Trade Correlation and System Evaluation
There is an important element to consider in system evaluation that has the unpleasant side effect of making a clear conclusion obvious. In a perfect world, the observed trading strategy distribution would come from a normal distribution and the distribution shape and mean would never change. However, even in such a perfect world, we cannot accurately model and evaluate such a system if the trade distribution is not independent. A normal distribution makes this very assumption–that if one win’s on a recent trade, there is no linkage to the probability that one will win on a subsequent trade. This makes everything like a roulette wheel where we can try martingale strategies (doubling down on a given color after a loss) but will never change the odds of winning/losing but rather the shape of profits and losses. Effectively we can create option-like payoffs by manipulating our bet size based on the previous profit or loss but will not accomplish the task of changing the expected value.
The market is a far different beast that is driven at rapid speeds by computer generated liquidity, and the emotions of the masses. It is an environment that creates self-reinforcing feedback loops that can periodically generate substantial auto-correlation (read:trending) in returns. The tendency for mean-reversion or follow-through itself is a form of dependency that would not be expected if the series of daily returns were random. Stepping away from these obvious points, is that different trading strategies whether short-term or long-term, trending or mean-reversion, will have a tendency to have either a correlated or un-correlated trade series. Part of the correlation in this trade series is driven by the market macro and micro-structure, while some of the correlation is idiosyncratic. It is up to the trader to figure out which is which.
However, the effect that a correlated trade series has on system evaluation is that it can cause you to systematically overstate or understate your analysis of the short-term performance of the system. Imagine for a second that I was short-sighted and looked at the past 5 trades of an indicator or system to determine its usefulness. I watch closely, and 4 out of 5 are winners– fantastic, sign me up! I look at the long-term performance of the system or indicator, and it has a very good track record—again this bodes very well right? Well, not if you are trading many short-term mean-reversion systems, in this case exceptional short-term performance is especially bad for the next trade. This is because the series of trades is often negatively correlated. This also has the side effect of distorting the ability to “turn-off” the equity curve of the system, because ultimately doing so requires a clear trend signal. We would have to strip the correlation effect out of the system in order to clean up the signals. Note that in some types of systems, the trade returns are positively correlated, and you have the reverse effect happening. Winners follow winners and losers follow losers. This type of system lends itself very well to using a traditional equity curve based system.
Nonetheless, it gets much more abstract that this–life and markets are never what they first seem. In fact, you may look at a terrible and inconsistent strategy by conventional metrics such as the Sharpe Ratio, or Profit Factor and mistakenly conclude that it is worth discarding. To the extent that the trading system has a predictable cycle or a high correlation between trade batches, you may be able to devise an extremely profitable system just from trading the equity curve of this “crappy” system. Even stranger is that you can combine two “crappy” systems using various co-efficients to create a very good system without having to trade the equity curves. Anything is possible, after all any given stock or instrument is just an equity curve itself–all of our attempts to use indicators to trade a stock is a means of manipulating or taking a derivation of that equity curve. Taking the same derivative approach to systems has the exact same effect. What is key to being successful here is that there must be some form of correlation that produces a systematic effect–otherwise we will face the same situation as with the roulette wheel where we are feverishly executing money management strategies in the hopes of taking advantage of random effects.