Case Study
The shares of two companies, K and L have the following expected returns: Prob Return K Return L 0.3 20% 6% 0.5 15% 10% 0.2 5% 12% The covariance of the returns of K and L is: Question 4Select one: a. -5.97 b. 0 c. 2.99 d. 5.97
To calculate the covariance of the returns of companies K and L, we can use the following formula:
[ \text{Cov}(X, Y) = E[XY] - E[X]E[Y] ]
Where:
Expected Return for K (E[X]): [ E[X] = (0.3 \times 20%) + (0.5 \times 15%) + (0.2 \times 5%) ] [ E[X] = (0.3 \times 0.20) + (0.5 \times 0.15) + (0.2 \times 0.05) ] [ E[X] = 0.06 + 0.075 + 0.01 = 0.145 \text{ or } 14.5% ]
Expected Return for L (E[Y]): [ E[Y] = (0.3 \times 6%) + (0.5 \times 10%) + (0.2 \times 12%) ] [ E[Y] = (0.3 \times 0.06) + (0.5 \times 0.10) + (0.2 \times 0.12) ] [ E[Y] = 0.018 + 0.05 + 0.024 = 0.092 \text{ or } 9.2% ]
Now we calculate (E[XY]): [ E[XY] = (0.3 \times 20% \times 6%) + (0.5 \times 15% \times 10%) + (0.2 \times 5% \times 12%) ] [ E[XY] = (0.3 \times 0.20 \times 0.06) + (0.5 \times 0.15 \times 0.10) + (0.2 \times 0.05 \times 0.12) ] [ E[XY] = (0.3 \times 0.012) + (0.5 \times 0.015) + (0.2 \times 0.006) ] [ E[XY] = 0.0036 + 0.0075 + 0.0012 = 0.0123 ]
Now we can calculate the covariance: [ \text{Cov}(K, L) = E[XY] - E[X]E[Y] ] [ \text{Cov}(K, L) = 0.0123 - (0.145 \times 0.092) ] [ \text{Cov}(K, L) = 0.0123 - 0.01334 = -0.00104 ]
The covariance of the returns of K and L is approximately -0.00104, which does not match any of the provided options. However, if we consider the values given in the options, it seems there might be a misunderstanding or miscalculation in the options provided.
If we round the covariance to two decimal places, it would be close to zero, but since the options provided are specific values, we can conclude that the closest answer is:
b. 0
This indicates that the covariance is very close to zero, suggesting that the returns of K and L are not significantly correlated.