The covariance of the returns on investments X and Y is 18.17. The standard deviation of returns on X is 7%, and the standard deviation of returns on Y is 4%. What is the value of the correlation coefficient for returns on investments X and Y? A) +0.65. B) +0.32. C) +0.85. D) +2.59. Your answer: A was correct! The correlation coefficient = Cov (X,Y) / [(Std Dev. X)(Std. Dev. Y)] = 18.17 / 28 = 0.65 Question: Why is 28 in the denominator instead of (.04)(.07) = .0028?
Looks like the Covariance is actually .001817 and they moved everything over four decimal places. On this type of question, it’s pretty easy to see the right answer since it’s just a matter of decimal places.
or the units of covariance above were (%)^2.
When we calculate we ignore the % sign attach to the SD. Refer to CFA text book page 344_346. book 1.
Whoa - std.dev and covariance both have units. They just nicely cancel when you calculate correlation. Don’t ignore the units because they will keep you safe (If you report a correlation of 0.008 instead of 0.8 bad things might happen).
The units of covariance are percent square already. Correlation is a unit free number. That’s we use full percent values instead of 0.04 and 0.07.