# 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.

Here are the steps:- 1.First you need to calculate the historical return series for your portfolio from the historical return series for each fund by adding the returns for each fund on a daily basis taking weights into consideration. 2. Calculate the historical return series for your benchmark. 3. Calculate the difference between the returns of your portfolio and the benchmark for each day. 4. Once you get the return series for the difference between the two, calculate the standard deviation of this series.

I hope this helps. • Thanks for the response. I could be wrong but I thought the method you described is for ex post TE, whereas I'm looking for ex ante TE. Do you know anything about an ex ante method? – GT213 Dec 14 '16 at 13:38
• The above answer is for ex ante TE only . Please refer to the screenshot above in my answer which I have now included. – Manish Dec 14 '16 at 19:17
• Manish is right, the above methodology is ex ante (based on forecasts rather than actual results), since you assume historical relationship will persist in the future. Ex post analysis, would be to compare your realized (vs. historical simulated returns) to benchmark – user18489 Dec 14 '16 at 19:25
• This is ex post though isn't it, alright it might be simulated but it's still historical data? – Simon Nicholls Feb 15 '19 at 11:09

both of them are right，and Danish gives one way to compute ex ante tracking error。the importance is，at a given period （t1，t2），ex ante use information before t1（such as return series to compute cov matrix），however，ex post uses information between this period，and this is what “realized” means。

• Hi APOSTATE LOYAL, we expect answers to stand on their own, i.e. not refer to other answers. Could you edit your question to stand on its own and also remove the weird punctuation? – Bob Jansen Oct 30 '20 at 18:21