Using SPY data for 2013 and 2014, and dividing trading day into 7 equal time intervals of about 56 minutes the percentages of highs and lows (and theoretical from arcsine law) are as follows:
| highs | lows | theoretical |
|---|---|---|
| 30% | 42% | 25% |
| 11% | 14% | 11% |
| 9% | 8% | 10% |
| 6% | 4% | 9% |
| 7% | 7% | 10% |
| 11% | 9% | 11% |
| 27% | 16% | 25% |
So the numbers are clearly different, especially for beginning of the day, and for daily lows. However, if we divide every day into 7 buckets of equal volume, the distribution of highs and lows is actually much closer to theoretical:
| highs | lows | theoretical |
|---|---|---|
| 23% | 28% | 25% |
| 12% | 15% | 11% |
| 10% | 14% | 10% |
| 9% | 10% | 9% |
| 11% | 11% | 10% |
| 13% | 11% | 11% |
| 23% | 11% | 25% |
Both highs and lows are quite similar to what is predicted by theory. But as Rich noted in the comment, lows tend to happen more often at the start of the day than predicted by theory, even if we normalize the data by volume. This, I believe, is a legitimate pattern - although I'm not sure how to systematically capitalize on it.
This is very interesting regarding high/low asymmetry. Given that it looks similar to what I found in the DAX - which is a different market in a different time zone over a different historical period (I can't remember but I believe I used 2001-2011) I'd say it is a real effect. Could it simply be because down moves tend to be higher volume? Although given my understanding of how you've done the analysis I expect that is not the explanation. The biggest deviation from theoretical is the low in the final bucket. Given the high in the final bucket is near theoretical you might capitalise on this by going long for the final bucket if you are currently far from the day's high. Even though you don't know when the bucket starts until after the fact, you could still come up with a simple trading strategy to capture this effect for testing. One other idea I'd be interested to see is to split out days based on above or below 200 DMA, my suspicion being this is more of a bull market effect. You'd have to extend the historical period to do that of course :).
ReplyDelete