From the June 2013 issue of Futures Magazine • Subscribe!

Setting stops the Bayesian way

Setting stops

To determine an effective stop, you have to make some more forecasts. When you set a stop, you really are forecasting the path of prices from now until your trade horizon. There’s no glory in being right three months from now if you get wiped out in the meantime. By setting a GLD stop at say, 160, you are forecasting that the price path is unlikely ever to go below that level.

Forecasting price paths can be challenging. Keep it simple. Assume that if your forecast is right, then the market should gradually move up to your forecasted level. This gives you a time series of gold forecasts from trade initiation until the trade end date. Each week’s forecast is a little higher than the previous one.

That said, you have to use common sense. For example, if you are making a bet on the outcome of a market-moving number, you may want to use a level path until the number comes out.

In practice, any reasonably straight path will work. In our gold example, we think that GLD will rise by five points in eight trading weeks. So the simple path is a gain of five-eighths, or about 0.625 per week. You could use any frequency to adjust your stop, but weekly is a practical default number.

The stop process works like this. On week zero, we determine our prior distribution and initiate the trade. On week one, we assume that GLD should have gone up to 165.00 + 0.625 = 165.63. Instead, it actually fell to 164.13. We use this new price to update our posterior probability distribution. On week two we assume that gold should have gone up to 165 + 2 x 0.625 = 166.25 and update our posterior again.

The last part of the analysis is a decision rule. This will tell us when to take action and exit the position. There are many possible rules, but this one works for me: When the mean of the posterior distribution is below the originally forecasted price path, get out. This could happen over a period of many small weekly declines or in one big crash. In fact, we would be stopped out even if gold moved sideways for long enough because the posterior mean eventually would fall below the path. 

Another rule might be that if you wanted to be more conservative, you could use a rule that got you stopped out when the mean fell only halfway between the current and forecasted prices, or you could recalculate the stop daily.

If GLD fell to 162.5 in week two, we would have the table in “Evolution of the trade” (below). As GLD fell from 165.00 to 160.33 in week two, the mean of our posterior probability falls to 166.43. Because our week two stop was at 166.25, we would do nothing. Then in week three it recovered to 162.02, but we get stopped out. The reason is that our week three stop is 165.00 + 3 x 0.625 = 166.88. The mean of the week three posterior is 164.72.

Before we move on to these calculations, there is one important pitfall to note. Numerous studies of probability assessments show that most people think they know more than they do. In other words, most people assess a prior that is too “skinny.” You may think that GLD is highly likely to be between 155 and 175. In reality, a world event might cause it to go to 300. You should take these fat-tailed scenarios into account when assessing your prior.

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