At Newfound, we are strong proponents of rules-based investing. However, rules-based investing in and of itself is not a panacea. The best rules will be defensible both in theory and in practice and be robust to dynamic market environments.

The following chart shows for each month the percentage of times that the sign of that month’s S&P 500 return matched the sign of the return for the period starting in the beginning of that month and ending one year later.

For example, the January figure means that starting in 1950, 69.8% of the time the sign of the return from January 1st to February 1st of that year matched the sign of the return from January 1st of that year to January 1st of the next year.

MonthPercent
January69.8%
February63.5%
March73.0%
April58.7%
May65.1%
June61.9%
July54.0%
August55.6%
September52.4%
October65.1%
November65.1%
December76.2%

What can we learn from this data? March and December returns seem to have done a better job than January of predicting the return for the following one year period. However, we need to dig deeper to see if these statistics are meaningful both in theory and in practice.

From a theoretical perspective, if we make some simplifying assumptions about the distribution of S&P 500 returns then we can explicitly compute the values in the above table. For the following discussion, we assume:

• Returns are normally distributed
• Monthly returns are i.i.d. (the distribution of each monthly return is identical and then return in one month does not affect the returns of subsequent months)
• Annual S&P return has mean of 7% and volatility of 15%

If January’s return is very slightly positive, the probability of a positive annual return is 67.2%. If January’s return is 2.0%, the probability of a positive annual return increases to 72.1%. If January’s return is 5.0%, the probability of a positive annual return increases further to 78.7%.

The chart below shows the probability of a positive annual return given various January returns.

This illustrates that the historical data backing the heuristic that as goes January, so goes the year is an expected statistical artifact and provides no basis for generating value as an investment strategy. Strong market performance in January does not cause strong market performance in the following eleven months. Instead, strong market performance in January simply makes it more likely that the full twelve month return is positive in the same way that the team winning a football game at the end of the third quarter has a better chance of winning the game. Strong January returns give the full year return a head start, providing no forward looking information that can be used to trade profitably.

We can go a step further to evaluate the practical value of the heuristic by examining the performance of a related trading strategy. Consider the following strategies:

• Strategy A: Hold a 100% long position in the S&P 500
• Strategy B: Go long the S&P 500 in January every month. If the return is positive, go long the S&P 500 for the remainder of the year, otherwise go short.

Strategy B, based on the January heuristic, underperformed both on an absolute return basis and a risk-adjusted return basis.

MetricStrategy AStrategy B
Return7.1%5.2%
Volatility15.4%16.5%
Return/Vol0.460.32

1) Is there economic/financial rationale for why the heuristic holds?When evaluating a potential trading heuristic, it is always useful to ask these questions:

2) Can the supporting data be explained statistically or is it truly an outperformance opportunity?

3) How would a trading strategy based on the heuristic have performed historically? If it has performed well, what are future market scenarios that could pose risks to its continued success and what are the magnitudes of these risks?

For another take on the January effect using conditional probabilities, see our weekly commentary.

### Justin Sibears

From 2012-2019, Justin Sibears served as Managing Director and Portfolio Manager at Newfound Research. At Newfound, Justin was responsible for portfolio management, investment research, strategy development, and communication of the firm's views to clients. Justin holds a Master of Science in Computational Finance and a Master of Business Administration from Carnegie Mellon University as a well as a BBA in Mathematics and Finance from the University of Notre Dame.