The Seasonality Problem (Part Eight)
November 30, 2007 by MTM
Not All Days Are Equal
One thing that significance will not tell you is whether the information you have just found is worth anything in the practical sense. To find that out, you have to examine and analyze your data.
Let’s revisit the table again:
Apart from the win:loss ratio, which gives you the batting average of each month, it’s also important to know the average magnitude of the returns (average wins/loss) for us to judge the worth of the results. In both cases, October outperforms the other months. Also note something: all of the months have a win:loss ratio higher than 1—meaning the number of winning trades is larger than losing trades. But what makes the winner is the reward:risk ratio—or the size of the wins vs. the size of the losses. In the case of the worst performing months (January and February), even if the number of winning trades exceeded the losing trades, the average size of the wins were smaller than the losses.
Let’s add a third dimension to the table, and spread the average returns out over years in the sample:
Consistency is cool. We can see from this table the consistency of average returns from year to year. Although October was not the best performer year on year, it was the most consistent. For the sub-performing years, they were worst in the one year and best in others, but overall the average returns were suboptimal. The real value is if we compound the months—meaning what if we bought every year during those months and liquidated after 180days, and repeated this every year. To simulate actual trading we applied a 5% fee for buying and selling, for a total of 10% hurdle rate per completed trade:
Let’s see if we compare the returns to a buy and hold strategy. We bought the PSEi on January 3, 2000 at a price of 2,141.77 and sold it on November 22, 2007 at a price of 3,478.94 for a total gross return of 62%. This was over 2,880 calendar days or 7.89 years which comes to an equivalent annual compounded growth rate of 6.34%. If we factor in fees (5% buying and 5% selling to be conservative), the total return would have been 52%, and the annual growth rate down to 5.5%.
Without question, timing purchases on certain months outperformed an outright buy and hold strategy which DISPROVES our null hypothesis convincingly.
Next: Reflections On An Unfinished Experiment…
In your table, if I understood it right, the exercise shows that if you bought the hypothetical psei stock in October and sell it after 6 months, you get that best returns as shown. Ever since I watched a video of Larry Williams regarding his study on seasonality on trading days of the month, I always wanted to do some study on our local market. After reading your blog, I decided to finally do some initial tests. It was nothing fancy, just simple tabulation, sorting and summation. I took the psei data from 1994 to present and sorted those with the psei closing higher, that is, close-open = value. I then sorted again based on that positive gains/losses for the day.
Here are the results of this unscientific approach for the psei:
best gains per day = thursday followed by friday
worst losses per day = tuesday followed by monday
best gains based on week = dec. 13-20
worst losses based on week = oct. 3-10
What’s interesting I noticed is that in your table, October is the best time to buy which corresponds to the month where I found that the psei experiences its worst losses.
Thanks for your feedback. Boss serval, seems your own observations shed further light on the Seasonality Problem. If October is usually (or should i say unusually) the month the index experiences its losses, then it might help investors in buying at good prices?
Your observation is also that December registers the best gains, so if I amended my table and checked for 3-month returns instead, would buying in October and selling in December appear the best times I wonder?
This kind of inquiry begs a more general question (which could cover the results of both our surveys): is buying the index during times of big losses (like a crash) a good trading strategy? And over what holding period?
The last frontier is the “Why?” What happens in October anyway that leads our independent studies to point to the same thing?
Boss MTM, October would indeed be a good candidate if one is positioning long term on FA stocks or if the stocks and indices are showing signs of bottoming out or are building bases. Buying just because it’s October maybe risky, or I wonder if it’s worth the risk?
The sorting I made is for 1 day gains only, so holding for 6 months could still give a better return than 3 months. I’m just guessing, only a mathematical computation could clearly show us that.
That’s a difficult one, buying in a crash? Like the old saying of “buying when there’s blood in the streets?” If one has deep pockets maybe he can spare a portion. The problem is what if the prices keep falling? For FA guys, that may not be an issue and for those with deep pockets. Like what Larry Williams said in the video, seasonal effects can give us a head’s up on possible opportunities, if the effect materializes or not as scheduled, I guess that’s a another matter. Maybe if we combine it with other tools, the odds would be greater that investing/trading on such seasons is worthwhile.
And the “why” part, FA guys particular to seasonal effects might have some insights.