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Sunday, March 5, 2023

Gresham's law

From Wikipedia, the free encyclopedia

In economics, Gresham's law is a monetary principle stating that "bad money drives out good". For example, if there are two forms of commodity money in circulation, which are accepted by law as having similar face value, the more valuable commodity will gradually disappear from circulation.

The law was named in 1860 by economist Henry Dunning Macleod after Sir Thomas Gresham (1519–1579), an English financier during the Tudor dynasty. Gresham had urged Queen Elizabeth to restore confidence in then-debased English currency. The concept was thoroughly defined in medieval Europe by Nicolaus Copernicus and known centuries earlier in classical Antiquity, the Middle East and China.

"Good money" and "bad money"

Under Gresham's Law, "good money" is money that shows little difference between its nominal value (the face value of the coin) and its commodity value (the value of the metal of which it is made, often precious metals, nickel, or copper).

The price spread between face value and commodity value when it is minted is called seigniorage. As some coins do not circulate, remaining in the possession of coin collectors, this can increase demand for coinage.

On the other hand, "bad money" is money that has a commodity value considerably lower than its face value and is in circulation along with good money, where both forms are required to be accepted at equal value as legal tender.

In Gresham's day, bad money included any coin that had been debased. Debasement was often done by the issuing body, where less than the officially specified amount of precious metal was contained in an issue of coinage, usually by alloying it with a base metal. The public could also debase coins, usually by clipping or scraping off small portions of the precious metal, also known as "stemming" (reeded edges on coins were intended to make clipping evident). Other examples of bad money include counterfeit coins made from base metal. Today virtually all circulating coins are made from base metals, known as fiat money. While virtually all contemporary coinage is composed solely of base metals, during certain contemporary, 21st century years in which copper values were relatively high, at least one common coin (the U.S. nickel) still maintained "good money" status (largely depending on market rates).

In the case of clipped, scraped, or counterfeit coins, the commodity value was reduced by fraud, as the face value remains at the previous higher level. On the other hand, with a coinage debased by a government issuer, the commodity value of the coinage was often reduced quite openly, while the face value of the debased coins was held at the higher level by legal tender laws.

The old saying "a bad penny always turns up" is a colloquial recognition of Gresham's Law.

Theory

The law states that any circulating currency consisting of both "good" and "bad" money (both forms required to be accepted at equal value under legal tender law) quickly becomes dominated by the "bad" money. This is because people spending money will hand over the "bad" coins rather than the "good" ones, keeping the "good" ones for themselves. Legal tender laws act as a form of price control. In such a case, the intrinsically less valuable money is preferred in exchange, because people prefer to save the intrinsically more valuable money.

If a customer purchases an item which costs five pence, and possesses several silver sixpence coins. Some of these coins are more debased, while others are less so – but legally, they are all mandated to be of equal value. The customer would prefer to retain the better coins, and so offers the shopkeeper the most debased one. In turn, the shopkeeper must give one penny in change, and has every reason to give the most debased penny. Thus, the coins that circulate in the transaction will tend to be of the most debased sort available to the parties.

A stack of twenty Walking Liberty half dollars (left), which contain 90% silver. In an example of Gresham's law, these coins were quickly hoarded by the public after the Coinage Act of 1965 debased half dollars to contain only 40% silver, and then were debased entirely in 1971 to base cupronickel (right).

If "good" coins have a face value below that of their metallic content, individuals may be motivated to melt them down and sell the metal for its higher intrinsic value, even if such destruction is illegal. The 1965 United States half-dollar coins contained 40% silver, in previous years these coins were 90% silver. With the release of the 1965 half-dollar, which was legally required to be accepted at the same value as the earlier 90% halves, the older 90% silver coinage quickly disappeared from circulation, while the newer debased coins remained in use. As the value of the dollar (Federal Reserve notes) continued to decline, resulting in the value of the silver content exceeding the face value of the coins, many of the older half dollars were melted down or removed from circulation and into private collections and hoards. Beginning in 1971, the U.S. government abandoned including any silver in half dollars, as the metal value of the 40% silver coins began to exceed their face value, which resulted in a repeat of the previous event, as the 40% silver coins also began to vanish from circulation and into coin hoards.

A similar situation occurred in 2007, in the United States with the rising price of copper, zinc, and nickel, which led the U.S. government to ban the melting or mass exportation of one-cent and five-cent coins.

