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The Fourth Quadrant: No Realm for the Normal

| | Posted in: Big Ideas

New sample points from the past two months are substantially shifting correlations in several our past analyses of relationships between indicators and future stock returns (published updates pending). Here are some recent relevant observations from Nassim Taleb’s September 2008 essay in Edge entitled “The Fourth Quadrant: A Map of the Limits of Statistics”. In the aftermath of the collapse of Fannie Mae, Bear Stearns and Lehman Brothers, he observes that:

“…not only have economists been unable to prove that their models work, but no one managed to prove that the use of a model that does not work is neutral, that it does not increase blind risk taking, hence the accumulation of hidden risks.”

“…if you look long enough almost all the contribution [to statistical metrics] in some classes of variables will come from rare events…”

“Fourth Quadrant [complex payoffs from fat-tailed distributions]: …Welcome to the Black Swan domain. Here is where your limits are. Do not base your decisions on statistically based claims.”

“For rare events, the confirmation bias (the tendency…of finding samples that confirm your opinion, not those that disconfirm it) is very costly and very distorting. Why? Most of histories of Black Swan prone events is going to be Black Swan free! Most samples will not reveal the black swans except after if you are hit with them…”

“What Is Wise To Do (Or Not Do) In The Fourth Quadrant

  1. Avoid optimization, learn to love redundancy. …redundancy is like long an option. You certainly pay for it, but it may be necessary for survival.
  2. Avoid prediction of…payoffs from remote parts of the distribution. …no model should be better than just any model.
  3. Beware the ‘atypicality’ of remote events.
  4. It takes much, much longer for a time series in the Fourth Quadrant to reveal its properties. At the worst, we don’t know how long.
  5. Beware moral hazard…[a] series of bonuses betting on [or against] hidden risks in the Fourth Quadrant…
  6. [Beware] conventional metrics… [Metrics] like “standard deviation” are not stable and do not measure anything in the Fourth Quadrant. [Likewise] “linear regression“…, “Sharpe ratio“, Markowitz optimal portfolio, ANOVA…, least squares, etc.
  7. Where is the skewness? If we suspect right [(left)]-skewness, the true mean is more likely to be underestimated [(overestimated)] by measurement of past realizations, and the total potential is likewise poorly gauged.
  8. Do not confuse absence of volatility with absence of risks.
  9. Beware presentations of risk numbers. …risk perception is subjected to framing issues that are acute in the Fourth Quadrant.”

For elaboration, read the entire essay.

In summary, “normal” statistical metrics and associated risk management methods do not work in the realm of Black Swans (including financial markets). Redundancy, not optimization, helps manage risk in this realm.

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