Minimum Tracking Error Volatility

Investors assign part of their funds to asset managers that are given the task of beating a benchmark. The risk management department usually imposes a maximum value of the tracking error volatility (TEV) in order to keep the risk of the portfolio near to that of the selected benchmark. However, risk management does not establish a rule on TEV which enables us to understand whether the asset manager is really active or not and, in practice, asset managers sometimes follow passively the corresponding index. Moreover, the benchmark is sometimes difficult to be beaten when the risk managers only check that portfolio managers do not exceed a fixed level of relative risk. I derive analytical methods that could be used to understand whether the strategy used by the portfolio manager is active that allows him/her to have an excess return above the benchmark large enough to cover the commission paid by investors and, concurrently, that allows him/her to restrict the portfolio's variance to be not more than the benchmark's variance in order to avoid an excess return merely due to a higher risk level (using variance as risk indicator). These equations are a necessary (but not suffiient) condition to beat the benchmark's return, without increasing the overall variance of the portfolio. This is also a generalization of the model of Jorion (2003) with the use of commissions. I apply these equations to an Italian liquidity fund and I find that the fees are too high and the TEV is low. In fact, all the funds in the liquidity category show similar problems that often render the portfolio unable to cover the fees without increasing the variance.