The Black Swan: The Impact of the Highly Improbable

Fitting processes:for the philosophy of the problem, Taleb and Pilpel (2004). See also Pisarenko and Sornette (2004), Sornette et al. (2004), and Sornette and Ide (2001).

Poissonjump:sometimes people propose a Gaussian distribution with a small probability of a “Poisson” jump. This may be fine, but how do you know how large the jump is going to be? Past data might not tell you how large the jump is.

FIGURE 15: TYPICAL DISTRIBUTION WITH POWER-LAW TAILS (HERE A STUDENT T)

FIGURE 16

The two exhaustive domains of attraction: vertical or straight line with slopes either negative infinity or constant negative a. Note that since probabilities need to add up to 1 (even in France) there cannot be other alternatives to the two basins, which is why I narrow it down to these two exclusively.

My ideas are made very simple with this clean cut polarization—added to the problem of not knowing which basin we are in owing to the scarcity of data on the far right.

Small sample effect:weron (2001). officer (1972) is quite ignorant of the point.

Recursivity of statistics:taleb and pilpel (2004), blyth et al. (2005).

Biology:modern molecular biology pioneers Salvador Luria and Max Delbruck witnessed a clustering phenomenon with the occasional occurrence of extremely large mutants in a bacterial colony, larger than all other bacteria.

Thermodynamics:entropy maximization without the constraints of a second moment leads to a Levy-stable distribution—Mandelbrot’s thesis of 1952 (see Mandelbrot [1997a]). Tsallis’s more sophisticated view of entropy leads to a Student T.

Imitation chains and pathologies:an informational cascade is a process where a purely rational agent elects a particular choice ignoring his own private information (or judgment) to follow that of others. You run, I follow you, because you may be aware of a danger I may be missing. It is efficient to do what others do instead of having to reinvent the wheel every time. But this copying the behavior of others can lead to imitation chains. Soon everyone is running in the same direction, and it can be for spurious reasons. This behavior causes stock market bubbles and the formation of massive cultural fads. Bikhchandani et al. (1992). In psychology, see Hansen and Donoghue (1977). In biology/selection, Dugatkin (2001), Kirpatrick and Dugatkin (1994).

Self-organized criticality:bak and chen (1991), bak (1996).

Economic variables:bundt and murphy (2006). most economic variables seem to follow a “stable” distribution. They include foreign exchange, the GDP, the money supply, interest rates (long and short term), and industrial production.

Statisticians not accepting scalability:flawed reasoning mistaking for sampling error in the tails for a boundedness: Perline (2005), for instance, does not understand the difference between absence of evidence and evidence of absence.

Time series and memory:you can have “fractal memory,” i.e., the effect of past events on the present has an impact that has a “tail.” It decays as power-law, not exponentially.

Marmott’s work:marmott (2004).

CHAPTER 18

Economists:weintraub (2002), Szenberg (1992).

Portfolio theory and modernfinance:markowitz (1952, 1959), huang and Litzenberger (1988) and Sharpe (1994, 1996). What is called the Sharpe ratio is meaningless outside of Mediocristan. The contents of Steve Ross’s book (Ross [2004]) on “neoclassical finance” are completely canceled if you consider Extremistan in spite of the “elegant” mathematics and the beautiful top-down theories. “Anecdote” of Merton minor in Merton (1992).

Obsession with measurement:crosby (1997) is often shown to me as convincing evidence that measuring was a great accomplishment not knowing that it applied to Mediocristan and Mediocristan only. Bernstein (1996) makes the same error.

Power laws infinance:mandelbrot (1963), Gabaix et al. (2003), and Stanley et al. (2000). Kaizoji and Kaizoji (2004), Véhel and Walter (2002). Land prices: Kaizoji (2003). Magisterial: Bouchaud and Potters (2003).

Equity premium puzzle:if you accept fat tails, there is no equity premium puzzle. Benartzi and Thaler (1995) offer a psychological explanation, not realizing that variance is not the measure. So do many others.

Covered writes:a sucker’s game as you cut your upside—conditional on the upside being breached, the stock should rally a lot more than intuitively accepted. For a representative mistake, see Board et al. (2000).

Nobel family:“nobel Descendant Slams Economics Prize,” The Local, September 28, 2005, Stockholm.