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New Book: 150 Most Frequently Asked Questions on Quant Interviews - Baruch MFE faculty

dstefan

dstefan

Baruch MFE Director
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We are happy to announce the release of 150 Most Frequently Asked Questions on Quant Interviews, whose authors, Dan Stefanica, Rados Radoicic, and Tai-Ho Wang, are professors and colleagues in the Baruch MFE Program, and have vast experience educating students who are very successful interviewing for quantitative positions (95% employment rate for 2007-2013 Baruch MFE graduates).

The book contains over 150 questions covering the core body of knowledge required for successfully interviewing for a quant type position. These questions are frequently and currently asked on interviews for quantitative positions, and cover a vast spectrum, from C++ and data structures, to finance, brainteasers, and stochastic calculus.

The book can be ordered for $25 for all orders placed before December 6 (15% discount from the $29.50 list price) from www.fepress.org/150iqs and from Amazon US and Amazon UK and Europe; links below.
___________________________________________________

Topics covered:
• Mathematics, calculus, differential equations
• Covariance and correlation matrices. Linear algebra
• Financial instruments: options, bonds, swaps, forwards, futures
• C++, algorithms, data structures
• Monte Carlo simulations. Numerical methods
• Probability. Stochastic calculus
• Brainteasers
________________________________________________________________

Title: 150 Most Frequently Asked Questions on Quant Interviews
Authors: Dan Stefanica, Rados Radoicic, Tai-Ho Wang
Softcover: 224 pages
Publisher: Financial Engineering Press
FE Press webpage: http://www.fepress.org/150iqs
FE Press Price: $25.00 (List Price: $29.50)
Amazon US page: http://tinyurl.com/mwgofj4
Amazon UK page: http://tinyurl.com/mz2kxsa
Also available on amazon.de amazon.fr amazon.it amazon.es
 
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A four questions sample:

1. Put options with strikes 30 and 20 on the same underlying asset and with the same maturity are trading for $6 and $4, respectively. Can you find an arbitrage?

2. The number \(2^{29}\) has 9 digits, all different. Without computing \(2^{29}\), find the missing digit.

3. Let \(W_t\) be a Wiener process, and let \(X_t = \int_0^t W_\tau d \tau\).
What is the distribution of \(X_t\)? Is \(X_t\) a martingale?

4. Alice and Bob stand at opposite ends of a straight line segment. Bob sends 50 ants towards Alice, one after another. Alice sends 20 ants towards Bob. All ants travel along the straight line segment. Whenever two ants collide, they simply bounce back and start traveling in the opposite direction. How many ants reach Bob and how many ants reach Alice? How many ant collisions take place?
 
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Sounds interesting, too bad the only payment method is Paypal and not possible to pay directly via credit card. Might pick it up though anyways seems it seems to comprise many relevant topics.

By the way, is there an ETA for when the other books of the Financial Engineering Series (Probability Primer, Numerical Linear Algebra Primer etc.) will be published? Big fan of the Primer of Mathematics, provides a really comprehensive introduction to the basics.
 
Thanks Dan.

Fantastic compilation of problems, structured solution with mathematical approach. Especially, problems around Brownian motion and its application, no other similar books in the market has covered in that detail as this one has.

Covers all mathematical problem that can be applied to finance, not just the popular ones, gives a solid revision to those who had been out of college for long. The size of the book makes it very handy to carry around, if that helps you, to me it does.
 
ashwani said:
Thanks Dan.

Fantastic compilation of problems, structured solution with mathematical approach. Especially, problems around Brownian motion and its application, no other similar books in the market has covered in that detail as this one has.

Covers all mathematical problem that can be applied to finance, not just the popular ones, gives a solid revision to those who had been out of college for long. The size of the book makes it very handy to carry around, if that helps you, to me it does.
Click to expand...
Thank you, Ashwani, glad to hear you like the book!

Other than the careful choice of questions, we presented solutions that are best suited to be given on an interview. One such example is the first of three solutions to the very often asked question of finding parameter values for a matrix to be covariance matrix:

Find all the values of \(\rho\) such that
\[ \Omega ~=~ \large( \begin{array}{ccc} 1 & 0.6 & -0.3 \\ 0.6 & 1 & \rho \\ -0.3 & \rho & 1 \end{array} \right) \]
is a correlation matrix.

Solution using Sylvester's Criterion:
A symmetric matrix with diagonal entries equal to 1 is a correlation matrix if and only if the matrix is symmetric positive semidefinite (spd). Thus, we need to find all the values of \(\rho\) such that \(\Omega\) is spd.

