Slippage and market impact are not the same cost

Most backtests carry a single cost number. Some basis points per trade, subtracted at execution, chosen because it seemed conservative. That number is doing the work of at least three separate quantities that behave differently, respond to different remedies, and scale differently with order size. Collapsing them loses the only component that execution work can actually improve.

Slippage is a measurement, not a mechanism

Slippage is the difference between a benchmark price and the price achieved. That is all it is. It says nothing about why the difference occurred, and it is not defined until the benchmark is.

The choice of benchmark is not neutral. Measured against the arrival price, the price at the moment the order was released, slippage captures everything that happened during execution, including market drift that had nothing to do with the order. Measured against the interval VWAP, it captures only how well the order was scheduled relative to the day's volume, and a strategy that systematically trades in one direction will look good on this measure for reasons that have nothing to do with execution quality. Measured against the decision price, the price when the signal fired, it also captures the delay between deciding and acting, which is a real cost but a different one.

A backtest that subtracts "slippage" without naming the benchmark has subtracted an undefined quantity. Worse, the benchmark is usually implicit and self-serving: the fill is assumed at the price the strategy was looking at, which makes the decision price and the arrival price identical by construction and removes an entire cost component by assumption.

Market impact is a mechanism, and it is yours

Market impact is the part of the price move that the order itself caused. It is a counterfactual claim: the price would have been elsewhere had the order not been sent. That makes it real but unobservable, since the counterfactual path is never available.

The standard decomposition splits it in two, and the split matters because the two halves have different remedies.

Temporary impact is the concession paid for demanding liquidity faster than it naturally arrives. It reflects the depletion of the book and the time it takes for resting interest to replenish. It decays after the order stops. Crucially, it is a function of the rate of trading rather than the total quantity: the same size worked over a day costs less in temporary impact than the same size worked in ten minutes.

Permanent impact is the part that does not decay, because the market has inferred something from the order flow and repriced. It is information leakage rather than liquidity consumption. It is approximately linear in total quantity and largely indifferent to how slowly the order is worked, because the information gets out either way.

The practical consequence is that trading more slowly reduces temporary impact and does almost nothing to permanent impact, while exposing the order to more price risk over a longer window. That tension is the entire content of optimal execution, and it is why scheduling is an optimisation problem rather than a preference.

Why a flat basis-point assumption fails in a known direction

A fixed cost per trade is flat in size and flat in participation rate. Real cost is neither.

The widely used empirical form for temporary impact is concave in quantity, commonly approximated as proportional to volatility multiplied by the square root of the ratio of order size to average daily volume. Concavity means that doubling the order does not double the cost. A flat per-trade assumption therefore overstates cost for small orders and understates it for large ones, and the crossover point sits wherever the constant was calibrated.

That is not a random error. It biases in a specific and dangerous direction: capacity. A strategy tested with a flat cost assumption will appear to scale linearly, because the only thing that grows with size in the model is the notional the flat cost is applied to. Real impact grows faster than that at first and then concavely, and the interaction with participation rate is where a strategy that works at one size stops working at ten times the size. The backtest cannot show this, because nothing in it depends on participation.

The measurement problem, stated honestly

Permanent and temporary impact cannot be separated from a single execution. The counterfactual is missing, and any decomposition depends on assumptions about how the price would have evolved.

What is available is weaker but usable. Post-trade price decay analysis, tracking where the price settles at increasing horizons after the order completes, gives an estimate of the split: the portion that reverts was temporary, the portion that persists was either permanent impact or drift. Separating the last two requires a control, which in practice means comparing against periods with similar conditions and no order, and accepting that the result is an estimate with a wide interval rather than a number.

This is worth stating plainly because impact models are often presented with a precision they do not have. A fitted impact coefficient carries real uncertainty, and the curvature of that fit around the estimate says how much the number can be relied on. A flat likelihood there means the coefficient was never identified, which is the same argument the firm's method makes about any other fitted parameter.

What to model instead

The minimum useful replacement for a flat number has three parts, kept separate because they behave differently.

• Spread cost, which is mechanical and observable. Crossing the spread costs half the quoted spread relative to the mid, before anything else happens. This part needs no model, only the correct quote at the correct timestamp.
• Temporary impact, modelled as a function of participation rate and volatility rather than of notional. Participation rate is the quantity the strategy actually controls, and expressing cost in those terms is what makes the scheduling decision visible.
• Permanent impact, modelled as roughly linear in total size and treated as a floor. It does not respond to scheduling and should not be presented as though it does.

Then vary all three rather than fixing them. A single assumption produces a single number and no information about its stability. A sweep across plausible impact coefficients and participation rates produces a response surface, and the shape of that surface is the finding. A strategy whose result survives a threefold change in the impact coefficient is a different object from one that inverts, and the difference is invisible if only one value was tested.

The connection to what gets built

None of this is only a research concern. A production execution system that cannot report realised cost against a stated benchmark, decomposed into spread and residual, cannot tell whether its scheduling is working. Measurement has to be designed in, because reconstructing it afterwards requires order-level timestamps and quote snapshots that were either captured at the time or lost.

The related question of what the delay itself costs, as distinct from what the order costs once it arrives, is covered in latency and slippage.