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).

 

	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%

5 day historical volatility by weeks of the year

I did a quick study to see the how seasonal volatility was during the year. For this study, I looked at the standard deviation of the logarithm of the price changes for the prior 5 days, using only on the last trading day of the week for the chart. I used the SPX since 1994 from Yahoo! Finance. Here is a graph of the average, median, and top and bottom 25 percentile.  In the above change, 101 is week 1, which I am using as the week with the first Friday of the new year.  Overall, looking at the average (grey line) there is a slight downward slope from the end of January through July, then slight pick up through mid October, and then finally a slight fall until year end – except a bit of a bump around the first week in December.  The line for the bottom 25 percentile is fairly flat all year long, while the top 25% percentile has much more variability.

SPY vs USO – daily direction

I was curious about how often the direction (ignoring magnitude) was the same for USO vs SPY, using data from Yahoo!.  The chart below indicates, over a 10 day period, how often the two moved together.  The first set of data is the last 2500 days, second set tries to eliminate  overlaps and takes the every 10th data point, and the last column looks a back over the last 25o trading days (about 1 year).  For example, the direction (either up or down) being the same six times in the past 10 days happens about 21% of the time.  Overall there is a slight bias to going in the same direction.

DAYS	2500	2500 (EVERY 10)	LAST 250
1	0.35%	0.00%	0.00%
2	1.60%	1.50%	2.40%
3	3.45%	3.50%	2.80%
4	7.90%	8.00%	8.40%
5	12.40%	11.00%	8.40%
6	21.05%	24.50%	18.80%
7	25.20%	23.00%	27.60%
8	20.00%	21.00%	24.80%
9	6.85%	7.00%	4.00%
10	1.15%	0.50%	1.60%

SPY open – predictions on close

I was curious how the SPY performed based on comparing the open vs prior close. In particular, I was curious if the open was lower, what is the likelihood that the close would also be lower than the prior day’s close.  I grouped the differences into 3 groups, down > .1%, up > .1% and where the change was less than .1%.  Using Yahoo Finance, adjusted data, I found

 

	cls < prior cls	cls similar p cls	cls > prior cls
open < prior close	64%	6%	30%
open unchanged	43%	10%	47%
open > prior close	28%	4%	68%

each row is sums to 100%, so for the first row, if the open was more than .1% below the prior day’s close, then 64% of the time the close was also below the prior day’s close, 6% the change was less than +/- .1% and 30% the close was more than .1% greater than the prior day’s close.

I looked to see if being above or below some simple moving average made a difference, and there wasn’t too much, of the numbers I looked at the 100 day had the most impact.

below 100 SMA
62%	4%	34%
42%	6%	52%
30%	2%	68%
above 100 SMA
64%	7%	29%
43%	11%	46%
28%	5%	68%

The value of the Vix was slightly more significant, but the movement was generally from closing down for the day to closing unchanged (about 3% chance of unchanged with vix>24.9 vs 9% chance when the vix is < 13.25)

vix > 24.9 (about 20% of the time)
67%	3%	30%
46%	2%	52%
28%	2%	70%
vix < 13.25 (about 20% of the time)
59%	9%	32%
37%	11%	51%
29%	7%	65%

So, it appears that the market will close lower about 2/3 of the time if it opens lower, and similarly if it opens higher, about 2/3 of the time it will close higher.  Not surprisingly, a low VIX environment will have more little changed occurrences.

SPX 52 week High in November / December

I was looking at the Yahoo! data for SPX going back to 1960, to see how often there were new 52 week highs in November & December.

28 times (out of 55 years) there weren’t any new 52 week highs, 23 new years had a new high in November, 20 times a new high in December, and 16 times both November and December.  So, over the 55 years, there is about 50% chance at least one new 52 week high; and if there is a new high in November, then it is likely to have a higher high in December nearly 70% of the time.

However, if July – August time frame of the year didn’t have any new 52 week highs (20 years), only 4 years had a new high in November/December (1961, 1984, 2004, 2010).  the odds rise slightly if only look at those where you also had a 52 week high in January – March, but none July-August (3 times out of 9).

