# Portfolio risk estimation through variance covariance matrix

Is the portfolio risk calculated through variance covariance matrix an estimate of the current risk of the portfolio? Suppose I am using the weights as of today, and I have estimated the variance covariance matrix from historical returns of the assets and I calculate portfolio risk as wVw'. Is it an estimate of the future risk in the portfolio?

How does this estimate relate to the realized portfolio risk i.e. the standard deviation of the portfolio returns?

The calculation you provide is the realized historical variance of the portfolio. The volatility would be the square root of this calculation and would be equal to the realized portfolio risk.

If one views that the future will look like the historical period which was used to calculate the volatility you describe, one can use this as an estimate of future risk. There are other methods to estimate future risk such as GARCH.

• Thanks. But does this hold over multi-periods? Given that the weights in the portfolio would change based on relative performance over time, would the estimate be equal to the realized vol. I did some simulations (generated monthly returns over a period of 36 months) and used the resulting VCV and the closing weights to estimate portfolio variance. It did not match the variance of the portfolio returns. Feb 21 '18 at 14:32
• @ragster: Rarely does any future look like exactly like the past. Using recent historical data is one way of estimating what the near future will look like. However, it would be dumb luck if that number would be exactly the future realized volatility. You identified one reason that your realized volatility would not be identical than your calculated volatility--which is that the performance (and hence the weights) of your constituent portfolio would change. Feb 21 '18 at 14:37