Aggregating a day of fills into a P&L

Question

Over a day you get 2{,}000 fills, averaging 500 shares each. On each fill you collect a 4-cent half-spread. But 15\% of fills are informed, and each informed fill suffers an average 20-cent adverse move against your position. What is your expected daily P&L per share, per fill, and in total? Annualize it.

Accepted Answer

Expected profit per share. You collect the half-spread s = 0.04 on every share; on the 15\% of flow that's informed you lose an extra L = 0.20 per share: E[	ext{per share}] = s - pL = 0.04 - 0.15(0.20) = 0.04 - 0.03 = \0.01. A net 1 cent per share survives adverse selection, a quarter of your gross half-spread, three-quarters eaten by toxicity. Per fill. At 500 shares per fill: 0.01 	imes 500 = \5 	ext{ per fill.} Daily total. Across 2{,}000 fills: \5 	imes 2{,}000 = \10{,}000 	ext{ per day.} Equivalently, total shares traded = 2{,}000 	imes 500 = 1{,}000{,}000, times 1 cent net = \10{,…

Aggregating a day of fills into a P&L

Your answer

More Market Making questions