Question

A bond analyst is looking at historical returns for two bonds, Bond 1 and Bond 2. Bond 2’s returns are much more volatile than Bond 1. The variance of returns for Bond 1 is 0.012 and the variance of returns of Bond 2 is 0.308. The correlation between the returns of the two bonds is 0.79, and the covariance is 0.048. If the variance of Bond 1 increases to 0.026 while the variance of Bond B decreases to 0.188 and the covariance remains the same, the correlation between the two bonds will:

A. remain the same.
B. decrease.
C. increase.

Answer 1

The correlation between Bond 1 and Bond 2 will decrease if the variance of Bond 1 increases to 0.026 while the variance of Bond 2 decreases to 0.188, given that the covariance remains the same.

Step-by-step explanation:

The correlation between two bonds can be calculated using the formula for the correlation coefficient, which is the covariance divided by the product of the standard deviations of each bond's returns. When the variance of Bond 1 increases to 0.026 and the variance of Bond 2 decreases to 0.188, while the covariance remains at 0.048, the correlation between the two bonds will change. To assess whether the correlation increases or decreases, we need to evaluate the change in standard deviations, which are the square roots of their variances, and then determine the impact on the correlation coefficient.

For the original variances, the standard deviations would be sqrt(0.012) and sqrt(0.308) for Bond 1 and Bond 2 respectively. For the new variances, they would be sqrt(0.026) and sqrt(0.188) respectively. Since the covariance is constant, an increase in the standard deviation of one bond and a decrease in the other would lead to a decrease in the correlation coefficient, as the denominator of the correlation coefficient increases.