Cost-To-Trade Curves And Depth Metrics

Ask a trader "how liquid is this stock?" and the quoted bid-ask spread only answers part of the question. The spread tells you the cost of a trade small enough to fit inside the best quote. It says nothing about what happens if you need to buy 50,000 shares right now and the best offer only has 500 shares sitting on it. A cost-to-trade curve answers that harder, more useful question directly: for an order of size $X$, executed immediately by sweeping the book, what's the average price paid relative to the pre-trade midpoint?

Building the curve

Take a snapshot of the limit order book. Starting from the best offer, walk up through each price level, accumulating shares until you reach the order size you're testing. The cost is the volume-weighted average execution price minus the midpoint, usually expressed in basis points. Repeat for order sizes of 100 shares, 1,000 shares, 10,000 shares, and so on, and plot cost against size — that's the curve. It's flat and near zero for tiny orders (they fill within the spread) and rises, often steeply, as size grows and the order has to reach into thinner price levels further from the midpoint.

Worked example

Suppose the midpoint is $100.00 and the offer side looks like: 500 shares at $100.02, 800 shares at $100.05, 2,000 shares at $100.12. A 500-share buy order costs 2 cents per share above midpoint — 2 basis points. A 1,300-share order fills 500 shares at $100.02 and 800 at $100.05, a volume-weighted average price of about $100.037, or roughly 3.7 basis points. Push the order to 3,300 shares and it has to reach the $100.12 level too, pulling the average cost above 6 basis points. Plotting cost at 500, 1,300, and 3,300 shares traces a curve that bends upward — exactly the shape a trader needs to see before deciding how aggressively to work a large order.

What this means in practice

Cost-to-trade curves are how execution desks and liquidity researchers compare markets fairly. Two stocks can share an identical one-cent spread while one has ten times the depth behind it — their curves diverge immediately past the first few hundred shares, and that divergence is exactly the difference a large trader cares about. The curve also sets a natural boundary between "just cross the spread" and "work the order slowly to avoid walking the book," since the point where the curve steepens is roughly where market impact starts to dominate the spread cost.