SPX monthly ranges

The high low range of the SPX for the month of August 2016 was 2.1% (computed using Yahoo! data = (high – low)/open), the 9th smallest range since 1950 (800 months worth of data).  I was curious how it varied by month, and also what happens after a low range month. Over all months, the average range is 6.4%, with a median value of 5.6% and standard deviation of 3.5%.  If the month range was less than 3% (56 times out of the 800), then the next month’s average was 4.5%, median of 4.4% and standard deviation was 1.6%. So if this September 2016 is typical, there should be around a 100 point (+/-35 pts) range in the SPX.  While the bottom 10% of the month’s ranges seem to be around 3.2% (with standard deviation of .3%), the 90% value of the months is at 10.3% with a standard deviation of 2.3%.  October, with an average range of 8.2%, exceeds January (at 7%) by a hefty margin, although the median for October at 5.8% is slightly above all months (January at 6.3% comes in first).

monthly ranges for spx

 

average median std dev count 10.00% 90.00%
all 6.4% 5.6% 3.5% 800 3.2% 10.3%
after <3% 4.5% 4.4% 1.6% 56 2.8% 6.3%
January 7.0% 6.3% 3.3% 67 3.3% 11.5%
February 5.5% 5.0% 2.5% 67 2.9% 8.2%
March 6.1% 5.4% 3.6% 67 2.8% 8.7%
April 6.0% 5.3% 2.7% 67 3.6% 9.6%
May 6.1% 5.5% 3.2% 67 3.1% 9.2%
June 5.9% 5.2% 2.3% 67 3.1% 9.4%
July 6.3% 5.5% 3.1% 67 3.5% 10.2%
August 6.7% 5.9% 3.7% 67 3.2% 12.9%
September 6.6% 5.9% 3.2% 66 3.2% 10.3%
October 8.2% 5.8% 6.0% 66 3.3% 16.8%
November 6.8% 6.0% 3.7% 66 3.4% 10.3%
December 5.5% 5.2% 2.5% 66 2.6% 9.1%
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