Taleb Distribution
   HOME

TheInfoList



OR:

In
economics Economics () is the social science that studies the production, distribution, and consumption of goods and services. Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analyzes ...
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 Martin Harry Wolf (born 16 August 1946 in London) is a British journalist of Austrian-Dutch descent who focuses on economics. He is the associate editor and chief economics commentator at the ''Financial Times''. Early life Wolf was born in ...
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 ''Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets'' is a book by Nassim Nicholas Taleb that deals with the fallibility of human knowledge. It was first published in 2001. Updated editions were released a few years later. ...
''. 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 Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speakin ...
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 In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with respect to something that humans value (such as health, well-being, wealth, property or the environm ...
and steady
returns Return may refer to: In business, economics, and finance * Return on investment (ROI), the financial gain after an expense. * Rate of return, the financial term for the profit or loss derived from an investment * Tax return, a blank document or t ...
. It is a combination of
kurtosis risk In statistics and decision theory, kurtosis risk is the risk that results when a statistical model assumes the normal distribution, but is applied to observations that have a tendency to occasionally be much farther (in terms of number of standar ...
and
skewness risk Skewness risk in financial modeling is the risk that results when observations are not spread symmetrically around an average value, but instead have a skewed distribution. As a result, the mean and the median can be different. Skewness risk ca ...
: 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 Business cycles are intervals of expansion followed by recession in economic activity. These changes have implications for the welfare of the broad population as well as for private institutions. Typically business cycles are measured by examini ...
. 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 The ''Journal of Behavioral Finance'' is a quarterly peer-reviewed academic journal that covers research related to the field of behavioral finance. It was established in 2000 as ''The Journal of Psychology and Financial Markets''. The founding ...
'' 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 risk of ruin that approaches eventual certainty over time. 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 A hedge fund is a pooled investment fund that trades in relatively liquid assets and is able to make extensive use of more complex trading, portfolio-construction, and risk management techniques in an attempt to improve performance, such as sho ...
.


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 An economic bubble (also called a speculative bubble or a financial bubble) is a period when current asset prices greatly exceed their intrinsic valuation, being the valuation that the underlying long-term fundamentals justify. Bubbles can be ...
, 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 Kay has likened
securities trading A security is a tradable financial asset. The term commonly refers to any form of financial instrument, but its legal definition varies by jurisdiction. In some countries and languages people commonly use the term "security" to refer to any for ...
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 is the action of a driver driving behind another vehicle while not leaving sufficient distance to stop without causing a collision if the vehicle in front stops suddenly. The safe distance for following another vehicle varies depend ...
, 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 The carry of an asset is the return obtained from holding it (if positive), or the cost of holding it (if negative) (see also Cost of carry). For instance, commodities are usually negative carry assets, as they incur storage costs or may suffer fro ...
and has claimed that along with
mark-to-market accounting Mark-to-market (MTM or M2M) or fair value accounting is accounting for the " fair value" of an asset or liability based on the current market price, or the price for similar assets and liabilities, or based on another objectively assessed "fai ...
and other practices, constitute part of what
John Kenneth Galbraith John Kenneth Galbraith (October 15, 1908 – April 29, 2006), also known as Ken Galbraith, was a Canadian-American economist, diplomat, public official, and intellectual. His books on economic topics were bestsellers from the 1950s through t ...
has called "innocent fraud".


Moral hazard

Some critics of the
hedge fund A hedge fund is a pooled investment fund that trades in relatively liquid assets and is able to make extensive use of more complex trading, portfolio-construction, and risk management techniques in an attempt to improve performance, such as s ...
industry claim that the compensation structure generates high fees for
investment strategies In finance, an investment strategy is a set of rules, behaviors or procedures, designed to guide an investor's selection of an investment Portfolio (finance), portfolio. Individuals have different profit objectives, and their individual skills make ...
that follow a Taleb distribution, creating
moral hazard In economics, a moral hazard is a situation where an economic actor has an incentive to increase its exposure to risk because it does not bear the full costs of that risk. For example, when a corporation is insured, it may take on higher risk ...
. 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. ;unobserved events: This is Taleb's central contention, which he calls
black swans Black swan is the common name for ''Cygnus atratus'', an Australasian waterfowl. (The) Black Swan(s) may also refer to: Film and television * ''The Black Swan'' (film), a 1942 swashbuckler film * ''Black Swans'' (film), a 2005 Dutch drama film * ...
– because extreme events are rare, they have often not been observed yet, and thus are not included in
scenario analysis Scenario planning, scenario thinking, scenario analysis, scenario prediction and the scenario method all describe a strategic planning method that some organizations use to make flexible long-term plans. It is in large part an adaptation and gener ...
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 In finance, leverage (or gearing in the United Kingdom and Australia) is any technique involving borrowing funds to buy things, hoping that future profits will be many times more than the cost of borrowing. This technique is named after a lever ...
: 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 refers to epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable ...
, in economics called
Knightian uncertainty In economics, Knightian uncertainty is a lack of any quantifiable knowledge about some possible occurrence, as opposed to the presence of quantifiable risk (e.g., that in statistical noise or a parameter's confidence interval). The concept acknow ...
.


