It’s been three weeks since I last posted. My hard disk drive on my laptop failed and it took dozens of hours to get all my data back. With the stroke of luck, I was able to retrieve everything.
I’m fairly diligent in backing up my files and photos, particularly of my 14-month old son, Viktor. I also have 18 years of my work – research papers, communiqués, spreadsheets and financial models, all of which are personally very valuable.
One night, my wife and I decided to consolidate all the photos and files between our two laptops. In the process of reorganizing the file folders, I cleared my external hard disk back-up drive so that we didn’t have redundant files and copies upon copies of photos. The 12 hours I exposed myself to no back-ups my laptop hard disk drive failed. Years of diligently backing up my files, the one day I risk reformatting the external hard disk drive and boom, my internal hard disk fails. Wow! What are the odds?
The situation reminds of the Black Swan. Former Wall Street stock options trader, Nassim Taleb, wrote his now famous book, The Black Swan, highlighting market risks that most financial models fail to incorporate. In the business, they’re known as fail-tail risk, the event of an event. Taleb correctly pointed out that risk is far greater and more frequent than current financial and statistical models estimate, and that investors fail to assess this catastrophic risk in valuing assets. I wrote about flawed financial modeling in my post, Mea Copula.
An example.
Most financial models use statistics, particularly regression analysis and the normal distribution curve. Generally, regression analysis and normal distribution take a series of data, say, past daily closing stock prices, finds the average daily change within a degree of volatility, known as the standard deviation. Thus, a stock that has an average daily price change of +1% and with a standard deviation of +/-2% should result in a -1% and +3% daily price range. In others words, 68.2% of the time, or just more than two-thirds, said stock is expected to fall within the range of -1% and +3% per day. At two standard deviations, or +/- 4%, the range should account for 95.4% of all daily prices changes around its average. Moving further, six standard deviations, or +/-12% from the average 1% gain, accounts for 99.999999% of all daily closing prices (Six standard deviations is more popularly known as Six Sigma and is also used in quality control of production in effort to keep defects down significantly).
Taleb points out that the fluctuation of stock prices do not fall into a normal distribution that modern financial statistics estimate. There are days that stocks fall more than 20%, perhaps on bad earnings, a labor strike or a sudden product recall, which are known as event risks. There are years that stocks can decline 90%, much like many financials and bank stocks did in 2008. Triggered by an ‘event of an event’ — in this case a perfect storm of the bursting housing bubble, ensuing credit crunch, resulting financial crisis and declining economic growth — stocks were figured to decline by the magnitude they did once in several centuries. Yet we’ve seen stocks collapse much more often – the 1987 Black Tuesday, the Internet Bubble and the recent stock market decline.
Since 1926, as measured by the S&P 500 Index, stocks, on average, increased roughly 10% per year with a standard deviation of about +/-18%. Thus, 68% of the time, the annual S&P 500 change should fall within a -8% and +28% range. At two standard deviations, or 95% of the time, the S&P 500 should fall within a -26% and +46% change. At three standard deviations, or 99.7% of the time, the Index should fall within an annual price change of -44% and +64%. The S&P 500 declined 38% in 2008, and from its October 2007 high of 1565, the S&P 500 fell to a low of 666 in March 2009, a drastic decline of 57%.
The odds of 2008’s stock market decline fall far outside what financial statistics predict. Even the untrained eye can see that. Yet, since the 1950s, Modern Portfolio Theory and financial modeling have for too long underestimated risk.
Just to be certain, I’m saving this post to my back-up drive to protect me from the risk of losing it.
Keep pressing,
Chris Monoki
