Tracking error can be calculated as the standard deviation of the difference between a portfolio’s returns and its benchmark’s returns:-
Where TE refers to the tracking error and s(Rp – RB) indicates that we take the sample standard deviation (indicated by s) of the time series of difference between the portfolio return, Rp, and the benchmark return, RB.
We should be careful that active return and tracking error are stated on the same time basis.
Tracking error can be caused by two reasons. First, by the trading cost and second, by improperly replicating the index.
For an ETF, tracking error is the deviation in performance of the fund and its index. It occurs primarily because of the ETF’s total expense ratio (a kind of trading cost).
Tracking error from erroneous replicating an index creeps in when the index gets rebalanced and repopulated with a new makeup of securities, but the fund’s basket of securities is yet to be changed to reflect that.