# How to calculate ex Ante Tracking Error

I'm looking to find the correct way to calculate the ex ante tracking error of a portfolio.

If say I have 10 funds, and their historical returns series (used to calculate mean return, standard deviation and correlations/ covariances or anything else needed) how would I calculate the ex ante tracking error for a portfolio made up of the 10 funds, with weights fixed?

Thank you

For ex-ante tracking error, you need a forecast covariance matrix $C$. Then the quantity you require is $\sqrt{w^{T}Cw}$, where $w$ is a vector of excess weights relative to the benchmark. You can construct a forecast covariance matrix from realized covariances if you think historical relationships will persist, or you use other methods, for example factor models.