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Quant Firm Interview Question

We roll three, 8 sided dice. If same face appears 3 times we win 80 dollars. We have a bank of 10,000 dollars. How much are we willing to pay to play? What if we increase the prize to 80,000 dollars? My thinking is as follows.

  • EV is 1.25 dollars. Therefore we pay anything less than 1.25. (Risk is very low so not accounted for)
  • When prize is 80,000 the EV is 1250 but the variance has also increased?
  • Therefore we would pay less than 1250 but I am unsure how much

My questions are how much compensation is required to take on the extra risk? Is there a correct answer here? What method can I use to calculate what I'm willing to pay if I know my risk tolerance?

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