"I can state the supreme law of Mediocristan as follows: When your sample is large, no instance will significantly change the aggregate or the total. In Extremistan, inequalities are such that one single observation can disproportionately impact the aggregate, or the total." Nassim Nicholas Taleb

On "The Black Swan" N.N.Taleb elaborates extensively on the limits of forecasting in the fat-tailed land of extremistan, to which economic variables such as earnings and dividends belong. Part of the reason is based on the faulty cognitive gear we humans have been endowed with by evolution; part of it is due to the extremely lumpy nature of economic variables that, among other things, tend to exhibit high kurtosis. The higher the kurtosis, the more irrelevant measures of dispersion (StdDev & Var) become. The higher the kurtosis, the higher the uncertainty and the higher our error rate becomes when trying to forecast economic variables.

We've all seen how stock prices tend to exhibit high kurtosis (with freak events as the 23-sigma crash of 1987), falsifying thereby any theory that assumes Gaussian distributions such as CAPM and BlackScholesMerton.

To analyze and forecast price behavior is, to a great extent, the study of the market's expectations. But what about the underlying economic variables that prices try to estimate? Here I show you some really interesting numbers anyone can compute relating to the statistical behavior of the S&P 500's dividends and earnings change throughout time. I think that constantly reminding me of these figures makes a humbler, more rational investor.

----------------------------------

DIVIDENDS:

Mean= 3.92%

StdDev= 11.16%

Skewness= -0.09

Kurtosis= 6.03%

----------------------------------

EARNINGS:

Mean= 9.21%

StdDev= 53.05%

Skewness= 10.37

**Kurtosis= 140.60** <====== O__O!

----------------------------------

[Source: www.econ.yale.edu/~shiller/data.htm]

[Statistical Computation performed with STATA]

In the last 140 years of financial history, the average earnings' year-to-year growth has been of 9.21%. Dividends grew, on average, about 3.92% a year. But how relevant are these figures when it comes to forecasting future earnings/dividends/cashflows? Orthodox financial theory would mislead you to look for the standard deviation of each respective time series. But to do that, you first need to assume that standard deviation is not completely irrelevant. How to figure that out? A simple rule of thumb is to look at kurtosis. If excess kurtosis is high enough, the more irrelevant variance becomes owing to the large impact that rare events can carry when they take place.

I find the earnings kurtosis to be an extremely interesting datum. Earnings exhibit a kurtosis of 140, which is insanely high, reflecting the disturbingly uncertain nature of corporate profits. More importantly, company management can [and almost always do] perform earnings smoothing. But as analysts what we actually care about are cashflows. Cashflows, too, can be "managed" in the way earnings are, but generally to a smaller degree. Cashflows effectively are more volatile, making me guess that cashflows' kurtosis is even higher than the earnings' 140 kurtosis.

When you buy a stock, you're buying a fractional ownership in the company's profits. Value investing involves figuring out how much a business is worth, and buying its stock for a lower price. But can you reliably value a company's future cashflows, when they exhibit a kurtosis of 140 or higher? Of course not! On an aggregate level, such as the S&P 500, or the macroecon, is pretty much unpredictable. You may get it fairly right 9 out of 10 times. But when you fail, you will usually fail severely bad, making your error rate monstrous.

Furthermore, when you try to value a single business (and not the S&P aggregate) statistics teaches us that estimating 1 single event (single company's results) will always carry a higher error margin than estimating an average (the performance of a collection of companies that even each other out because of imperfect correlation).

I don't think this means one should abandon the investing business altogether, but it definitely means that we should seriously consider what circle of competence means for us as business analysts. We all know that we should stick to our circle of competence. Warren Buffett (aka "The Lord") claims he doesn't understand 90% of the businesses out there trading in the markets. If Warren's circle of competence is about 10%, I guess my prospects as a mere mortal are definitely below that.

Takeaway: Don't undervalue your circle of competence and margin of safety, DO UNDERVALUE your skills. Because odds are that the overconfidence cognitive heuristic is always lurking in the back office of your mind. ^^

Peace!