Question

a risky security has a variance of 0.036190 and a covariance with the market of 0.0222. the variance of the market is 0.01975. what is the correlation of the risky security of the market?

Answer 1

In this case, let X be the risk security and Y be the market.

where Corr (X,Y) is the correlation of X and Y.

CoV (X,Y) is Covariance of X and Y = 0.0222,

Sigma (x) is the standard devaition of X

and Sigma (Y) is the standard deviation of Y.

Now, given in the question is variance of X and Y respectively.

Standard deviation is the square root of variance,

Therefore, Std Deviation of X = Sigma (x) = = 0.190237

and Std Deviation of Y = = 0.140535

Then, as given in the problem, CoV (X,Y) = 0.0222,

then Corr (X,Y) =

=0.0222 / (0.190237 *  0.140535)

= 0.830377