Fat Tails and Risk Estimate Distortions
By contrast to fat tail distributions, the normal distribution posits events that deviate from the mean by five or more standard deviations ("5-sigma event") are extremely rare, with 10- or more sigma being practically impossible. On the other hand, fat tail distributions such as the Cauchy distribution (and all other stable distributions with the exception of the normal distribution) are examples of fat tail distributions that have "infinite sigma" (more technically: "the variance does not exist").
Thus when data naturally arise from a fat tail distribution, shoehorning the normal distribution model of risk—and an estimate of the corresponding sigma based necessarily on a finite sample size—would severely understate the true risk. Many—notably Benoît Mandelbrot as well as Nassim Taleb—have noted this shortcoming of the normal distribution model and have proposed that fat tail distributions such as the stable distribution govern asset returns frequently found in finance.
The Black–Scholes model of option pricing is based on a normal distribution. If the distribution is actually a fat-tailed one, then the model will under-price options that are far out of the money, since a 5 or 7 sigma event is much more likely than the normal distribution would predict.
Read more about this topic: Fat Tails
Famous quotes containing the words fat, tails, risk and/or estimate:
“Call the bald man, “Boy;” make the sage thy toy;
Greet the youth with solemn face; praise the fat man for his grace.”
—Helen Rowland (1875–1950)
“All along the backwater,
Through the rushes tall,
Ducks are a-dabbling,
Up tails all!”
—Kenneth Grahame (1859–1932)
“The Englishman’s strong point is his vigorous insularity; that of the American his power of adaptation. Each of these attitudes has its perils. The Englishman stands firmly on his feet, but he who merely does this never advances. The American’s disposition is to step forward even at the risk of a fall.”
—Thomas Wentworth Higginson (1823–1911)
“Shall we then judge a country by the majority, or by the minority? By the minority, surely. ‘Tis pedantry to estimate nations by the census, or by square miles of land, or other than by their importance to the mind of the time.”
—Ralph Waldo Emerson (1803–1882)