Black swan theory - AbsoluteAstronomy.com

The black swan theory or theory of black swan events is a metaphor that encapsulates the concept that The event is a surprise (to the observer) and has a major impact. After the fact, the event is rationalized by hindsight.

The theory was developed by Nassim Nicholas Taleb to explain:

The disproportionate role of high-impact, hard-to-predict, and rare events that are beyond the realm of normal expectations in history, science, finance and technology
The non-computability of the probability of the consequential rare events using scientific methods (owing to the very nature of small probabilities)
The psychological biases that make people individually and collectively blind to uncertainty and unaware of the massive role of the rare event in historical affairs

Unlike the earlier philosophical "black swan problem", the "black swan theory" refers only to unexpected events of large magnitude and consequence and their dominant role in history. Such events, considered extreme outlier

Outlier

In statistics, an outlier is an observation that is numerically distant from the rest of the data. Grubbs defined an outlier as: An outlying observation, or outlier, is one that appears to deviate markedly from other members of the sample in which it occurs....

s, collectively play vastly larger roles than regular occurrences.

Background

Black swan events were characterized by Nassim Nicholas Taleb in his 2007 book (revised and completed in 2010), The Black Swan. Taleb regards almost all major scientific discoveries, historical events, and artistic accomplishments as "black swans"—undirected and unpredicted. He gives the rise of the Internet

Internet

The Internet is a global system of interconnected computer networks that use the standard Internet protocol suite to serve billions of users worldwide...

, the personal computer

Computer

A computer is a programmable machine designed to sequentially and automatically carry out a sequence of arithmetic or logical operations. The particular sequence of operations can be changed readily, allowing the computer to solve more than one kind of problem...

, World War I

World War I

World War I , which was predominantly called the World War or the Great War from its occurrence until 1939, and the First World War or World War I thereafter, was a major war centred in Europe that began on 28 July 1914 and lasted until 11 November 1918...

, and the September 11 attacks as examples of Black Swan Events.

The term black swan derives from a Latin expression—its oldest known reference comes from the poet Juvenal's

Juvenal

The Satires are a collection of satirical poems by the Latin author Juvenal written in the late 1st and early 2nd centuries AD.Juvenal is credited with sixteen known poems divided among five books; all are in the Roman genre of satire, which, at its most basic in the time of the author, comprised a...

characterization of something being "rara avis in terris nigroque simillima cygno" (6.165). In English, this Latin phrase means "a rare bird in the lands, and very like a black swan." When the phrase was coined, the black swan was presumed not to exist. The importance of the simile

Simile

A simile is a figure of speech that directly compares two different things, usually by employing the words "like", "as". Even though both similes and metaphors are forms of comparison, similes indirectly compare the two ideas and allow them to remain distinct in spite of their similarities, whereas...

lies in its analogy to the fragility of any system of thought. A set of conclusions is potentially undone once any of its fundamental postulates is disproved. In this case, the observation of a single black swan would be the undoing of the phrase's underlying logic, as well as any reasoning that followed from that underlying logic.

Juvenal's phrase was a common expression in 16th century London as a statement of impossibility. The London expression derives from the Old World

Old World

The Old World consists of those parts of the world known to classical antiquity and the European Middle Ages. It is used in the context of, and contrast with, the "New World" ....

presumption that all swan

Swan

Swans, genus Cygnus, are birds of the family Anatidae, which also includes geese and ducks. Swans are grouped with the closely related geese in the subfamily Anserinae where they form the tribe Cygnini. Sometimes, they are considered a distinct subfamily, Cygninae...

s must be white because all historical records of swans reported that they had white feathers. In that context, a black swan was impossible or at least nonexistent. After a Dutch expedition led by explorer Willem de Vlamingh

Willem de Vlamingh

Willem Hesselsz de Vlamingh was a Dutch sea-captain who explored the central west coast of Australia in the late 17th century.- Vlamingh and the VOC :...

on the Swan River

Swan River (Western Australia)

The Swan River estuary flows through the city of Perth, in the south west of Western Australia. Its lower reaches are relatively wide and deep, with few constrictions, while the upper reaches are usually quite narrow and shallow....

in 1697, discovered black swans in Western Australia

Western Australia

Western Australia is a state of Australia, occupying the entire western third of the Australian continent. It is bounded by the Indian Ocean to the north and west, the Great Australian Bight and Indian Ocean to the south, the Northern Territory to the north-east and South Australia to the south-east...

, the term metamorphosed to connote that a perceived impossibility might later be disproven. Taleb notes that in the 19th century John Stuart Mill

John Stuart Mill

John Stuart Mill was a British philosopher, economist and civil servant. An influential contributor to social theory, political theory, and political economy, his conception of liberty justified the freedom of the individual in opposition to unlimited state control. He was a proponent of...

used the black swan logical fallacy as a new term to identify falsification.

Specifically, Taleb asserts in the New York Times:

What we call here a Black Swan (and capitalize it) is an event with the following three attributes.

First, it is an outlier
Outlier
In statistics, an outlier is an observation that is numerically distant from the rest of the data. Grubbs defined an outlier as: An outlying observation, or outlier, is one that appears to deviate markedly from other members of the sample in which it occurs....

, as it lies outside the realm of regular expectations, because nothing in the past can convincingly point to its possibility. Second, it carries an extreme impact. Third, in spite of its outlier status, human nature makes us concoct explanations for its occurrence after the fact, making it explainable and predictable.

I stop and summarize the triplet: rarity, extreme impact, and retrospective (though not prospective) predictability. A small number of Black Swans explains almost everything in our world, from the success of ideas and religions, to the dynamics of historical events, to elements of our own personal lives.

