Investing Anomalies

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Investing is historically chock-full of strategies based on absurd anomalies. These include the January effect, the Super Bowl Indicator, the Harvard MBA Indicator, and “Sell in May and Go Away.”  If you take a large number of “indicators” (I wince as I use that word loosely), some of them will exhibit a correlation with market returns by chance alone. Geeks even have a name for this--“spurious correlation.”

Even though statistics allows us to remove the subjective nature of decision making, a fundamental reasoning should underlie a relationship between two variables. For instance, Index Funds Advisors' investment recommendations utilize small cap and value stocks to a greater extent than their natural weight in the total US stock market. Finding two equity categories that outperformed the overall Market is insufficient for the purpose of making an investment recommendation. The fundamental logic behind the higher historical returns for small cap and value is that these stocks are riskier and thus have a higher cost of capital. These higher returns are neither free nor guaranteed; they are expected compensation for the additional risk borne.

Regarding the calendar anomalies, I have yet to see a robust and logical explanation. Consider that if all months had the identical average return, it would be equally suggestive of a non-random process. The key requirement is that these time periods would have to outperform by more than chance alone would predict. A recent paper by Ronnie Shah of Dimensional Funds Advisors1 analyzed the “Sell in May and Go Away” anomaly identified by Bourman and Jacobsen (2002). The anomaly states that the stock market shows stronger growth in the winter period from November through April than May through October2. Shah tested whether the seasonality in returns could have been expected by chance based on randomly sampling identical returns distributions and testing these returns with out of sample data.

The difference between these high (winter period) and low (summer period) six-month periods for the total U.S. Market is 4.11% which seems sufficiently large to motivate selling in May and buying back in November. However, before logging in to your online brokerage account, it is crucial to understand that stock market returns are extremely noisy, and a question worth asking is whether a randomly generated sample of monthly returns could reproduce the anomaly observed over the last 83 years. Of course, doing it once does not tell you anything, so rinse and repeat 10,000 times as Shah did, and you can actually expect results comparable to the “Sell in May and Go Away” anomaly 24.2% of the time1. For comparison sake, this is about as uncommon as flipping a coin and it landing on heads 2 times in a row.

Shah’s data was derived from one of the two popular US Market data series, the Center for Research in Securities Prices (CRSP). To test the anomaly out of sample, the other popular data set was used--Robert Shiller’s S&P 500 returns which dates back to 1871. In the November 1871-October 1926 out of sample period winter period is only larger than the summer period by 1.06%. This is much lower than the original data set’s results of 4.11%. The relationship is substantially weaker out of sample.

What does this mean for your portfolio? For the most part, nothing-- it’s really just a reminder of the types of odd things that will happen by chance alone. Considering the sheer number of random variables in the universe, somebody sneezing at breakfast is going to be correlated with market returns by chance alone. Just for laughs, we sorted the 2011 returns of the 500 constituents of the S&P 500 Index based on the first letter of the company name, and we found that stocks that begin with “v” had a 29.8% higher return than stocks that begin with “z”. Needless to say, we would not recommend this as a long/short strategy. The only true driver of market returns is risk; you should expect to lose money at times if you want to make money. Market prices are always working for participants to price securities fairly for the amount of risk assumed, regardless of who wins the Super Bowl, or whether it’s spring, summer, winter or fall.

1 Ronnie R. Shah, “Sell in May and Go Away? Market Timing and Stock Return Seasonality.” (Private Site), May 2012.

2Bouman, Sven and Ben Jacobsen, “The Halloween Indicator, ‘Sell in May and Go Away’: Another Puzzle.” American Economic Review 92: 1618–1635, 2002.