Strategy Capacity Estimation Before Scaling Capital

When to Use

Use this skill when deciding how much capital a quantitative strategy can absorb before its own trading destroys its edge. As AUM scales, traded notional scales with it, and execution cost per dollar traded grows with the square root of participation. That drag compounds against a fixed gross alpha, so net return per dollar falls and the realized Sharpe ratio decays. The engine walks an AUM grid, prices half-spread and market-impact drag at each level, and reports the largest AUM that still clears both a minimum net Sharpe gate and a maximum ADV participation cap — along with which of the two bound first.

Reach for it before an allocation increase, when sizing a new strategy's target book, or when a research backtest run at $1M is about to be promoted to institutional size.

When NOT to Use

• As an alpha-decay model. annual_gross_return_pct is assumed invariant to AUM. Real gross alpha decays with size independently of execution cost — signal capacity exhausts, the book dilutes into worse names, and crowding erodes the edge. Every capacity number this engine produces is therefore an upper bound. Treat it as a ceiling to stay under, never a target to reach.
• As a per-name liquidity check. The engine compares aggregate portfolio turnover against a single aggregate avg_daily_volume_usd. A real book spreads turnover across names whose ADVs differ by orders of magnitude, and capacity binds on the least liquid names long before it binds on the aggregate. Pair with liquidity-adjusted-position-sizing and concentration-risk-single-name-limits.
• With an uncalibrated impact_gamma. The square-root prefactor $Y$ is the single largest lever on the result and the default sits at the optimistic end of the empirical range. An unfitted value produces a confident but meaningless capacity figure.
• As an execution scheduler or a risk control. Nothing here slices orders, sets a participation schedule, or halts anything. For scheduling see execution-algo-twap-vwap-slicing and multi-day-execution-schedules-for-very-large-orders; for enforcement see kill-switch-and-drawdown-circuit-breakers.
• For a strategy that never clears its Sharpe gate at any size. That result comes back as BELOW_MIN_SHARPE_AT_ALL_SIZES and is a strategy-quality verdict, not a capacity limit — more liquidity would not relieve it.

Prerequisites

• Strategy performance parameters (StrategyParameters: strategy_id, annual_gross_return_pct, annual_volatility_pct, daily_turnover_pct, avg_daily_volume_usd, avg_daily_volatility_pct, half_spread_bps, max_participation_rate_pct, min_acceptable_sharpe, risk_free_rate_pct).
• Unit contract: returns, volatilities, and turnover are fractions (0.25 = 25%); half_spread_bps is in basis points; max_participation_rate_pct is a percentage (5.0 = 5% of ADV). avg_daily_volume_usd must be in the same currency as AUM.
• daily_turnover_pct is one-way notional traded per day as a fraction of AUM, paired with a half-spread charged once on that notional. If your turnover figure is two-way, halve it before passing it in or you double every cost in the model.
• An impact_gamma fitted to your own realized slippage. Empirical values for stocks and futures fall roughly in $0.5 \dots 1.0$; the 0.5 default is the optimistic end.

Workflow

1. Fix the unit and horizon contract before anything else:
   • Non-finite inputs are rejected, not priced. A NaN return propagates to a NaN Sharpe, and because every comparison against NaN is False the gate silently passes — the engine would otherwise report a confident capacity for an unpriced strategy.
   • Zero volatility and zero ADV are rejected rather than divided by. Zero volatility is a division by zero, not an infinitely good strategy; zero ADV is an untradeable instrument, not one of unbounded capacity.
   • Decide whether annual_gross_return_pct is a total or an excess return. If total, set risk_free_rate_pct; leaving it at 0.0 credits the risk-free rate to the strategy and overstates every Sharpe by $r_f/\sigma$.
2. Daily friction modelling at each AUM level:
   • Daily one-way notional $Q = \text{AUM} \times \text{turnover}$; participation $= Q / \text{ADV}$.
   • Square-root impact law: $I(Q) = Y \cdot \sigma_{\text{daily}} \cdot \sqrt{Q / V}$ — not Almgren-Chriss, which is a linear-impact optimal-execution model (see references/standards.md).
   • Half-spread cost $= Q \times \text{half_spread_bps} / 10^4$, charged once on one-way notional.
   • Both are annualised over 252 trading days. Crypto and FX venues do not follow that convention.
3. AUM grid construction:
   • The grid is $\text{step}, 2 \times \text{step}, \dots \le \text{max_search}$, index-derived rather than accumulated — repeated += on a non-representable step drifts and can drop the final point.
   • A non-positive step and a step wider than the search range are rejected: the first never terminates, the second yields an empty curve whose zero capacity is indistinguishable from a real answer.
4. Net Sharpe decay: $\text{Sharpe}{\text{net}} = (R{\text{net}} - r_f) / \sigma_{\text{strategy}}$, using gross strategy volatility. Costs are modelled as a deterministic drag, so realized impact variance is ignored and net Sharpe is biased upward.
5. Capacity limit and limiting factor:
   • Capacity is the largest AUM with an unbroken feasible run beneath it — the search stops at the first breach. Taking the last feasible point anywhere on the grid would jump across a breached region.
   • Classify the binding constraint: ADV_PARTICIPATION_LIMIT, MIN_SHARPE_BREACH, BELOW_MIN_SHARPE_AT_ALL_SIZES, or SEARCH_RANGE_EXHAUSTED. The last means no gate broke inside the searched range — the answer is censored by the loop bound and is not evidence of unlimited capacity. Widen max_search_aum_usd and re-run before treating it as anything.
6. Read the optimum correctly: optimal_sharpe_capacity_aum_usd maximises net dollar PnL among feasible points only. Net dollar PnL keeps climbing well past the point where the strategy breaches its own gates, so the unconstrained peak is reported separately as unconstrained_max_pnl_aum_usd — a diagnostic, never an allocation target.
7. Execution output: structured StrategyCapacityReport, carrying capacity_resolution_usd, search_range_exhausted, and the impact_gamma and risk_free_rate_pct actually used, so the number is auditable rather than merely reported.

