Quantitative Analyst Interview Questions | Glassdoor

# Quantitative Analyst Interview Questions

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Quantitative analyst interview questions shared by candidates

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

Jan 21, 2014
 What's the best unbiased estimator for a series random variables?5 AnswersI guess it is just a Gaussian distribution (Normal dist.). Since it has the smallest uncertainty (from quantum point of view) or variance.I guess it is just a Gaussian distribution (Normal dist.), since it has the smallest uncertainty (from quantum point of view) or variance.It is the OLS estimator (with Gauss-Markov approximations and normality), by Fisher's theorem on Maximum Likelihood Estimators.Show More ResponsesIt didn't mention linear. if it's linear, then ols. if not, CEF, conditional expectation function.It didn't mention linear. if it's linear, then ols. if not, CEF, conditional expectation function.

Jun 15, 2015

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

May 14, 2011

Sep 12, 2015

Aug 24, 2009
 What is the probability of breaking a stick into 3 pieces and forming a triangle?8 AnswersIts 1/4. Here is the key idea for my analysis of the problem: If we consider the original stick to be of unit length, then we can form a triangle whenever the longest stick is less than a half unit long.Suppose x is the length of the first piece and y is the length of the second piece (both must be nonnegative). Then y will be <= 1-x, and to be able to form a triangle, y must be <= .5 - x with x <= .5. The probability of being able to form a triangle is the area of the second set of (x,y) pairs divided by the area of the first set of (x,y) pairs, which is .125/.5 = .25.The probability is 0 given that it is a question about the probability of 2 breaking points falling on 1st thirdth and 2nd thirdth point. For any continuous variable, the probability of the variable equal to countable points (including indefinite countable numbers) equal to 0Show More ResponsesFor one time evet, the probability is 0I think, the probability is 1/2: Breaking a stick into three pieces corresponds to selecting three real positive numbers with a+b+c=1, and, w.l.o.g., a>=b>=c. The triangle inequation, that any two sides are longer than the third one (i.e., a= 0.5, then b+c a, so we cannot form a triangle. - If a 0.5 > a. The other two inequations a+b>c and a+c>b also hold because a>=b>=c: b is positive and so from a>=c we have a+b>c, similarly, as c>0, a+c>b holds. Hence, we can form a triangle iff a<0.5. Ultimately, selecting a number 0nothing in the question said it had to be equilateral triangle so the probability is 100%1.a+b>c 2.b+c>a 3.a+c>b A Triangle is formed when all three are true. As there are three pieces, so a>0, b>0 and c> 0 Only possibilities are: 1.T,T,F i.e one is bigger than sum of 2 2. T,T,T I.e all thee equations are valid Favorable possibility is T,T,T So answer = 1/2 = 0.5try this simulation in R: checkTri c & a+c>b & b+c>a, 1, 0) ) } mean(replicate(100, checkTri())) Theoretically, we have conditions that a+b>1/2, a<1/2, b<1/2. If you can draw this area in an coordinate axis, you can calc the probability.

Nov 11, 2011

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

Dec 19, 2010
 The price of a stock is \$10 now. It has .6 prob. increasing to 12 and .4 prob. going down to 8. Interest rate is 0. What's the value of a call option with strike \$10?8 AnswersFirst compute risk neutral prob.10.40Calculate first the risk neutral probability. (I.e you are assuming the current stock price is efficiently priced in) With the stock price tree, risk neutral probability Pi: Its \$10 = pi * \$12 + (1-pi)*\$8 Solving for Pi = 0.5 Then to calculate the value of call: Substitute Pi with the payoffs (\$2 = \$12 - 10 and \$0 as option is worthless at <\$10) C(0) = (pi*(\$2) + (1pi)*\$0 )/ r = 0.5 * 2 = \$1 (Since r = 1, 0 interest rate) A normal expected value of the option (non risk neutral) will just be 0.6*\$2 + (0.4)*\$0 = \$1.2.Show More Responses\$1Expectation under any measure is equivalent. That's why we change measures to calculate things as the result will be same. Answer is 1It's easy to get an answer 1.2, but it's wrong. Answer is 1.Can someone explain why the answer is 1 and not 1.2:?Jim, because you get 1.2 with physical probabilities, and 1 with risk neutral probabilities. To use the binomial tree pricing approach you should use the risk neutral probabilities. Th calculations are provided above.

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

Feb 22, 2011
 From (0,0,0) to (3,3,3) in 3D space how many paths are there if we move only right, forward or up?7 Answers1449! / (3! 3! 3!)Can you explain that please?Show More ResponsesA dynamic programming solution is applicable here. Considering each decision hop (a point where a decision is made whether to move right/up/forward) is placed unit length apart, the number of decision hops one might encounter in moving from (0,0) to (3,3) is 4 , making it a length=5 path.Also, there are 3 directions of movement corresponding to the 3 dimensions. A 2-Dimensional *dynamic programming based Forward Table* of length 5 along the X-axis (5 steps from (0,0) to (3,3)) and length 3 along the Y-axis (3-directions of movement), can be used to solve the problem.here is a MUCH easier way to think of this, no dynamic programming required: Consider a much simpler problem - you have 2 white books and 2 black books and want to arrange them on a shelf. How many ways can you do this? Basic permutation theory tells us that when you have m distinct groups of n items, the number of ways they can be arranged is given by: n! / (i_1)!(i_2)!...(i_m)! where i_x is the number of items in group x. So, the answer to this problem is 4! / 2!2! = 6. Now, let's return to the original problem: you can ONLY move forward, right, or up. This means you MUST get closer to (3,3,3) each move. It doesn't take a rocket scientist to figure out that this will ALWAYS require 3+3+3 = 9 moves. Now, with these 9 moves, you MUST do 3 moves of each type. Now, using the formula given above you get 9! / 3!3!3!If this was 2 dimensional, ie a square instead of a cube, the answer would be 2. The coordinate of the far corner can be at (1,1), (3,3) or (1000, 1000), there are only two distinct paths to get from (0,0) to the far corner, if we can only move up and right. Same deal for the cube. There are a total of 8 distinct paths.We know there has to be 3 up, 3 forward and 3 right to arrive at the final destination, the only difference is how many combinations are there for up, forward and right. So we choose 3 up from 9 steps, that is C{_9}{^3}, then we choose 3 forward from the following 6 steps, which is C{_6}{^3}, lastly the three steps have to be right, which is C{_3}{^3}. So the total is 1680 paths.

Feb 22, 2011