Identifying a black swan event

Based on the author's criteria:

The event is a surprise (to the observer).
The event has a major impact.
After its first recording, the event is rationalized by hindsight, as if it could have been expected (e.g., the relevant data were available but not accounted for).

Coping with black swan events

The main idea in Taleb's book is to not attempt to predict Black Swan Events, but to build robustness against negative ones that occur and be able to exploit positive ones. Taleb contends that banks and trading firms are very vulnerable to hazardous Black Swan Events and are exposed to losses beyond those predicted by their defective models.

After the second edition of The Black Swan, Taleb provides "Ten Principles for a Black-Swan-Robust Society".

Taleb states that a Black Swan Event depends on the observer. For example, what may be a Black Swan surprise for a turkey is not a Black Swan surprise to its butcher; hence the objective should be to "avoid being the turkey" by identifying areas of vulnerability in order to "turn the Black Swans white".

Epistemological approach

Taleb's black swan is different from the earlier philosophical versions of the problem, specifically in epistemology, as it concerns a phenomenon with specific empirical and statistical properties which he calls, "the fourth quadrant".

Taleb's problem is about epistemic limitations in some parts of the areas covered in decision making. These limitations are twofold: philosophical (mathematical) and empirical (human known epistemic biases). The philosophical problem is about the decrease in knowledge when it comes to rare events as these are not visible in past samples and therefore require a strong a priori, or what one can call an extrapolating theory; accordingly events depend more and more on theories when their probability is small. In the fourth quadrant, knowledge is both uncertain and consequences are large, requiring more robustness.

Before Taleb, those who dealt with the notion of the improbable, such as Hume

David Hume

David Hume was a Scottish philosopher, historian, economist, and essayist, known especially for his philosophical empiricism and skepticism. He was one of the most important figures in the history of Western philosophy and the Scottish Enlightenment...

, Mill

John Stuart Mill

, and Popper

Karl Popper

Sir Karl Raimund Popper, CH FRS FBA was an Austro-British philosopher and a professor at the London School of Economics...

focused on the problem of induction

Problem of induction

The problem of induction is the philosophical question of whether inductive reasoning leads to knowledge. That is, what is the justification for either:...

in logic

Logic

In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...

, specifically, that of drawing general conclusions from specific observations. Taleb's Black Swan Event has a central and unique attribute, high impact. His claim is that almost all consequential events in history come from the unexpected—yet humans later convince themselves that these events are explainable in hindsight

Hindsight bias

Hindsight bias, or alternatively the knew-it-all-along effect and creeping determinism, is the inclination to see events that have already occurred as being more predictable than they were before they took place. It is a multifaceted phenomenon that can affect different stages of designs,...

(bias).

One problem, labeled the ludic fallacy

Ludic fallacy

The ludic fallacy is a term coined by Nassim Nicholas Taleb in his 2007 book The Black Swan. "Ludic" is from the Latin ludus, meaning "play, game, sport, pastime." It is summarized as "the misuse of games to model real-life situations." Taleb explains the fallacy as "basing studies of chance on the...

by Taleb, is the belief that the unstructured randomness found in life resembles the structured randomness found in games. This stems from the assumption that the unexpected

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...

may be predicted by extrapolating from variations in statistics based on past observations, especially when these statistics are presumed to represent samples from a bell-shaped curve. These concerns often are highly relevant in financial markets, where major players use value at risk

Value at risk

In financial mathematics and financial risk management, Value at Risk is a widely used risk measure of the risk of loss on a specific portfolio of financial assets...

models, which imply normal distributions, although market returns typically have fat tail

Fat tail

A fat-tailed distribution is a probability distribution that has the property, along with the heavy-tailed distributions, that they exhibit extremely large skewness or kurtosis. This comparison is often made relative to the ubiquitous normal distribution, which itself is an example of an...

distributions.

More generally, 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...

, based on a fixed universe or a model of possible outcomes, ignores and minimizes the effect of events that are "outside model". For instance, a simple model of daily stock market returns may include extreme moves such as Black Monday (1987)

Black Monday (1987)

In finance, Black Monday refers to Monday October 19, 1987, when stock markets around the world crashed, shedding a huge value in a very short time. The crash began in Hong Kong and spread west to Europe, hitting the United States after other markets had already declined by a significant margin...

, but might not model the breakdown of markets following the September 11 attacks of 2001. A fixed model considers the "known unknowns", but ignores the "unknown unknowns".

Taleb notes that other distributions are not usable with precision, but often are more descriptive, such as the fractal

Fractal

A fractal has been defined as "a rough or fragmented geometric shape that can be split into parts, each of which is a reduced-size copy of the whole," a property called self-similarity...

, power law

Power law

A power law is a special kind of mathematical relationship between two quantities. When the frequency of an event varies as a power of some attribute of that event , the frequency is said to follow a power law. For instance, the number of cities having a certain population size is found to vary...

, or scalable distributions and that awareness of these might help to temper expectations.

Beyond this, he emphasizes that many events simply are without precedent, undercutting the basis of this type of reasoning altogether.

Taleb also argues for the use of counterfactual reasoning when considering risk.

External links

The Fourth Quadrant and The Limits of Statistics -Taleb's concept of the limits of statistics
Ten Principles for a Black Swan Robust World

The source of this article is wikipedia, the free encyclopedia. The text of this article is licensed under the GFDL.

Background

Identifying a black swan event

Coping with black swan events

Epistemological approach

See also

Books by Taleb

External links