Make a market on the number of sixes in 60 rolls

Question

Interviewer: "A fair die is rolled 60 times. Make me a market on the number of sixes. I will trade either side, one contract settling at the realized count." Give a bid and ask, and explain what sets your width.

Accepted Answer

Fair value. The number of sixes is Binomial(60, 	frac16), so E[X] = np = 60 \cdot 	frac16 = 10. Your fair value is 10, exactly. As with any fair random draw, there is no informed counterparty, the outcome is unknowable in advance, so you can quote tight around 10. Your risk is settlement variance, not being wrong about fair value. What sets the width. The standard deviation of the count: \sigma = \sqrt{np(1-p)} = \sqrt{60 \cdot 	frac16 \cdot 	frac56} = \sqrt{	frac{300}{36}} = \sqrt{8.33} \approx 2.89. A single contract typically settles about 3 away from 10. If you sell one at 11, you co…

Make a market on the number of sixes in 60 rolls

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