The answer is a single inequality:
$$IR \cdot TE > \text{Fee differential vs. passive benchmark}$$
If the fund's Information Ratio multiplied by its Tracking Error — definition">tracking error exceeds the extra cost you pay over a passive index fund in the same category, the active fee is worth paying. If not, the index fund wins on pure economics. [2]
IR (Information Ratio) = alpha ÷ tracking error. It measures how efficiently the manager converts active risk into active return. [10]
TE (Tracking Error) = Volatility — definition">volatility of the fund's returns relative to its benchmark. A TE below 3% signals a closet indexer; above 6% signals genuinely active, high-conviction bets. [3]
Fee differential = active fund's Expense Ratio — definition">expense ratio minus the cheapest index fund in the same category.
| Large-Cap Active | Mid-Cap Active | |
|---|---|---|
| Active fund expense ratio | 1.2% | 1.0% |
| Index fund expense ratio | 0.10% | 0.20% |
| Fee differential | 1.1% | 0.8% |
| Demonstrated IR | 0.2 | 0.6 |
| Tracking error | 4% | 6% |
| Expected alpha (IR × TE) | 0.8% | 3.6% |
| After fee differential | −0.3% (fail) | +2.8% (pass) |
The large-cap fund doesn't clear the hurdle. The mid-cap fund does. [2]
Mid-cap and small-cap categories have lower analyst coverage, higher residual volatility, and more information asymmetry — the conditions where a skilled manager's edge actually compounds into alpha. [4]
Apply this → Go to Explore Funds, sort by 5-year Information Ratio, and run the $IR \times TE > \text{fee differential}$ test against the appropriate benchmark for each fund you hold.