Portfolio Risk: Covariance and Correlation
Data for two assets are provided. The risk-free rate is 1.75%:
| Asset | Variance |
|-------|----------|
| G | 487 |
| H | 138 |
Assuming the covariance between Stocks G and H is half of the mean of the variances of the two stocks, the correlation coefficient between G and H is _closest_ to:
Incorrect.
The covariance is not negative; therefore, the correlation coefficient cannot be negative.
Correct.
There are three parts to this solution. First, the covariance between Stocks G and H must be computed. Covariance is given as half of the mean of the variances.
$$\displaystyle \mbox{Cov}[r_G{,}r_H]=\frac{1}{2}(\frac{\mbox{Variance}_G+ \mbox{Variance}_H}{2})$$
$$\displaystyle \mbox{Cov}[r_G{,}r_H]=\frac{1}{2}(\frac{487+138}{2})=156.25$$
Second, the standard deviation for Stocks G and H must be identified. Standard deviation is the square of the variance.
$$\displaystyle \sigma_G=\sqrt{487}=22.068\%$$
$$\displaystyle \sigma_H=\sqrt{138}=11.747\%$$
Third, the correlation coefficient between Stocks G and H can be determined using the following equation:
$$\displaystyle \rho({G{,}H})= \frac{\mbox{Cov}[r_G,r_H]}{\sigma_G\sigma_H}$$
$$\displaystyle \rho({G{,}H})=\frac{156.25}{(22.068)(11.747)}=0.60274$$.
Stocks G and H are cycling similarly.
Incorrect.
This answer choice is a calculation of the correlation coefficient; however, the covariance is given as equal to the mean of the variances, and the variances were subtracted during calculation of the mean.
-0.545.
0.603.
0.673.
