# Why do we need the covariance when calculating portfolio VaR?

I was recently learning about value at risk and how to calculate it, and one of the steps was to calculate the covariance of the returns of the securities making up the portofolio. This makes sense because if we consider the return of the securities as random variables ( and dont assume independence between them ) and the return of the portofolio is a random variable which is a weighted sum of the security random variables, we would need the covariance matrix. However, if all we need is the portofolio returns variance, why not just estimate directly? i.e get returns of the securities, weight sum them and use the sum along with a simple variance estimator to estimate the variance. I ran a couple of dummy simulation with 2 securities ( returns generated from a normal distribution), the first one where the 2 distributions are indepdent and the second where there was a covariance between them and both method estimated almost the same variance.

• Remember that equity returns are non-gaussian before you attempt to use this for anything important (like managing real money). Jul 22 at 11:46
• yea, i am currently looking at other distributions ( like johnson SU) that better fits the returns Jul 23 at 9:42