# Math Help - Correlation Coefficient Question

1. ## Correlation Coefficient Question

Hi Everyone

Need a bit of help on a correlation coefficient question I came across during revision:

Shares A and B have the following Variance-Covaraince matrix.

$
\left[
\begin{array}{cc}
\sigma_{a^2} & \sigma_{ab} \\
\sigma_{ba} & \sigma_{b^2}
\end{array}
\right] = \left[\begin{array}{cc}
0.02 & -0.005 \\
-0.005 & 0.01
\end{array}
\right]$

What is the correlation coefficient between A and B?

(a) .35
(b) .125
(c) -.35
(d) -25

If anyone could enlighten me with the answer and the method for getting the answer it would be much appreciated!

2. ## Correct answer

c. is correct. Denote X=sigma_ab - non-diagonal component of covariance matrix and Y=sigma^2_a*sigma^2_b - product of two diagonal components of cov matrix. Then Pearson correlation coeff is the ratio of X and square root of Y.