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Dave Evans

I'm not sure how to use this, or the implications of it, but I though the following was worth sharing. 

I've been looking at the day's trading range as a predictable variable for trade management purposes and was struck by often daily range size appeared to be mean reverting, just like markets can be (or were) in terms of gains or losses. By mean reversion I mean a big range day is likely to be followed by a day with a smaller trading range and vice versa. The day's range is simply the difference between the high and the low. 

I wanted to put some numbers to the pattern I was eyeballing on various markets. The data below is on the SPX cash index. 

Since 2007, today's trading range has been 116% of yesterday trading range on average (16% bigger). 100% would mean that today's range is exactly the same as yesterday's. In other words, on average daily ranges have been expanding, with the credit crunch forming part of this time period, there is little surprise in this and the average no doubt hides a trend for the range decreasing since the volatility of 2009. 

What is more interest is the impact of the prior day's range on day's range relative to this trend. 

Yesterday's range bigger than previous days: 
69.3% chance of today's range being smaller than yesterday's. 
Average range today is 87.26% of yesterdays (Smaller).

Yesterday's range smaller than previous days: 
69.64% chance of today's range being bigger than yesterday's. 
Average range today is 146.54% of yesterdays (bigger). 

So interestingly, even in a period of expanding daily ranges, range is mean reverting. Essentially, if today's range is bigger than the previous day's range, tomorrow's session is 69% likely to have a range smaller than today's. If today's range is smaller than the previous day's range, tomorrow's session is 69.64% likely to have a range bigger than today's.

What if you get two back to back days of trading ranges expading, or contracting?

Trading range has expanded for two days in a row : 
79% chance of today's range being smaller than yesterday's. 
Average range today is 78% of yesterdays (Smaller). 

Trading range has contracted for two days in a row
75% chance of today's range being bigger than yesterday's. 
Average range today is 153% of yesterdays (bigger). 

When the trading range expands or contracts for two sessions in a row, the reversion effect is amplified both in terms of accuracy and size of effect. 

How to use this?

Right now I'm not sure. This will no doubt be picking up some of the directional mean reversion seen in recent years, but I dont think that explains it all. I've tested it on FX markets which are not mean reverting in a direction sense and still found a range reversion effect. 

Perhaps this could be used as a trade size management tool. If for example you get a sell signal and you are long and the range pattern is signalling an expansive day, then you might trim your trade size slightly. 

I know that it has been written elsewhere that volatility is relatively easy to predict, but I've not seen any compelling ideas on how to make use of this. Any thoughts dear reader?


2 Responses to “Mean Reversion In Trading Ranges”


  1. Hi,
    Are you using absolute ranges or did you normalize the range to price? Absolute ranges will increase as the index rises. Instead I would like at Range as a percent of Price and do the analysis. This would mean that a range of 10 points when S&P was at 400 is 2.5% would be the same as a range of 35 points with S&P at 1400. The absolute range increased, but volatility stayed the same.
    BTW, I use ATR% as vol measure.
    just a thought


  2. Hi Nick
    The range difference calc is comparing today to yesterday so I’m not sure normalising the range would make too much difference.
    I’ve done a quick check and expressing the range comparison as a % of the price doesn’t make any significant difference.
    Thanks for the suggestion