In praise of day-trading

A recent article by Mark Hulbert in the NYTimes talked about the Value Line's rankings, and how this system is under-performing the market index in recent years. Mr. Hulbert asked Professor David Aronson of Baruch College whether this drop in performance means that the system has stopped working. Prof. Aronson says no: he believes that it takes 10 or more years [my emphasis] of under-performance of this strategy before one can say that it has stopped working! This statement, if taken out-of-context, is so manifestly untrue that it warrants some elaboration.

To evaluate whether a strategy has failed bears a lot of resemblance to evaluating whether a particular trade has failed. In my previous article on stop-loss, I outlined a method to determine how long it takes before we should exit a losing trade. This has to do with the historical average holding period of similar trades. This kind of thinking can also be applied to a strategy as a whole. If your strategy, like the Value Line system, holds a position for months or even years before replacing it with others, then yes, it may take many years to find out if the system has finally stopped working. On the other hand, if your system holds a position for just hours, or maybe just minutes, then no, it takes only a few months to find out! Why? Those who are well-versed in statistics know that the larger the sample size (in this case, the number of trades), the smaller the percent deviation from the mean return.

Which brings me to day-trading. In the popular press, day-trading has been given a bad-name. Everyone seems to think that those people who sit in sordid offices buying and selling stocks every minute and never holding over-night positions are no better than gamblers. And we all know how gamblers end up, right? Let me tell you a little secret: in my years working for hedge funds and prop-trading groups in investment banks, I have seen all kinds of trading strategies. In 100% of the cases, traders who have achieved spectacularly high Sharpe ratio (like 6 or higher), with minimal drawdown, are day-traders.

Index tracking, arbitrage, and cointegration

Mr. Lange, a reader of mine from Germany, alerted me to the following paper regarding a strategy related to index arbitrage that involves the EUROStoxx50 index. It is a nice illustration of a common application of cointegration techniques to statistical arbitrage trading. I have written an exposition of this paper, together with an additional index arbitrage strategy not discussed in the original paper, which I posted to my subscribers only area. (Mr. Lange has graciously allowed me to share this exposition with other readers of this blog.)

Cointegration between oil and bond yield? Not!

An article in the Feb 1 issue of the Economist magazine suggested that there may be a link between crude oil price and long-dated US treasuries. Their reasoning is that if oil price is high, OPEC will need to re-invest the pile of cash that they generate, and eventually a lot of this ended up invested in US 10-year bond. Therefore, when crude prices go up, 10-year yield should go down. As I explained before, the fact that these 2 numbers are anti-correlated do not prevent them from being cointegrated. And in fact, the Economist article plotted the crude oil prices together with bond yield over the last year together, and they seem tantalizingly close to being cointegrated.

My curiosity piqued, I proceeded to get a longer history of these data to examine.

In the graph above, I plotted the (normalized) difference between the 10-year treasury yield and oil price. One can see that over the last year and a half, they are indeed cointegrated to a good degree. (To see that, notice the spread is range-bound, or mean-reverting, from mid-2005 to the present.) But this relationship breaks down completely over the longer history.

Though I think that the Economist magazine is doing a disservice to its readers for plotting this graph over just one year and making innuendos of linkage, it is a nice illustration of the danger of studying cointegration over a short window.