In addition to being melted down for its bullion value, money that is considered to be "good" tends to leave an economy through international trade. International traders are not bound by legal tender laws as citizens of the issuing country are, so they will offer higher value for good coins than bad ones. The good coins may leave their country of origin to become part of international trade, escaping that country's legal tender laws and leaving the "bad" money behind. This occurred in Britain during the period of adoption of the gold standard - in 1717 Isaac Newton, then Master of the Mint, declared the gold guinea to be worth 21 silver shillings. This overvalued the gold guinea in Britain, making it "bad", and encouraged people to send "good" silver shillings abroad, where it could buy more gold than at home. This gold was then minted as currency, which bought silver shillings, which were sent abroad for gold, and so on. For a century hardly any silver coins were minted in Britain, and Britain moved onto a de facto gold standard.

History of the concept

Gresham was not the first to state the law which took his name. The phenomenon had been noted by Aristophanes in his play The Frogs, which dates from around the end of the 5th century BC. The referenced passage from The Frogs is as follows (usually dated at 405 BC):

It has often struck our notice that the course our city runs
Is the same towards men and money. She has true and worthy sons:
She has good and ancient silver, she has good and recent gold.
These are coins untouched with alloys; everywhere their fame is told;
Not all Hellas holds their equal, not all Barbary far and near.
Gold or silver, each well minted, tested each and ringing clear.
Yet, we never use them! Others always pass from hand to hand.
Sorry brass just struck last week and branded with a wretched brand.
So with men we know for upright, blameless lives and noble names.
Trained in music and palaestra, freemen's choirs and freemen's games,
These we spurn for men of brass...

According to Ben Tamari, the currency devaluation phenomenon was already recognized in ancient sources. He brings some examples which include the Machpela Cave transaction and the building of the Temple from the Bible and the Mishna in tractate Bava Metzia (Bava Metzia 4:1) from the Talmud.

In China, Yuan dynasty economic authors Yeh Shih and Yuan Hsieh (c. 1223) were aware of the same phenomenon.

Ibn Taimiyyah (1263–1328) described the phenomenon as follows:

If the ruler cancels the use of a certain coin and mints another kind of money for the people, he will spoil the riches (amwal) which they possess, by decreasing their value as the old coins will now become merely a commodity. He will do injustice to them by depriving them of the higher values originally owned by them. Moreover, if the intrinsic values of coins are different it will become a source of profit for the wicked to collect the small (bad) coins and exchange them (for good money) and then they will take them to another country and shift the small (bad) money of that country (to this country). So (the value of) people's goods will be damaged.

Notably this passage mentions only the flight of good money abroad and says nothing of its disappearance due to hoarding or melting. Palestinian economist Adel Zagha also attributes a similar concept to medieval Islamic thinker Al-Maqrizi, who offered, claims Zagha, a close approximation to what would become known as Gresham's law centuries later.

In the 14th century it was noted by Nicole Oresme c. 1350, in his treatise On the Origin, Nature, Law, and Alterations of Money, and by jurist and historian Al-Maqrizi (1364–1442) in the Mamluk Empire.

Johannes de Strigys, an agent of Ludovico III Gonzaga, Marquis of Mantua in Venice, wrote in a June 1472 report che la cativa cazarà via la bona ("that the bad money will chase out the good").

In the year that Gresham was born, 1519, it was described by Nicolaus Copernicus in a treatise called Monetae cudendae ratio: "bad (debased) coinage drives good (un-debased) coinage out of circulation". Copernicus was aware of the practice of exchanging bad coins for good ones and melting down the latter or sending them abroad, and he seems to have drawn up some notes on this subject while he was at Olsztyn in 1519. He made them the basis of a report which he presented to the Prussian Diet held in 1522, attending the session with his friend Tiedemann Giese to represent his chapter. Copernicus's Monetae cudendae ratio was an enlarged, Latin version of that report, setting forth a general theory of money for the 1528 diet. He also formulated a version of the quantity theory of money. For this reason, it is occasionally known as the Gresham–Copernicus law.

Sir Thomas Gresham, a 16th century financial agent of the English Crown in the city of Antwerp, was one in a long series of proponents of the law, which he did to explain to Queen Elizabeth I what was happening to the English shilling. Her father, Henry VIII, had replaced 40% of the silver in the coin with base metals, to increase the government's income without raising taxes. Astute English merchants and ordinary subjects saved the good shillings from pure silver and circulated the bad ones. Hence, the bad money would be used whenever possible, and the good coinage would be saved and disappear from circulation.

