The book shows 100 lots at 19.98 and 300 at 19.96 on the bid, and 100 at 20.02 and 300 at 20.04 on the offer. A 400 lot market buy arrives. What effective spread does it pay, and why does the quoted spread understate trading costs in this book?

The book shows 100 lots at 19.98 and 300 at 19.96 on the bid, and 100 at 20.02 and 300 at 20.04 on the offer. A 400 lot market buy arrives. What effective spread does it pay, and why does the quoted spread understate trading costs in this book?

Approach: Walk the order through the offer levels to get the size-weighted average fill price, then compare that average with the mid to get the effective half spread and double it.

7 cents. The 400 lot buy takes 100 at 20.02 and 300 at 20.04, an average of (100 * 20.02 + 300 * 20.04)/400 = 8014/400 = 20.035. The mid is 20.00, so the effective half spread is 3.5 cents and the effective spread is 7 cents against a quoted spread of 4 cents. The quoted spread prices only the first 100 lots, so it describes a trade nobody in this name is doing: with a 400 lot average order, walking the book adds 3 cents a share that the touch never shows. Book depth is why depth-weighted or size-conditional spread measures are the right comparison across venues, since a venue can post a tight touch on tiny size and look cheap on the headline number.

Follow-up: How would you compute a depth-weighted spread for a book with hidden midpoint liquidity you cannot see?

Key concepts: effective spread, quoted spread, book depth, walking the book.