Actual interview brainteaser at a top flight shop

Discussion in 'Professional Trading' started by sjfan, Dec 22, 2009.

  1. sjfan


    Since once in a (short) while there's a question about what the interviews are like at an actual investment shop (ie, IB, hedge fund, asset manager, not "prop"), I figured I'd share one in the spirit of the holiday. This is an actual interview brain teaser used by one of the top 5 trading shop in the world in an interview for a strategist (5y+ experience, 300k+/yr):

    You are playing this coin game: a fair coin will be flipped five times in a row. You will win on the 3rd head. You will lose on the 2nd head. (ie, if 1 is head and 0 is tail, if the flip comes out 111, you win. if it comes out 1011, you win. if it comes ou t 1000 you lose).

    You start out with $100. You can bet any amount, but no more than what you have on hand at the time, before each flip. If head, you double what you bet. If tail, you lose what you bet.

    You want to double your initial $100 stake if you win the game (3 heads).

    Question: what is the size of the first bet that you should make?

    Hint: there is ONE right answer. It will require you coming up with the full betting strategy.
  2. sjfan


    Btw, if you already work for a financial institution, please don't post your solution (but I'll be happy to tell you via PM whether it's right). I'd rather let the just-of-school want-a-shot-at-being-hated-by-the-populist guys have a shot
  3. first bet zero..

    after the second head comes up, next flip bet $100
  4. What is this firm's annualized net return to investors in the coin-flip betting market?
  5. sjfan


    Not even close. Say you got head on the first flip. You bet nothing. Head on the second flip. You bet it all. Tail on the third flip, you are out of all of your money. Head on the Fourth flip - you won the game, but you lost all your money instead of doubling it.

  6. question_

    you have three US dollar coins for a total of 76 cents, one is not a half dollar.

    >>what coins do you have??
  7. sjfan


    In case this wasn't sarcastic, it should be trivially easy to figure out once you figure out the correct answer to the above :)

  8. take the hundo and run for the hills.
  9. sjfan


    Sign... not this old cliche of a question again (the other coin is a half $). What to start your own thread?

  10. betting zero, waiting for the first two heads then going all in wins 50% of the time, the flip will have a EV of 0
    #10     Dec 22, 2009