According to the economist George Selgin in his paper "Gresham's Law":

As for Gresham himself, he observed "that good and bad coin cannot circulate together" in a letter written to Queen Elizabeth on the occasion of her accession in 1558. The statement was part of Gresham's explanation for the "unexampled state of badness" that England's coinage had been left in following the "Great Debasements" of Henry VIII and Edward VI, which reduced the metallic value of English silver coins to a small fraction of what it had been at the time of Henry VII. Owing to these debasements, Gresham observed to the Queen, that "all your fine gold was convayed out of this your realm".

Gresham made his observations of good and bad money while in the service of Queen Elizabeth, with respect only to the observed poor quality of British coinage. Earlier monarchs, Henry VIII and Edward VI, had forced the people to accept debased coinage by means of legal tender laws. Gresham also made his comparison of good and bad money where the precious metal in the money was the same metal, but of different weight. He did not compare silver to gold, or gold to paper.

In his "Gresham's Law" article, Selgin also offers the following comments regarding the origin of the name:

The expression "Gresham's Law" dates back only to 1858, when British economist Henry Dunning Macleod (1858, pp. 476–8) decided to name the tendency for bad money to drive good money out of circulation after Sir Thomas Gresham (1519–1579). However, references to such a tendency, sometimes accompanied by discussion of conditions promoting it, occur in various medieval writings, most notably Nicholas Oresme's (c. 1357) Treatise on money. The concept can be traced to ancient works, including Aristophanes' The Frogs, where the prevalence of bad politicians is attributed to forces similar to those favoring bad money over good.

Reverse of Gresham's law (Thiers' law)

The experiences of dollarization in countries with weak economies and currencies (such as Israel in the 1980s, Eastern Europe and countries in the period immediately after the collapse of the Soviet bloc, or Ecuador throughout the late 20th and early 21st century) may be seen as Gresham's law operating in its reverse form (Guidotti & Rodriguez, 1992) because in general, the dollar has not been legal tender in such situations, and in some cases, its use has been illegal.

Adam Fergusson and Costantino Bresciani-Turroni (in his book Le vicende del marco tedesco, published in 1931) pointed out that, during the great inflation in the Weimar Republic in 1923, as the official money became so worthless that virtually nobody would take it, people simply stopped accepting the currency in exchange for goods. That was particularly serious because farmers began to hoard food. Accordingly, any currency backed by any sort of value became a circulating medium of exchange. In 2009, hyperinflation in Zimbabwe began to show similar characteristics.

Those examples show that in the absence of effective legal tender laws, Gresham's Law works in reverse. If given the choice of what money to accept, people will accept the money they believe to be of highest long-term value, and not accept what they believe to be of low long-term value. If not given the choice and required to accept all money, good and bad, they will tend to keep the money of greater perceived value in their own possession, and pass the bad money to others.

In short, in the absence of legal tender laws, the seller will not accept anything but money of certain value (good money), but the existence of legal tender laws will cause the buyer to offer only money with the lowest commodity value (bad money), as the creditor must accept such money at face value.

Nobel Prize winner Robert Mundell believes that Gresham's Law could be more accurately rendered, taking care of the reverse, if it were expressed as: "Bad money drives out good if they exchange for the same price."

The reverse of Gresham's Law, that good money drives out bad money whenever the bad money becomes nearly worthless, has been named "Thiers' law" by economist Peter Bernholz in honor of French politician and historian Adolphe Thiers. "Thiers' Law will only operate later [in the inflation] when the increase of the new flexible exchange rate and of the rate of inflation lower the real demand for the inflating money."

Analogs in other fields

The principles of Gresham's law can sometimes be applied to different fields of study. Gresham's law may be generally applied to any circumstance in which the true value of something is markedly different from the value people are required to accept, due to factors such as lack of information or governmental decree.

Vice President Spiro Agnew used Gresham's law in describing American news media, stating that "Bad news drives out good news", although his argument was closer to that of a race to the bottom for higher ratings rather than over- and under-valuing certain kinds of news.

Gregory Bateson postulated an analogue to Gresham's law operating in cultural evolution, in which "the oversimplified ideas will always displace the sophisticated and the vulgar and hateful will always displace the beautiful. And yet the beautiful persists."

