Taleb Distribution
Encyclopedia
In economics
and finance
, a Taleb distribution is a term coined by U.K. economists/journalists Martin Wolf
and John Kay
to describe a returns profile that appears at times deceptively low-risk with steady returns, but experiences periodically catastrophic drawdowns. It does not describe a statistical probability distribution
, and does not have an associated mathematical formula. 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). The corresponding situation is also known as the peso problem.
The term describes dangerous or flawed trading strategies. The Taleb distribution is named after Nassim Taleb
, based on ideas outlined in his Fooled by Randomness
. 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."
This has also been referred to as "picking up pennies in front of a steamroller".
has likened securities trading to bad driving, as both are characterized by Taleb distributions. Drivers can make many small gains in time by taking risks such as overtaking on the inside and tailgating
, however, they are then at risk of experiencing a very large loss in the form of a serious traffic accident. Kay has described Taleb Distributions as the basis of the carry trade and has claimed that along with mark-to-market accounting and other practices, constitute part of what JK Galbraith has called "innocent fraud".
industry claim that the compensation structure generate high fees for investment strategies
that follow a Taleb distribution, creating moral hazard
. In such a scenario, the fund can claim high asset management and performance fees until they suddenly 'blow up', losing the investor significant sums of money and wiping out all the gains to the investor generated in previous periods; however, the fund manager keeps all fees earned prior to the losses being incurred – and ends up enriching himself in the long run because he does not pay for his losses.
presence of extreme adverse events: The very presence or possibility of adverse events may pose a problem per se, which is ignored by only looking at the average case – a decision may be good in expectation (in the aggregate, in the long term), but a single rare event may ruin the investor: one is courting disaster.
unobserved events: This is Taleb's central contention, which he calls black swans
– because extreme events are rare, they have often not been observed yet, and thus are not included in scenario analysis
or stress testing
.
hard-to-compute expectation: A subtler issue is that expectation is very sensitive
to assumptions about probability: a trade with a $1 gain 99.9% of the time and a $500 loss 0.1% of the time has positive expected value; while if the $500 loss occurs 0.2% of the time it has approximately 0 expected value; and if the $500 loss occurs 0.3% of the time it has negative expected value. This is exacerbated by the difficulty of estimating the probability of rare events (in this example one would need to observe thousands of trials to estimate the probability with confidence), and by the use of financial leverage: mistaking a small loss for a small gain and magnifying by leverage yields a hidden large loss.
More formally, while the risks for a known distribution can be calculated, in practice one does not know the distribution: one is operating under uncertainty
, in economics called Knightian uncertainty
.
not exposing oneself to large losses using the barbell strategy
: For instance, only buying options
(so one can at most lose the premium), not selling them. Many funds have started offering "tail protection" such as the one advocated by Taleb .
performing sensitivity analysis
on assumptions: This does not eliminate the risk, but identifies which assumptions are key to conclusions, and thus meriting close scrutiny.
scenario analysis
and stress testing
: Widely used in industry, they do not include unforeseen events but emphasize various possibilities and what one stands to lose, so one is not blinded by absence of losses thus far.
using non-probabilistic decision techniques: While most classical decision theory
is based on probabilistic techniques of expected value
or expected utility, alternatives exist which do not require assumptions about the probabilities of various outcomes, and are thus robust. These include minimax
, minimax regret, and info-gap decision theory
.
altering pay structure to reduce moral hazard: For workers in the financial industry whose strategies follow a Taleb distribution, linking success to long-term (not cash) rewards, which can be withdrawn in the event of intervening failure.
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
and finance
Finance
"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...
, a Taleb distribution is a term coined by U.K. economists/journalists Martin Wolf
Martin Wolf
Martin Wolf, CBE is a British journalist, widely considered to be one of the world's most influential writers on economics. He is associate editor and chief economics commentator at the Financial Times.-Early life:...
and John Kay
John Kay (economist)
John Kay is a leading British business economist of centrist persuasion.Kay was educated at the Royal High School, Edinburgh University, and Nuffield College, Oxford...
to describe a returns profile that appears at times deceptively low-risk with steady returns, but experiences periodically catastrophic drawdowns. It does not describe a statistical probability distribution
Probability distribution
In probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values....
, and does not have an associated mathematical formula. The term is meant to refer to an investment returns profile in which there is a high probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
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
Expected value
In probability theory, the expected value of a random variable is the weighted average of all possible values that this random variable can take on...
