Interview #11: Job Interview of an Associate (junior Quant)
Team Latte March 18, 2011
The following conversation occurred in a recent interview in a European bank, where the interviewer was the Head of Structuring of a Commodities desk and the interviewee was an intern in the same desk and was being interviewed for an Associate’s job. The interviewee had a Ph.D. in theoretical physics from a top name university. What the intern / interviewee did not know was that the interviewer was not only the Head of Structuring and an experienced quant but also had a Master’s degree in Electrical Engineering and a Master’s degree in Applied Math from another top school. He was also one of those rarest of the rare Managing Directors in banks who had practically no ego.
In the following conversation, Question refers to the question asked by the interviewer and Answer refers to the corresponding answer given by the interviewee.
Question :
Marcus tells me great things about you. He’s quite impressed. And he says you love paper and a pencil.
Answer :
Yes, I think too much knowledge that’s lost within the computer programs and all these systems. Mind is a better computer…and somehow I can think clearly away from a computer screen. I need paper and pencil to work out. And this scientific calculator does all my work.
Question :
But you can write code. Marcus told me that you are good with C++ and C#.
Answer :
Yes, I can write C++ and some C# but for that you need to put a gun to my head.
Question :
This is the bank, mate. You got to live with these screens. That’s all you have. Screens and numbers, nothing else.
Answer :
I know. As long as the numbers are real and not imaginary, I am happy. (smiles all around). And of course, we have the prime numbers.
Question :
Right, we have the prime numbers. What’s the application of Prime numbers in finance?
Answer :
This is a rather trivial question. Of course, everybody knows that we use random numbers in Monte Carlo simulation engine. All uniform random numbers are generated using some algorithm involving Prime numbers.
Question :
Great! So how many Prime numbers are there between zero and, 1000.
Answer :
(The interviewee uses the scientific calculator for a second and then answers) ....about 333 Prime numbers.
Question :
And are they evenly distributed?
Answer :
Distribution of Prime numbers is a complex and detailed topic. It’ll take some math to explain that. Suffice it to say that the average spacing between the Prime numbers from 0 to 1,000 is about 3.
Our Comment:
The interviewee is correct. Prime number theorem states that the number of primes less than is given by: . And the average spacing between the primes is given by (in the limiting case when ): . Using the above formulas, we can see that there are around 333 prime numbers less than 1000. And the average spacing would be given by which is equal to 3.
Question :
OK, sounds good! So you have a lot of experience of using random numbers. I’m sure you can write a couple of robust algorithms of your own to generate pseudorandom numbers.
Answer :
Yes, I can. But I need to use C++. If you have a C compiler or Visual Studio I can generate a low discrepancy sequence…..or I can write a couple of lines of code on this piece of paper….
Question :
Oh, that won’t be necessary. I trust you. (smiles all around). But you said low discrepancy sequence. Right? What’s that? Is it some kind of a random number generation algorithm?
Answer :
No, a low discrepancy sequence is not a sequence of random numbers. These are deterministic sequences but their discrepancy is low. That’s why they are called “quasi random numbers” as opposed to “pseudo random numbers” which are generated by say, Microsoft Excel’s =rand() algorithm. But such a low discrepancy sequence can be a very good proxy for a realistic random number sequence…better than a pseudo random number sequence. Halton sequence and Sobol sequence are two good examples of low discrepancy sequences.
Question :
Cool. Tell me something. You’ve used matrices in your physics days as well as here while you were doing some stuff for Marcus.
Answer :
Yes, I have used matrices a lot. I am familiar with matrices and linear transformations.
Question :
Say, I have an square matrix, . Or just take a matrix. Let’s keep things simple. Now I populate all the elements of this matrix with random normal numbers (Gaussian deviates) with mean zero and standard deviation of one, all the cells of this 3 by 3 matrix are Gaussian random numbers.
Answer :
I think this would be an example of what they call a “random matrix”.
Question :
Yes, yes that’s right. It is indeed a random matrix. That’s the technical name. But is it possible for me to generate another “random matrix” from the original matrix, whose diagonal elements are also Gaussian deviates with distribution, and off diagonal elements are Gaussian deviates with distribution?
Answer :
I am sorry, I am not too familiar with Random Matrix Theory. But I know they use it in Nuclear Physics and some other fields in physics.
Question :
Actually, you’d be surprised to know that Random Matrix Theory (RMT) has applications in Quantitative Finance and Portfolio theory as well. Of course, RMT is used in wireless communication theory as well. But, in finance as well.
Answer :
So, what is the answer to your question? Can you generate another random matrix from the original matrix with N(0,1) and N(0,0.5) distributions?
Question :
Yes, you can. In fact, if is a square, random matrix with all elements of it being Gaussian deviates of order and is transpose of then a matrix given by is another random matrix (symmetric, of course) whose diagonal elements will have a distribution and off diagonal elements will have the distribution . It’s called a Wigner matrix.
Answer :
Isn’t that quite trivial. I mean, will give that by construction.
Question :
Yes, but this random matrix is of great significance. It’s part of Gaussian Orthogonal Ensemble. It’s used in Nuclear physics.... I think when you study heavy nuclei dynamics or something like that.
Answer :
I have very little exposure to Nuclear physics.
Question :
No problem. We are good here. How do you like working for Marcus? He’s pretty clued on. I think you can learn a lot from him…the so called tricks of the trade. We need someone who can do a lot of calibration work.
Answer :
Yes, I know. Marcus was telling me that. I did some in the last few weeks. But I think double mean reverting models are going to take a long time and I have a feeling that the Feller condition will be violated more often than not (like Anna was telling me about the FX options market).
Question :
Jonathan, you’ll do fine. I got to run and I’ll leave you to Marcus to sort out all those model related issues. Calibration, mate. Models come dime a dozen, it’s how you calibrate them to the real life data that makes or breaks a desk. Let’s catch up for a drink sometimes....the three of us.
End of the Interview.
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