Looking at the distance from the prior 52 week high the October close, the average (median) close on the last day of October was -2.2% (-1.5%)  below the prior 52 week high when it had a new high in November/December (SPX was about -2.4% below the high this past October 30).  The average (median) close for October for months that didn’t make a new high in November/December was -12% (-10%), with only 3 years (2007 @ -1.0%, 1994 @-2.0%, 1988 @-1.6%, ) that had a close above  this year that didn’t make a new high.  Here is a breakdown by distance from prior 52 week high at the close of October.

below prior	52 week high	# of years	new 52 week high nov/dec
0%	-2%	18	89%
-2%	-4%	9	89%
-4%	-6%	6	33%
-6%	-8%	4	50%
-8%	-10%	3	0%
-10%	-12%	3	0%
-12%	-14%	2	0%
-14%	-16%	3	0%
-16%	-18%	1	0%
-18%	-20%	0
-20%	-22%	0
-22%	-24%	1	0%
-24%	-26%	2	0%
-26%	-28%	1	0%
-28%	-30%	0
-30%	-32%	1	0%
-32%	-34%	0
-34%	-36%	0
-36%	-38%	1	0%

So, if you are looking at the fact we haven’t had new 52 week SPX high while in several months, it seems unlikely one will happen in November/December.  But if you look at the distance from the 52 week high the October close was, then it looks likely to have a higher high before year end.

Four day vs Five day trading weeks

A brief look at four day trading weeks vs five day.  I looked at SPY data from Yahoo! and categorized all weeks into either 4 day or 5 day.

For the time period I looked at,

	4 day	5 day
% weeks up	58.76%	55.48%
average change	0.41%	0.16%
median change	0.43%	0.28%
95%	4.52%	3.95%
5%	-2.98%	-3.78%
hi low range median	2.41%	2.77%
hi low range > prior 4 week median	40.91%	51.39%
abs week change vs prior 4 week median	51.70%	48.73%

 

So, the conclusions I draw for 4 day trading weeks are that the SPY is slightly more likely to have an up week, and the high-low range [(high-low)/prior week close] is going to be slightly less the preceding 4 weeks.  I compared against the preceding 4 week median to try to adjust for different volatility.  There were 175 4 week periods in the study and 867 5 week periods, going back to 1994
.

SPX drawdowns

I was looking at how often during a 10 day period, there was 3 % and 5 % down move.  The excel formula was =C20/MAX(C20:C29)-1 where column C contained the closes. I then removed those cases where the move was within 10 days of another similar move, using the excel formula =IF(AND(H20<-3%, H20=MIN(H10:H30)),H20,””), where column H are the results of the previous calculation.  I took the data and grouped and charted by year:

The chart has some ebb and flo, the median 3% drop is 6 per year and 5% drop is 2 per year.  2014 was fairly close to median, at 5 & 2 (although 4.95% is awfully close).

I also looked at a 3% move in a 5 day period, and the results were similar to the 3% in 10 day period, the median was 7 per year, due in part to clustering – 8/2011 – 10/2011 had 2 10 day moves of over 3% down, but 5 5 day moves of over 3% down.  The VIX was in the mid 30’s so the larger number of moves isn’t surprising.

December Daily Performance – 2013 edition

Similar to September, first 15 trading days and last 5.

SPY

Since 1993, the average SPY has been up for December overall.  The low of the month is spread throughout the month (although as the month progresses, the 5 days that have the lows decreases – starts with 30% for first 5 days, and goes to 20% final 5 days).  On the other hand, there is a distinct history of the high of the month falling in the last 5 trading days (55% of the time).  Beware of the last 2 days, as they are more often negative than normal.  The prior few days are generally positive though, with the 4th to last trading day up 80% of the time. 30% of the time December’s closing low is above November’s close.

IWM has been stronger than SPY, and the high of the month often comes in the last 5 days (11 out of 13, although last year it wasn’t in the last 5 trading days.)

Month of SPX High of the Year

I was curious what month the high of the year occurred, and if a year to date high occurred in a given month, how often did it get eclipsed in a later month? The second column is the count of the number of years the SPX index (based on Yahoo! data – 1951 – 2012) that had that month as achieving the high of the year. The third column is the number of years where there was a higher high in a subsequent month given that month had a year to date high.

Since August 2013 had a year to date high, then it is fairly likely there will be a higher high later this year.

	highest high of year	high later
January	11	51
february	1	32
march	2	28
april	1	29
may	2	25
june	0	24
july	3	25
august	3	20
september	4	20
october	6	15
november	7	18
december	22

September Daily Performance – 2013 edition

Similar to last month, first 15 trading days and last 5.

SPY

Since 1993, the average September SPY has been down slightly, but the median is positive. 40% of the time the low has been in the first 5 trading days (only 10% in the second 5 trading days), while there doesn’t seem to be a pattern for the high of the month – each group of 5 days has around 25% chance of being the high of the month. In 5 of 20 years, the lowest close of the month was above the August month end close, and 5 years the highest close of the month was below the August month end. As far as daily changes, the 8th and 9th trading days had the highest percent of up days while the end of the month had weakness (particularly the last day of the month)

For IWM, September the average and median is negative for the month, with the average only positive the first couple of days of the month.