Quantitative Analyst Interview Questions | Glassdoor.co.uk

# Quantitative Analyst Interview Questions

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Quantitative analyst interview questions shared by candidates

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

21 Mar 2012
 a, b, c are integers. Such that a^2 + 2bc = 1; b^2 + 2ac=2012, find all the possibles values of c^2 + 2ab. 7 Answers2011 is primeMore details in addition to the last post. 1) subtracting the 1st equation from the 2nd one gives: (b-a)*(b+a-2c)＝2011 2) 2011 is prime, so there are only two possibilities: b-a=1, b+a-2c=2011; or b-a=2011, b+a-2c=1 3) subtracting the 1st equation from the 3rd equation gives: (c-a)(c+a-2b)=x-1 4) plugging c-a=0.5*[(b-a)-(b+a-2c)], c+a-2b=(c-a)-2(b-a) into 3) gives you xIn 2) there should be four rather than two possibilities. Both terms could be negative.Show more responses2 cand: heavy one... I have no idea how did you figure out that 2011 is prime! Do you remember the table of prime numbers from 2 to 10000?? I easily found trivial solution b=0 a=+-1, and then got stucked. however, later I found that this is unique solution, and (3)=c^2= 1006^2. I've used your approach. You've got a 4 possibilities, +-1 +-2011 and +-2011 +-1, but 2 of them lead to complex roots. You see, sum (1)+(2)+(3) gives you (a+b+c)^2=1+2012+x, thus x>=-2013, so (b-a) may be only +-1, not +-2011. The answer is (3)=1012036In the equation a^2 + 2bc = 1, obviously, a is either 1 or -1 and either b or c is zero. Then if you derive b from the second equation, b = sqrt(2012 - 2ac), c can't be zero, because sqrt(2012) is not an integer. Therefore b = 0. So, in order for b to be 0, 2012 - 2ac should be zero or 2ac = 2012. => it's either a = -1 and c = -606 or a =1 and c = 606. In any case, because b is zero, 2bc term in the 3rd equation disappears and c^2 gives an answer 367236.To the comment above, 2ab term in the 3rd equation, of coursesimple eq: (a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca. from given eq, we know: (a+b+c)^2 = (2012 + 1 + UNKNOWN) = K^2 with K being anything larger than 45. 45*45 = 2025 46*46 = 2116 .. so you can figure out the missing term by: (K^2 - 2013)

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

4 Nov 2011
 You have a deck of 52 cards, and you keep taking pairs of cards out of the deck. if a pair of cards are both red, then you win that pair; if a pair of cards are both black, then I win that pair; if a pair of cards has one red and one black, then it's discarded. If, after going through the whole deck, you have more pairs than I do, then you win \$1, and if I have more pairs than you do, I win \$1. What is the value of this game in the long run?7 Answers00 lol. nice oneby symmetry, probability of losing = probability of winning therefore, -1p(lose)+1p(win)=0. done, ko, finished, fiendin'Show more responsesNo one bothered to ask if you're paying the loser -- e.g. when you win, you get \$1, but when you lose, are you losing \$1? It's not clear from the question above, though the interviewer may have been more specific.good point J.D It can either be 0 or 0.5 depending on how you interpret the questionI think you will always have the same number of pairsWhy is it 0 for us dumb people pls

