SIG (Susquehanna)–styleTraderTrading InternQuestion #85
A painting has an 80% chance of being fake. If it is real, it is worth $500,000; if fake, it is worth $10,000. The seller asks for $120,000. Based on this information, should you buy the painting?
Free worked solution · Quant Blueprint
Do not buy at $120,000 under a risk-neutral expected-value criterion: the expected value is $108,000.
- The painting is real with probability 0.2 and fake with probability 0.8.
- Its expected resale value is 0.2 × $500,000 + 0.8 × $10,000 = $108,000.
- Subtract the purchase price: expected profit is −$12,000, before fees. This conclusion assumes those valuations can be realized and the probabilities are reliable.
Common mistake
Comparing the $500,000 upside alone with the price ignores the much more likely fake outcome. Expected value also does not describe an individual’s utility or ability to bear losses.
Follow-up
The break-even real probability p solves 500,000p + 10,000(1−p) = 120,000, so p = 11/49 ≈ 22.45%.
Original educational explanation for this practice question. Reviewed . Firm-style practice; the label describes the collection’s preparation context.
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