Learn / Library / Market making

Variance of sold die contracts

Market makingMedium

A contract pays, in dollars, the number shown on one roll of a fair $6$ -sided die. A market maker sells $12$ units, each tied to its own independent roll, at the fair price. What is the variance of the total payout in squared dollars?

Checking an answer needs JavaScript. The hint and the solution open without it.

Hint

Independent variances add; the variance of one roll is E[X²] − E[X]².

Solution

One roll has variance $\frac{91}{6} - (3.5)^{2} = \frac{35}{12}$ .
The variances of independent rolls add up over the units.
The variance of the total is $12 \times \frac{35}{12} = 35$ .

Answer: $35$

Next question Back to the library