Sales and trading summer analyst Interview Questions | Glassdoor

# Sales and trading summer analyst Interview Questions

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sales and trading summer analyst interview questions shared by candidates

## Top Interview Questions

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Mar 11, 2011
 You are playing a game where the player gets to draw the number 1-100 out of hat, replace and redraw as many times as they want, with their final number being how many dollars they win from the game. Each "redraw" costs an extra $1. How much would you charge someone to play this game?10 Answers10?redraw 10 times and get the payoff around 77?the average draw will pay out$50.50Show More ResponsesEvery time when you are deciding whether to play once more, we consider the two options: stop now, then you get current number (the cost of $1 is sunk cost); continue, then the expectation of benefit would be$50.50-1=49.50. This means, as long as you have get more than $50 (inclusive), then you should stop the game. Suppose the game ends after N rounds (with probability (49%)^(N-1) x 51%, and in the last round, the expected number is (50+100)/2=75, and thus the expected net benefit would be 75-N . This shows N<=74. Then we take the sum:$Sigma_{N=1}^{74} (49%)^(N-1) x 51% x (75-N), which is 73.Every time when you are deciding whether to play once more, we consider the two options: stop now, then you get current number (the cost of $1 is sunk cost); continue, then the expectation of benefit would be$50.50-1=49.50. This means, as long as you have get more than $50 (inclusive), then you should stop the game. Suppose the game ends after N rounds (with probability (49%)^(N-1) x 51%, and in the last round, the expected number is (50+100)/2=75, and thus the expected net benefit would be 75-N . This shows N<=74. Then we take the sum:$Sigma_{N=1}^{74} (49%)^(N-1) x 51% x (75-N), which is 73.All of the above answers are way off. For a correct answer, see Yuval Filmus' answer at StackExchange: http://math.stackexchange.com/questions/27524/fair-value-of-a-hat-drawing-gameYuval Filmus proves that the value of the game is 1209/14=86.37 and the strategy is to stay on 87 and throw again on 86 and below..Let x be the expected value and n be the smallest number you'll stop the game at. Set up equation with x and n, get x in terms of n, take derivative to find n that maximizes x, plug in the ceiling (because n must be integer) and find maximum of x. ceiling ends up being 87, x is 87.357, so charge $87.36 or moreI guess the question asks for the expected value of the game given an optimal strategy. I suppose the strategy is to go on the next round if the draw is 50 or less. Hence, the expected value of each round is: (1) 1/2*1/50(51 + 52 + ... + 100) (2) 1/2*1/2*1/50(51 + 52 + ... + 100) - 1/2 (3) 1/2^3 * 1/50 (51 + 52 + ... + 100) - 1/4 .... Sum all these up to infinity, you'd get 74.50.This is all very interesting and I'm sure has some application...but to trading? I don't think so. I own a seat on the futures exchange and was one of the largest derivatives traders on the floor. Math skills and reasoning are important but not to this level. I would associate day trading/scalping more to race car driving i.e. getting a feel for what's going on during the day, the speed at which the market is moving and the tempo for the up and down moves. If I were the interviewer at one of these firms, I throw a baseball at your head and see if you were quick enough and smart enough to duck. Then if you picked it up and threw it at my head I'd know that you had the balls to trade. I know guys who can answer these questions, work at major banks, have a team of quants working for them and call me up to borrow money from me because they're not making money. At the end of the day, if you want to be a trader then...be a trader. If you want to be a mathematician then be a mathematician. It's cool to multiply a string of numbers in your head, I can do this also, but never in my trading career did I make money because in an instant I could multiply 87*34 or answer Mensa questions which...realistically the above answer is: it depends on the market as the market will dictate the price. You may want to charge$87 to play that game but you'd have to be an idiot to play it. In trading terms this means that when AAPL is trading at $700 everyone would love to buy it at$400. Now that it's trading at $400 everyone is afraid that it's going to$0. Hope this helps. No offense to the math guys on this page, just want to set the trading record straight.

