Mathematical finance | Types of probability distributions
Taleb distribution
In economics and finance, a Taleb distribution is the statistical profile of an investment which normally provides a payoff of small positive returns, while carrying a small but significant risk of catastrophic losses. The term was coined by journalist Martin Wolf and economist John Kay to describe investments with a "high probability of a modest gain and a low probability of huge losses in any period." The concept is named after Nassim Nicholas Taleb, based on ideas outlined in his book Fooled by Randomness. According to Taleb in Silent Risk, the term should be called "payoff" to reflect the importance of the payoff function of the underlying probability distribution, rather than the distribution itself. The term is meant to refer to an investment returns profile in which there is a high probability of a small gain, and a small probability of a very large loss, which more than outweighs the gains. In these situations the expected value is very much less than zero, but this fact is camouflaged by the appearance of low risk and steady returns. It is a combination of kurtosis risk and skewness risk: overall returns are dominated by extreme events (kurtosis), which are to the downside (skew). Such kind of distributions have been studied in economic time series related to business cycles. More detailed and formal discussion of the bets on small probability events is in the academic essay by Taleb, called "Why Did the Crisis of 2008 Happen?" and in the 2004 paper in the Journal of Behavioral Finance called "Why Do We Prefer Asymmetric Payoffs?" in which he writes "agents risking other people’s capital would have the incentive to camouflage the properties by showing a steady income. Intuitively, hedge funds are paid on an annual basis while disasters happen every four or five years, for example. The fund manager does not repay his incentive fee." (Wikipedia).
