A recent Globe and Mail blog repeats an oft-cited claim that the U.S. stock market is weaker in mid-term election years (MTEYs). According to this blog, stock markets “have traditionally been weaker than normal during mid-term election years. Price returns during these four-year cycle lows have been atypically negative in January, but then frequently favorable in February. What’s more, March also typically posted an gain, just before a string of sub-par performances from April through September, with two-thirds of these months recording average declines.”
This is, in fact, one version of the presidential election market cycle theory first proposed by Yale Hirsch in the late 1960s. Hirsch analyzed a number of instances of cyclical behavior in the stock market and founded the influential Stock Trader’s Almanac.
In our previous blog, we found that one specific claim of Hirsh (the “Halloween indicator”) is not reliable. Other discrepancies between some of Hirsch’s predicted market cycle are discussed elsewhere, for example in this Forbes column and in this CBS News column.
This is not to say that Hirsch is not serious about the analysis presented in the Stock Trader’s Almanac. In most cases, the cyclical behavior he highlights does fit well with the historical facts in the period during which it was analyzed. However, these cycles are often in a monthly time frame. For such a time frame, a few decades of historical data is simply too short to make statistically reliable conclusions. This makes such analyses prone to overfitting, the theme of the paper featured in our previous Mathematical Investor blog.
Let us take the cyclic behavior of mid-term election year alluded in the Globe and Mail blog as an example. Here, obviously, the author has done his homework to verify the phenomena provided in the above summary. But let us delve into it deeper.
First we take the S&P500 index data available to us and calculate the average monthly returns in four year cycles for the 48 years from 1963 to 2010 (see a summary in the table below). We can see that the average monthly return for the mid-term election year matches the description of the cyclic behavior closely—so far so good.
|Month||3rd year||E||1st year||MTEYs|
|1st year –1st year of presidency|
|E–presidential election years|
|3rd year –3rd year of presidency|
|MTEYs – mid-term election years|
Next we divide the 48 years into three blocks each consists of 16 years: 1963-78, 1979-84 and 1985-2010 and list monthly average returns for each period side-by-side with the 48 year averages in the next table.
Now we see that the “January weakness” almost disappears in the third block, and the favorable performance in February and March reduces to statistical errors in the first two blocks. The “swoon by June,” as indicated by the title of the Globe and Mail blog, more likely occurs in May, if we examine the first and third blocks and is shifted to September in the second block.
The root cause of this instability, of course, is that the sample is too short: in the 48 years of historical data, there are only 12 mid-term election years. We certainly cannot expect “cyclic behaviors” observed on 12 samples to have any statistical significance.
In other words, this is a classic example of backtest overfitting, as we analyzed in our paper Pseudo-mathematics and financial charlatanism. Refer to this paper for a detailed technical analysis.