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The risk management department usually imposes to asset managers a maximum value of the tracking error volatility (TEV), but it does not establish a rule on TEV to understand whether portfolio managers are active.

Analytical methods are derived to understand whether the asset allocation is active allowing to have an excess return above the benchmark large enough to cover the commission paid by investors and, concurrently, allowing to restrict the variance of the portfolio to be no more than the benchmark’s variance, in order to avoid an excess return merely due to a higher risk level. These equations are a necessary (but not sufficient) condition to beat the benchmark’s return, without increasing the overall variance of the portfolio.

This is also a generalisation of the Jorion (2003) model with the use of commissions.

These equations are applied to a liquidity fund and the fees are found to be too high.