Covariance of random variables (returns)

Question

How large are the correlations between each pair of the securities?

I only know how to calculate their correlations if I knew their joint (discrete) distributions,since I need $E(K_jK_i), j \neq i$ . But is there any other way to get their pairwise correlations?

Answer 1

The covariance between $K_1$ and $K_2$ is

$Cov(K_1,K_2)=0.1\cdot (0.1053-\overline r_1)\cdot (0.0723-\overline r_2)$

$+0.3\cdot (0.1378-\overline r_1)\cdot (0.1057-\overline r_2)+0.6 \cdot (0.1182-\overline r_1)\cdot (0.1215-\overline r_2)$

$\overline r_1$ is the average return. $\overline r_1=0.1\cdot 0.1053+0.3\cdot 0.1378+0.6 \cdot 0.1182$

Similar for $\overline r_2$

And $Var(r_1)=0.1\cdot (0.1053-\overline r_1)^2+0.3\cdot (0.1378-\overline r_1)^2+0.6 \cdot (0.1182-\overline r_1)^2$

Finally you know that $Corr(K_1,K_2)=\frac{Cov(K_1,K_2)}{\sqrt{Var(K_1)\cdot Var(K_2)}}$