Covariance of a stock portfolio

Question

I need to find the covariance of two stocks in a portfolio. I know you can calculate covariance as: cov = 1/(n-1)[(summation:Xi-(mean of X))*(summation:Yi-(mean of Y))]

However, I don't think I can use the formula above for the question I have. In the question I am trying to answer I am given the following information about two stocks (Asset A and Asset B):

                    A    B
Portfolio weight:  0.71   0.29 (i.e. 71% of the portfolio is invested in asset A, 29% in B)

Variances:        0.2209 0.3721

Standard Deviation: 0.47  0.61

Hopefully the above formatting is clear.

So, I need to figure out the co variance of the two assets, given the portfolio weight, variances, and standard deviation. Any help is much appreciated. Thanks.

Answer 1

If it is a $\text{minimum variance portfolio}$, then the equation for asset A is

$x_1=\frac{\sigma_2^2-\sigma_{12}}{\sigma_1^2+\sigma_2^2-2\sigma_{12}}$

where $x_1$ is the portfolio weight of asset A and $\sigma_{12}$ is the covariance between asset A and asset B.

Similar formula for the weight of asset B:

$x_2=\frac{\sigma_1^2-\sigma_{12}}{\sigma_1^2+\sigma_2^2-2\sigma_{12}}$

You only need one of the equations to determine the value of the covariance.