A tracking error tells you how much a portfolio moves differently from its benchmark. It does not tell you how differently it is built. Cremers and Petajisto's contribution, published in the Review of Financial Studies in 2009, was to measure the holdings directly:
Active Share = 0.5 x sum over i of |w_P,i - w_B,i|
How is active share calculated and read?
Half the sum of the absolute deviations, taken over the union of names in the portfolio and the benchmark. For a long-only, fully invested portfolio it has two equivalent readings that are worth carrying, because either can be the faster route on a given data set. It equals the sum of the overweights, since overweights and underweights are equal in size and opposite in sign. And it equals one minus the overlap, 1 - sum of min(w_P,i, w_B,i), which is the fraction of the portfolio that is not simply the benchmark in disguise.
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The interpretation is direct. A portfolio identical to the benchmark has an active share of zero. A portfolio sharing no holdings with it has an active share of 100 percent. A long-only fund's active share is bounded above by one minus its overlap with the index, which means a fund benchmarked to a concentrated ten-name index cannot reach the same active-share levels as one benchmarked to a five-hundred-name index even if both are equally opinionated. The commonly quoted thresholds, roughly 60 percent as the boundary below which a fund starts to look like an index tracker and 90 percent as genuinely stock-picking, were calibrated on broad US equity benchmarks. Applying them unchanged to a sector fund or a concentrated index is a mistake, and Worked Example 1 shows a genuinely aggressive Indian book landing at 64 percent for exactly this structural reason.
How does active share split into sector and stock bets?
Active share also splits into two economically different bets, and the split is the useful part. For a name i in sector s, write its active weight as the sum of a within-sector deviation and a sector deviation:
w_P,i - w_B,i = [w_P,i - (W_P,s / W_B,s) x w_B,i] + [(W_P,s / W_B,s) - 1] x w_B,i
The first bracket is what the manager did inside the sector after her sector weight was fixed, which is stock selection. The second is her sector bet. Summing absolute values gives a within-sector active share and an across-sector active share, the latter equal to 0.5 x sum over sectors of |W_P,s - W_B,s|.
The two components bound the total rather than adding to it, because absolute values do not add: a name whose selection deviation and sector deviation point in opposite directions contributes less to the total than the two parts add up to. On Worked Example 1's book the across-sector figure is 28.0 percent, the within-sector figure 57.59 percent, and the total 64 percent, so 21.59 points of the parts cancel. The reading is what matters: 28 of the 64 points of active share, or 43.75 percent of it, is a sector bet that a cheap sector-rotation product could reproduce, and the client should know that before paying a stock-picker's fee for it.
What goes wrong when you calculate active share?
Two failure modes are worth naming because both are common. Active share computed against the wrong benchmark variant is meaningless, and the variant question is the same one that governs any alpha computation: same universe, same date, same treatment of cash and derivatives. And active share computed on a stale holdings file measures where the fund was, not where it is. Most jurisdictions require holdings disclosure with a lag, monthly for Indian mutual funds and quarterly for US funds through their portfolio-holdings filings, so an active share is always a statement about a past date and should be dated when quoted.