Cory Doctorow wrote that a similar effect to Gresham's law occurred in carbon offset trading. The alleged information asymmetry is that people find it difficult to distinguish just how effective credits purchased are, but can easily tell the price. As a result, cheap credits that are ineffective can displace expensive but worthwhile carbon credits. The example given was The Nature Conservancy offering cheap, yet "meaningless", carbon credits by purchasing cheap land unlikely to be logged anyway, rather than expensive and valuable land at risk of logging.

In the market for used cars, lemon automobiles (analogous to bad currency) will drive out the good cars. The problem is one of asymmetry of information. Sellers have a strong financial incentive to pass all used cars off as good cars, especially lemons. This makes it difficult to buy a good car at a fair price, as the buyer risks overpaying for a lemon. The result is that buyers will only pay the fair price of a lemon, so at least they reduce the risk of overpaying. High-quality cars tend to be pushed out of the market, because there is no good way to establish that they really are worth more. Certified pre-owned programs are an attempt to mitigate this problem by providing a warranty and other guarantees of quality. The Market for Lemons is a work that examines this problem in more detail.

Miracle

From Wikipedia, the free encyclopedia

A miracle is an event that is inexplicable by natural or scientific laws and accordingly gets attributed to some supernatural or praeternatural cause. Various religions often attribute a phenomenon characterized as miraculous to the actions of a supernatural being, (especially) a deity, a magician, a miracle worker, a saint, or a religious leader.

Informally, English-speakers often use the word miracle to characterise any beneficial event that is statistically unlikely but not contrary to the laws of nature, such as surviving a natural disaster, or simply a "wonderful" occurrence, regardless of likelihood (e.g. "the miracle of childbirth"). Some coincidences may be seen as miracles.

A true miracle would, by definition, be a non-natural phenomenon, leading many writers to dismiss miracles as physically impossible (that is, requiring violation of established laws of physics within their domain of validity) or impossible to confirm by their nature (because all possible physical mechanisms can never be ruled out). The former position is expressed (for instance) by Thomas Jefferson, and the latter by David Hume. Theologians typically say that, with divine providence, God regularly works through nature yet, as a creator, may work without, above, or against it as well.

Definitions

The word miracle is usually used to describe any beneficial event that is physically impossible or impossible to confirm by nature. Wayne Grudem defines a miracle as "a less common kind of God's activity in which he arouses people's awe and wonder and bears witness to himself." A deistic perspective of God's relation to the world defines a miracle as a direct intervention of God into the world.

Naturalistic explanations

A miracle may just be fake information or simply a fictional story, rather than something that truly happened. A miracle experience may be due to cognitive errors (e.g. overthinking, jumping to conclusions) or psychological errors (e.g. hallucinations) of witnesses. Use of some drugs such as psychedelics (e.g. ecstasy) may produce similar effects to religious experiences.

Law of truly large numbers

Statistically "impossible" events are often called miracles. For instance, when three classmates accidentally meet in a different country decades after having left school, they could consider this as "miraculous". However, a colossal number of events happen every moment on Earth; thus, extremely unlikely coincidences also happen every moment. Events that are considered "impossible" are therefore not impossible at all – they are just increasingly rare and dependent on the number of individual events. British mathematician J. E. Littlewood suggested that individuals should statistically expect one-in-a-million events ("miracles") to happen to them at the rate of about one per month. By his definition, seemingly miraculous events are actually commonplace.

Supernatural explanations

A miracle is a phenomenon not explained by known laws of nature. Criteria for classifying an event as a miracle vary. Often a religious text, such as the Bible or Quran, states that a miracle occurred, and believers may accept this as a fact.

Philosophical explanations

Aristotelian and Neo-Aristotelian

The Aristotelian view of God has God as pure actuality and considers him as the prime mover doing only what a perfect being can do, think. Jewish neo-Aristotelian philosophers, who are still influential today, include Maimonides, Samuel ben Judah ibn Tibbon, and Gersonides. Directly or indirectly, their views are still prevalent in much of the religious Jewish community.

Baruch Spinoza

In his Tractatus Theologico-Politicus Spinoza claims that miracles are merely lawlike events of whose causes we are ignorant. We should not treat them as having no cause or of having a cause immediately available. Rather the miracle is for combating the ignorance it entails, like a political project.

