Sunday, September 12, 2010

Quants and Black Swans

I've left this blog unattended for more than a year. It's refreshing to read the questions I've had a year ago with regards to the feasibility of using mathematics in trading.

In the past year, I've:

1. gone from working for a software vendor developing retail banking software (loans accrual, general ledger transactions, account origination workflow, etc), which deals with retail banking clients, to working for a fund service provider developing data connectivity solutions (portfolio reconciliation, instrument/trade/price loading, broker instructs), which deals with hedge funds and prime brokers.

2. entered the world of stocks and derivatives trading (and put forex trading on hold for now), bought a Jul40 covered call on BP when it was trading at $31, made the mistake of rolling it into an Oct35 call when the stock price continued to fall before bottoming out at $26 (its now trading at $38), but also bought Mar11 SSFs on BP and RIG and an Apr21 call on MSFT which look pretty underpriced despite the present economic climate.

3. learnt about a mathematician called Paul Wilcott and the course which he's started, read Scott Paterson's 'The Quants', read Nassim N Taleb's 'Fooled by Randomness', started reading 'The Black Swan' by the same author, decided to enroll for the MFE program, scored 1500 on the GRE, looked up my former professors for recommendation letters, and registered for the GRE Maths Subject test.

Looking back on my 1st 2 posts, I realized that the idea of using statistical analysis - of "crunching numbers" - for making trading decisions fall squarely into the field of quantitative finance. I was describing, albeit simplistically, a concept which may already be in place in quantitative strategies today. I'd like to think that a firm like Renaissance Technologies would invoke regression-to-the-mean in some of its trading decisions, especially if it really is a contrarian fund as Paterson suggests.

I've also realized that I need to enter the world of quants if I am to pursue my interest in this area. Or rather, if I am to achieve my goal of being mathematically certain of the probabilities involved in my trading decisions, ideally by being able to discover trades in which the expected profits is x with a margin of error less than x (in other words, trades with guaranteed profits).

But, as demonstrated in 1998 and 2007, mathematical models can go horribly wrong. I've learnt from Taleb's books that these collapses can be attributed to "Black Swan" events. It is very easy to create quantitative models which are incorrect, because stock prices and other financial statistics belong in "Extremistan", an analogy used by Taleb to describe populations of data points in which a single extreme value can severely disrupt any prevailing assumptions about the population mean (eg making statements about the average annual income of Americans after analyzing a sample of 1 (or 10, or 100) million Americans, and then adding Bill Gates to the sample). In my own words, it is important not to underestimate the standard deviation of any models used in making investment decisions.

Nevertheless, I will still need an education in mathematical finance. The knowledge gained from people who'd already done the same thing before me, coupled with the necessary temperance to avoid over-reliance on statistical assumptions, should enable me to develop a quantitative model with which I can trade profitably. So here we go.