Is this quote actually making money?

Question

You quote a 4-cent half-spread, so on any fill you collect \0.04 up front. But a quarter of your fills come from informed traders: when one of them trades against you, the value moves against your position by an average of \0.20 before you can react. The other 75\% of fills are harmless noise flow. What is your expected profit per fill? What half-spread would break you even?

Accepted Answer

Set up the EV. On every fill you collect the half-spread s = 0.04. On an informed fill you additionally suffer an adverse move of L = 0.20, the true value was really beyond your quote, so you're now holding a loser. Let p = 0.25 be the informed fraction. E[	ext{profit per fill}] = \underbrace{s}{	ext{always collected}} - \underbrace{p \cdot L}{	ext{expected toxic hit}} = 0.04 - (0.25)(0.20). = 0.04 - 0.05 = -\0.01. You are losing a penny per fill, even though every trade "collects" the spread. The four cents of edge simply isn't enough to cover the toxic quarter of your flow. Break-even ha…

Is this quote actually making money?

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