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
Kurtosis risk
Kurtosis risk in statistics and decision theory denotes the fact that observations are spread in a wider fashion than the normal distribution entails...
and skewness risk
Skewness risk
Skewness risk in financial modeling denotes that observations are not spread symmetrically around an average value. As a result, the average and the median can be different...
: overall returns are dominated by extreme events (kurtosis), which are to the downside (skew). The corresponding situation is also known as the peso problem.
The term describes dangerous or flawed trading strategies. The Taleb distribution is named after Nassim Taleb
Nassim Taleb
Nassim Nicholas Taleb is a Lebanese American essayist whose work focuses on problems of randomness and probability. His 2007 book The Black Swan was described in a review by Sunday Times as one of the twelve most influential books since World War II....
, based on ideas outlined in his Fooled by Randomness
Fooled by Randomness
Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets is a book written by Nassim Nicholas Taleb about the fallibility of human knowledge.-Reaction:The book was selected by Fortune as one of the 75 "Smartest Books of All Time."...
. 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."
Criticism of trading strategies
Pursuing a trading strategy with a Taleb distribution yields a high probability of steady returns for a time, but with a near certainty of eventual ruin. This is done consciously by some as a risky trading strategy, while some critics argue that it is done either unconsciously by some, unaware of the hazards ("innocent fraud"), or consciously by others, particularly in hedge funds.Risky strategy
If done consciously, with one's own capital or openly disclosed to investors, this is a risky strategy, but appeals to some: one will want to exit the trade before the rare event happens. This occurs for instance in a speculative bubble, where one purchases an asset in the expectation that it will likely go up, but may plummet, and hopes to sell the asset before the bubble bursts.This has also been referred to as "picking up pennies in front of a steamroller".
"Innocent fraud"
John KayJohn Kay (economist)
John Kay is a leading British business economist of centrist persuasion.Kay was educated at the Royal High School, Edinburgh University, and Nuffield College, Oxford...
has likened securities trading to bad driving, as both are characterized by Taleb distributions. Drivers can make many small gains in time by taking risks such as overtaking on the inside and tailgating
Tailgating
Tailgating is the practice of driving on a road too close to the vehicle in front, at a distance which does not guarantee that stopping to avoid collision is possible...
, however, they are then at risk of experiencing a very large loss in the form of a serious traffic accident. Kay has described Taleb Distributions as the basis of the carry trade and has claimed that along with mark-to-market accounting and other practices, constitute part of what JK Galbraith has called "innocent fraud".
Moral hazard
Some critics of the hedge fundHedge fund
A hedge fund is a private pool of capital actively managed by an investment adviser. Hedge funds are only open for investment to a limited number of accredited or qualified investors who meet criteria set by regulators. These investors can be institutions, such as pension funds, university...
industry claim that the compensation structure generate high fees for investment strategies
Investment strategy
In finance, an investment strategy is a set of rules, behaviors or procedures, designed to guide an investor's selection of an investment portfolio...
that follow a Taleb distribution, creating moral hazard
Moral hazard
In economic theory, moral hazard refers to a situation in which a party makes a decision about how much risk to take, while another party bears the costs if things go badly, and the party insulated from risk behaves differently from how it would if it were fully exposed to the risk.Moral hazard...
. In such a scenario, the fund can claim high asset management and performance fees until they suddenly 'blow up', losing the investor significant sums of money and wiping out all the gains to the investor generated in previous periods; however, the fund manager keeps all fees earned prior to the losses being incurred – and ends up enriching himself in the long run because he does not pay for his losses.
Risks
Taleb distributions pose several fundamental problems, all possibly leading to risk being overlooked:presence of extreme adverse events: The very presence or possibility of adverse events may pose a problem per se, which is ignored by only looking at the average case – a decision may be good in expectation (in the aggregate, in the long term), but a single rare event may ruin the investor: one is courting disaster.
unobserved events: This is Taleb's central contention, which he calls black swans
Black swan theory
The black swan theory or theory of black swan events is a metaphor that encapsulates the concept that The event is a surprise and has a major impact...
– because extreme events are rare, they have often not been observed yet, and thus are not included in scenario analysis
Scenario analysis
Scenario analysis is a process of analyzing possible future events by considering alternative possible outcomes . Thus, the scenario analysis, which is a main method of projections, does not try to show one exact picture of the future. Instead, it presents consciously several alternative future...
or stress testing
Stress testing
Stress testing is a form of testing that is used to determine the stability of a given system or entity. It involves testing beyond normal operational capacity, often to a breaking point, in order to observe the results...
