Quant Interview Questions | Glassdoor.co.uk

# Quant Interview Questions

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Quant interview questions shared by candidates

## Top Interview Questions

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14 Apr 2015
 How do you check if your regression parameters are significant? Given a number's prime number decomposition, how many ways are there of factorizing it into two different factors?3 Answersanswer to prime number question: I am assuming that the 2 factors you factorize it into are relatively prime, in that they have no common factors. For a number N, suppose it is represented as a product of prime number N=\Pi_i p_i^(e_i), where p_i is a prime number and e_i represents the number of such primes in N's prime number factorization. For N=xy, we see that for each p_i, we can choose whether ALL p_i factors go to x or go to y (2 choices). it cannot be that we take some of the p_i factors and give them to x, then give the others to y because otherwise x and y will have common factors. Thus, for each p_i we have 2 choices as to where it can go: x or y. So nominally we have 2^n possibilities. However, since (a)(b) and (b)(a) are considered the same factorization, we over count by a factor of 2, so really we have 2^(n-1) possibilities.regarding my above answer: the upper limit on the product \Pi should be n. That is, \Pi_{i=1}^nyour assumption of relatively prime makes the problem easy...i don't think that's the goal...try to answer the actual question without making sweeping assumptions!!

### Quant at J.P. Morgan was asked...

14 Nov 2012
 What is the expected number of coin tosses required before 3 heads in a row show up?2 AnswersTry it for 1 head first. Let X be the expected number of flips until you get heads. What are the possible outcomes after 1 flip? There's 1/2 chance of getting heads (H), and there's 1/2 of getting tails (T). We stop when we get H. In other words, you can get H or TH or TTH, etc. Getting T means you've wasted one go, and you still have X flips to go. So, lets define X recursively as X = (1/2)(1) + (1/2)(X+1). This says, "If you've got H the first time, you're done. If you've got T, you've wasted one go and you flip again, hence 1+X." Solving for X, we get X=2. Getting 2 consecutive heads is similar, but you need to add an extra possibility: Getting HT means you've wasted 2 go's and we're still not done. So then we have X = (1/4)(2) + (1/2)(X+1) + (1/4)(X+2). This says, "If you get HH, you're done. If you get T, you've wasted a go and you're not done. If you get HT, you've wasted 2 go's and you're not done." Solving for X gives us X=6. For 3 consecutive heads, it's similar. Think about getting HHT and how this would look mathematically in our equation for X. The expected number of flips is X=14. See if you get the same :)If you like working with power series, an alternative - but arguably more laborious approach is laid out in 1.42 here www.math.umn.edu/~gennady/hw2.pd

### Quant at Winton Group was asked...

11 Apr 2010
 Definition of eigenvalues/eigenvectors. Requirements for stability of a dynamical system. 2 Answersby the Koopman von Neumann Theorem, a dynamical system S is ergodic iff 0 is a simple eigenvalue of A (the infinitesimal generator of S). And S is weakly mixing iff 0 is the only eigenvalue of A.fack u!

### Entry Level Quant Developer at Cantab Capital Partners was asked...

6 Nov 2011
 What is d x^x/dx?2 AnswersIf y = x x and x > 0 then ln y = ln (x x) Use properties of logarithmic functions to expand the right side of the above equation as follows. ln y = x ln x We now differentiate both sides with respect to x, using chain rule on the left side and the product rule on the right. y '(1 / y) = ln x + x(1 / x) = ln x + 1 , where y ' = dy/dx Multiply both sides by y y ' = (ln x + 1)y Substitute y by x x to obtain y ' = (ln x + 1)x xsorry, i copy pasted this, the x x is is really a x^x. Essentially this is just a logarithmic differential exercise, exploiting the fact that d/dx ln f(x) = f'(x) / f(x) so that f'(x) = d/dx ln(f(x)) * f(x)

### Summer Internship Quant Analyst at J.P. Morgan was asked...

1 Jan 2013
 What is a 'pure virtual function'? - Was the only difficult one for me as I am not as familiar with C++ as other languages. :/ 1 AnswerAlso asked about current JPM stock price ( @ \$41.22 then )

15 Aug 2018
 A reasonably easy question about sorting lists.1 AnswerHow to estimate the how biased a coin is. The quant guy was very annoying

11 Mar 2014
 find declarative algo from recursive one1 Answeruse stacks

8 Aug 2019
 You have a scale and 18 balls. One of the balls is slightly heavier than the rest. The rest are identical. What is the minimum number of times you need to use the scale to determine which ball is the heavy ball?1 Answer3 times: first divide 18 balls into 3 groups, 6 each, take two groups and weigh, if equal, then the heavier ball is the in the 3rd group, then divide the 3rd group into 2 groups of two's, take two groups and weigh, either equal or not you know the pair of balls containing the heavy one, just one more weigh. If the initial weigh is not equal, take the heavy 6-ball group and do the same as above, still 2 more weighs. So you can find the ball in 3 weighs

5 Oct 2016