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A 2015 study* argues that a simplified measure of activeness, termed active weight, is even more effective than active share. Unlike active share, it does not need to assume an appropriate benchmark index, but simply compares the weights of the stocks held by a fund with the weights these stocks would have had if they had been weighted in proportion to their market capitalizations.
The empirical results presented in the study support the claim that active weight is more effective than active share, and captures something different. However, it may be prone to the same issues that plague active share. For instance, active weight also tends to be higher for small-cap funds than for large-cap funds, and it is unclear how effective the measure is within these categories. It is also unclear what would happen if we adjusted active weight appropriately for differences in active risk and fee levels.
*Doshi, Elkamhi & Simutin, “Managerial Activeness and Mutual Fund Performance”, Review of Asset Pricing Studies 5 (2), 2015, pp. 156-184