Active Share

An investor pays a fund 1% a year in fees for active management. How would they check that the fund is actually doing something different from just buying the benchmark index for free? One direct way: compare the fund's holdings, name by name and weight by weight, against the benchmark's holdings, and measure how much of the portfolio simply overlaps. That comparison is active share, introduced by Cremers and Petajisto in 2009 specifically to catch "closet indexers" — funds that charge active fees while holding a portfolio nearly identical to their benchmark.

The formula

$$\text{Active Share} = \frac{1}{2} \sum_i |w_{p,i} - w_{b,i}|$$

In words: for every stock in either the portfolio or the benchmark, take the absolute difference between the portfolio's weight and the benchmark's weight in that stock, add all those differences up, and divide by two. The divide-by-two matters: without it, every overweight in one stock is matched by an underweight somewhere else (weights must sum to 100% on both sides), so summing raw differences double-counts the same active decision once as an overweight and once as an underweight.

Worked example

A three-stock world. The benchmark holds Stock A at 50%, Stock B at 30%, Stock C at 20%. The fund holds Stock A at 30%, Stock B at 30%, and a new Stock D (not in the benchmark) at 40%, holding none of Stock C.

1. Stock A difference. $|30\% - 50\%| = 20\%$.
2. Stock B difference. $|30\% - 30\%| = 0\%$.
3. Stock C difference. $|0\% - 20\%| = 20\%$.
4. Stock D difference. $|40\% - 0\%| = 40\%$.
5. Sum and halve. $(20\% + 0\% + 20\% + 40\%) / 2 = 80\% / 2 = 40\%$.

This fund has 40% active share: 60% of its portfolio, in a weight-matching sense, could be reconstructed by just buying the benchmark, and 40% represents genuine active bets.

What this means in practice

Cremers and Petajisto's original research found that funds with the highest active share, combined with reasonably low turnover, tended to outperform their benchmarks net of fees, while low-active-share funds essentially never did once fees were subtracted, since there was almost no active decision-making to generate excess return in the first place. Institutional investors now routinely screen for active share before hiring a manager, specifically to avoid paying active fees for what amounts to indexing, and some regulators have pushed fund disclosure rules partly motivated by the closet-indexing problem active share made visible.