David Hume

According to the philosopher David Hume, a miracle is "a transgression of a law of nature by a particular volition of the Deity, or by the interposition of some invisible agent". The crux of his argument is this: "No testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous, than the fact which it endeavours to establish." By Hume's definition, a miracle goes against our regular experience of how the universe works. As miracles are single events, the evidence for them is always limited and we experience them rarely. On the basis of experience and evidence, the probability that miracle occurred is always less than the probability that it did not occur. As it is rational to believe what is more probable, we are not supposed to have a good reason to believe that a miracle occurred.

Friedrich Schleiermacher

According to the Christian theologian Friedrich Schleiermacher "every event, even the most natural and usual, becomes a miracle as soon as the religious view of it can be the dominant".

Søren Kierkegaard

The philosopher Søren Kierkegaard, following Hume and Johann Georg Hamann, a Humean scholar, agrees with Hume's definition of a miracle as a transgression of a law of nature, but Kierkegaard, writing as his pseudonym Johannes Climacus, regards any historical reports to be less than certain, including historical reports of miracles, as all historical knowledge is always doubtful and open to approximation.

James Keller

James Keller states that "The claim that God has worked a miracle implies that God has singled out certain persons for some benefit which many others do not receive implies that God is unfair."

Religious views

According to a 2011 poll by the Pew Research Center, more than 90 percent of evangelical Christians believe miracles still take place. While Christians see God as sometimes intervening in human activities, Muslims see Allah as a direct cause of all events. "God’s overwhelming closeness makes it easy for Muslims to admit the miraculous in the world."

Buddhism

The Haedong Kosung-jon of Korea (Biographies of High Monks) records that King Beopheung of Silla had desired to promulgate Buddhism as the state religion. However, officials in his court opposed him. In the fourteenth year of his reign, Beopheung's "Grand Secretary", Ichadon, devised a strategy to overcome court opposition. Ichadon schemed with the king, convincing him to make a proclamation granting Buddhism official state sanction using the royal seal. Ichadon told the king to deny having made such a proclamation when the opposing officials received it and demanded an explanation. Instead, Ichadon would confess and accept the punishment of execution, for what would quickly be seen as a forgery. Ichadon prophesied to the king that at his execution a wonderful miracle would convince the opposing court faction of Buddhism's power. Ichadon's scheme went as planned, and the opposing officials took the bait. When Ichadon was executed on the 15th day of the 9th month in 527, his prophecy was fulfilled; the earth shook, the sun was darkened, beautiful flowers rained from the sky, his severed head flew to the sacred Geumgang mountains, and milk instead of blood sprayed 100 feet in the air from his beheaded corpse. The omen was accepted by the opposing court officials as a manifestation of heaven's approval, and Buddhism was made the state religion in 527 CE.

The Honchō Hokke Reigenki (c. 1040) of Japan contains a collection of Buddhist miracle stories.

Miracles play an important role in the veneration of Buddhist relics in Southern Asia. Thus, Somawathie Stupa in Sri Lanka is an increasingly popular site of pilgrimage and tourist destination thanks to multiple reports about miraculous rays of light, apparitions and modern legends, which often have been fixed in photographs and movies.

Christianity

The Miracle of the Slave, a 1548 painting by Tintoretto, from the Gallerie dell'Accademia in Venice. It portrays an episode of the life of Saint Mark, patron saint of Venice, taken from Jacobus de Voragine's Golden Legend. The scene shows a saint intervening to make a slave who is about to be martyred invulnerable.

The gospels record three sorts of miracles performed by Jesus: exorcisms, cures, and nature wonders. In the Gospel of John, the miracles are referred to as "signs" and the emphasis is on God demonstrating his underlying normal activity in remarkable ways. In the New Testament, the greatest miracle is the resurrection of Jesus, the event central to Christian faith.

Jesus explains in the New Testament that miracles are performed by faith in God. "If you have faith as small as a mustard seed, you can say to this mountain, 'move from here to there' and it will move." (Gospel of Matthew 17:20). After Jesus returned to heaven, the Book of Acts records the disciples of Jesus praying to God to grant that miracles be done in his name for the purpose of convincing onlookers that he is alive. (Acts 4:29–31).

