Statistical arbitrage capacity is a slippage problem disguised as an alpha problem. The Statistical Arbitrage Capacity engine on this pair (mean-reversion half-life 7 days, 36 trades/year, 8bp alpha, $10M daily volume, 2% daily volatility) returns a maximum theoretical position of about $25,000 per name at the strategy's 4bp slippage, and a capacity curve that runs $169,000 at zero slippage, $121,000 at 1bp and $81,000 at 2bp. The square-root impact model lands on retail-scale numbers because the edge left after costs is thin: 2.5bp of an 8bp alpha survives slippage and fees. The binding constraint is net edge per trade; the half-life sets how often that edge is collected.
TL;DR
- Scenario: mean-reversion half-life 7 days, 36 trades/year, 8bp alpha, $10M daily volume, 2% daily volatility.
- Engine maxAum: about $25,000 per name at 4bp slippage; practical AUM (half the alpha kept) is $0, because costs already take more than half the edge.
- Capacity curve at 0/1/2/3/5 bps slippage: $169,000 / $121,000 / $81,000 / $49,000 / $9,000.
- The curve crosses zero by 8bp: at 8bp and above the engine returns $0 capacity.
- Capacity scales with the square of the edge left after costs and linearly with dollar volume, so a thin-edge pair is small by construction.
- The binding constraint is net edge per trade; half-life sets the trade count, not the per-trade ceiling.
The scenario
A market-neutral pairs strategy on US equities1 with a 7-day mean-reversion half-life, executing 36 trades per year (3 per month, roughly matching the half-life-bounded turnover), 8bp alpha per trade against a $10M daily-volume name with 2% daily volatility, 1.5bp fees and an impact coefficient of 0.25. The Statistical Arbitrage Capacity tool returns a theoretical capacity curve.
| Slippage assumption | Theoretical AUM per name |
|---|---|
| 0 bps | $169,000 |
| 1 bp | $121,000 |
| 2 bps | $81,000 |
| 3 bps | $49,000 |
| 5 bps | $9,000 |
| 8 bps | $0 |
| 12 bps | $0 |
The engine's maxAum field returns about $25,000 at the strategy's 4bp slippage. The curve shows how capacity drops as the assumed slippage rises. At 5bp slippage it is already down to $9,000, and by 8bp, a realistic retail fill cost on mid-cap pairs, the engine returns $0: the average trade's slippage and fees have fully cancelled its alpha.
Why the curve drops
The model holds alpha per trade fixed and lets market impact grow with the square root of position size relative to daily volume, scaled by daily volatility: impact = 0.25 × 2% × √(position ÷ $10M). Fixed slippage and fees come off the top. Capacity is the position at which impact uses up the edge that slippage and fees leave, so it moves with the square of that remaining edge.
The curve is steep because the remaining edge is small: every basis point of extra slippage removes a large share of the 2.5bp that is left. Half-life enters through the trade itself: a 7-day half-life means the trade must close inside 7 days, and the alpha captured is bounded by the mean-reversion gap. Longer half-life pairs (30+ days) tend to carry larger per-trade alpha and can absorb more slippage before the curve crosses zero. The Cointegration Half-Life Solver gives the formal mapping from cointegration residual to half-life.
What retail capacity really looks like
The engine's number is already retail-scale for this pair, and even that overstates deployable capital. Two effects make it worse:
Slippage is much higher
Retail fills on mid-cap pairs typically realise 15-30 bps of slippage including spread, commissions, and impact. The engine's curve has already crossed zero by 8bp on this pair, so at a 15-30bp retail fill the model says there is no profitable capacity at all: the per-trade alpha is fully consumed by execution cost. The 8bp alpha-per-trade assumption is itself optimistic for retail; a higher-alpha, longer-half-life pair is what keeps the curve positive at realistic slippage.
For retail-scale capital (€10k-1M), the question is not "what is the maximum AUM" but "what is the minimum AUM at which the strategy is worth the effort." Below roughly €50k of capital deployed per pair, the per-trade dollar profit drops below the cost of execution and monitoring.
Half-life sets the trade count
A 7-day half-life implies roughly 50 round-trips per year per pair under perfect re-entry. The engine's 36 trades/year is the practical version with re-entry friction. Running 10 pairs simultaneously gives 360 trades/year — which is high enough to dominate the trader's attention budget without giving a meaningful Sharpe lift over 3-5 well-chosen pairs.
The empirical pattern in published stat-arb research: pair count above ~20 starts to be dominated by maintenance overhead rather than alpha2. The retail sweet spot is 3-8 carefully validated pairs, each with verified half-life and PBO < 0.3.
The cointegration prerequisite
Before any capacity number means anything, the pair must actually be cointegrated. The Engle-Granger test, the Johansen test, or a half-life-based stationarity check on the spread are the standard diagnostics3. A pair that fails cointegration is not a stat-arb pair; it is two random walks that happen to look correlated on a backtest window.
The Pair Trading Tester runs cointegration and half-life checks on uploaded price series. Half-life under 1 day is suspicious (probably a microstructure artefact); half-life over 60 days is too slow for a retail strategy to capture before regime change kills the relationship.
