221 + 0.023231)^0.50

                     = 44.54%

Portfolio beta = Sum of weight x stock beta

                       = 0.70 x .80   + 0.30 x 1.20

                        = 0.92

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