This post was originally made on April 18, 2006 on a former blog of mine. I will update the numbers through 2007 when I have time. I will also add Total Return.

Most longer term investors have always heard the old mantra that the majority of long term gains have come in very few days (say 90) and that if you missed those days you would miss a substantial return. This is one popular argument on the “buy and hold” side of the fence.

Back in December I decided to look at some of these market dynamics. I downloaded the S&P 500 data from Yahoo Finance and ran some numbers that might interest you.

The data only goes back to 1950 (the actual S&P 500 did not start until 1957). There were 14,090 trading days during that time. Of those, 52.5% were UP days, 46.4% were DOWN days, and 1.1% were no change. If you factor in the daily highs and lows the truth is that at any one point in time you have about a 50/50 shot of randomly entering the market on an up day. The AVERAGE daily return is only 0.035% with a standard deviation of 0.895%. This means roughly 68% of all the daily return figures fell between .93% and -.86%. 95% fell between 1.83% and -1.76%.

The compound return for that period (not including dividend reinvestment) was 8.01%. If you remove the top 100 best days the compound return drops down to an extremely poor 1.49%. If you remove the worst 100 days the compound return is a handsome 15.37%.

The extreme days mentioned above (top 100 and worst 100 days) started at roughly +/- 3 standard deviations. While trying to devise an algorithm to avoid the down days I noticed something peculiar about these extreme days. They all seemed to be clustered together. In fact roughly 1/2 of all extreme days come within 15 days of another extreme day (either up or down).

What does that mean? Unless your crystal ball is fine tuned, avoiding the down days will also involve avoiding the up days. In fact, if you remove both the top 100 and worst 100 days, the compound interest rate becomes 8.41% for the data. Only slightly better than not avoiding them at all.

An example - the worst day of all, October 19, 1987 (-20.47%) was immediately followed by two of the top 4 best days October 20, 1987 (+5.33%) and October 21, 1987 (+9.10%).

To my surprise, a few days after I made this intuitive discovery I happened upon the book, The (Mis) Behavior of Markets by Benoit Mandlebrot the father of fractal geometry. In his book he talks about this clustering of extreme days.

I will leave you with this notion from his book. Volatility is Volatile. Extreme periods of volatility have a large probability of spawning more extreme days.

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