Full procedure: see references/workflows.md. Standards reference: see references/standards.md. Printable pre-flight checklist: see assets/checklist.md.

Common Pitfalls

• Calling the square-root law "Almgren-Chriss". Almgren and Chriss (2000) solve optimal liquidation under linear temporary and permanent impact; they do not propose a square-root law. The $\sigma\sqrt{Q/V}$ form is a separate empirical regularity from Torre/BARRA (1997) and Grinold and Kahn (1999). Earlier versions of this skill made exactly this mis-attribution. Citing the wrong paper hides that the exponent is an empirical fit — and one that Almgren et al. (2005) and Kyle and Obizhaeva (2016) put nearer $0.6$ than $0.5$.
• Shipping the default impact_gamma. Impact drag is linear in $Y$, but capacity is not: where the Sharpe gate binds it scales as $Y^{-2}$, so moving from the $0.5$ default to the top of the measured $0.5\dots1.0$ range cuts estimated capacity roughly fourfold — on the reference parameters, from $133M to $33M. Running uncalibrated does not produce a rough estimate; it produces a systematically optimistic one, and the direction of the error is always toward over-allocation. (Where the participation cap binds instead, capacity is independent of $Y$ — check the limiting_factor before deciding how much the calibration matters.)
• Reading SEARCH_RANGE_EXHAUSTED as unlimited capacity. It means the loop ended, not that the strategy scales. Scaling to max_capacity_aum_usd in that state is scaling to a function argument you chose arbitrarily.
• Allocating to the unconstrained PnL peak. With the reference parameters, net dollar PnL is still rising at $100M against a true capacity of $25M. Bigger is more profitable right up until the participation cap makes the fills unachievable, and the dollar-PnL curve gives no warning at that boundary.
• Treating max_capacity_aum_usd as exact. It is a grid point. True capacity lies within capacity_resolution_usd above it, and 0.0 means "below one grid step", not "exactly zero".
• Dividing total return by volatility and calling it Sharpe. A Sharpe ratio is an excess return per unit of risk (Sharpe 1994). At a 4% risk-free rate against 15% volatility, omitting $r_f$ adds $+0.27$ — enough on its own to carry a strategy over a 1.0 gate it does not clear.
• Believing the 5% ADV cap is a rule. It is a practitioner risk convention with no general regulatory backing. The US ADV-anchored limit that does exist — SEC Rule 10b-18's 25% ADTV volume condition — is a non-exclusive safe harbour for issuer repurchases and does not apply here. See references/standards.md.
• Applying an aggregate ADV to a diversified book. Comparing total portfolio turnover against a single blended ADV hides the illiquid tail, which is where capacity actually binds first.
• Projecting a frictionless backtest Sharpe onto institutional AUM. A strategy that shows 1.67 at $1M is not a 1.67 strategy at $100M, and the gap is not a rounding error.

Verification

• Instantiate StrategyCapacityEstimatorEngine(impact_gamma=0.5) with a 25% gross / 15% vol strategy, 10% one-way daily turnover, $50M ADV, 1.5% daily volatility, 1 bp half-spread, 5% participation cap. Verify frictionless Sharpe $1.67$ at $r_f = 0$.
• At AUM $$25\text{M}$, verify against the hand derivation: participation exactly $5.00%$, spread cost $$63{,}000$, impact cost $$1{,}056{,}542.12$, net PnL $$5{,}130{,}457.88$, net Sharpe $1.3681221015$.
• Verify the participation cap is inclusive: $$25\text{M}$ is feasible and $$26\text{M}$ is not, giving max_capacity_aum_usd $= $25\text{M}$ and limiting_factor $=$ ADV_PARTICIPATION_LIMIT.
• Verify optimal_sharpe_capacity_aum_usd $\le$ max_capacity_aum_usd, while unconstrained_max_pnl_aum_usd reaches the $$100\text{M}$ search ceiling — the feasible optimum must not follow the dollar-PnL curve past the cap.
• Set $r_f = 0.04$ and verify frictionless Sharpe drops to exactly $1.40$, and that every curve point drops by $0.04/0.15$.
• Verify impact obeys the square-root law: quadrupling traded notional exactly doubles impact, and doubling impact_gamma exactly doubles it.
• Verify a search that breaches nothing returns SEARCH_RANGE_EXHAUSTED with search_range_exhausted=True, never UNLIMITED.
• Verify NaN/Inf inputs, zero volatility, zero or negative ADV, negative turnover, a non-positive aum_step_usd, and a step wider than the search range all raise rather than returning a report.
• Run python -m unittest discover -s skills/strategy-capacity-estimation-before-scaling-capital/scripts.

Related Skills

• portfolio-construction-with-transaction-cost-awareness
• incremental-capital-deployment-for-new-strategies
• liquidity-adjusted-position-sizing
• execution-cost-model-recalibration-cadence
• capital-reallocation-based-on-live-performance