A signal that predicts a price move of ten basis points is worthless if trading on it costs twelve. Execution research exists to measure that cost precisely and to minimise it — and the cost of trading is frequently the deciding factor in whether a strategy is viable at all.
§01Measuring cost: implementation shortfall
Perold (1988) proposed measuring execution quality as implementation shortfall: the difference between the return of a hypothetical paper portfolio traded instantly at the decision price and the return actually achieved. Shortfall captures every component of cost in one number:
- Explicit costs — commissions, exchange and clearing fees.
- Spread — the cost of crossing from mid-price to the opposite quote.
- Market impact — the adverse price move caused by the order itself, partly temporary and partly permanent.
- Timing and opportunity cost — price drift while the order is worked, and the cost of any quantity left unfilled.
§02The square-root law
One of the most robust empirical regularities in market microstructure is that the impact of a large order grows roughly with the square root of its size relative to market volume, not linearly:
As a worked example: with 2% daily volatility and an order equal to 1% of daily volume, the formula gives an impact of roughly 1 × 2% × 0.1 = 0.2%, or 20 basis points. The law has been documented across equities, futures and other markets (Tóth et al., 2011); direct estimates on equity orders by Almgren, Thum, Hauptmann and Li (2005) found an exponent close to 0.6. Constants vary by market and must be calibrated on one's own executions.
§03Optimal scheduling: the Almgren–Chriss trade-off
Trading quickly minimises exposure to price drift but maximises impact; trading slowly reduces impact but extends exposure. Almgren and Chriss (2000) formalised this trade-off as a mean-variance problem over the execution schedule. With linear temporary impact and a risk-aversion parameter λ, the optimal remaining holding decays smoothly:
The result is an efficient frontier of schedules, each minimising expected cost for a given variance of cost. A risk-neutral trader chooses the straight-line schedule; a more risk-averse trader trades faster at the start.
§04From model to system
- Pre-trade: estimate expected cost and its uncertainty before a signal is accepted, using impact models calibrated on actual fills.
- In-trade: adapt the schedule to live conditions such as spread, depth and volatility, within limits set by risk controls.
- Post-trade: attribute realised shortfall to its components and feed the result back into the impact model.
