Trader Trainee Technical Question
Hey guys,
I came across this really interesting teaser at glassdoor.com. Anyone have much of an idea on what would be the best answer to some of these q's.
“You have a single dice. You have a single roll. If you choose to play the game, you will be paid out in dollars of the value of whatever face the dice shows after the roll (1 = $1, 5 = $5, etc.). A) What is the value of this game? B) If you were bidding on this game, what bid price would you submit? C) At this bid price, what would your expected profit be if you played for 12 hours? D) If you were allowed two chances to roll. i.e. you could roll the first dice, if you don't like the number, you can elect to roll again. What is the expected value?”
Fairly straight forward EV question.
a) The value of this game = EV of the dice. The answer is $3.50. The work out is that : 1/6 * $1 + 1/6*$2 +.....+ 1/6 * $6 = 3.5
b) Your bid price would be $3.50. Over the long run if you could pay anything less than $3.50 you would generate profits.
c) So say you bid $3.4 for this game. As you want to maximize the number of dice rolls (as you are playing a +EV game) you want the money to be settled at the end of the 12 hour period. A dice roll takes 5 seconds to execute fairly. In 12 hours, you will have 8640 rolls. Thus, as your expected profit per roll is .10, your expected profit over 12 hours is $864.00.
d) This is tricky as it makes it a conditional probability. The EV of your first roll is 3.50. Thus, if you got 1, 2, or 3 in your first roll you would elect to roll again as your EV on the next roll is greater than your present value. On the other hand, if you rolled a 4, 5, or 6 you would be content as you don't want to give away the higher than EV profit you already have. So 50% of the time you would elect to roll again, while 50% of the time you would keep your first roll values.
So the answer would be: first roll (4,5,6) + second roll everything0.5 => 1/64 +1/65 + 1/66 + 3.5/2 => $4.25.
Mahran-How would you do it if you were given three roles?
recursively from the last roll: EV of 3rd roll= 3.5 On 2nd roll take 4, 5, 6, otherwise roll again for a chance of expected 3.5 of the third roll => EV before 2nd roll is (4+5+6)=15+3.5(3)=25.5/6=4.25 On 1st roll take 5 or 6, otherwise roll again for a chance of expected 4.25 =>EV before 1st roll is 5+6+4.25(4)=17+11=28/6=4+4/6= 4 and a third
4+4/6 is = 4 and two thirds
btw, where can we get a list of questions that one might expect in a trading interview?
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