Buying a Coin-Flip Asset

Market Making

Fair Value

Medium

An asset pays

0

100

, each with probability

0.5

. A dealer buys one unit at

44

. What is the expected P&L?

Hint 1

The expected payoff is the average of the two outcomes.

Hint 2

The buyer earns E[value] minus the price.

Show worked solution

1. Expected value
$0.5 (0) + 0.5 (100) = 50$
2. Buyer's P&L
$50 - 44 = 6$
3. Key idea
Buying below fair value is positive expected value even when the payoff is very risky.

Answer: 6

1. Expected value