.
hard-to-compute expectation: A subtler issue is that expectation is very sensitive
Sensitivity analysis
Sensitivity analysis is the study of how the variation in the output of a statistical model can be attributed to different variations in the inputs of the model. Put another way, it is a technique for systematically changing variables in a model to determine the effects of such changes.In any...
to assumptions about probability: a trade with a $1 gain 99.9% of the time and a $500 loss 0.1% of the time has positive expected value; while if the $500 loss occurs 0.2% of the time it has approximately 0 expected value; and if the $500 loss occurs 0.3% of the time it has negative expected value. This is exacerbated by the difficulty of estimating the probability of rare events (in this example one would need to observe thousands of trials to estimate the probability with confidence), and by the use of financial leverage: mistaking a small loss for a small gain and magnifying by leverage yields a hidden large loss.
More formally, while the risks for a known distribution can be calculated, in practice one does not know the distribution: one is operating under uncertainty
Uncertainty
Uncertainty is a term used in subtly different ways in a number of fields, including physics, philosophy, statistics, economics, finance, insurance, psychology, sociology, engineering, and information science...
, in economics called Knightian uncertainty
Knightian uncertainty
In economics, Knightian uncertainty is risk that is immeasurable, not possible to calculate.Knightian uncertainty is named after University of Chicago economist Frank Knight , who distinguished risk and uncertainty in his work Risk, Uncertainty, and Profit:- Common-cause and special-cause :The...
.
Mitigants
A number of mitigants have been proposed, by Taleb and others. These include:not exposing oneself to large losses using the barbell strategy
Barbell strategy
In finance, a Barbell strategy is formed when a Trader invests in Long and Short duration bonds, but does not invest in the intermediate duration bonds....
: For instance, only buying options
Option (finance)
In finance, an option is a derivative financial instrument that specifies a contract between two parties for a future transaction on an asset at a reference price. The buyer of the option gains the right, but not the obligation, to engage in that transaction, while the seller incurs the...
(so one can at most lose the premium), not selling them. Many funds have started offering "tail protection" such as the one advocated by Taleb .
performing sensitivity analysis
Sensitivity analysis
Sensitivity analysis is the study of how the variation in the output of a statistical model can be attributed to different variations in the inputs of the model. Put another way, it is a technique for systematically changing variables in a model to determine the effects of such changes.In any...
on assumptions: This does not eliminate the risk, but identifies which assumptions are key to conclusions, and thus meriting close scrutiny.
scenario analysis
Scenario analysis
Scenario analysis is a process of analyzing possible future events by considering alternative possible outcomes . Thus, the scenario analysis, which is a main method of projections, does not try to show one exact picture of the future. Instead, it presents consciously several alternative future...
and stress testing
Stress testing
Stress testing is a form of testing that is used to determine the stability of a given system or entity. It involves testing beyond normal operational capacity, often to a breaking point, in order to observe the results...
: Widely used in industry, they do not include unforeseen events but emphasize various possibilities and what one stands to lose, so one is not blinded by absence of losses thus far.
using non-probabilistic decision techniques: While most classical decision theory
Decision theory
Decision theory in economics, psychology, philosophy, mathematics, and statistics is concerned with identifying the values, uncertainties and other issues relevant in a given decision, its rationality, and the resulting optimal decision...
is based on probabilistic techniques of expected value
Expected value
In probability theory, the expected value of a random variable is the weighted average of all possible values that this random variable can take on...
or expected utility, alternatives exist which do not require assumptions about the probabilities of various outcomes, and are thus robust. These include minimax
Minimax
Minimax is a decision rule used in decision theory, game theory, statistics and philosophy for minimizing the possible loss for a worst case scenario. Alternatively, it can be thought of as maximizing the minimum gain...
, minimax regret, and info-gap decision theory
Info-gap decision theory
Info-gap decision theory is a non-probabilistic decision theory that seeks to optimize robustness to failure – or opportuneness for windfall – under severe uncertainty, in particular applying sensitivity analysis of the stability radius type to perturbations in the value of a given estimate of the...
.
altering pay structure to reduce moral hazard: For workers in the financial industry whose strategies follow a Taleb distribution, linking success to long-term (not cash) rewards, which can be withdrawn in the event of intervening failure.