What is active share and how does it help detect closet indexing?
CFA Level II mentions 'active share' as a measure of how different a fund is from its benchmark. How is it calculated and what does it tell you about a fund manager's approach?
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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