The “Monthly W” (in Video)
Included on our monthly seasonality map is a weak observation I call the Monthly W.
In a nutshell, at this moment in history, the beginning, middle and end of each month (excluding the very last day) tend to be bullish, and the times in between bearish. The effect isn’t strong enough all by itself to justify a trade, but I do think it deserves to be one of many tools in the trader’s toolbox.
To illustrate, the following graph shows average excess return per day of the month for the S&P 500 over the last 20 years. Obviously every month doesn’t have exactly 21-days so I’ve normalized the data to always fit our 21-day chart (see geek notes below).
See the W?
Returns tend to be higher at the beginning, middle and end of the month (excluding the very last day), and negative in between. Here we’re looking at excess average return, but other metrics (median return, volatility-adjusted return, etc.) all paint a similar picture.
Geek notes: I’ve massaged the data quite a bit to make it more useful: (a) I’ve fit all months to 21 days; months with less have been stretched and months with more have been compressed. And (b) it doesn’t make sense to be overly precise with something that’s by its nature not, so I’ve smoothed results by averaging each day’s average return with the day before and after. For example, the result on day 5 is actually the average of days 4, 5, and 6.
The evolution of the W…
The video below shows how the Monthly W has evolved since 1950. Each frame covers 20 years, so frame one is from 1950 to 1969, frame two from 1951 to 1970, etc. Click to play.
Observations…
1. The beginning and end of the month have remained consistently bullish over the entire 60 years (read more about Turn of the Month seasonality).
2. It’s difficult to catch because of how I’ve smoothed the data, but in the last 20 years or so the very last day of the month has been very blah (read more about the Last Day of the Month Blahs).
3. Earlier in the sample, the month resembled more of a “U” shape with lower returns for the entire middle of the month. This flattened out in the 70’s and 80’s, and finally, over the last 20 years we see a strong “W” shape emerge.
Again, I would reiterate that I don’t think monthly seasonality is strong enough all by itself to justify a trade, but as the video shows, these effects have tended to stay consistent enough that I think they deserve to be one of many tools in the trader’s toolbox.
You can see our own take on the Monthly W and other seasonality plays on our monthly seasonality map.
Happy Trading,
ms
P.S. a big THANKS to Nick Gogerty for showing me how to put together the time lapse chart. You were right sir, not as difficult as it looked.
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Filed under: Evolving Markets, Time-based | 16 Comments
Michael:
Thank you. Great work…
Speculation for the W effect changing over time is the growing influence of monthly option expirations in the context of delta hedging.
“3. Earlier in the sample, the month resembled more of a “U” shape with lower returns for the entire middle of the month. This flattened out in the 70’s and 80’s, and finally, over the last 20 years we see a strong “W” shape emerge.”
RE to Tom: very insightful.
When I first intro’ed this “mid-month hump” I connected it with options expiration week (http://marketsci.wordpress.com/2008/12/17/options-expiration-week-stock-market-strength/) but after running the numbers when I created the Monthly Seasonality Map I found it looked more like a calendar effect than related to OE week.
I’m going to rerun the numbers b/c it’s been a while and maybe put t/g a post to discuss.
Thanks for the comment,
michael
Michael:
In Nassim Taleb’s book “The Black Swan” (pages 176 to 178), he discusses “The Three Body Problem.” Included as Figure 2 is this image ( http://www.scribd.com/doc/30971768 ). Integrating David Cowen’s shatter plot image and your Monthly W, I guess the effect is a Three Body Problem in time.
The month starts out and I frame up the first few days as the “Initial Balance” (Pete Steidlmayer) and the market ball keeps moving with more information coming into the process until mid-month. This process is just exploring the space until mid-month where prices become influenced by option expiration. Although option expiration is relatively fixed at the 3rd Friday of every month, it forces me to make choices under the duress of Gamma swings. Option Expiry becomes the “Second Body” in time and then the market ball moves towards month end influenced by the Initial Monthly Balance Range, Option Expiry, and new information.
Your Monthly W chart and the above narrative match my experience trading options. I typically feel lost during the week 2 and going into month end. In other words, I feel a loss of effectiveness in my time framing and this affects me emotionally. In addition, declines in market velocity (bar ranges, volume, and interest), affects my ability to focus during these “low interest” periods.
Nice work.
A relatively useless observation is that day 16 has been as consistently negative as the month ends have been positive.
RE to Blue: I haven’t run the numbers, but I’d bet that there’s a very high probability of that being the day-after options expiration which, as we’ve talked about before, has historically been very bearish. See, not a useless observation at all! =) michael
That’s fascinating. I wonder if 401k plan contributions tend to bunch at the beginning and middle of the month, and could create some portion of this type of seasonality…
Thanks for the post Michael:
Please enlighten me as to how you made the”time lapse chart”. Looks very cool!
RE to rkhanen: sure…here are the instructions from Nick. Seems complicated (at least it did when I first read it), but is actually pretty quick & simple when you think about it.
1. pick a variable to iterate over time
2. select and create the chart you want and fix the axis so they won’t jump or re-scale
3. write a small loop macro to iterate the variable cell with or without a pause in it using VBA
4. connect the VBA macro to a button near the chart
5. getting a free screen movie capture program from download.com
6. start the screen capture program with a capture area set to the chart.
7. push the button to iterate the series
8. import the movie into windows moviemaker (free program)
9. using movie maker add titles
10. using movie maker slow down or speed up the time elapsed for your narative
11. drop in a music track to suit your tastes
12. trim off beginning and end of the film etc.
13. publish to youtube
michael
Thx! VBA loop macro…oh dear. I have to study a bit I can hear :)
cool presentation!
Love the vid/time-lapse too – thanks for the step-by-step also
Why do i feel that this might be related to the biweekly paycheck cycles and the 401k investments associated with them
Michael
I’ve tried playing with adjusting variable “length” of trading month in the past and never found an esy/accurate way of getting over this problem. Would you mind sharing a little more on how you “strecth” and “compress” the longer and shorter months?
thanks
fm
It would be nice if you answer Fernando.
Take the trading day of the month, divide it by the total number of trading days in the month, multiply it by 21, and round to the nearest integer.
In months that have 20 trading days, there will be no day 10. In months that have 22 days, there will be two day 11s.
michael