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An investor can design a risky portfolio based on two shares, A and B
An investor can design a risky portfolio based on two shares, A and B. The standard deviation of Share A is 24% while the standard deviation of Share B is 12%. The correlation coefficient between the returns on A and B is -1. The expected return on Share A is 15% while on Share B it is 9%. What is the expected return of the minimum variance portfolio?
a.
15%
b.
12%
c.
11%
d.
9%
Expert Solution
| Computation of Expected Return of the Minimum Variance Portfolio: | ||
| Given, | ||
| Standard Deviation of Share A = | 24% | |
| Standard Deviation of Share B = | 12% | |
| Variance of Share A = | 0.0576 | =24%^2 |
| Variance of Share B = | 0.0144 | =12%^2 |
| Correlation (r ) = | -1 | |
| Covariance (Cov) | -0.0288 | =24%*12%*-1 |
| Weight of Share A = | 0.333333333 | =(0.0144-(-0.0288))/(0.0576+0.0144-(2*-0.0288) |
| Weight of Share B = | 0.666666667 | =1-0.33333333 |
| So, | ||
| Expected return of Minimum Variance Portfolio = | 11.00% | =(0.3333333*15%)+(0.666667*9%) |
So, the correct option is C "11%".
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