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Breakeven retail share

Market makingMedium

Each order is from a retail trader or an informed trader. A retail order earns the market maker $1$ and an informed order costs $3$ . What share of orders must be retail for the expected profit per order to be exactly zero? Give a fraction.

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Hint

Let $r$ be the retail share and set the expected profit to zero.

Solution

The expected profit per order is $1 \times r - 3 \times (1 - r)$ .
Setting it to zero gives $4 r = 3$ .
The retail share is $\frac{3}{4}$ .

Answer: $\frac{3}{4}$

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