Sample Portfolio Problems

Calculate the covariance of returns in a joint distribution. Given the following equally likely outcomes for two joint variables, A and B.

Instance Return of Return of Ret A - EV(A) Ret B - EV(B) (Ret A - EV(A))(Ret B - EV(B))
Security A Security B
1 0.24 0.15 -0.0025 -.0.0625 0.0000391
2 0.16 0.12 -0.0825 -0.0925 0.0019078
3 0.26 0.25 0.0175 0.0375 0.0001641
4 0.31 0.33 0.0675 0.1175 0.0019828
- - - - - -
EV = 0.2425 0.2125 covariance = 0.0040938

Calculate the correlation coefficient, $\rho$, between the returns on two securities A and B if you know the covariance between them to be 24. The variance of security A is 25 and the variance of security B is 36.

Recall
(1)
\begin{align} \rho=\frac{cov(A,B)}{\sigma_A\times\sigma_B} \end{align}
Recall
(2)
\begin{align} \sigma=\sqrt{variance} \end{align}
Thus
(3)
\begin{align} \rho=\frac{24}{\sqrt{25}\times\sqrt{36}}=\frac{24}{5\times6}=0.8 \end{align}