IWM cross history based on open position in prior day range

This table is based on the last 2000 trading days of IWM (from Yahoo!).

The left most column is where the current day’s open is based on yesterday’s range (open – yesterday’s low) / (yesterday’s high – yesterday’s low). Each row is 10%, starting with -30%.
The other columns are the percent of times the range value was crossed, with 0 being yesterday’s low and 1 being yesterday’s high.

1.69% -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
-0.4
-0.3 89.66% 79.31% 62.07% 44.83% 31.03% 20.69% 10.34% 3.45% 0.00% 0.00% 0.00%
-0.2 80.77% 92.31% 76.92% 46.15% 42.31% 34.62% 26.92% 7.69% 3.85% 3.85% 0.00%
-0.1 61.36% 100.00% 88.64% 70.45% 56.82% 50.00% 34.09% 18.18% 13.64% 13.64% 13.64%
0 56.96% 82.28% 93.67% 69.62% 48.10% 31.65% 21.52% 12.66% 7.59% 5.06% 2.53%
0.1 55.67% 69.07% 94.85% 77.32% 51.55% 27.84% 22.68% 12.37% 7.22% 4.12% 4.12%
0.2 40.46% 58.78% 82.44% 93.13% 62.60% 45.80% 29.77% 13.74% 9.92% 5.34% 2.29%
0.3 28.79% 49.24% 68.18% 90.15% 77.27% 53.79% 34.85% 21.97% 12.88% 8.33% 6.06%
0.4 27.27% 40.91% 55.30% 78.03% 94.70% 71.21% 48.48% 33.33% 26.52% 14.39% 8.33%
0.5 22.83% 35.43% 52.76% 67.72% 90.55% 77.17% 53.54% 32.28% 22.05% 14.96% 3.94%
0.6 20.00% 33.10% 44.83% 60.00% 80.00% 91.72% 67.59% 46.90% 32.41% 20.69% 10.34%
0.7 14.63% 20.12% 34.76% 50.00% 68.29% 93.90% 76.22% 51.83% 35.98% 26.83% 18.90%
0.8 13.29% 18.50% 28.90% 41.04% 57.80% 80.35% 94.22% 68.21% 46.82% 28.90% 20.81%
0.9 10.34% 14.37% 21.84% 29.89% 47.70% 64.37% 89.66% 77.59% 53.45% 34.48% 21.84%
1 8.33% 8.93% 15.48% 22.02% 38.69% 55.36% 78.57% 92.86% 69.64% 43.45% 25.60%
1.1 8.70% 11.30% 13.04% 20.87% 29.57% 50.43% 63.48% 96.52% 73.04% 53.04% 31.30%
1.2 8.33% 11.11% 13.89% 25.00% 36.11% 51.39% 66.67% 86.11% 84.72% 55.56% 30.56%
1.3 4.65% 9.30% 13.95% 23.26% 32.56% 41.86% 58.14% 83.72% 90.70% 62.79% 34.88%
1.4 3.03% 9.09% 12.12% 12.12% 27.27% 36.36% 57.58% 66.67% 87.88% 96.97% 60.61%

As a (busy) chart:

Here are the cross chances for the today and tomorrow:

1.69% -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
-0.4
-0.3 96.55% 86.21% 72.41% 62.07% 44.83% 31.03% 24.14% 6.90% 6.90% 3.45% 3.45%
-0.2 88.46% 96.15% 84.62% 57.69% 46.15% 42.31% 30.77% 15.38% 15.38% 11.54% 11.54%
-0.1 68.18% 100.00% 90.91% 79.55% 68.18% 56.82% 43.18% 31.82% 29.55% 25.00% 20.45%
0 72.15% 86.08% 94.94% 73.42% 56.96% 45.57% 34.18% 21.52% 17.72% 16.46% 13.92%
0.1 63.92% 77.32% 95.88% 84.54% 64.95% 51.55% 37.11% 27.84% 21.65% 16.49% 10.31%
0.2 54.96% 68.70% 86.26% 96.18% 77.10% 66.41% 47.33% 37.40% 26.72% 17.56% 9.16%
0.3 46.21% 64.39% 79.55% 94.70% 84.85% 70.45% 50.76% 37.12% 25.76% 19.70% 15.15%
0.4 44.70% 59.85% 69.70% 84.09% 96.97% 84.85% 66.67% 52.27% 43.18% 33.33% 22.73%
0.5 44.09% 56.69% 72.44% 81.89% 95.28% 82.68% 68.50% 51.18% 38.58% 29.13% 17.32%
0.6 31.03% 42.76% 54.48% 67.59% 86.90% 93.79% 81.38% 66.90% 51.72% 44.14% 33.79%
0.7 34.15% 40.85% 53.05% 64.63% 75.00% 94.51% 84.15% 71.95% 57.32% 44.51% 32.32%
0.8 29.48% 38.73% 49.71% 59.54% 71.68% 86.71% 94.80% 79.19% 62.43% 50.29% 36.99%
0.9 21.26% 29.89% 37.36% 45.40% 58.62% 69.54% 90.80% 86.21% 70.69% 55.17% 40.23%
1 17.26% 22.62% 27.98% 33.33% 51.19% 66.67% 83.33% 95.83% 81.55% 63.10% 44.64%
1.1 16.52% 22.61% 31.30% 36.52% 45.22% 62.61% 73.04% 98.26% 84.35% 70.43% 52.17%
1.2 16.67% 20.83% 29.17% 34.72% 48.61% 59.72% 75.00% 90.28% 90.28% 66.67% 52.78%
1.3 23.26% 30.23% 34.88% 44.19% 51.16% 67.44% 74.42% 86.05% 93.02% 67.44% 55.81%
1.4 18.18% 24.24% 33.33% 36.36% 48.48% 60.61% 72.73% 75.76% 87.88% 96.97% 66.67%

