Can you solve this fiendishly difficult hedge fund interview question?

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Hedge fund interview questions are tricky. They involve maths, logic and reasoning. Here is an example that was given by a former Wall Street hedge fund trader. See if you can solve it.

It's called "two-envelope problem".

There are two envelopes in front of you. Each has some money in it. The amount of money in one envelope is twice the amount in the other. You then select one envelope, open it and find there are ten dollars in it. The question is, if you are allowed to exchange the current envelope in your hand for the other one, would you do it?

And the next question immediately following it would be: there are still two envelopes, one with the amount of money double that of the other. You then select one envelope, but you are not allowed to open it to see how much money it has inside. The question remains the same: if you are allowed to exchange the current envelope in your hand for the other one, would you do it?

This is obviously a question about maths. But the purpose of asking this question is "to see if the candidate can see through the tricks here", according to the trader, who asked to be anonymous.

So what are the tricks?

The maths itself is not too complicated, says the trader. Some probability calculations will tell you it's worth exchanging the current envelope in the first instance, but not in the second. The trick is, however, when one is repeatedly asked the same question, with the general prerequisites remain the same but other information constantly changing, how long would it be before you stop continuing with the same logic?

To better illustrate the situation, it's just like buying shares. You have a view that the price of a certain share is too low, so you buy. The share price then continues to fall for a few more days. Would you keep buying? The answer should be "yes" according to your previous logic. Then assume the share price falls further, would buy even more? If you keep buying, and assume the share price keep falling, when are you going to stop buying and start to review your logic?

That, suggests the trader, is a very important quality of a trader that hedge funds are looking for.

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