Back(ward?)-Testing

I have a passing interest in finance and investing. This is somewhat of a dirty secret; while scientist are no more or no less interested in money than anybody else, and much of our lives revolves around finding enough money from grants and fellowships to support our research, we are nevertheless supposed to look down on the finance sector. Researchers who abandon sleepy* Cambridge for bigger salaries found at London financial institutions are regarded as sell-outs, throwing away the good they could do for humanity in search of a quick buck.

I’m not going to weigh in on the debate of whether our financial system and the stock markets is unethical, ethical or immoral, and whether participating in it directly is a sin. But I do enjoy learning about the market, and considering the properties of this immensely complex thing that we’ve created, which follows seemingly simple rules such as a supply and demand economics, but nevertheless behaves in entirely unpredictable ways.

All this is just a long-winded introduction to explain why I came across this article on backtesting on The Value Perspective. Backtesting is easily explained; it simply involves looking at historical data to see how your chosen investment strategy would have performed, had you applied it then. So, if, let’s say, you plan to only buy stocks that start with the letter ‘A’. Now you do a back-test over the last say 25 years, and check the returns for portfolios that only contain A-stocks. If they perform significantly better than stocks picked at random, then you might think that your strategy is a winner.

Of course, there is a pretty serious problem here. Leaving aside issues such as trading fees, dividend yields that may or may not be priced in, and the fact that past performance may not be an indicator of future performance, any statistician will tell you that the real problem with this strategy is that it is prone to overfitting. In fact, as the blog post I linked points out, a group of respected academics have told the world exactly this. Bailey et al. simply point out something that we’ve known for decades: you cannot test your model on the same data that you use to choose your strategy.

Let’s say you keep backtesting different strategies: portfolios starting with ‘B’, with ‘C’, … eventually you will find something that performs well on your backtesting period. Odds are, however, that this good performance is mostly random. What you need is an out-of-sample test set; another period that you haven’t tested on. This is why in machine learning, people split their datasets into training set, validation set and test set. The training set trains your model (maybe not needed if you’re only comparing a set of simple strategies with no learned parameters), the validation set helps you select the settings for any pre-set parameters (in my example, which letter the stocks name should start with), and the test set tells you if your selection works on new data. Of course, we would usually use cross-validation to cover the whole dataset. While Bailey et al. explain some of the difficulties with directly applying these approaches to financial models, it boggles the mind that many academic papers apparently don’t use out of sample test sets at all.

If I ever get bored with biostatistics (unlikely as that may be), it seems that there’s a lot of work still to be done in financial modelling.

*It’s not really that sleepy these days, but let’s pretend.

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