How to use the strategy capacity calculator
- Describe the liquidity. With one typical instrument, enter its average daily dollar volume (ADV), daily volatility and the number of positions held at once. With a list of instruments, enter each name with its ADV and daily volatility; every row is one equal-weight position.
- Set the maximum participation rate, the largest share of a day’s volume one trade may take. Limits of 1% to 10% are common, depending on how patient the execution is.
- Set the acceptable impact per trade in basis points, applied to each entry and each exit.
- Enter the average holding period in days. It sets how many round trips each position makes a year.
- Enter the impact coefficient Y, the gross alpha per trade and the fixed costs per round trip (spread and commissions). Gross alpha is the expected return of one round trip before any costs, as your backtest would show it at small size.
How capacity is calculated
The model assumes equal weights: with assets A and N positions, every trade is A ÷ N and is completed within one day. Impact follows the square-root law:
Each constraint gives a maximum fund size. With a list of instruments the least liquid one sets the limit:
Impact budget: A ≤ N × Vi × (I ÷ (Y × σi))²
Capacity = the smaller of the two, over all instrumentsρ is the maximum participation rate and I the acceptable impact per trade, as fractions.
The net alpha of a round trip pays fixed costs once and impact twice, on entry and on exit:
Zero net alpha: A* = N × ((α − c) ÷ (2Y × k))²
Largest dollar profit: A = 4/9 × A*
Annual net return = Net alpha × 252 ÷ holding periodα is the gross alpha per round trip and c the fixed costs. The profit-maximizing size comes from maximizing A × Net alpha(A).
A worked example
A strategy holds 20 equal positions in stocks that trade about $50,000,000 a day with 2% daily volatility, and holds each position for 10 days. It expects 50 bps of gross alpha per round trip and pays 4 bps in spread and commissions.
- A 5% participation limit allows $50.00M.
- A 20 bps impact budget allows only $10.00M, so capacity is $10.00M, set by impact, with trades of $500,000 per position.
- At that size, each trade nets 6.0 bps, or 1.51% a year on the fund.
- Dollar profit peaks at $5.88M, where the fund earns 3.86% a year ($227,117), and the edge disappears entirely at $13.23M.
The impact budget usually binds first
With the square-root law, impact rises quickly from the first dollar. A 20 bps budget on a stock with 2% daily volatility allows a trade of only 1% of ADV; the 5% participation limit would allow five times that. Participation limits keep execution practical; impact decides what the trades cost. That is why capacity estimates built only on “x% of volume” are usually far too generous for strategies with short holding periods.
The constraints also have to agree with the alpha. In the example the impact budget allows $10.00M, but at that size impact takes most of the edge. Tightening the budget to 10 bps lowers capacity to $2.50M and leaves 26.0 bps per trade. A strategy with only 30 bps of gross alpha has a zero-alpha size of $4.22M, below the impact-budget capacity, so the budget should be set from the alpha rather than chosen independently.
What changes capacity most
| Change from the example | Capacity | Zero net alpha | Largest profit at |
|---|---|---|---|
| The example | $10.00M | $13.23M | $5.88M |
| Impact coefficient Y of 0.5 | $40.00M | $52.90M | $23.51M |
| 50 positions | $25.00M | $33.06M | $14.69M |
| Gross alpha of 30 bps | $10.00M | $4.22M | $1.88M |
| List of six stocks | $639,053 | $2.95M | $1.31M |
Capacity scales with 1 ÷ Y², so halving the impact coefficient quadruples every figure: the calibration of Y matters more than any other input, and it is the least certain one. Spreading the book over more positions raises capacity in proportion. With a list of instruments and equal weights, the least liquid name sets the limit for the whole book; in the example list it is Stock D, with the smallest volume and the highest volatility. Weighting positions by liquidity would raise capacity, at the cost of concentrating the book in the most traded names.
Assumptions and limitations
- The square-root law is an average. It describes the typical impact of metaorders across many trades; individual orders scatter widely around it, and the coefficient differs by market, time period and execution style. Calibrate Y against your own fills where you can, using the market impact calculator.
- Each trade is completed within one day, entries and exits alike. Spreading trades over several days relaxes the participation limit, but impact under the square-root law depends on the total size relative to daily volume, not on the speed, so it barely helps the impact budget.
- Equal weights and constant liquidity. Volume and volatility change over time; capacity shrinks in quiet markets and in stress, exactly when exits matter most.
- No crowding or decay. Other traders running similar signals share the same liquidity, and alpha that is widely known tends to shrink. Both lower real capacity below these estimates.
- Gross alpha comes from somewhere. A backtest that looks good at small size may be overfitted; test it before scaling, for example with the backtest overfitting calculator.