And here are the cross chances for the next 5 days:

1.69% -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
-0.4
-0.3 96.55% 89.66% 82.76% 79.31% 62.07% 51.72% 44.83% 31.03% 31.03% 27.59% 24.14%
-0.2 88.46% 96.15% 88.46% 84.62% 65.38% 57.69% 50.00% 42.31% 34.62% 34.62% 23.08%
-0.1 70.45% 100.00% 95.45% 88.64% 81.82% 72.73% 61.36% 47.73% 43.18% 40.91% 38.64%
0 78.48% 88.61% 98.73% 87.34% 77.22% 64.56% 56.96% 46.84% 41.77% 39.24% 29.11%
0.1 76.29% 85.57% 96.91% 91.75% 80.41% 73.20% 61.86% 56.70% 45.36% 35.05% 24.74%
0.2 69.47% 78.63% 90.84% 98.47% 86.26% 80.92% 67.18% 61.07% 49.62% 41.22% 31.30%
0.3 64.39% 77.27% 85.61% 97.73% 93.18% 84.85% 71.97% 62.88% 56.06% 48.48% 36.36%
0.4 61.36% 71.21% 77.27% 87.88% 98.48% 88.64% 79.55% 73.48% 67.42% 59.09% 50.76%
0.5 63.78% 74.02% 80.31% 88.98% 96.85% 89.76% 82.68% 71.65% 62.20% 53.54% 46.46%
0.6 52.41% 60.69% 73.79% 81.38% 91.03% 97.93% 90.34% 82.07% 76.55% 71.03% 58.62%
0.7 51.83% 62.20% 68.29% 80.49% 85.37% 96.95% 90.85% 82.32% 72.56% 60.98% 53.66%
0.8 49.71% 55.49% 65.32% 74.57% 82.66% 92.49% 97.69% 83.82% 76.30% 69.36% 57.80%
0.9 41.95% 45.98% 52.30% 59.20% 68.97% 81.03% 93.68% 90.80% 79.31% 71.84% 60.92%
1 33.33% 39.29% 44.05% 52.38% 67.26% 76.79% 87.50% 97.02% 89.29% 79.76% 69.64%
1.1 32.17% 36.52% 45.22% 50.43% 62.61% 73.04% 84.35% 98.26% 87.83% 80.87% 72.17%
1.2 37.50% 48.61% 51.39% 58.33% 69.44% 77.78% 83.33% 94.44% 95.83% 83.33% 68.06%
1.3 39.53% 48.84% 53.49% 62.79% 65.12% 76.74% 81.40% 90.70% 93.02% 79.07% 69.77%
1.4 33.33% 39.39% 51.52% 60.61% 66.67% 75.76% 84.85% 87.88% 96.97% 96.97% 69.70%

In other words, if the opening price today was the same as yesterday’s low price (the “0” row) , then there is an 82.28% chance it would reach a value that is 20% of yesterdays’ range lower than the low. and 69.62% chance of reaching a price 20% of yesterday’s range above the low.   Looking over 2 days, the odds raise to 86.08%,  73.42% respectively, and over the next 5 days 88.61%  and 87.34%   respectively and  77.22% it will cross the 40% of yesterday’s range value.  The median open is at  61%  of yesterday’s range above the low (the .7 line covers the values above .6 and below or equal to .7).

As a final note, these are the chances a particular price will be crossed over the next day, two days or five trading days. It doesn’t indicate where the close will be. These are historical chances, but when I divide the set into 2 groups of 1000, using the odds of the first (in time) 1000 as a predictor of a price point being crossed, they were fairly close – that is if you look at the price points where the historical odds where 70% or greater, then the prediction came true over 80% of the time (vs predicted (70 + 100)/2 = 85%, although I’m not sure that is the proper calculation but it is a good rough estimate) of the time.

Having said this does not predict the future closing prices, I looked at closing price in relationship to the daily range and found this (for the past 1000 IWM trading days):

close relative position next day percentage change close vs close number of up days
0% 0.51% 30
4% 0.43% 32
8% 0.21% 28
13% 0.40% 29
20% -0.18% 23
27% 0.09% 27
33% 0.09% 26
40% 0.03% 26
46% 0.25% 31
52% -0.39% 17
58% 0.13% 29
63% 0.34% 28
68% -0.22% 21
73% -0.31% 20
79% -0.05% 23
83% -0.10% 22
88% 0.15% 30
92% 0.13% 29
95% 0.51% 31
98% 0.14% 27

So, by my rough calculation, if you shorted at close when the closing price was in the 68% – 88% of the daily range, and were long at other times, you would have improved over buy and hold (excluding transaction fees).   The results don’t seem to be generally true, I looked at the SPY for the last 4000  trading days (since September 1994)  and the bias did not exist (you would have done worse then buy and hold).  It could be that the mean reversion was stronger over the last few years (although it seems to be weakening of late).

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