S&P 500 Performance By Day Of Week And The Changing Nature Of Trading Tuesdays

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Includes: SPY, SSO
by: Dr. Duru

After the S&P 500 (NYSEARCA:SPY) dropped as much as 0.4% on Monday, April 30, 2012, I decided to take a shot at trading what seemed to be the double whammy of technical trades: the tendency for Tuesday's to trade up and the tendency of the beginning of the month to trade up. Tuesday, May 1 delivered in a big way as the S&P 500 soared as high as 1.2% before closing with a much smaller gain of 0.6%. (As I covered in my tweets, I sold early into that advance and quickly regretted it until the fade into the close.) The index has continued to sell off ever since in what I am now thinking is the beginning of a topping pattern.

This trade was so successful, I decided to go back to the original article from 2011 that pointed out the anomaly of Tuesday's outperformance. I could not find it, so I decided to run my own numbers to check into the history of this trade and to investigate more deeply any related nuances. My apologies to the author of the original analysis for not being able to give you specific credit!

It turns out that the Tuesday anomaly was not just special to 2011, it has been special since at least 1950.

Average Daily Price Change of the S&P 500 Based On Day of Week and Performance of Previous Days (Jan 3, 1950 to May 4, 2012)Click to enlarge

Average Daily Price Change of the S&P 500 Based On Day of Week and Performance of Previous Days (Jan 3, 1950 to May 4, 2012)

There are many things to notice in this chart, so I will list them in bullet point form after defining the chart's elements.

The S&P 500 daily price data comes from Yahoo!Finance from January 1, 1950 to May 4, 2012. Daily performance is calculated as the price change from one trading day to the next. Holidays are automatically excluded. This means that Monday's and Friday's have far fewer data points than the rest of the week.

I segmented these calculations along several dimensions. The "Overall" segment describes the average daily price change across the entire set of data. For example, the overall .08% average daily price change for Wednesday means that from 1950 to 2012, on average, one can expect the S&P 500 to gain .08% in price at the close of trading on Wednesdays. I made the same calculation for the "Previous Day Down" segment. This provides the average daily price change given the previous trading day delivered a negative price change. Similarly, "Previous Day Up" provides the average daily price change given the previous trading day delivered a positive price change. I did not calculate the impact of a perfectly flat trading day.

I next turned up the dial on the "Previous Day Down" category by conditioning on the previous trading day closing with a -0.5% price change or lower and finally a -1.0% or lower price change. Each segment lists the average daily price change in the same order from Monday to Friday, from left to right. I follow this same format for all related charts.

Some immediate observations:

  • The overall average daily performances are all very small, well within a band of -0.1% to +0.1%. (For those who are statistically inclined, I conducted an analysis of variance, ANOVA single factor, on the average daily price changes segmented by day of the week and found the differences to be statistically significant. That is, I was able to reject the null hypothesis that the means of the daily performances are statistically indistinguishable).
  • Mondays trade at a near consistent disadvantage to all other days of the week across categories.
  • Tuesdays outperform all other days when the previous trading day closes with a loss. This outperformance appears to grow the greater the sell-off in the previous trading day.
  • There is an overall bias to trade up - this is consistent with a stock market that has risen significantly over the past 60+ years.

I also looked at the range of price changes for a given day of the week. It was startling to get a reminder of 2008′s drama. That year holds the record (since 1950) for the largest price changes, positive and negative, for all but two scenarios. The crash of 1987 delivered the largest down day for Monday (October 19, -20.5%) and, two days later, the largest up day for Wednesday (9.1%).

I next looked at recent years to see how well these averages have played out since 2007, the year before the last recession began. This analysis showed substantial variation in the daily trading performance. In other words, you are not likely to build a consistently winning trading strategy year-in and year-out simply trying to play the overall averages. For example, since 2007, Tuesday has only delivered outperformance in two years: 2008 and 2011.

Average Daily Price Change of the S&P 500 Based On Day of Week and Year (Jan 3, 2007 - May 4, 2012)Click to enlarge

Average Daily Price Change of the S&P 500 Based On Day of Week and Year (Jan 3, 2007 - May 4, 2012)

Note that 2008 and 2011 were years full of macro-economic and geo-political drama that played out over the weekends. Markets would react poorly on Monday and bargain hunters would swoop in on Tuesday. The author who identified the outperformance of Tuesdays in 2011 offered up this explanation, and it seems to make sense to me.

The next charts break down the data segments by year covering 2007-2012. Again, note well that the relationships across the days of the week can change dramatically from year-to-year. Hopefully given the discussion so far, the unique features of these charts should stand out! (Feel free to ask any clarifying questions).

I will say that the small amount of data for 2012 seems to suggest that the "Tuesday trade" is only reliable if Monday closes down…but not too low. Wednesday is this year's more reliable recovery day. However, there are currently only a few data points, so this week should be a great test. If the European drama flares up again this summer, I suspect we will see a lot of down Mondays. At the time of writing, elections in France and Greece have helped the Nikkei drop almost 2% on Sunday evening in the U.S. Assuming the U.S. markets react in similar fashion, I will be looking to buy some calls in the ProShares Ultra S&P500 (NYSEARCA:SSO) at Monday's close and add on any weakness on Tuesday.

Average Daily Price Change of the S&P 500 Based On Day of Week and Year When Previous Trading Day Closes Down (Jan 3, 2007 - May 4, 2012)Click to enlarge

Average Daily Price Change of the S&P 500 Based On Day of Week and Year When Previous Trading Day Closes Down (Jan 3, 2007 - May 4, 2012)

Average Daily Price Change of the S&P 500 Based On Day of Week and Year When Previous Trading Day Closes Up (Jan 3, 2007 - May 4, 2012)Click to enlarge

Average Daily Price Change of the S&P 500 Based On Day of Week and Year When Previous Trading Day Closes Up (Jan 3, 2007 - May 4, 2012)

Average Daily Price Change of the S&P 500 Based On Day of Week and Year When Previous Trading Day Closes -0.5% Or Lower (Jan 3, 2007 - May 4, 2012)Click to enlarge

Average Daily Price Change of the S&P 500 Based On Day of Week and Year When Previous Trading Day Closes -0.5% Or Lower (Jan 3, 2007 - May 4, 2012)

Average Daily Price Change of the S&P 500 Based On Day of Week and Year When Previous Trading Day Closes -1.0% Or Lower (Jan 3, 2007 - May 4, 2012)Click to enlarge

Average Daily Price Change of the S&P 500 Based On Day of Week and Year When Previous Trading Day Closes -1.0% Or Lower (Jan 3, 2007 - May 4, 2012)

The strong rally of 2012 has not yet generated many large down days. To date, there have been 12 trading days closing with a price change of -0.5% or lower and only 5 trading days closing with a price change of -1.0% or lower. No Thursday has yet closed with a price change of -1.0% or lower.

Be careful out there!

Disclosure: I am long SDS.