Statistical Arbitrage Capacity: Examples
Net edge enters the capacity formula squared, which means small changes in costs or the impact coefficient move capacity dramatically. That sensitivity is what these scenarios are designed to show. Inputs are alpha per trade in basis points, slippage, fees, a market-impact coefficient, and daily dollar volume traded against. Max AUM is the level at which net alpha is fully consumed; practical AUM applies a 50% haircut as a safety margin. The large capacity figures reflect institutional dollar-volume universes, not retail scale.
Worked Examples
See the inputs and outcome together
Each scenario keeps the starting point, the outcome, and the actual lesson in one place so the page reads like a decision notebook, not a data dump.
- 1
Baseline mid-frequency strategy
A 20-basis-point edge per trade against a $50M daily-volume universe, with 5 bps slippage, 2 bps fees, a five-day signal half-life and a moderate impact coefficient.
Max AUM $845B, practical AUM $45B, trades per year 50.4.
Alpha per trade
20 bps
Slippage
5 bps
Fees
2 bps
Impact coefficient
0.1
Daily volume
$50M
Signal half-life
5 days
Net edge of 13 bps over an impact coefficient of 0.1 gives 130, and 130 squared times $50M is the $845B ceiling. The practical $45B is far lower because the 50 percent alpha haircut cuts net edge to 3 bps, and capacity moves with the square. The safety margin is not a 50 percent cut to capacity; it is a 95 percent cut.
- 2
Same strategy, twice the market impact
Identical edge and costs, but the impact coefficient doubles from 0.1 to 0.2, modeling a less liquid name or a more aggressive execution style.
Max AUM $211B, practical AUM $11.25B, trades per year 50.4.
Alpha per trade
20 bps
Slippage
5 bps
Fees
2 bps
Impact coefficient
0.2
Daily volume
$50M
Signal half-life
5 days
Doubling the impact coefficient quarters the capacity, from $845B to $211B, because impact enters the denominator and is then squared. Execution quality is not a minor tuning knob; halving your market footprint quadruples how much you can run.
- 3
Fast signal, thinner universe
A one-day half-life signal trading a smaller $10M-volume universe with a 15-basis-point edge. High turnover, less liquidity.
Max AUM $64B, practical AUM $250M, trades per year 252.
Alpha per trade
15 bps
Slippage
5 bps
Fees
2 bps
Impact coefficient
0.1
Daily volume
$10M
Signal half-life
1 day
The thinner universe and lower edge drop max capacity to $64B, but the practical figure craters to $250M because the alpha haircut leaves only 0.5 bps of net edge to square. Fast, thin strategies look large on paper and tiny once you apply a realistic safety margin.
- 4
Edge too thin to survive the haircut
A marginal 10-basis-point edge with 5 bps slippage and 3 bps fees, leaving only 2 bps net. The strategy works at full alpha but not with a safety margin.
Max AUM $20B, practical AUM $0, trades per year 50.4.
Alpha per trade
10 bps
Slippage
5 bps
Fees
3 bps
Impact coefficient
0.1
Daily volume
$50M
Signal half-life
5 days
At full alpha there is a $20B ceiling, but the 50 percent haircut wipes out the 2 bps net edge entirely, so practical capacity is zero. A strategy whose practical capacity is zero is not undersized; it has no margin for the costs you have not measured yet.
Patterns
Try These Tools
Run the numbers next
Execution Simulator
Model realistic order fills — square-root market impact, linear temporary impact, latency jitter, partial fills, and queue position. See the real cost.
Cointegration Half-Life Solver
Engle-Granger residual ADF + Ornstein-Uhlenbeck half-life from any two price/return series. Hedge ratio, p-value, spread chart. Browser-only.
Sources & References
- Optimal Execution of Portfolio Transactions — Almgren, R. and Chriss, N., Journal of Risk (2001)
- Direct Estimation of Equity Market Impact — Almgren, Thum, Hauptmann and Li (2005)
Related Content
Keep the topic connected
Slippage
Slippage as the gap between expected and executed price: the components (spread, market impact, latency), and how to model each in a backtest.
Latency Arbitrage
Latency arbitrage: cross-venue price discrepancies exploited by being faster than the slowest replicator. Why the game is mostly won at the cable layer.
Bid-Ask Spread
Bid-ask spread defined: quoted vs effective vs realized spread, why the touch isn't the cost you actually pay, and how to measure each.