Mitigants

A number of mitigants have been proposed, by Taleb and others. These include: ;not exposing oneself to large losses using the
barbell strategy In finance, a barbell strategy is formed when a trader invests in long- and short-duration bonds, but does not invest in intermediate-duration bonds. This strategy is useful when interest rates are rising; as the short term maturities are rolled o ...
: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 Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be divided and allocated to different sources of uncertainty in its inputs. A related practice is uncertainty anal ...
on assumptions: This does not eliminate the risk, but identifies which assumptions are key to conclusions, and thus meriting close scrutiny. ;
scenario analysis Scenario planning, scenario thinking, scenario analysis, scenario prediction and the scenario method all describe a strategic planning method that some organizations use to make flexible long-term plans. It is in large part an adaptation and gener ...
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 Decision theory (or the theory of choice; not to be confused with choice theory) is a branch of applied probability theory concerned with the theory of making decisions based on assigning probabilities to various factors and assigning numerical ...
is based on probabilistic techniques of expected value or
expected utility The expected utility hypothesis is a popular concept in economics that serves as a reference guide for decisions when the payoff is uncertain. The theory recommends which option rational individuals should choose in a complex situation, based on the ...
, alternatives exist which do not require assumptions about the probabilities of various outcomes, and are thus
robust Robustness is the property of being strong and healthy in constitution. When it is transposed into a system, it refers to the ability of tolerating perturbations that might affect the system’s functional body. In the same line ''robustness'' ca ...
. These include minimax,
minimax regret In decision theory, on making choice, decisions under uncertainty—should information about the best course of action arrive ''after'' taking a fixed decision—the human emotional response of regret is often experienced, and can be measured as th ...
, and
info-gap decision theory Info-gap decision theory seeks to optimize robustness to failure under severe uncertainty,Yakov Ben-Haim, ''Information-Gap Theory: Decisions Under Severe Uncertainty,'' Academic Press, London, 2001.Yakov Ben-Haim, ''Info-Gap Theory: Decisions Unde ...
. ;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. For example, paying banks staff in long-term stock options in their bank rather than in cash bonuses. ;adding to asset allocation a strategy with a holy grail distribution of returns:Adding a complementary strategy with a performance pattern that helps reduce the impact of market performance shocks (holy grail distribution)


See also

*
Fat-tailed distribution A fat-tailed distribution is a probability distribution that exhibits a large skewness or kurtosis, relative to that of either a normal distribution or an exponential distribution. In common usage, the terms fat-tailed and heavy-tailed are someti ...
*
Gambler's ruin The gambler's ruin is a concept in statistics. It is most commonly expressed as follows: A gambler playing a game with negative expected value will eventually go broke, regardless of their betting system. The concept was initially stated: A per ...
*
Holy grail distribution In economics and finance, a holy grail distribution is a probability distribution with positive mean and right fat tail — a returns profile of a hypothetical investment vehicle that produces small returns centered on zero and occasionally exhi ...
*
Kurtosis risk In statistics and decision theory, kurtosis risk is the risk that results when a statistical model assumes the normal distribution, but is applied to observations that have a tendency to occasionally be much farther (in terms of number of standar ...
*
Skewness risk Skewness risk in financial modeling is the risk that results when observations are not spread symmetrically around an average value, but instead have a skewed distribution. As a result, the mean and the median can be different. Skewness risk ca ...
*'' The Black Swan: The Impact of the Highly Improbable''


References

{{Nassim Nicholas Taleb Financial risk Mathematical finance Types of probability distributions Nassim Nicholas Taleb