Selling Above Expected Value

Market Making

Fair Value

Medium

An asset settles at

110

with probability

0.4

and

90

otherwise. A dealer sells one unit at

100

. Find the expected dealer P&L.

Hint 1

First compute the expected settlement.

Hint 2

A seller profits by the sale price minus the expected payoff.

Show worked solution

1. Expected payoff
$0.4 (110) + 0.6 (90) = 98$
2. Seller's P&L
The dealer receives $100$ and expects to deliver value $98$ .
$100 - 98 = 2$
3. Key idea
Seller P&L = price - E[value]; buyer P&L = E[value] - price.

Answer: 2

1. Expected payoff