Pre-Trade Cost Models

A portfolio manager wants to buy 200,000 shares of a stock. Average daily volume (ADV) is 4,000,000 shares, the stock trades at $50.00 with a quoted spread of $0.02, and its daily volatility is 2%. Before the order goes anywhere, the desk needs a number: roughly what will this cost, and does that number change if we trade it over one hour instead of one day? That estimate — made before a single share trades — is a pre-trade cost model.

The order is $200{,}000 / 4{,}000{,}000 = 5\%$ of ADV. That participation rate, call it $X$, drives almost everything. A standard model splits expected cost into three pieces:

$\text{spread cost} = \tfrac{1}{2} \times \text{spread} \times \text{shares}$

$\text{impact cost} = \sigma \times \eta \sqrt{X} \times \text{shares} \times \text{price}$

$\text{timing risk} = \sigma \times \sqrt{T} \times \text{shares} \times \text{price}$

In words: spread cost is what you pay crossing the bid-ask on the way in (half the spread per share, roughly, for an order that isn't purely passive). Impact cost is the square-root impact law — cost grows with the square root of how large your order is relative to the market, scaled by volatility $\sigma$ and a stock-specific constant $\eta$ (typically fit from historical data, often around 0.5–1). Timing risk isn't a cost you pay on average, it's the standard deviation of your outcome — the price can drift against you simply from holding an unfinished order open for time $T$ (measured as a fraction of a trading day), and that risk shrinks the faster you trade.

Worked example

Plug in the numbers. Spread cost: $\tfrac{1}{2} \times 0.02 \times 200{,}000 = 2{,}000$, i.e. $2,000 — half a cent per share crossing the spread.

Impact cost, trading over a full day ($X = 0.05$, take $\eta = 0.75$): $0.02 \times 0.75 \times \sqrt{0.05} \times 200{,}000 \times 50 = 0.02 \times 0.75 \times 0.2236 \times 10{,}000{,}000 \approx 33{,}540$, i.e. roughly $33,500 — about 3.4 basis points of notional.

Timing risk, trading over a full day ($T=1$): $0.02 \times \sqrt{1} \times 10{,}000{,}000 = 200{,}000$, i.e. $200,000 of standard deviation around the expected cost — this is not money you expect to lose, it's the width of the distribution of outcomes if the market happens to run away from you while the order is still open.

Now compare to trading it in one hour instead ($T = 1/6.5$ of a 6.5-hour session, so participation rate roughly quadruples to $X \approx 0.20$ if volume is spread evenly through the day, though real intraday volume is front- and back-loaded). Impact cost rises to $0.02 \times 0.75 \times \sqrt{0.20} \times 10{,}000{,}000 \approx 67{,}000$, i.e. $67,000 — impact roughly doubles because it scales with $\sqrt{X}$. But timing risk falls to $0.02 \times \sqrt{1/6.5} \times 10{,}000{,}000 \approx 78{,}400$, i.e. $78,400 — a quarter of the full-day number, because $\sqrt{T}$ shrinks fast.

Where this is used in practice

• Algo selection. The pre-trade estimate is what tells a trader to route to a VWAP algo over the full day versus an aggressive liquidity-seeking algo over twenty minutes — the model's cost-vs-speed curve is the menu.
• Best execution and compliance. Funds are often required to document that expected costs were considered before trading, and the pre-trade estimate becomes the benchmark that post-trade TCA is measured against.
• Portfolio construction. If a signal's expected edge is 10 bps and the pre-trade model says trading the position costs 15 bps, the honest answer is not to trade it — pre-trade models are as much a filter on which ideas are worth acting on as they are an execution tool.

In interviews

Expect to be asked to build the estimate from scratch: participation rate first (order size over ADV), then spread cost as a flat half-spread charge, then impact as $\sigma \eta \sqrt{X}$, then timing risk as $\sigma \sqrt{T}$. The key insight to state explicitly is that impact and timing risk move in opposite directions with speed, so "optimal execution" is a risk-aversion choice, not a pure minimization — tie it back to Permanent Versus Temporary Impact if asked why impact doesn't simply reverse once the order is done.