Question

The correlation coefficient between two stocks, C and D, is-1. The variances are: 10 and 40, respectively.

The variance of a portfolio consisting these two stocks will be zero if the investment in stock C will be:
a. 33.333%
b. None of the answers is correct
c. 25%
d. 50%
e. 66.667%

Answer 1

To achieve a portfolio variance of zero with two negatively correlated stocks (correlation coefficient of -1) and variances of 10 and 40, the weight of stock C must be 66.667%, which corresponds to option e.

Step-by-step explanation:

The student asked about the variance of a portfolio consisting of two stocks C and D with a correlation coefficient of -1 and variances of 10 and 40, respectively. To achieve a portfolio variance of zero, the investment weights must be such that the product of the weight of stock C, the standard deviation of stock C, the weight of stock D, and the standard deviation of stock D equals the negative of their individual variances.

Given the variances (VarianceC = 10 and VarianceD = 40), let us denote the weight of stock C as wC and stock D as wD = 1 - wC. The portfolio variance formula when the correlation coefficient is -1, is:

Var(Portfolio) = (wC^2 * VarianceC) + (wD^2 * VarianceD) - (2 * wC * wD * StdDevC * StdDevD)

A portfolio variance of zero will occur when:

0 = (wC^2 * 10) + ((1 - wC)^2 * 40) - (2 * wC * (1 - wC) * √10 * √40)

Solving for wC, we find that wC = 0.667 or 66.667%, which corresponds to option e.