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Daily profit from mixed flow

Market makingEasy

A market maker receives $500$ orders in a day. A share $0.7$ of them are from retail traders and earn $0.5$ each, and the rest are from professionals and lose $0.8$ each. What is the expected daily profit?

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Hint

Compute the expected profit per order, then scale.

Solution

The profit per order is $0.7 \times 0.5 - 0.3 \times 0.8 = 0.35 - 0.24 = 0.11$ .
The day has $500$ orders.
The expected daily profit is $500 \times 0.11 = 55$ .

Answer: $55$

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