Oct 4, 2011
 Say I take a rubber band and randomly cut it into three pieces. What's the probability that one of the pieces has length greater than 1/2 of the original circumference of the rubber band.9 Answers3/4Suppose you have two cuts on the rubber band placed randomly. The probability of having one segment greater than half the circumference is the probability that the third cut will be inside the combined range of 90* to either side of the cuts. Since the average distance between the first two cuts is also 90*, the combined range is 270*, or 3/4 of the circle.You need 3 cuts to end up with 3 pieces. The first cut doesn't matter. The second cut can also be anywhere and the largest piece will still be at least half the circumference. What matters is the third cut, which should lie in the same half as the second cut. So the probability is actually 1/2.Show More ResponsesThe correct answer is 3/4, as this problem is equivalent to the famous 3-points-on-semicircle problem. Why? If one of the pieces has length greater than 1/2 the circumference, then the three points of cutting must lie in the same semicircle. On other hand, if the three points of cutting lie on the same semicircle, then the longest piece must be at least 1/2 of the circumference.For reference to the 3-points-on-same-semicircle problem, see e.g., http://godplaysdice.blogspot.com/2007/10/probabilities-on-circle.html1/4 1 -3/4suppose I have two points whose minor arc distance is t <= 1/2. Then the range of semicircles covering both points gives an arc length of (1/2+1/2)-t = 1-t. say we fix the first point, tracing the second point around gives minor arc lengths from 0 to 1/2 and then 1/2 to 0. Therefore the answer is 2*integral (1-t) from 0 to 1/2, which is 2(1/2-1/8) = 3/4It's 3/4. Cut it into 1 piece make a line. Cut it close. Pretend the length is 100. If you cut the first at x=1, as long as it isn't between x=50-51, it will have a length greater than 50% so there's 99% chance. You can imagine that if the cut was infinitely close to the end it would be about 100%. Now cut at x=2 you can't do between x=50-52. For x=3 it's 50-53 etc. So when you get to right to infinitely close to 50 it is pretty much between x=50-100 so there is a 50% chance you hit your spot. (obviously 50-50 is 100%, but since this length is continuous there's little chance it lands on that point). Obviously since this is symmetrical you can see this pattern going from 50% to 100% at the other end. Since each point on the continuous line has the same probability of happening the answer is clearly 75%.This problem is also equivalent to the probability that, if you have a line segment from 0 to 1 and you make 2 random cuts on that line segment, what is the probability that the three resulting pieces do NOT make a triangle?

Feb 8, 2014

Nov 7, 2012
 This wasn't difficult, but it's the only specific question I can remember. You're playing basketball and you're down by 2. You know you can hit a 2-pointer to tie the game with 28% probability, and then go on to win the game in overtime with 50% probability. Alternatively, you know you can hit a 3-pointer and win with 15% probability. Which do you take?2 AnswersThe 3-pointer3-pointer. First option has a probability of 14% of wining (0.28x0.5) whilst the second option gives you a probability of 28%.

### Sales and Trading Summer Analyst at Bank of America was asked...

Mar 22, 2011
 What is BofA currently trading at?1 Answer(Lookup price before you go into the interview)

Apr 27, 2020
 They asked questions about technical projects on resumé and statistics based questions. Some mathematics brain teasers. e.g. describe penalty term for lasso regression/sum natural numbers up to 100.2 AnswersI described my projects by framing them with respect to what I learned through them. Discussed the L1 penalty which penalizes the absolute value of the sum of non-zero coefficients. Explained the derivation of n(n+1)/2 formula for the sum of the first n natural numbers.How long before they responded with a decision?

### Sales Trading and Quantitative Analysis Summer Analyst at Citi was asked...

Dec 1, 2014
 what is the square root of 64,000?3 Answersdon't say 80.Wrong Above~ The point is to get the answer without a calculator! The fairly easy way is to use Newton's method or Taylor expansion to get sqrt(10). One or more comments have been removed. Please see our Community Guidelines or Terms of Service for more information.

May 14, 2020
 Explain what a bond is to a child2 AnswersUsed a lemonade stand business to explain the concept.What is the age of that child & which child of d*nkey asked this question.