How Statistical Arbitrage Capacity works

Square-root impact

The dominant empirical pattern across equity, futures, and crypto markets is square-root market-impact — first formalised in Almgren-Chriss (2000) and confirmed across thousands of trades by Frazzini-Israel-Moskowitz (2018):

impact_bps ≈ K · √( participation )
participation = traded_notional / daily_volume

The constant K ranges 0.10–0.30 across studies. We default to K = 0.20.

Breakeven AUM

Capacity is defined as the AUM at which gross alpha equals friction:

α_per_trade = slippage + fees + K · √(participation)
participation* = ( (α − slippage − fees) / K )²
AUM_max = participation* · daily_volume

The "practical AUM" is the same calculation with the LHS reduced by 50% — the AUM where net alpha is half of gross.

Trades per year and half-life

trades_per_year ≈ trading_days / half_life_days

Capacity is calculated per trade, not per year — turnover is implicit in the participation constraint.

References

• Kyle, A. S. (1985). "Continuous auctions and insider trading." Econometrica 53(6): 1315–1335. DOI: 10.2307/1913210.
• Almgren, R., Chriss, N. (2000). "Optimal execution of portfolio transactions." Journal of Risk 3(2): 5–39.
• Frazzini, A., Israel, R., Moskowitz, T. J. (2018). "Trading costs." SSRN 3229719.
• Bouchaud, J.-P., Farmer, J. D., Lillo, F. (2009). "How markets slowly digest changes in supply and demand." Handbook of Financial Markets: 57–160.

Limitations

• Ignores market regime — capacity shrinks dramatically in stressed markets.
• Single-name input; multi-name strategies have correlated impact that requires a portfolio-level model.
• Impact constant K is asset-class-dependent; verify K against your live execution data.

External resources

• Statistical Arbitrage in the U.S. Equities Market (Avellaneda & Lee 2010, SSRN)