Basic, lesson 1 of 3
Quoting on anything
A market is a fair value plus a width. The fair value comes from expected value; the width comes from how unsure you are and who might be on the other side.
9 min, 3 checks
1Fair value first, width second
Asked for a market, say the fair value to yourself first. Then pick a width that reflects your uncertainty: tight when the value is well defined (a sum of dice), wide when it is a guess (the height of a building you have never seen).
Quote it as bid at ask, with a size if they ask: "16 at 19, ten up" means you buy ten at 16 and sell ten at 19.
Worked example
Market on the number of red cards in the top 10 of a shuffled deck
- 1Each card is red with chance 1/2, so the mean is 10 x 1/2 = 5.
- 2Without replacement, the variance is 10 x 0.25 x (42/51) = 2.06, so the standard deviation is about 1.4.
- 3A market one standard deviation wide around 5 is about 4.3 at 5.7. In whole numbers, 4 at 6.
4 at 6. If the interviewer wants tighter, 4.5 at 5.5 is still sensible because the distribution is symmetric around 5.
Check 1
Where should the middle of your market be on the sum of five fair dice?
Check 2
What is the standard deviation of the sum of four fair dice? Three decimals.
2Markets on things you cannot know
Fermi markets (the weight of all the cars in a parking garage, the number of words in a novel) test whether you will commit. Break the quantity into pieces you can estimate, give a wide market, and say which piece you are least sure of. When the interviewer trades, that trade is information: tighten around it.
Check 3
You are asked for a market on a number you have almost no idea about. What is the best first move?
Terms in this lesson: Expected value, Standard deviation.
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