Seasonality — Old And New January Effect
Man’s curiosity is insatiable. We need a reason for everything and can never take things as it is. To fulfill our thirst for answers, we will venture into the darkest corners and leave no stones unturned. But unfortunately, many phenomenon in this world, including some stock market anomalies, are still not well understood even today.
Seasonality in stock performance is one of them. Early investors observed that markets seem to behave in a certain way during specific times of the year. For example, in US, stocks tend to do better in January and worse in May. For the latter, there is even a common saying in the market “Sell in May and go away”. Even though these seasonal or calendar effects have faded away, they are quite well documented. Among them, the January effect on the US market is probably the most prominent. However, these observations are mere hypothesis as deterministic evidence remain elusive.
What is the big deal about January?
January effect refers to the seasonal rally of the US stock market in, as the name says it, January. The impact seems to be more pronounced for small caps. No one knows exactly why the market behave the way it did. But analysts have postulated a few explanations:
- Individual investors liquidate losing stocks in December to reduce capital gains tax, and then reinvest the proceeds in January.
- People invest into the stock market in January after taking their year-end bonus.
- The start of a new year has a bigger psychological appeal to commence new resolutions which include investing in stocks.
Anyone can try to rationalize and come up with a reason. But at the end of the day, no one can be sure what is really going on. And if you believe that markets are efficient, then such effects should not exist, or at least not for long.
Does January effect apply to the S&P 500?
Records of January effect centers around the outperformance of small caps against the broader market. So has it ever hold for the large cap S&P 500 stocks? To find out out, I used the historical price of S&P 500 index dating back to the 1950s to conduct some analysis. (Note: I am using the price index).
The table above displays the average return of each month over its corresponding 10 year period. As an example, if we look at the period 2001–2010 for the month of January, we get -1.61%. This means that the average return for January over that period is -1.61%. At a glance, January looks fine, but it certainly does not seem to deserve all the attention it is getting. It might have done well from the 70s to 90s but results have since tapered off. If anything, the seasonality “champion” should be awarded to December, November, April or March. The average of these months were consistently positive throughout all the 10-year periods.
And if we look at the entire period since 1951, it is also quite obvious that January is not the most outstanding month. In fact, December is the clear winner. November, April and March are also better off in many of the metrics. Why is December such a stellar month? Maybe investors start positioning themselves in December in anticipation of a rally in January. And when the bulk of the money are put to work in December, then January gets watered down, and the effect fizzles out. Instead, what you get now is a December effect. But by that reasoning, shouldn’t December effect also disappear as investors shift to position themselves earlier in November and then in October and so on? To cut it short, I have absolutely no idea why.
It might also be worth to take a look at the month of May. It did not fare too well from the 60s-70s, but the picture turns rosier starting in the 80s. While May’s performance looks mediocre, it is definitely not the worst month. August and September, without a doubt, look more miserable. So maybe they should change the saying to “Sell in August and don’t come back till October”.
How has each month performed since the 1951?
We can get a better picture of how each month performed by creating a NAV series for each month. To understand how these NAVs are created, let me use the January NAV as an example. The NAV of January is constructed by assuming we start with $1 in 1951. We then invest all our capital only during the month of January each year till 2017. In all other months, we sit on cash. For simplicity, let us also assume that these cash does not earn us any interest. The NAVs for the other months are constructed using the same approach.
These NAV series paint a distinct picture. As noted earlier, December is undeniably the leader of the pack. September is also clearly the worst of the lot. Meanwhile, if we look at January, we will notice that all is well until a marked deterioration in its performance after year 2000. And as for the month of May, it is evidently the top loser until the mid-80s where it started trending up. Is it pure coincidence that January and May appear to have the most apparent and extended departure in their paths? Or is this the result of market obsession due to heightened publicity of these 2 months where everyone tries to exploit a known pattern?
I have no answer. But it does not really matters. If we want to make any deductions based on these observations, perhaps all we can say is that the seasonality effects are possibly present earlier from 70s-90s. But as of today, the game has changed and these effects have waned. This should not come as a surprise. If you carry a Nokia or Motorola mobile phone more than a decade ago, they are seen as the in thing. Today, after the advent of smart phones and rise of companies like Apple and Samsung, we hardly hear of Nokia and Motorola anymore. In fact, unable to move fast enough to tackle competition, both have sold off their mobile phone businesses.
A less well-known January effect
There is something a little less well known about January for S&P 500. And what is that?
January looks positively correlated to the total returns delivered by the remaining 11 months. That means that if January is up, there is good chance the total returns of the remaining 11 months is up. The S&P 500 is up 76% of the time between February to December from 1951 to 2017. But if January is a positive month, the odds increases to 88%. In total, there are 40 years with positive January, out of which 35 carry on to churn out profits for the remaining months.
