A Sharpe ratio is size-invariant; returns are not. Capacity converts “does it work?” into “does it matter?”: the AUM at which the strategy’s own trading moves prices enough to consume its edge. The arithmetic needs four numbers you can estimate from any honest backtest — edge, turnover, the daily volume your orders could touch, and the signal’s decay — plus a participation cap, which forces execution to stretch over days and pays for the lower impact in decayed alpha. Defaults are editable and dated October 2026; the reasoning is in the capacity guide and the seven reasons a high Sharpe is not investable. Everything runs in your browser; nothing is uploaded.
The strategy
The market
Capacity
AUM at which net return hits the hurdle
AUM where the net Sharpe halves
Shared capacity
Dollar alpha — the fund-sized question
AUM that maximizes net dollar P&L
Peak net dollar alpha
Net return and dollar alpha against AUM
net return (%/yr, left axis) net dollar alpha ($/yr, right axis) dashed = capacity at hurdle
The AUM ladder
| AUM | 1-day participation | Execution days | Alpha captured | Impact drag | Explicit drag | Net return | Net Sharpe | Dollar alpha |
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Download the full net-return-vs-AUM curve as CSV.
Assumptions (edit me — defaults dated October 2026)
Per rebalance, the two-way notional traded is 2 × AUM × turnover. Executed in one day it would be that notional ÷ ADV of participation; if that exceeds the cap, execution stretches over H = participation ÷ cap days at the cap. Impact per dollar traded is k · σ_daily · √(daily participation); annual impact drag = rebalances × notional × impact ÷ AUM. Alpha captured over an H-day execution against a signal with half-life h is the average of 2^(−t/h) over t ∈ [0, H], normalized to a one-day execution (the backtest's convention), so stretching execution decays the edge while impact per dollar stays at the cap. Net = captured edge − explicit costs − impact; capacity is the largest AUM with net ≥ hurdle (net is monotone in AUM). Shared capacity divides by the number of others running the trade. Net Sharpe = net ÷ gross volatility.
How to read this
The arithmetic. Each rebalance trades 2 × AUM × turnover of notional. Divided by the daily volume you can actually touch, that is your participation; the square-root law prices every dollar traded at roughly k · σ · √participation, so the annual impact bill grows with the square root of AUM. Capacity is where that bill, plus explicit costs, equals the edge. The guide’s worked example — fifty liquid names with $50M of combined ADV, 10% daily turnover, a 6% gross edge — lands in single-digit millions here too; the point is not the constants but that five minutes of arithmetic bounds what a Sharpe is worth.
The cap turns impact into decay. Below the participation cap, more AUM means more impact per dollar. Above it, execution stretches over more days, impact per dollar stays at the cap, and the cost shifts to alpha that decays before you have finished trading. A five-day half-life loses a quarter of its edge to a four-day execution; a sixty-day half-life barely notices. This is why the capacity hierarchy runs from HFT (edge measured in ticks, capacity in millions) to low-turnover factors (edge in low single digits, capacity in billions): fast decay forces urgency, and urgency is impact.
Three different AUM numbers. The capacity at hurdle says where the strategy stops earning. The Sharpe-halving AUM is what to ask every paper that leads with its ratio. The dollar-alpha maximum is the fund-sized number: net return times AUM peaks well below capacity, and growing past it earns fewer dollars for more risk. A 3-Sharpe strategy earning 4% on $500k is a salary; this tool is the difference between that and a fund, stated in advance.
Capacity is shared. Your model prices your participation; the market bills aggregate participation in the trade. Published strategies are shared strategies, which is the mechanism behind post-publication decay and the reason the backtest’s capacity is an upper bound. Exit capacity in a stressed market is a fraction of calm-market ADV, and it is the binding constraint on the days that define the drawdown.
What it does not know. Whether the edge survives the slicing it assumes (the alpha-capture curve is a model, not a measurement), what your fills actually cost (calibrate k to them), and whether the gross edge is real: the deflated Sharpe calculator handles the last question, the transaction-cost calculator the explicit-cost line at fixed size. The capacity guide has the questions to ask a paper; why a high Sharpe may not be investable has the other six links in the chain.
Model: square-root impact with k · σ_daily · √(daily participation), execution capped at a daily participation rate and stretched over days, exponential alpha decay averaged over the execution window and normalized to the backtest’s one-day fill. October 2026 defaults are order-of-magnitude, not quotes.