At Newfound, we are strong proponents of rules-based investing. However, rules-based investing in and of itself is not a panacea. Investors must be diligent in evaluating any rules that may be used for investing purposes.
The best rules will be defensible both in theory and in practice and be robust to dynamic market environments. Investors can evaluate candidate heuristics by asking the following questions:
- Is there economic/financial rationale for why the heuristic should hold?
- Is the market insight upon which the heuristic is based statistically significant?
- 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?
We can walk through this framework by evaluating the popular rule of thumb: "As goes January, so goes the year..."
The common explanation for the success of this rule is that the start of a new year creates a clean slate in terms of investor sentiment. January performance then sets the tone for sentiment for the rest of the year. Intuitively, there is no reason to believe that events after January can have just as much if not more impact on year end performance. For example, February could be a significant month in 2013 with the looming debt ceiling issues.
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.
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. 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:
- S&P 500 annual returns are normally distributed with a mean of 7% and volatility of 15%
- Monthly returns are i.i.d. (the distribution of each monthly return is identical and the return in one month does not affect the returns of subsequent months)
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.
|Metric||Strategy A||Strategy B|
While rules-based investing is a great tool for investors to achieve consistent and desirable portfolio behavior, it is imperative that individual heuristics are objectively evaluated as we did with the "As goes January, so goes the year..." heuristic in this post.
Note that to some extent "wrong" heuristics may persist just because investors/traders follow them and that in and of itself may provide short term rationale for following them. However, this type of reasoning can potentially lead to large losses once the myth of the heuristic is exposed and market participants cease following it.
Business relationship disclosure: Newfound Research is a quantitative asset management firm. This article was written by Justin Sibears, one of our Managing Directors in our Product Development & Quantitative Strategies Group. We did not receive compensation for this article (other than from Seeking Alpha), and we have no business relationship with any company whose stock is mentioned in this article.