Interview #12: Job Interview of an Options Trader
Team Latte March 18, 2011
The following is the transcript of a discussion during the job interview of a trainee trader. In 2005, after the completion of their global boot camp in London and New York, Delhi Bombay bank (DB), short listed 15 candidates for their credit derivatives desk based in London. These fifteen exceptionally bright individuals, all of whom had either a Ph.D. in Math / Physics or advanced degree in Engineering from a top tier university, were supposed to be the next generation traders who would be producing ideas and dollars by the bucketful. And they would all work under the youngest Managing Director ever in the history of Delhi Bombay bank. This man, a math and computer science whiz kid from the top Ivy league school in the States, a champion chess player, a star and a demigod within DB, would ultimately cause havoc by inflicting a loss of around $2 billion thereby causing the entire credit derivatives desk to fold in 2008. But in 2005 he was the Master of the Universe.
This is the job interview of one of those trainees. The interviewer was of course the M.D. and the head of the desk.
Managing Director:
What is common between the functions and where is a constant?
Trainee:
Well, they are both nonlinear.
Managing Director:
Nonlinear as in exponential, logarithmic, quadratic, what? They don’t look same to me. Do these two functions share any particular property?
Trainee:
They are both convex functions.
Managing Director:
Can you prove it?
Trainee:
Sure, just plot the two functions and you can see both these functions will have a convex shape. A certain curvature. The curvature would be different in both cases and the exact shape would also be different but both will have convexity. Therefore, they both belong to the class of convex functions.
Managing Director:
No graph. Just using numbers, can you show that they are both convex? [At this point there is a long silence ......]
Trainee:
I mean, we can take different values of and then estimate at those values, then take the gradient and then see how that gradient changes. I guess we can take different values and intervals over which we can do this for each of the functions and show that the gradient of each function actually changes, which can prove convexity.
Managing Director:
I am not interested in that. Can you simply define a convex function and then using numbers, purely numbers for various values of and corresponding values of , show that both these functions satisfy the definition of a convex function in an exact manner.
Trainee:
No, I can’t.
Managing Director:
Then you should be working with those guys in Finance and not on the trading desk. If someone cannot use numbers to explain every single thing happening in the Universe then he has no business being a trader in a bank. [The trainee looks flustered at this stage and has gone a bit red in the face]
Managing Director:
Say, the bank has designed a contract that pays the square of S&P500 at maturity, something like the payoff function, , and the current value of is normalized to 100. OK? SP500 is trading at 100 today and you have a contract that pays off, the square of SP500 at the end of one year. Will such a payoff have a fair value, or an inherent value, today, at ? If a client asks you for a price would you be able to quote him a price on this contract?
Trainee:
This contract will have a fair value. There is an inherent value in this contract because of the inherent convexity. So I guess the expected value of the contract should be the fair value.
Managing Director:
You mean expected value of SP500 or expected value of SP500 squared?
Trainee:
I think it is the expected value of SP500 squared.
Managing Director:
OK, say, at maturity, SP500 can only take 5 values, 100, 110, 120, 130, 140 or 150. What is the fair value of the contract today?
Trainee:
We’ll calculate the square of all these five values because that is the function and then average them. Right?
Managing Director:
You tell me. [Clearly the M.D. has by now lost interest in the interview and is distracted. They say this is the sign of a genius that he cannot stay focused on one topic for too long.]
Managing Director:
If you have two contract payoffs, and , where is constant, then which of these is more risky?
Trainee:
The first payoff is more risky, because it is more convex.
Managing Director:
What’s "more convex"? There’s nothing like "more convex" or "less convex" in trading. You need numbers, figures. It’s like saying I made some profit. How much? Ten dollars, hundred dollars, how much, profit? There’s a world of a difference between ten dollars and hundred dollars! On my screen ten dollars is not the same as hundred dollars. ["Ten dollars" is the banking jargon for Ten Million dollars. Similarly, "hundred dollars" mean a hundred million dollars.] [The trainee is determined to soldier on and makes one last attempt at a light hearted joke]
Trainee:
Yes, there’s a lot of difference or maybe that your computer’s got a bug.
Managing Director:
Excuse me? My computer’s got a bug. Oh, I see, my computer’s got a bug. [An awkward pause for about 20 seconds. And then the Managing Director asks:] Tell me something. Why can’t I get an antivirus program for my computer and get rid of all the bugs and viruses. I mean, no antivirus program – not the best one ever invented on this planet – can ever get rid of all the viruses and bugs in my operating system. Can you tell me why?
Trainee:
I don’t have a clue. But honestly, is this knowledge also required for being a trader?
Managing Director:
No, it’s required only if you want to start a software company and turn it into a Microsoft. By the way, it’s a math question and not a software one.
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