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.
To find out the factors and marginal change if one of the constraints or assumption breaks.
Understanding the covariance of a portfolio is important because it allows investors to assess the risk of the portfolio and make informed decisions about how to allocate their investments.
When you make decision to put more money into one stock, you have to sacrifice the alternative investment. That may reduce your maximum return of your portfolio