Questions / Quant trading, Information & Bayes
Learn from the side of a trade
A contract pays 60 or 100, equally likely. A customer is informed 50% of the time; an informed customer buys only in the high state, while an uninformed customer buys or sells at random. What is expected value given a buy?
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Answer: 90 points
- P(high | buy) = (1 + 0.5) / 2 = 0.75. Value is 0.75 × 100 + 0.25 × 60 = 90.
Interview shortcut. A buy is 3 times as likely in the high state (0.75 vs 0.25), so P(high) goes to 3/4.
In the app this has a follow-up where one thing about the setup changes. Try the follow-up.