Quantitative research analyst Interview Questions | Glassdoor

# Quantitative research analyst Interview Questions

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Oct 26, 2017

### Quantitative Analyst at Goldman Sachs was asked...

Aug 4, 2010
 What is the expected value of tosses to get 3 heads in a row?4 Answers14can be found using markov chains and fundamental matrics matlab code A = [1/2 1/2 0; 1/6 1/2 1/3; 0 1/3 1/2]; E=[1 0 0; 0 1 0; 0 0 1]; X=(E-A)^(-1); P = [1; 1; 1]; C = X*P; PS = [1/8 3/8 3/8]; F = PS* C; display(C); display(F); so 14.5 average number of steps14，2^(n+1)-2,with n denotes number of headsShow More ResponsesDenote H as an expected number of tosses. The key is to solve an appropriate equation. First toss, if you get tails than the expected number of tosses is (H+1), since you have to start from the beginning.. If you get heads than you move to the next throw with the same logic: H=0.5*(H+1) + 0.5*(0.5(H+2)+0.5(0.5(H+3)+0.5*3)) H=14

### Quantitative Risk Analyst at Goldman Sachs was asked...

Oct 2, 2010
 gambling question, whether it makes sense to gamble, if the chances are very small. Calculate the odds someone will take the grand prize if one million people goes, and odds are 1 in 1 million for each entry.4 Answers1/e = 0.3 1/1000000 is very small, so actual odd approaches the limiting case of 1/e.Odds are: 0.3678792572210609 that no one wins, i.e. 0.632120742778939 that someone wins. The number e is not related to this problem; it is the limit of (1+1/n)^n. Here we have odds of (1-1/n)^n that no one wins.poisson as limiting cxase if binomial distribut5ion. Large number of trials with small prob. Thus Lambda = 1. find prob n = 0 in poisson with lambda = 1 = 1-1/e.Show More ResponsesYou're all wrong. 1) Answer one makes no sense, where are you getting 1/e= 0.3? (I assume this is related to answer 3) 2) Lotteries are not binomially distributed, since lottery numbers are typically unique to each ticket. Therefore you are sampling without replacement. 3) Poisson is indeed the limiting case of the poisson, and using this approximation will give you the same answer as two, which since I was bored I calculated as p=0.3678794 that no one wins, but is wrong for the same reason in my view. If we are sampling without replacement, the problem becomes much easier, and you won't need to bring a slide-rule or pocket calculator to your interview. If the odds for each player are one in one million, then one million tickets must have been issued. If there are one million players, then all tickets have been issued, and thus with certainty someone has won.

### Quantitative Finance Summer Associate at Morgan Stanley was asked...

Aug 5, 2010
 There are two stocks with the same expected value, with variance 0.3 and 0.2 and correlation 0.5. What proportion of each stock do you invest in to yield a minimum risk portfolio? 4 Answers100% in stock 2, with the smaller variance.No, if you can short, the variance could be reduced even further since the stocks are correlated.17/44 of the stock with variance of .3 and 27/44 from the stock with variance of .2Show More ResponsesCovariance = 0.3 * 0.2 * 0.5 = 0.03 Cov Matrix = c = [0.3 0.03; 0.03 0.2] Inv Cov Matrix = c_inv = [2000/591 -100/197; -100/197 1000/197] Answer = (c_inv * [1; 1])/([1 1] * c_inv * [1; 1]) = [17/44; 27/44]

### Quantitative Analyst at Morgan Stanley was asked...

Jan 24, 2011
 expectation of max value of two dices4 Answers161/36if D1=D2: EV1 = sum_{i=1}^6 i/36=21/36 O.W.: EV2 = sum_{i=2}^6 i(i-1)/36=140/36 => EV=EV1+EV2=161/36;161/36. I did it by finding pdf of max(x1,x2).Show More ResponsesWhat is the expression for probability(max =n)? P(max=n)=P(1st=n, 2nd

### Quantitative Researcher at Jane Street was asked...

Oct 1, 2016
 Expected length of the longest segment of a unit-length stick broken in 2 places.4 AnswersMapped the probability measure to a 3D polytope and calculated the center of mass.0.75 by common senseLet L and R be the left and right half of the broken stick (resp.) The probability that L is longer than R is equal to the probability that R is longer than L (these halves are symmetric, and so this probability is 1/2). This implies that the expected length of the longer side is 3/4.Show More Responses11/18, also verified by simulation, but I don't know how to do it without 15minutes of calculus

### Quantitative Research at J.P. Morgan was asked...

Feb 18, 2012
 You play a game with someone, the rule is to take turns to put a quarter on a round table ( can be any size, but must be of symmetrical shape). You are trying to cover the table up with quarters, you lose when there's no place for you to put down the quarter. Should you be the first person to play ?3 AnswersNo. You should be the second to play. The symmetry of round table guarantees the space for a 2nd coin for every coin placed.be the first to play with the coin dead center Then the symmetry rules will apply for the the rest of the coinsbe the first to play with the coin dead center Then the symmetry rules will apply for the the rest of the coins

Oct 15, 2015