# VaR Calculation - Covariance matrix is not positive semidefinite

This is a basic question.

I have three assets, equally weighted, and all the mutual covariances are -1. Then, the covariance matrix looks like -

 1  -1  -1
-1   1  -1
-1  -1   1


Now, to calculate the VaR, I need to calculate the portfolio variance.

Am I correct in concluding that I can't calculate the portfolio variance because this matrix is not positive semidefinite? Here is some R code -

v = matrix(c(1, -1, -1, -1, 1, -1, -1, -1, 1), ncol=3)
eigen(v)
> $eigenvalues > 2 2 -1 library(micEcon) semidefiniteness(v) > FALSE  My next question is: Given ANY symmetric matrix by a user, how do I figure out if I can use it to calculate portfolio variance (or the covariance matrix)? Additionally, given the three assets, I can use them to create a weighted time series for the portfolio and calculate the mean and variance of that, and use that to calculate the VaR. How is that different from calculating VaR using teh covariance method? • Be careful to distinguish the variance of a portfolio and its VaR that stand for Value At Risk. I guess your are trying to compute the Variance$\sigma^2\$, and this question is hence barely on-topic, since it is basic quantitative finance. – SRKX Aug 19 '13 at 7:23