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Suppose the expected returns and standard deviations of Stocks A and B are E(RA) = 0
Suppose the expected returns and standard deviations of Stocks A and B are E(RA) = 0.087, E(RB) = 0.147, σA = 0.357, and σB = 0.617. (Do not round intermediate calculations. Round the final answers to 2 decimal places.)
a-1. Calculate the expected return of a portfolio that is composed of 32 percent A and 68 percent B when the correlation between the returns on A and B is 0.47.
Expected return %
a-2. Calculate the standard deviation of a portfolio that is composed of 32 percent A and 68 percent B when the correlation between the returns on A and B is 0.47.
Standard deviation %
b. Calculate the standard deviation of a portfolio with the same portfolio weights as in part (a) when the correlation coefficient between the returns on A and B is −0.47.
Standard deviation %
Expert Solution
| Expected return%= | Wt Stock A*Return Stock A+Wt Stock B*Return Stock B | ||||
| Expected return%= | 0.32*0.087+0.68*0.147 | ||||
| a-1Expected return%= | 12.78 | ||||
| Variance | =( w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB)) | ||||
| Variance | =0.32^2*0.357^2+0.68^2*0.617^2+2*0.32*0.68*0.357*0.617*0.47 | ||||
| Variance | 0.23414 | ||||
| Standard deviation= | (variance)^0.5 | ||||
| a-2Standard deviation= | 48.39% |
| Variance | =( w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB)) |
| Variance | =0.32^2*0.357^2+0.68^2*0.617^2+2*0.32*0.68*0.357*0.617*-0.47 |
| Variance | 0.14403 |
| Standard deviation= | (variance)^0.5 |
| b. Standard deviation= | 37.95% |
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