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

13 May 2013
 You have 10 mice and 1000 bottles of wine. You also have 24 hours before a party, and one of the bottles has been tainted with a slow acting poison, which takes 24 hours to kill a mouse. In the 24 hours you have remaining, how many bottles can you guarantee safe for human consumption (assume humans and mice react identically)? Assume the lethal dosage is insignificant relative to the size of the bottle.9 AnswersI'll say 500. Since the dosage is insignificant, I'll divide the number of bottles in half, take samples from each of the first 500 bottles, mix them up, divide by 10 and feed to each mouse. If no mouse dies after 24 hours, then the first batch is safe. else, the second batch would be served.999. It is like a binary problem. First mouse tests the first #1-500 (mixed). Second tests #1-250 and #501-750. Third one tests #1-125, #251-375, #501-625, #751-875, and so on. 10 mice with 2 status each (death/alive) could encode number of bottles up to 2^10=1024. So 10 mice is enough to find out the single bottle that tainted.http://advanceddiscrete.wikispaces.com/Mice+and+WineShow more responsesChapter 7.2, P.183 in Zhou's bookEncode the wine bottle numbers in binary. Give each mouse is a combination based on this table: | mouse | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |-----------|---|---|---|---|---|---|---|---|---|---|---| | wine 1 | - | - | - | - | - | - | - | - | - | - | - | - | | wine 2 | - | - | - | - | - | - | - | - | - | - | - | + | | wine 3 | - | - | - | - | - | - | - | - | - | - | + | - | | wine 4 | - | - | - | - | - | - | - | - | - | - | + | + | ... | wine 1000 | + | + | + | + | + | - | + | - | - | - | If none of the mice die, wine bottle 1 contains the poison. If only mouse 10 dies, wine bottle 2 contains the poison. ... If mice 1-5 and 8 die, wine bottle 1000 contains the poison. That systems allows for an additionally 24 bottles to be encoding, 2^10=1024.Answer is 900 10 mices vs 1000 bottles 1 mice per 100 bottles 24 hiurs one dies 9 alive 100*9=900The answer is 900. You have 1000 bottles divided between 10 mice. as dosage doesn't matter, 100 bottles can contribute to a single dosage, in which case, one mouse will die meaning the tainted batch needs to be discarded and 900 are confirmed untainted.The answer is 1023. You need to think in bit-wise way. 1023 can be represented in binary as (1111111111). Your goal should be: representing each wine label (i-th number) to each binary representation. 1000th wine will be represented with 1111101000 meaning (1,2,3,4,5,7th) mices will be used to check the toxicity of this wine. In binary way, you can assign label to up to 1023 wines. So by analysing the rats that die after 24 hrs, you can actually identify which wine is toxic or not. hope this helps.Brian was quite close, but to represent 1024 wines, you actually need 11 mice. So the maximum # of wines that one can guarantee is up to 1023.

19 Oct 2011
 derive the formula for the variance of OLS from scratch4 Answersdelta^2*(x'x)^(-1)I think you meant: sigma^2*(x'x)^-1Both of these are wrong. Beta_hat = (X'X)^(-1)(X'Y)Show more responseshttps://en.wikipedia.org/wiki/Proofs_involving_ordinary_least_squares

17 Jul 2013

### Junior Quantitative Analyst at AXA was asked...

9 Jan 2011
 What is the theta of an option?1 AnswerTheta is the time value of an option, or the sensitivity of the price of the option to a change in time, getting closer to the date of expiry of the option.

### Quantitative Analyst at GSA Capital was asked...

21 Mar 2012
 What would you do as a trading strategy?1 Answer(I think this is completely stupid. First of all what kind do you want. I offered equity market neutral, event-based, statistical arbitrage, macroeconomic, market inefficiencies, what do you want? He did not answer, said that he didn't really think to constrain the question -- obviously this was pulled out of his a\$\$ last minute, he has no idea what he wants to hear. But he will be critical and dissatisfied in any case, guaranteed.

### Quantitative Analyst at Bank of America was asked...

28 Feb 2019
 What is the volatility?1 AnswerHistorical vol, local vol, stochastic vol

### Senior Quantitative Risk Analyst at npower was asked...

24 Aug 2012
 Why did you chose npower?1 AnswerHealthy atmosphere.

### Quantitative Analyst at Credit Suisse was asked...

3 Nov 2013
 If you bought an Equity Call Option with a Down-and-In Barrier, are you Long Skew or Short Skew? Please provide explanation as well.1 AnswerWould be very helpful if someone can explain to me what does "Long Skew" "Short Skew" means. Thanks.
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