What is active share and how does it help detect closet indexing?

Active share measures the percentage of a portfolio's holdings that differ from the benchmark. It's a powerful tool for detecting "closet indexers" — managers who charge active fees but essentially replicate the index.

Formula:

Active Share = (1/2) × Σ |w_portfolio,i - w_benchmark,i|

Where the sum is over all securities in both the portfolio and benchmark.

Interpretation:

Active Share	Interpretation
0%	Exact index replication
20-40%	Closet indexer — mostly mimics benchmark
40-60%	Moderate active management
60-80%	Truly active — significant stock selection bets
80-100%	Highly active — concentrated, benchmark-agnostic

Example: Osprey Capital manages a US equity fund benchmarked to the S&P 500.

Stock	Osprey Weight	S&P 500 Weight	Difference
Titan Tech	5.0%	3.5%	+1.5%
Nova Motors	2.8%	0.0%	+2.8%
Atlas Bank	0.0%	2.2%	-2.2%
Meridian Health	1.5%	1.5%	0.0%
... (all other stocks)	...	...	Sum of absolute differences = 140%

Active Share = 140% / 2 = 70%

Osprey is truly active — 70% of its portfolio differs from the benchmark.

Active share vs. tracking error:

Metric	What It Measures	Limitation
Active share	Degree of holdings overlap	Doesn't capture factor bets
Tracking error	Volatility of return differences	Doesn't show position-level differences

The 2x2 matrix:

	Low Active Share	High Active Share
Low Tracking Error	Closet indexer	Diversified stock picker
High Tracking Error	Factor bet (macro tilts)	Concentrated stock picker

Closet indexing is a problem because:

• Investors pay active fees (1%+) for near-index returns
• After fees, closet indexers almost always underperform the benchmark
• Studies show that high active share funds have a better chance of outperforming (though not guaranteed)

Research finding: Cremers and Petajisto (2009) found that funds with the highest active share outperformed their benchmarks by ~1.5% per year, while those with the lowest active share underperformed after fees.

Exam tip: Know how to calculate active share from a table of weights, interpret the result, and distinguish it from tracking error. CFA Level II often tests the 2x2 classification framework.

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