Not an implementation claim. Capacity analysis is the arithmetic that converts “does it work?” into “does it matter?” — the question that separates academic from implementable and the number conspicuously absent from most published backtests.
Definition. A strategy’s capacity is the asset level at which expected net returns fall to some threshold (zero, or an opportunity-cost hurdle) because the strategy’s own trading moves prices against it. It exists for every strategy, because impact grows with participation while edges don’t.
The estimation arithmetic
A serviceable first-order capacity model needs four numbers you can estimate from any honest backtest:
per-rebalance participation = (AUM × turnover_per_rebalance) / (universe ADV captured)
impact per rebalance ≈ k · σ · √participation (square-root law)
capacity: solve for AUM where annualized impact ≈ gross edge
Worked example: a daily-rebalanced strategy trading 50 liquid names ($50M combined relevant ADV), 10% daily turnover, gross edge 6%/yr, daily σ ≈ 1.5%, k ≈ 0.5. At $100M AUM: participation = 20% of ADV — deep in impact territory; the square-root law prices each rebalance at ~34 bps, ~85%/yr annualized — absurd, the strategy is far over capacity. Iterate downward and the viable AUM lands near single-digit millions. The point isn’t the constants (calibrate k to your own fills); it’s that five minutes of arithmetic bounds what a paper’s Sharpe is worth — and routinely reveals published strategies to be salary-sized, not fund-sized.
The capacity hierarchy
Capacity is set by holding period × universe liquidity — which orders the strategy world:
| Strategy type | Typical capacity order | Why |
|---|---|---|
| HFT / market making | $1–100M | Edge per trade ~ticks; participation caps are brutal |
| Tick/LOB signals | similar | Fast decay forces urgency; urgency is impact |
| Stat-arb / short-horizon equity | $100M–low $B | Breadth helps; turnover hurts |
| Momentum-family factors | $B-scale, contested | Turnover mid; crowding severe |
| Low-turnover value/quality tilts | $10B+ | Slow trading in liquid names |
| Beta | ~unbounded | Nothing to compete away |
The diagonal is the industry’s structure: high-Sharpe/low-capacity strategies fund proprietary desks; low-Sharpe/high-capacity ones become products. A paper’s implied position on this diagonal tells you who could possibly care about its result — and at what fee.
Capacity is shared: the crowding correction
Your capacity model prices your participation; the market bills aggregate participation in the trade. Published strategies are shared strategies, so effective capacity is divided among everyone running the signal — the mechanism behind post-publication decay and the reason crowding proxies belong in capacity estimates. Corollary: capacity estimated from a backtest (you alone) is an upper bound that publication itself erodes.
Common ways capacity fails in production
- The backtest’s fills assumed away the question: unconstrained position sizes in thin names mean the reported Sharpe was earned at an AUM near zero.
- Scaling changed the strategy: liquidity caps and participation limits added at size reshape the portfolio until realized returns decorrelate from the research version — you’re running a different, undertested strategy.
- Capacity consumed by success: the strategy works, AUM grows, returns decay on schedule, and the decay gets misdiagnosed as regime or alpha loss instead of self-impact. Track return-vs-AUM explicitly.
- Exit capacity ≠ entry capacity: positions accumulated patiently must sometimes exit urgently; stress liquidity is the binding constraint, and it’s a fraction of calm-market ADV.
Questions to ask a paper
- What AUM do the reported positions imply against the universe’s ADV?
- Does performance survive a 5%-of-ADV participation cap?
- Where does the strategy sit on the hierarchy, and does its Sharpe make sense for that seat?
- If this were published and adopted, what’s the shared capacity?
What our scoring captures
Capacity reporting is rare enough to be a top-decile rigor signal — papers with participation caps, liquidity-bucketed results, or explicit capacity estimates announce that the authors have met real order books. The hierarchy also explains a scoring pattern: HFT-hub papers can be simultaneously high-rigor and low-relevance to most readers — sound science about seats you can’t sit in. The score certifies the evidence; the arithmetic above tells you if the seat is yours.
Run your numbers: capacity estimator → · The impact law: transaction costs → · The consequence: why high Sharpe ≠ investable → · factor tradability →