Stock A has an expected return of 10% and a standard deviation of 10%. Stock B has an expected return of 15% and a standard deviation of 20%. The two stocks are perfectly negatively correlated ( $$\text { Q1,2 }$$ = -1). What set of weights yields a portfolio with a zero variance?
A)2/3 in Stock A; 1/3 in Stock B
B)2/3 in Stock B; 1/3 in Stock A
C)2 in Stock A; -1 in Stock B
D)2 in Stock B; -1 in Stock A
E)None of the above.

Question

Quizplus · Accepted Answer

When two assets are perfectly negatively correlated, a zero-variance portfolio can be achieved by setting the weights such that the weighted standard deviations cancel each other out. The weights are calculated as the inverse ratio of the standard deviations: $ w_A = \frac{\sigma_B}{\sigma_A + \sigma_B} $ and $ w_B = \frac{\sigma_A}{\sigma_A + \sigma_B} $. For Stock A and Stock B, this results in weights of 2/3 in Stock A and 1/3 in Stock B.

Stock a Has an Expected Return of 10% and a Standard