Trade-by-trade economics
For a single pair with half-life 7 days and $50k deployed per leg, the per-trade economics:
- Position notional: $50k per leg ($100k gross)
- Expected per-trade alpha: 30-80 bps of notional (typical for validated pairs)
- Slippage at retail: 15-30 bps round-trip
- Net per-trade alpha: 0-50 bps = $0-500 per trade
- 36 trades/year per pair: $0-18k annual P&L per pair
Multiply by 5 pairs: $0-90k annual P&L. The variance on this estimate is wide because slippage and alpha are both empirical. The Execution Simulator gives a slippage envelope on a chosen pair's order-book history.
When the strategy stops working
Stat-arb pairs decay. Three failure modes:
- Regime change. The underlying economic linkage that creates the cointegration breaks (corporate action, sector reclassification, macroeconomic regime). Half-life lengthens, then the relationship fails the cointegration test entirely.
- Crowding. Other traders find the same pair. Spread tightens, alpha shrinks, slippage stays the same. Capacity per trader drops.
- Microstructure shift. Tick-size change, exchange fee change, or a market-maker withdrawing from one side. Slippage rises, alpha is unchanged.
All three patterns show up as deteriorating live performance against backtest. The Walk-Forward Validator catches early signs by re-fitting the cointegration parameters on a rolling window — a half-life that drifts is a half-life that is about to fail.
Failure modes
- Treating maxAum as a deployable number. It is the theoretical ceiling at the modeled slippage, where net alpha is zero. Realistic retail slippage of 15-30bp sits past the 8bp zero-crossing, so the model says there is no profitable capacity at that fill cost.
- Sizing a strategy to the engine's slippage assumption without validating. Run the Execution Simulator on actual order-book snapshots to estimate true slippage at the chosen size.
- Ignoring the cointegration test. A pair that fails cointegration has no statistical foundation; the half-life is meaningless.
- Multi-pair correlation. Running 10 pairs that are all driven by the same factor is one bet at 10x leverage. Size the portfolio, not the trade.
FAQ
Why does the engine return such a small maxAum?
After 4bp of slippage and 1.5bp of fees, only 2.5bp of the 8bp edge is left for market impact. Square-root impact with a 0.25 coefficient on a 2%-volatility, $10M-a-day name uses that up at about $25,000 per position. The maxAum is the ceiling at the modeled slippage, not at zero friction. The practical number is lower still: realistic retail slippage of 15-30bp sits past the 8bp zero-crossing, where the model returns no profitable capacity.
What half-life is too short for retail?
Under 3 days, the round-trip execution cost typically exceeds the alpha. The strategy works on institutional infrastructure with sub-bp execution, not on retail platforms with 10-30 bp realised cost.
How do I check if my pair is actually cointegrated?
Run the Engle-Granger or Johansen test on the price series. The half-life of the spread residual should be stable across rolling windows. The Pair Trading Tester wraps these tests; for the formal test detail, the standard reference is Lopez de Prado's Advances in Financial Machine Learning4.
Connects to
- Walk-Forward Validation Cookbook: catches pair decay early.
- Backtest Overfitting LLM Strategies: PBO Explained: qualify the backtest first.
- Execution Simulation: Slippage Impact: slippage at retail scale.
- How to Read a Backtest Report: turn the capacity curve into a deployment decision.
- Statistical Arbitrage Capacity: re-run on your pair.
- Statistical Arbitrage Capacity methodology: full input/output specification.
References
Footnotes
-
Avellaneda, M., & Lee, J. H. (2010). "Statistical arbitrage in the U.S. equities market." Quantitative Finance 10(7), 761–782. tandfonline.com ↩
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Gatev, E., Goetzmann, W. N., & Rouwenhorst, K. G. (2006). "Pairs Trading: Performance of a Relative-Value Arbitrage Rule." Review of Financial Studies 19(3), 797–827. academic.oup.com ↩
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Engle, R. F., & Granger, C. W. J. (1987). "Co-Integration and Error Correction: Representation, Estimation, and Testing." Econometrica 55(2), 251–276. jstor.org/stable/1913236 ↩
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Lopez de Prado, M. (2018). Advances in Financial Machine Learning. Wiley. Chapter on mean-reversion strategies and pair trading. ↩
Verified engine output
Show the recompute-verified inputs and outputs
| signal_half_life_days | 7 |
|---|---|
| daily_volume_usd | 10000000 |
| daily_vol_pct | 2 |
| names | 1 |
| slippage_bps | 4 |
| fee_bps | 1.5 |
| alpha_per_trade_bps | 8 |
| impact_k | 0.25 |
| trading_days | 252 |
| max aum | 25000.000000000004 |
|---|---|
| practical aum | 0 |
| max aum per name | 25000.000000000004 |
| practical aum per name | 0 |
| trades per year | 36 |
| impact bps at practical aum | 0 |
| annual net return at practical aum | 0 |
| annual net pnl usd at practical aum | 0 |
| capacity curve (9 items) | [...] |
Computed live at build time.