The converse, however, does not seem to work that well. A negative January does not translate to a better chance of the index heading south for the rest of the year. Out of the 27 years that January produce negative returns, only 11 of these headed deeper into the red at year end. The results are summarized in the table below.
Does statistics back this up?
For those who are interested in how the numbers for each year looks like, you can have a look at the table below. It shows you how much returns S&P 500 made in the period of January and collectively during February-December each year.
To see if there is any linear relation between January and the total returns from the remaining 11 months of the year, we can run a simple regression using January as the independent variable (factor) and the following 11 months’ returns as the dependent variable.
From 1951–2017, we will have a total of 67 observations. The regression results shows January has a positive coefficient with a p-value below 0.05. This is statistically significant. Basically, the lower the p-value is, the stronger the statistical significance. It suggests that the returns of January and the remaining months may have a positive linear correlation.
R Square is another metric people scrutinize. It measures how much of the dependent variable’s moves can be attributed to the factor. It can range from 0% to 100%. 0% means the factor explains nothing about the moves of its dependent variable, while 100% means we absolutely nail the problem.
So if we look at our R Square of 6.4%, we may be led to believe that using January as a factor is a poor choice as it explains little of the subsequent 11-months’ return variability. However, we have to bear in mind that we are doing predictions and not explanations here. The independent and dependent variables occur at different time periods. For stock market predictions, we can forget about getting high R squares. Those are only seen in academic examples for different applications. If we think about it, there is a good reason why people say stock market is unpredictable. In the investment industry, we work with and accept uncertainty as part and parcel of our daily lives. And more often than not, we make do with finding just that slightest edge instead of wasting time to look for holy-grail solutions.
Does trading using this new January effect improve performance?
A simple way to assess is to run a historical backtest. In this backtest, we will start investing in February whenever January is up. We then close off our position at the end of December and repeat the same for the next year. Let’s call this the January Method, and doing this since 1951 delivered an annualized return of 6.7%. This is lower than what we would have received if we had just bought and hold an equivalent of S&P 500. For the same period, buying and holding S&P 500 returned an annualized 7.6%. But the January method fared better on a risk adjusted basis. It has a lower volatility of 9.5% and a higher Sharpe of 0.71 against 14.3% and 0.53 for the buy and hold method.
The results are not surprising. Lower volatility comes from sitting on cash for the 27 years where January was down. But to trail the market only less than 1% in annualized returns despite not being in it for that long is quite impressive. It is also good to have spare cash on hand that you can invest into other areas.
This is just one simple implementation. It does not mean it is the only way you can use this information.
Would I use such a strategy?
At the point of writing, I am not using it and has no near term intention to. Why?
1. The rationale is not strong enough.
I have touched on this point earlier. No one can explain why things happen the way it did. Just like I have no idea why the January effect seems to exist in the 70s-90s, I have no clue why it vanishes after 2000 either.
2. The sample size is quite small.
When fundamental reasoning fail, we turn to statistics. We have 67 years of data. It sounds like an awfully long period except that there is only 1 January per year. So there is only 67 observations to work with. There is no hard and fast rule for determining a good sample size. Basically, the more the merrier. This is so that we have a better chance of ruling out fluke results, in particular for cases that are not well understood.
3. One or two key events can shake up the results
Let’s take October as an example. It is not a particularly impressive month. But if we dive a bit deeper, we will realize that 2 key events have a major responsibility for where it is today — (1) Black Monday, (2) continued fallout from the collapse of Lehman Brother after September 2008. If we removed these 2 events, October would jump and become one of the top performers. Such events could have happened to any of the months.
4. It is difficult to determine when to pull the plug
Knowing when to call it quits and cut losses should be an integral part of everyone’s investment plan. This include answering fundamental questions like when to pull the plug on a strategy. In the case here, the premise of the strategy lies on using January as a predictor for the performance on the rest of the year. This is a one trade per year kind of strategy. To give such a strategy reasonable room to run, we are going to need many years before we can fairly decide if the premise is still valid. And none of us have that many years to give. So we may end up having to settle for less optimal criteria to decide whether the strategy goes or stay.
These are just my thoughts. It certainly does not represent what everyone thinks. For example, those with large portfolios and many different strategies may be less inhibited to try out new ideas as long as any fallout can be mitigated. At the end of the day, a lot boils down to our own investment philosophy and risk preference. There is no right or wrong answer. Meanwhile, we have strong a January this year, so let us see how this year is going to unfold.
Originally published at investmentcache.com on October 11, 2018.
Disclaimer: Any views or opinions represented in are personal and belong solely to me. It does not represent any other people, institutions or organizations that may or may not be associated with in professional or personal capacity. The views or opinions are not intended to offend or malign any religion, ethnic group, club, organization, country, company or individuals. The content is provided for informational purposes only. It is not intended to be, nor shall it be construed, as an offer, or a solicitation of an offer, to buy or sell an interest in any fund or security. I make no representations as to accuracy, reliability, completeness, suitability or validity of any information.
