Question

An investor can design a risky portfolio based on two stocks, A and B. The standard deviation of return on stock A is 20% while the standard deviation on stock B is 15%. The correlation coefficient between the return on A and B is 0%. The standard deviation of return on the minimum variance portfolio is _________.

- 17%

- 0%

- 6%

-12%

Answer 1

Correct Answer is 12%

Covariance (A,B) = Correlation (A,B) x Standard Deviation A x Standard Deviation B

Covariance (A,B) = (0) x 20 x 15 = 0

Minimum variance porfolio is

Weight of Security A =  

Weight of Security A =

                                 

Weight of Security A = 225/625 =0.36

Weight of Security A is 0.36

Weight of Security B = 1-0.36 = 0.64

S.D. of portfolio = (wA2 *σA2 + wB2 *σB2 + 2*wA*wB*σA*σB*corrAB)1/2

S.D. of portfolio = ((0.36)2(20)2 + (0.64)2 (15)2 +2 * 0.36 * 0.64 * 20 * 15 * 0 )1/2

S.D. of portfolio = [51.84 + 92.16 + 0]1/2

S.D. of portfolio = 12 or say 12%

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