Recall from Sylvester's criterion that a matrix is spd if and only if all its principal minors are greater than or equal to 0. Also, recall that the principal minors of a matrix are the determinants of all the square matrices obtained by eliminating the same rows and columns from the matrix. In particular, the matrix \(\Omega\) has the following principal minors:
\(det(1) = 1; det(1) = 1; det(1) = 1;\) \(det\large( \begin{array}{cc} 1 & 0.6 \\ 0.6 & 1 \end{array} \right) = 0.64; det\large( \begin{array}{cc} 1 &-0.3 \\-0.3 & 1 \end{array} \right) = 0.91; det\large( \begin{array}{cc} 1 & \rho \\ \rho & 1 \end{array} \right) = 1 - \rho^2; \) \(det(\Omega) = 1 - 0.36 \rho - 0.09 - 0.36 - \rho^2 = 0.55 - 0.36 \rho - \rho^2. \)

Thus, it follows from Sylvester's criterion that \(\Omega\) is spd if and only if
\(1 - \rho^2 \ge 0 \) and \(0.55 - 0.36 \rho - \rho^2 \ge 0,\)
which is equivalent to \(-1 \le \rho \le 1\) and \(\rho^2 + 0.36 \rho - 0.55 \le 0.\)
Since the roots of the quadratic equation \(\rho^2 + 0.36 \rho - 0.55 = 0\) are -0.9432 and 0.5832, we conclude that the matrix \(\Omega\) is spd, and therefore a correlation matrix, if and only if \(-0.9432 ~\le~ \rho ~\le~ 0.5832.\)
 
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Ole Bueker said:
By the way, is there an ETA for when the other books of the Financial Engineering Series (Probability Primer, Numerical Linear Algebra Primer etc.) will be published? Big fan of the Primer of Mathematics, provides a really comprehensive introduction to the basics.
Click to expand...

Thank you, Ole - the current plan is to release the Numerical Linear Algebra Primer for Financial Engineering some time next year.
 
4. Alice and Bob stand at opposite ends of a straight line segment. Bob sends 50 ants towards Alice, one after another. Alice sends 20 ants towards Bob. All ants travel along the straight line segment. Whenever two ants collide, they simply bounce back and start traveling in the opposite direction. How many ants reach Bob and how many ants reach Alice? How many ant collisions take place?

I hate questions like this. They are supposed to test how smart you are. Perhaps they do, I don't know. Google has finally admitted that questions of this sort were not predictors for how well someone did at Google.

Microsoft is famous for questions like this too. I was having a problem with Microsoft software the caused me to waste over an hour. I was reminded of how these questions have lead to such excellent software at Microsoft (Linux, live free or die).

The quant questions look like they are great review. I suspect that if you can do all the quant questions you have a good chance of doing well in interviews. But these brain teasers are endless. There is a good chance that an interviewer will have some silly question that you have not seen before and may stump you. I believe that there's book of brain teasers.

Personally, I'd rather not work in an organization that thinks that brain teasers are good interview questions. Unless they're going to make me rich. And that doesn't look too likely these days.
 
The point of these brain teaser questions isn't to find the right answer every time. The interviewer is interested in how you approach these questions and how you logically structure your solution.

Extrapolating from these questions to your problems with Microsoft software is ..I don't know how to say it nicely so I will refrain from commenting.
 
Ole Bueker said:
The point of these brain teaser questions isn't to find the right answer every time. The interviewer is interested in how you approach these questions and how you logically structure your solution.
Click to expand...

For the majority of the brainteasers from this book, you would have to get the right answer. On the other hand, at many interviews, the interviewer will probe until finding something the interviewee does not know, and then probe deeper.

Ian Kaplan said:
I hate questions like this. They are supposed to test how smart you are. Perhaps they do, I don't know. Google has finally admitted that questions of this sort were not predictors for how well someone did at Google.
Click to expand...

Since there are several different types of brainteasers, everyone has favorites and less than favorites. Focusing what the ones you like least, actually the ones you are less naturally inclined to, pays dividends in case such brainteasers are asked on the interview.
 
Hi

Thanks for this great book,I have a doubt about the 1st question :
In the plane (K,P(K)), these option values correspond
to the points (30, 6), (20, 4), and (0, 0), which are on the
line P(K) = 2/3*k
==> In my undertanding I think : P(k) =1/5*k , P(0)=0 , P(30) = 1/5*30 = 6 and P(20) = 1/5*20=4 ?
 
soufiane said:
Hi

Thanks for this great book,I have a doubt about the 1st question :
In the plane (K,P(K)), these option values correspond
to the points (30, 6), (20, 4), and (0, 0), which are on the
line P(K) = 2/3*k
==> In my undertanding I think : P(k) =1/5*k , P(0)=0 , P(30) = 1/5*30 = 6 and P(20) = 1/5*20=4 ?
Click to expand...

Indeed, P(k) =1/5*k; we will put together an Errata as soon as early December, including this correction.

The rest of the proof holds true, as does the principle of strict convexity of the option price (put or call) as function of strike which the arbitrage is based on.
 
dstefan said:
Indeed, P(k) =1/5*k; we will put together an Errata as soon as early December, including this correction.

The rest of the proof holds true, as does the principle of strict convexity of the option price (put or call) as function of strike which the arbitrage is based on.
Click to expand...

Many thanks for your update, I already bought your book and I 'm starting with the first questions ,I really like your book with challenging questions and the answers to those question are very clear and detailed
Thanks
 
damonloveavril said:
Hi Dan,

I just got the book earlier this week. Feel very honored to get your and Professor Wang's signatures. I am preparing my application now and hope we will have a chance to talk to each other next spring.
Click to expand...

And Professor Radoicic's signature, right? :)

Enjoy the book, and good luck!
 
Last Day: The book can be ordered for $25 for all orders placed before December 8 (15% discount from the $29.50 list price) fromwww.fepress.org/150iqs

All the books ordered from the link above before December 8 are signed by the authors.
 
I got the book this morning i have spent 20 minutes on first question because i found 1/5×K ... I saw their is an errata i was feeling stupid
 
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