Can you answer this cursed brainteaser from Balyasny's quant research head?

Brainteasers in quant job interviews often have a 'right' answer, but sometimes the goal is simply to figure out how you think. A recently unveiled brainteaser from Giuseppe Paleologo, head of quantitative research at hedge fund Balyasny on X, is closer to a social experiment than a test.

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His question reads as follows:

An evil witch has given you an evil curse. She tosses an evil coin. Your bank account has A right now. If it’s heads, your bank account increases by A/2. If tails, it is reduced by A/2. She repeats this every year, always plus or minus A/2 from year 1. 

“But” she adds “I am also greedy. If you give me x% of your bank account, I will remove the curse.” You accept if x=

A. 0%

B. 2%

C. 5%

D. 10%.

Responses to the question note that it is an example of a Martingale, a stochastic process in which the expected value of an action is equal to that of your current situation. As there is an equal chance of increasing or decreasing your bank account by A/2, expected values cancel each other out.

This is similar to a game allegedly played by Goldman Sachs in some job interviews. There, the interviewer would flip a coin; if it lands on heads, the interviewee pays them a dollar and the game ends, if it lands on tails, they pay a dollar and the game restarts, with the payout doubling. In this situation, the question is how much would you need to be paid upfront to start the game?

Paleologo says there's no right answer, and that he's "trying to understand haw much we are all willing to pay to remove uncertainty from our lives." More than a third of respondents only accepted if they had to give 0% of their bank account; perhaps they like risk, or perhaps they have a thing for witches.

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