Is the stock market predictable or inherently unpredictable? If you believe Nassim Taleb, author of The Black Swan, trying to predict the market is not only impossible, it is also a very risky proposition. I recently finished reading this thought provoking book and a number of interesting points stuck with me. One of these key points is Taleb's claim that the stock market is "Mandelbrotian" by nature, i.e. daily returns in the market are not "normally distributed", they don't follow a neat Gauss-like distribution, where daily returns don't stray too much from the average daily return.
Taleb's claim - which I tested for myself (but more about that in a second) - is that stock returns are "scale free". While on most days returns in the market remain in a relatively tight range, once in a while, a Black Swan strikes. A Black Swan is a completely unexpected event that greatly impacts the market in unforeseen ways, resulting in dramatic up or down days. These rare but dramatic events account for a large percentage of stock market returns over the long term.
I must admit that my assumption (even though I never really articulated it) was that while on a daily basis the market can swing up or down, these swings are largely confined to a pretty narrow range that would fall more or less neatly on a normal distribution curve. Well, Taleb claims (and I checked) that this is not the case.
Those that dislike statistics can skip this next paragraph, but for the rest of you, here goes: from Yahoo! Finance, I downloaded the daily returns for the S&P500 from January 3, 1950 to December 4, 2009. Almost 60 years of data. Through the miracle of Excel, I calculated the daily returns on the S&P500 (using closing prices in each case). From this population I calculated the average daily return (0.033%) and the standard deviation (0.966%). I then proceeded to calculate the z-score for each daily return figure. I won't bore you with all the results and analysis, but here are a few eye openers:
- I found a total of 90 days in which the z-score of daily returns exceeded 4 or -4. If stock market returns are normally distributed, we would expect to see one such event every approximately 143 year...
- I also found a total of 24 days in which the z-score of daily returns exceeded 6 or -6. Once again, if stock market returns were normally distributed we would expect to see one such event every approx. 4.6 million years...
- now here's a real doozy: on October 19, 1987 the S&P fell about 20.4% which translates to a z-score of -21.2 or one event every approximately... wait for it... 10 to the power of 93 years. For the sake of comparison, the age of the universe is estimated to be approximately 14.3 times 10 to the power of 17 seconds (or about 6000 years if you choose to get your information from certain unreliable sources). Another comparison point: the number of atoms in the universe is estimated to be approximately 10 to the power of 80...
Point spectacularly made. Stock market returns are NOT normally distributed.
Now, what are the implications of this discovery and what are we to do about it? Well, to be honest with you, I don't think I have good answers to this, but I will do my best to take a crack at some sort of answer over the next couple of days. Stay tuned.
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