The move in Apple’s stock over the past few years has been nothing short of unbelievable – going from $90 at the start of ’09 to near $600 today (566% gain), and from $400 just a short two and a half months ago (50% gain). But if you looked at all of the data from all of the stocks ever traded, you would likely find that the average stock rises about 10% to 15% over a three year period (we didn’t do this, but that would be our guess, and serves for purposes of this example). The odds of a stock doing what Apple has just done would be on the order of 1 in a million or so according to standard statistical methods.
But here’s the thing – these types of outlier moves (both up and down) happen way more frequently than once every million times, highlighting one of the often forgotten aspects of the investment world, that financial matters are not normally distributed. That is, you can’t use normal statistical measures (even when using the actual outlier data…) to make observations about what may happen moving forward. Here’s what we had to say about it in a 2010 newsletter:
Now, normally distributed is a statistical term meaning that any observations we see in a data set will be in a bell curve shape, with roughly 68% of the data points being 1 standard deviation above or below the average, and 95% being within 2 standard deviations of the average, and virtually no data points outside of 3 standard deviations above or below the average (just .027%).
Problem is – financial market returns are not normally distributed. If 2008 didn’t teach us that, consider the double digit sigma move during the flash crash on May 6th of this year, or the mother of all normal distribution killing moves – Black Monday in October of 1987. Using a normal distribution curve, there was a 1 in a trillion chance of prices being down more than 6% on 10/21/87, yet they fell -20% in a singled session.
Nassim Taleb, author of the fabulous book Black Swan separates normally distributed and non-normally distributed by saying that which belongs to normally distributed curves exists in mediocristan, and everything else exists in a place called extremistan. Unfortunately for the efficient frontier and any financial models assuming a normal curve – we live in extremistan!
Take the distribution of wealth as compared to the distribution of human height as an example. Consider that the tallest human ever recorded was 8’ 11”, or about 1.6 times the average, and 10 standard deviations outside of the average.
Now consider Bill Gates and his net worth of about $54 Billion. How tall do you think a person would have to be so that they are as much over the average in height, as Bill Gates is over the average in wealth? 10ft tall? 50? 1000? Would you believe 1.6 million feet, or 303 miles, tall… which is about the length of Lake Michigan. That is how much greater Bill Gates’ wealth is than the average American. He should literally not exist in a world which is normally distributed, being thousands of standard deviations above the average. But he does exist, and those $54 Billion are really his, making it painfully obvious for those of us down there within a few standard deviations of the mean that we are in fact in extremistan.
We’ll hope you forgive us for talking about Apple’s stock and Bill Gates in the same post… but the point remains whether you are talking about the former tech champion Microsoft’s leader’s net worth, or the price of the stock of the new tech leader – financial markets are NOT NORMALLY DISTRIBUTED. In the financial world, you are just as likely to run into a “300 mile tall man” as you are a “1 inch tall person.”