I must state at the outset that this post is inspired by the second chapter of Nate Silver’s book The Signal and the Noise. In that chapter, which is about election forecasting, Silver draws upon the old Russian parable of the hedgehog and the fox. According to that story, the fox knows several tricks while the hedgehog knows only one – curling up into a ball. The story ends in favour of the hedgehog, as none of the tricks of the unfocused fox can help him evade the predator.
Most political pundits, says Silver, are like hedgehogs. They have just one central idea to their punditry and they tend to analyze all issues through that. A good political forecaster, however, needs to be able to accept and process any new data inputs, and include that in his analysis. With just one technique, this can be hard to achieve and so Silver says that to be a good political forecaster one needs to be a fox. While this might lead to some contradictory statements and thus bad punditry, it leads to good forecasts. Anyway, you can know about election forecasting from Silver’s book.
The world of “quant” and “analytics” which I inhabit is again similarly full of hedgehogs. You have the statisticians, whose solution for every problem is a statistical model. They can wax eloquent about Log Likelihood Estimators but can have trouble explaining why you should use that in the first place. Then you have the banking quants (I used to be one of those), who are proficient in derivatives pricing, stochastic calculus and partial differential equations, but if you ask them why a stock price movement is generally assumed to be lognormal, they don’t have answers. Then you have the coders, who can hack, scrape and write really efficient code, but don’t know much math. And mathematicians who can come up with elegant solutions but who are divorced from reality.
While you might make a career out of falling under any of the above categories, to truly unleash your potential as a quant, you should be able to do all. You should be a fox and should know each of these tricks. And unlike the fox in the Old Russian fairy tale, the key to being a good fox is to know what trick to use when. Let me illustrate this with an example from my work today (actual problem statement masked since it involves client information).
So there were two possible distributions that a particular data point could have come from and I had to try and analyze which of them it came from (simple Bayesian probability, you might think). However, calculating the probability wasn’t so straightforward, as it wasn’t a standard function. Then I figured I could solve the probability problem using the inclusion-exclusion principle (maths again), and wrote down a mathematical formulation for it.
Now, I was dealing with a rather large data set, so I would have to use the computer, so I turned my mathematical solution into pseudo-code. Then, I realized that the pseudo-code was recursive, and given the size of the problem I would soon run out of memory. I had to figure out a solution using dynamic programming. Then, following some more code optimization, I had the probability. And then I had to go back to do the Bayesian analysis in order to complete the solution. And then present the solution in the form of a “business solution”, with all the above mathematical jugglery being abstracted from the client.
This versatility can come in handy in other places, too. There was a problem for which I figured out that the appropriate solution involved building a classification tree. However, given the nature of the data at hand, none of the off-the-shelf classification tree algorithms for R were ideal. So I simply went ahead and wrote my own code for creating such trees. Then, I figured that classification trees are in effect a greedy algorithm, and can lead to getting stuck at local optima. And so I put in a simulated annealing aspect to it.
While I may not have in depth knowledge of any of the above techniques (to gain breadth you have to sacrifice depth), that I’m aware of a wide variety of techniques means I can provide the solution that is best for the problem at hand. And as I go along, I hope to keep learning more and more techniques – even if I don’t use them, being aware of them will lead to better overall problem solving.