Covariance Matrix C given expected returns

Question

If I'm given the expected returns, standard deviations, and correlation coefficients how can I compute the covariance matrix C?

Answer 1

The covariance matrix of the returns $r_1, r_2, \ldots, r_n$ looks like

$$ \begin{pmatrix} \operatorname{Var}(r_1) & \operatorname{Cov}(r_1,r_2) & \cdots & \operatorname{Cov}(r_1,r_n) \\ \\ \operatorname{Cov}(r_2,r_1) & \operatorname{Var}(r_2) & \cdots & \operatorname{Cov}(r_2,r_n) \\ \\ \vdots & \vdots & \ddots & \vdots \\ \\ \operatorname{Cov}(r_n,r_1) & \operatorname{Cov}(r_n,r_2) & \cdots & \operatorname{Var}(r_n) \end{pmatrix}$$

And the correlation coefficient of $r_i$ and $r_j $ is

$$\large{\rho_{r_i,r_j}}\normalsize =\frac{Cov(r_i,r_j)}{\sqrt{Var(r_i)\cdot Var(r_j)}}, \quad 1\leq i,j \leq n$$

Since you know the variances and correlation coefficients the corresponding covariances can be calculated straightforward.