The Mystery of the Declining Instances

One question I get fairly often is “Why does the number of instances decline when you look further out in a study?” I’ve answered it on a few occasions but recently realized I should make it a post.

As an example I ran a simple study below that looks at performance following a 1% drop in the S&P 500.

Declining instances are common with some studies – especially studies like this with a large number of instances. The issue has to do with repeat occurrences of the setup. Here we see there were 454 occurrences that showed up with a 1-day holding period. 77 times it happened twice in a row, so when you look at the 2-day exit results now your number of instances drops to 377. Looking out 5 days the instances drops to 246, meaning after the 1st instance there were 208 times where you again had a 1% drop during the 4 days following all “initial” instances.

I do this to avoid double counting. When dealing with oversold statistics if you double (or triple, etc.) count them then your results will most often be skewed unfairly bullish. The 2nd instance you’re more oversold than the 1st and the 3rd even more so. Now when the bounce comes it’s being counted 3 times if you decide to track the stats on all 3.

The opposite holds true for overbought studies with bearish results. Double counting there would often skew them even more bearish.

So when I run the stats on such studies, I make the assumption that the 1st time it triggers it puts you “all in” and your exit will be X days later. You can’t get another buy trigger until the first one closes out.

So there you have it – “The Mystery of the Declining Instances” is finally solved.