Kaufman’s fractal efficiency ratio and market noise

I’ve been toying with Kaufman’s fractal efficiency ratio to see whether some time frames are noisier than others, as is generally asserted. The fractal efficiency ratio is derived by dividing the net change in price movement over n periods by the sum of all component moves, taken as positive numbers, over the same n periods. If the ratio approaches the value 1, the movement is smooth; if the ratio approaches 0, there is great inefficiency or noise.

I’m not talented at number crunching, and I haven’t taken this analysis very far. But here’s some not quite raw data. Click on the graphics to enlarge them.



The first spreadsheet shows the ten-minute price change on YM divided by the sum of all one-minute absolute price movements for the period between 10/14 and 11/2/2009. I have arbitrarily defined the trading day as starting at 8:30 EST and ending at 4:00. The particularly noisy 10-minute segments are colored yellow, the smooth segments are colored green. Beneath the rule is the average fractal efficiency ratio for each trading day and the standard deviation of the ratios. And then follows the 8:30 open and the 4:00 close, with the directional change, for each day. The average of the 14 average fractal efficiency ratios is 0.32; the average standard deviation is 0.22.



I then compared this very small sample with daily, weekly, and monthly SPY, GLD, and EEM data over the entire course of their trading history. Once again, I calculated the ten-period price change divided by the sum of its ten component moves. I highlighted the smoothest daily, weekly, and monthly price series with green, the smallest standard deviations with yellow.

Although I know that the tiny YM study isn’t statistically significant, I do find it interesting that its one-minute intraday price movements are very similar in terms of fractal efficiency to the one-day price movements on the SPY. This might offer some ammunition to day traders who are often accused of merely trading noise.

By the way, it seems that great minds think alike (and quite independently). David Varadi at CSS Analytics is experimenting with using fractal efficiency as the key component in a performance statistic. Of course, he knows what he’s doing, and I’m just mucking about.