In statistics, the best-known distribution measure is the normal distribution, often referred to as the bell curve because of its shape. The normal distribution is characterized by the majority of observations showing up in the middle of the curve and gradually falling off as you move up or down from the mean. This fine statistical tool lets me know that I am taller than about 41% of the U.S. male population -- or shorter than 59%, if you prefer to look at it that way.
When using a normal distribution, statisticians typically measure out two standard deviations from the mean in either direction, since this covers 95% of the observations in a normal distribution. As you look further out past two standard deviations on either side, the outcomes covered grow increasingly unlikely. In my example of male height, 95% of the U.S. male population falls roughly between 5'5'' and 6'2''. Once you start getting into NBA-type heights, you're talking about much smaller probabilities. That's why Sean Bradley and Manute Bol are so fascinating -- at 7'7'' and 7'6'', respectively, they are nearly 10 standard deviations away from the mean, a serious statistical improbability.
Stocks -- not so normal
Natural phenomena such as earthquakes and weather patterns have been shown to sport distributions outside the standard normal distribution. Observations in these areas do fall for the large part within the plus-or-minus-two standard deviation range, but there are far more occurrences of events outside this range than would be predicted by a normal distribution. Because of this, events such as Hurricane Katrina or the earthquake that caused the Asian tsunami not only happen, but also happen with a relatively high frequency.
Stock-market returns have been very much akin to these natural events, exhibiting a similar "fat tail" distribution. So while a majority of stock movements happen within the expected range, there are a lot of observations outside this range. Most of us are familiar with one such event -- the big crash of October 1987, an event that was around 30 standard deviations away from the average single-day change in the S&P. Unlikely market movements like this, though of somewhat smaller magnitude, happen quite often. In other words, when it comes to your portfolio in the short term, expect the unexpected.
Enter the 5-sigma
No, 5-sigma is not a new Star Trek spacecraft, and it also shouldn't be confused with Motorola's Six Sigma method for managing process variations. I'm simply using 5-sigma to refer to events that happen five standard deviations away from the mean on either side. In a standard normal distribution, an event that occurs five standard deviations or more from the mean has about a 1 in 3,488,555 chance in happening -- fairly unlikely, in other words. Yet plenty of stocks have seen more than their fair share of these lightning strikes.
KOS
Pharmaceuticals'
"OK," you're probably saying, "that's a gimme -- it's a volatile drug company, and it's now being acquired." With that in mind, I looked at a few other names. First Marblehead
The lightning rod of patience
I look at this as another vote for taking a long-term view on my portfolio. With the potential for stocks to be so drastically revalued in these quick, single-day spikes, it doesn't seem to make much sense to jump in and out of a stock as the wind blows -- missing even one day could seriously hurt my returns.
Using Cisco as an example, if you bought the stock last November and held it until Aug. 8 of this year, you might have been pretty disappointed with your -3% return. Hang on to that sucker one more day, though, and your 3% loss is suddenly a 10% gain -- not a bad nine-month performance all in one trading day. Or, even better, a look at Akamai
Even if you stay away from individual stocks and stick to the broader-market index funds, the results are no different. Over the past 56 years, the S&P 500 has seen 52 days with 5-sigma or greater movement, and three days in 1987 with changes that were 10-sigma or greater. Over the past five years, if you had invested in the S&P and held on to it, you would've seen a 23% return, or roughly 4% annually, not exactly something to get excited about. But if, instead of holding, you were jumping in and out and managed to miss the eight 5-sigma days (two of which were negative) over that time frame, then your annual return is slashed to 1%, a certifiably terrible performance.
So regardless of whether patience truly is a virtue, it certainly seems to be a friend of the investor when navigating the choppy waters of the stock market. That is unless, of course, you are clairvoyant and know when all of the big moves are coming.
If that's the case, though, I have to question why you're even reading this in the first place.
More patient Foolishness:
Johnson & Johnson is a Motley Fool Income Investor selection. Akamai Technologies is a Motley Fool Rule Breakers pick. First Marblehead is a Motley Fool Hidden Gems recommendation. Try out these or any of our other investing newsletter services free for 30 days.
Fool contributor Matt Koppenheffer rarely has the patience to let the microwave finish cooking before he pulls out his food. He does, however, aim to show a bit more self-control when working with Mr. Market. He does not own shares of any of the companies mentioned. The Fool's disclosure policy has far surpassed a Six Sigma level of greatness.
