covariance and correlation

The correlation coefficient for a series of returns on two investments is equal to 0.80. Their covariance of returns is 0.06974 . Which of the following are possible variances for the returns on the two investments? A) 0.04 and 0.19. B) 0.02 and 0.44. C) 0.08 and 0.37.

A! 0.04^2 * 0.19^2 * 0.8 = 0.06974

I got A as well, although I did it the opposite way than Sarah. .06974/((.04^.5)(.19^.5))= 0.8

The correlation coefficient is: 0.06974 / [(Std Dev A)(Std Dev B)] = 0.8. (Std Dev A)(Std Dev B) = 0.08718. Since the standard deviation is equal to the square root of the variance, each pair of variances can be converted to standard deviations and multiplied to see if they equal 0.08718. ã0.04 = 0.20 and ã0.19 = 0.43589. The product of these equals 0.08718.

B :slight_smile:

A. Damil4real, I think you forgot to take the square root of the variances before multiplying them together.


Very weird - I think I did this exact question last night - and yes A.