Suppose that the index model for stocks A and B is estimated from excess returns
ID: 2417560 • Letter: S
Question
Suppose that the index model for stocks A and B is estimated from excess returns with the following results: R_A = 2% + 040R_M + theta_A R_B = -1.8% + 0.9R_M + theta_B sigma_M =15%; R-square^A = 0.30; R-squares = 0.22 Assume you create portfolio with investment proportions of 0.70 in A and 0.30 in B. 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.) Standard deviation % What is the beta of your portfolio? (Do not round your intermediate calculations. Round your answer to 2 decimal places.) Portfolio beta What is the firm-specific variance of your portfolio? (Do not round your intermediate calculations. Round your answer to 4 decimal places.) Firm-specific.0253 What is the covariance between the portfolio and the market index? (Do not round your intermediate calculations. Round your answer to 3 decimal places.) CovarianceExplanation / Answer
1.Standard Deviation of the portfolio
This is calculated using the following formula
Square root of = (sA )2( WA) 2 + (sB) 2 ( WB) 2 + 2 sA sBWA WB * Correlation b/w A and B
Throughtout the solutions the notation (sA)(sB) indicates risk/standard deviation
(sA ) = Sq Rt of 0.3 = 0.547723
(sB ) = Sq Rt of 0.22 = 0.469
To computed correlation b/w A and B
Covariance b/w A and B = (sA ) (sB ) (sm )2 = 0.54*0.46*0.0225 = 0.00578
Correlation b/w A and B = Covariance b/w A and B divided by Risk of (sA ) (sB )
Therefore correlation = 0.00578/(0.024)*(0.1215) = 1.982
The values of 0.024 and 0.1215 have been calculated separately below
Therefore calculation = 0.3*0.49 + 0.22*0.09 + 2*0.54*0.469*0.7*0.3*1.982 =0.21084 = 21.084%
2.Beta of the portfolio
(sA )( WA) + (sB) ( WB) = 0.5477*0.7 + 0.46*0.3 = 0.52411
3.Firm Specific Variance
Firm specific risk is the difference between Firms total risk and systematic risk/market risk
Total Risk of Firm A = Explained Variance/Total Variance
(0.4)2(0.15) 2 /0.15 = 0.024
Systematic Risk for Firm A
(sA )2(sm) 2 = (0.4)2(0.15) 2 = 0.0036
Total Risk of Firm B = Explained Variance/Total Variance
(0.9)2(0.15) 2 /0.15 = 0.1215
Systematic Risk for Firm B
(sB )2(sm) 2 = (0.9)2(0.15) 2 = 0.018225
Firm specific risk of A = 0.024-0.0036 = 0.0204 = 2.04%
Firm specific risk of B= 0.01215-0.018225 = 0.103275 = 10.3275%
4.Covariance between portfolio and market index
(sportfolio ) (sm) 2 = 0.52411*(0.15)2 = 0.11792
1.Standard Deviation of the portfolio
This is calculated using the following formula
Square root of = (sA )2( WA) 2 + (sB) 2 ( WB) 2 + 2 sA sBWA WB * Correlation b/w A and B
Throughtout the solutions the notation (sA)(sB) indicates risk/standard deviation
(sA ) = Sq Rt of 0.3 = 0.547723
(sB ) = Sq Rt of 0.22 = 0.469
To computed correlation b/w A and B
Covariance b/w A and B = (sA ) (sB ) (sm )2 = 0.54*0.46*0.0225 = 0.00578
Correlation b/w A and B = Covariance b/w A and B divided by Risk of (sA ) (sB )
Therefore correlation = 0.00578/(0.024)*(0.1215) = 1.982
The values of 0.024 and 0.1215 have been calculated separately below
Therefore calculation = 0.3*0.49 + 0.22*0.09 + 2*0.54*0.469*0.7*0.3*1.982 =0.21084 = 21.084%
2.Beta of the portfolio
(sA )( WA) + (sB) ( WB) = 0.5477*0.7 + 0.46*0.3 = 0.52411
3.Firm Specific Variance
Firm specific risk is the difference between Firms total risk and systematic risk/market risk
Total Risk of Firm A = Explained Variance/Total Variance
(0.4)2(0.15) 2 /0.15 = 0.024
Systematic Risk for Firm A
(sA )2(sm) 2 = (0.4)2(0.15) 2 = 0.0036
Total Risk of Firm B = Explained Variance/Total Variance
(0.9)2(0.15) 2 /0.15 = 0.1215
Systematic Risk for Firm B
(sB )2(sm) 2 = (0.9)2(0.15) 2 = 0.018225
Firm specific risk of A = 0.024-0.0036 = 0.0204 = 2.04%
Firm specific risk of B= 0.01215-0.018225 = 0.103275 = 10.3275%
4.Covariance between portfolio and market index
(sportfolio ) (sm) 2 = 0.52411*(0.15)2 = 0.11792
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