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Retail versus informed flow

Market makingEasy

Each arriving order is from a retail trader with probability $0.8$ or from an informed trader with probability $0.2$ . A retail order earns the market maker $1$ and an informed order costs the market maker $3$ . What is the expected profit per order?

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Hint

Weight each outcome by the probability of the trader type.

Solution

Retail orders contribute $0.8 \times 1 = 0.8$ .
Informed orders contribute $0.2 \times (- 3) = - 0.6$ .
The expected profit is $0.8 - 0.6 = 0.2$ .

Answer: $0.2$

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