Forging a rapport with the interviewer is a good thing, but some interviews drift off topic as the people involved chat. However, there is a time budget for each interview, and most managers have specific objectives in checking your ability. If they don't get covered it can hurt your progress to the next stage. Although it is the interviewer's responsibility to get things done, it s your problem if he doesn't. This is where the politeness we mention elsewhere is important. When you feel that time is moving against you, ask to make sure that everything he needs to know is covered.
Actually there are stupid questions. Bad questions are ones which embarrass the interviewer, or force him into a corner; that's his job, not yours. Do not try to score points off the interviewer; either you fail and look silly, or worse still, you succeed. It s a bad idea to bring up any screw-ups that the bank has been involved in, or where the manager has to admit that he hasn't read your CV.
Your interrogator will often come from a similar background to you, but even within maths and physics there are many specializations that are mutually incomprehensible. You re just emerging from a discipline where you think in terms of these names and equations and it's easy to emit a stream of noises that your interviewer can barely understand. It's actually worse if he is from a similar background, since he may feel embarrassed to ask what you actually mean. You lose points here. But it is generally polite to enquire about the background of your audience when asked to explain some part of your work. This both shows consideration, and prevents you making this error.
Show some market insight
This doesn't mean you have to know the ticker symbols of all SP500 stocks, but it does mean you should be able to comment on the reliability of models, what are their common pitfalls and how the quant and the trader might communicate about this. If you can quantify some practical phenomenon that is rarely discussed in academic literature then you will impress. (Tip: Because banks are often delta hedging, everything usually boils down to gamma and/or volatility.)
It is also worth reading The Economist before the interview. Some interviewers are keen to see if you have awareness of the world in general. The Economist may disturb some people since it covers other countries and has no astrology column or coverage of golf.
There are several different types of brainteasers you might get asked, all designed to test how your mind works under pressure, and to try to gauge how smart you are, rather than how much you have learned.
• Straightforward calculation. Example: How many trailing zeros are there in 100 factorial?
• Lateral thinking. Example: Several coworkers would like to know their average salary. How can they calculate it, without disclosing their own salaries?
• Open to discussion. Example: What's the probability that a quadratic function has two real roots?
• Off the wall. Example: How many manhole covers are there within the M25?
Work through the Brainteaser Forum on wilmott.com. You can practice for IQ tests, and the more you do, the better your score. Brainteasers are no different. And you'd be surprised how often the same questions crop up.
It's worth having a few numbers at your fingertips for the 'manhole covers.' One manager recently told us in rather despairing tones of the stream of candidates who didn't have even a rough approximation to the population of the country they were born and educated in. Several put the population of Britain between 3 and 5 million (it's around 60 million). A good trick when 'estimating' is to pick numbers with which it is easy to do mental arithmetic. Sure you can multiply by 57, but why expose yourself to silly arithmetic errors.
In many types of question, the interviewer wants to hear your train of thought, and has simply no interest in the actual answer. Thus you need to share your thoughts about how you get to each stage. You also should 'sanity check' your answers at each step, and make sure he is aware that you're doing it. This is a soft skill that's very important in financial markets where the money numbers you are manipulating are rather larger than your credit card bill.
At entry level we also see people being asked what we call 'teenage maths.' You've probably been focusing on one area of maths for some years now, and to get this far you've probably been good at it. However, some banks will ask you to do things like prove Pythagoras' theorem, calculate n to a few decimal places, or prove that the sum of N numbers is N(N + 1)/2. That last fact being surprisingly useful in brainteasers.