A few years ago, my local library held a sale to purge old books from the shelves. I bought a 1976 book by Norman Fosback, Stock Market Logic, for a quarter. If Mr. Fosback is still alive, he might make a good Spec List member. His book is full of data and testable hypotheses. Best of all from a statistician's point of view, Mr. Fosback has done much of the testing, and one can go directly to out-of-sample testing.

In a chapter on seasonality, Mr. Fosback wrote that the US stock market tended to rise on the last trading day of the month, the first four trading days of a new month, and the two trading days before the market is closed for a holiday. He found that these days, which were only about 28% of all trading days, accounted for the entire advance in the S&P 500 from 1928 to 1975.

Using Mr. Fosback's definition to identify favorable days, I checked recent S&P 500 futures returns:

                               Favorable  Unfavorable
                                days          days
12/10/04-12/31/05        5.7%         -2.3%
2006                           2.7%          7.2%
2007                           5.3%         -5.1%
2008                         -21.9%       -22.2%
2009                           5.6%         18.5%
2010                          15.5%         -0.7%

The favorable days were clear winners in three of the six years. In 2006 and 2009, the per-day return was roughly equal on favorable and unfavorable days (remember that there are many more unfavorable days than favorable days). In 2008, the favorite was beaten as the per-day return of the favorable days was much worse than the unfavorable days. Over the entire period, S&P 500 returns were 9% on favorable days and -9% on unfavorable days.

Lars van Dort comments:

A slightly adopted version of Mr. Fosback's hypothesis of favorable days was tested by me for the Dutch stock market using the CBS Reinvestment Index for the period 1981-2003.

My definition of favorable days only included the last trading day of the month and the first four trading days of a new month. I excluded the two days before the market is closed for a holiday from the definition. (There are different holidays over here and frankly it would be a lot of work to identify them for the whole sample).

In this case favorable days account for 23% of all trading days, as opposed to 28% in Mr. Fosback's definition.

The results:

average return favorable day: 0.16% average return unfavorable day: 0.03%

Over the full sample, being long only on favorable days leads to a cumulative return of 714%. For the unfavorable days this was only 144%, while taking more than 3x as many trading days for this.

Of course, I'm aware of ever-changing cycles, but if this result would still hold, things would be very easy. Buy at close of the next-to-last trading day of a month. Sell at close of the fourth trading day of a month.


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