Suppose that the index model for stocks A and B is estimated from excess returns

Question

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


RA = 1.5% + 0.55RM + eA
RB = –1.4% + 0.6RM + eB
M = 18%; R-squareA = 0.25; R-squareB = 0.16
  

Assume you create portfolio P with investment proportions of 0.60 in A and 0.40 in B.


1.  
What is the standard deviation of the portfolio? (Do not round your intermediate calculations. Round your answer to 2 decimal places. Omit the "%" sign in your response.)
   



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




3.  
What is the firm-specific variance of your portfolio? (Do not round your intermediate calculations. Round your answer to 4 decimal places.)


   

4.  
What is the covariance between the portfolio and the market index? (Do not round your intermediate calculations. Round your answer to 3 decimal places.)

Explanation / Answer

Part –A

StdVA^2 =beta A^2 * stdVM^2 /R square-A;

stdVA^2 = 0.55^2 * 18^2/0.25 = 392.04

stdVA = sqrt(392.04) = 19.8%

StdVB^2 =beta B^2 * stdVM^2 /R square-B;

stdVB^2= 0.6^2*18^2/0.16 = 729

stdVB = sqrt (729) = 27%

Cov(rA, rB) = beta A* beta B * stdVm^2 = 0.55*0.6*18^2 = 106.92

Correlation(A,B) = Cov(rA,rB)/ (stdVA * stdVB)

Correlation (A,B) = 106.92/(27*19.8) = 0.2

Portfolio standard deviation = sqrt ( w1^2 * stdVA^2 + w2^2 * stdVB^2 + 2*w1*w2*corr(A,B)*stdVA*stdVB)

W1 =0.6 ;w2 =0.5; stdVA =19.8%; stdVB=27%; corr(A,B) =0.2

By substitution, we get Portfolio standard deviation as 17.58%

Part –B

Beta of the portfolio is 0.6*0.55 +0.4 *0.6 = 0.57

Part- C

Firm specific Variance of A = stdVA^2 = 392.04 ( as shown in Part 1)

Firm specific Variance of B = stdVB^2 = 729 ( as shown in Part 1)

Part- D

Covariance between portfolio and market index

Cov(rP, rM) = Corr * stdVP* stdVM

Cov(rP,rM) = 0.2*17.58*18 = 63.28

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