What is your stop loss strategy?

Are you sure whether setting a stop loss for a trading strategy is a good idea. I am a big fan of setting stop loss, but there are certainly myriad views on this.

One of my friends didn't believe in stop loss: his argument is that the market does not care about your personal entry price, so your stop price may be somebody else’s entry point. So stop loss, to him, is irrational. Since he is running a portfolio with hundreds of positions, he doesn’t regard preserving capital in just one or a few specific positions to be important. Of course, if you are an individual trader with fewer than a hundred positions, preservation of capital becomes a lot more important, and so does stop loss.

Even if you are highly diversified and preservation of capital in specific positions is not important, are there situations where stop loss is rational? I certainly think that applies to trend-following strategies. Whenever you incur a big loss when you have a trend-following position, it ususally means that the latest entry signal is opposite to your original entry signal. In this case, better admit your mistake, close your position, and maybe even enter into the opposite side. (Sometimes I wish our politicians think this way.) On the other hand, if you employ a mean-reverting strategy, and instead of reverting, the market sticks to its original direction and causes you to lose money, does it mean you are wrong? Not necessarily: you could simply be too early. Indeed, many traders in this case will double up their position, since the latest entry signal in this case is in the same direction as the original one. This raises a question though: if incurring a big loss is not a good enough reason to surrender to the market, how would you ever decide if your mean-reverting model is wrong? Here I propose a stop loss criterion that looks at another dimension: time.

The simplest model one can apply to a mean-reverting process is the Ornstein-Uhlenbeck formula. As a concrete example, I will apply this model to the commodity ETF spreads I discussed before that I believe are mean-reverting (XLE-CL, GDX-GLD, EEM-IGE, and EWC-IGE). It is a simple model that says the next change in the spread is opposite in sign to the deviation of the spread from its long-term mean, with a magnitude that is proportional to the deviation. In our case, this proportionality constant θ can be estimated from a linear regression of the daily change of the spread versus the spread itself. Most importantly for us, if we solve this equation, we will find that the deviation from the mean exhibits an exponential decay towards zero, with the half-life of the decay equals ln(2)/θ. This half-life is an important number: it gives us an estimate of how long we should expect the spread to remain far from zero. If we enter into a mean-reverting position, and 3 or 4 half-life’s later the spread still has not reverted to zero, we have reason to believe that maybe the regime has changed, and our mean-reverting model may not be valid anymore (or at least, the spread may have acquired a new long-term mean.)

Let’s now apply this formula to our spreads and see what their half-life’s are. Fitting the daily change in spreads to the spread itself gives us: