Forecasting Your Own Trading Costs

A signal that predicts a 15-basis-point move sounds tradeable until you realize it costs 20 basis points to get in and out of the position. Researchers spend enormous effort forecasting returns and comparatively little forecasting the other half of the ledger: what it will actually cost to act on those forecasts. A strategy is only as good as its edge net of costs, and costs are themselves a forecast — one that is easy to get wrong in the same direction, every time, toward optimism.

What drives the forecast

Trading cost has a predictable piece and a size-dependent piece. The predictable piece is the spread you cross and any exchange or broker fees — roughly constant per trade. The size-dependent piece is market impact: the price moves against you because you are trading, and it moves more the faster you try to trade and the larger your order is relative to normal volume. A common working form:

$$\text{Impact} \approx k \times \sigma \times \left(\frac{Q}{V}\right)^{\alpha}$$

In words: expected impact scales with how volatile the asset is ($\sigma$), grows with the size of your order ($Q$) relative to typical trading volume ($V$), and that size effect is sub-linear — doubling your order size less than doubles the cost per share, but it still costs more in total — governed by an exponent $\alpha$ typically estimated between 0.5 and 1 from a firm's own historical fills.

Worked example

A desk wants to buy 200,000 shares of a stock that trades 4 million shares a day, with daily volatility of 2%. Using $k=0.5$, $\alpha=0.6$: the participation rate is $Q/V = 200{,}000 / 4{,}000{,}000 = 0.05$. Then $(0.05)^{0.6} \approx 0.174$, and impact $\approx 0.5 \times 0.02 \times 0.174 = 0.00174$, about 17 basis points. If the desk's signal forecasts a 25-basis-point move over the holding period, the net expected edge after this one-way cost (and the same again to exit) is roughly $25 - 17 - 17 = -9$ basis points — the trade is not worth doing at that size, even though the raw signal looked profitable.

Backtest costs versus live costs

A backtest that charges a flat, generous-looking cost assumption (say, 5 basis points per side regardless of size) is really a different, easier strategy than the one that will trade live, because it ignores that the strategy's own trading moves the price. The honest fix is to fit a cost model to the firm's actual historical fills — comparing the price at decision time to the price actually achieved — and apply that fitted model inside the backtest, so that costs scale with order size the way they will in production.

Try increasing the exponent on the curve above — this is the shape of the impact-versus-size relationship: costs rise faster than linearly with size once an order becomes large relative to available liquidity.

What this means in practice

Signals with short holding periods and high turnover are hit hardest by cost forecasting error, because costs are paid on every rebalance while the return forecast only pays off if it's right. A strategy that looks excellent gross of costs but survives only under an optimistic cost model is not really a strategy — it is a bet that the researcher's cost assumptions, not the market's, will hold.