Consider two perfectly negatively correlated risky securities, K and L. K has an expected rate of return of 13% and a standard deviation of 21%. L has an expected rate of return of 10% and a standard deviation of 15%. The weights of K and L in the global minimum variance portfolio are _____ and _____, respectively.
A) 0.2411; 0.7261
B) 0.5000; 0.5000
C) 0.4167; 0.5833
D) 0.4532; 0.5511
E) 0.7665; 0.2488

Question

Quizplus · Accepted Answer

For two perfectly negatively correlated securities, the weights in the global minimum variance portfolio can be calculated using the formula: $w_K = \frac{\sigma_L}{\sigma_K + \sigma_L}$ and $w_L = \frac{\sigma_K}{\sigma_K + \sigma_L}$, where $w_K$ and $w_L$ are the weights of securities K and L, respectively, and $\sigma_K$ and $\sigma_L$ are the standard deviations of securities K and L, respectively. Plugging in the given standard deviations, $w_K = \frac{15}{21 + 15} = \frac{15}{36} = 0.4167$ and $w_L = \frac{21}{36} = 0.5833$.

Consider Two Perfectly Negatively Correlated Risky Securities, K and L