Other passages mention false prophets who will be able to perform miracles to deceive "if possible, even the elect of Christ" (Matthew 24:24). 2 Thessalonians 2:9 says, "And then shall that Wicked be revealed, whom the Lord shall consume with the spirit of His mouth, and shall destroy with the brightness of His coming: Even him, whose coming is after the working of Satan with all power and signs and lying wonders, and with all deceivableness of unrighteousness in them that perish; because they received not the love of the Truth, that they might be saved." Revelation 13:13,14 says, "And he doeth great wonders, so that he maketh fire come down from heaven on the earth in the sight of men, and deceiveth them that dwell on the earth by the means of those miracles which he had power to do in the sight of the beast; saying to them that dwell on the earth, that they should make an image to the beast, which had the wound by a sword, and did live." Revelation 16:14 says, "For they are the spirits of devils, working miracles, which go forth unto the kings of the earth and of the whole world, to gather them to the battle of that great day of God Almighty." Revelation 19:20 says, "And the beast was taken, and with him the false prophet that wrought miracles before him, with which he deceived them that had received the mark of the beast, and them that worshipped his image. These both were cast alive into a lake of fire burning with brimstone." These passages indicate that signs, wonders, and miracles are not necessarily committed by God. These miracles not committed by God are labeled as false(pseudo) miracles though which could mean that they are deceptive in nature and are not the same as the true miracles committed by God.

In early Christianity miracles were the most often attested motivations for conversions of pagans; pagan Romans took the existence of miracles for granted; Christian texts reporting them offered miracles as divine proof of the Christian God's unique claim to authority, relegating all other gods to the lower status of daimones: "of all worships, the Christian best and most particularly advertised its miracles by driving out of spirits and laying on of hands". The Gospel of John is structured around miraculous "signs": The success of the Apostles according to the church historian Eusebius of Caesarea lay in their miracles: "though laymen in their language", he asserted, "they drew courage from divine, miraculous powers". The conversion of Constantine by a miraculous sign in heaven is a prominent fourth-century example.

Since the Age of Enlightenment, miracles have often needed to be rationalized: C.S. Lewis, Norman Geisler, William Lane Craig, and other 20th-century Christians have argued that miracles are reasonable and plausible. For example, Lewis said that a miracle is something that comes totally out of the blue. If for thousands of years a woman can become pregnant only by sexual intercourse with a man, then if she were to become pregnant without a man, it would be a miracle.

There have been numerous claims of miracles by people of most Christian denominations, including but not limited to faith healings and casting out demons. Miracle reports are especially prevalent in Roman Catholicism and Pentecostal or Charismatic churches.

Catholic Church

The Catholic Church believes miracles are works of God, either directly, or through the prayers and intercessions of a specific saint or saints. There is usually a specific purpose connected to a miracle, e.g. the conversion of a person or persons to the Catholic faith or the construction of a church desired by God. The church says that it tries to be very cautious to approve the validity of putative miracles. The Catholic Church also says that it maintains particularly stringent requirements in validating the miracle's authenticity. The process is overseen by the Congregation for the Causes of Saints.

The Catholic Church has listed several events as miracles, some of them occurring in modern times. Before a person can be accepted as a saint, they must be posthumously confirmed to have performed two miracles. In the procedure of beatification of Pope John Paul II, who died in 2005, the Vatican announced on 14 January 2011 that Pope Benedict XVI had confirmed that the recovery of Marie Simon-Pierre from Parkinson's disease was a miracle.

Among the more notable miracles approved by the church are several Eucharistic miracles wherein the sacramental bread and wine are transformed into Christ's flesh and blood, such as the Miracle of Lanciano and cures in Lourdes.

According to 17th century documents, a young Spanish man's leg was miraculously restored to him in 1640 after having been amputated two and a half years earlier.

Another miracle approved by the church is the Miracle of the Sun, which is said to have occurred near Fátima, Portugal on October 13, 1917. According to legend, between 70,000 and 100,000 people, who were gathered at a cove near Fátima, witnessed the sunlight dim and change colors, and the Sun spin, dance about in the sky, and appear to plummet towards Earth, radiating great heat in the process. After the ten-minute event, the ground and the people's clothing, which had been drenched by a previous rainstorm, were both dry.

Velankanni (Mary) can be traced to the mid-16th century and is attributed to three miracles: the apparition of Mary and the Christ Child to a slumbering shepherd boy, the curing of a lame buttermilk vendor, and the rescue of Portuguese sailors from a violent sea storm.

In addition to these, the Catholic Church attributes miraculous causes to many otherwise inexplicable phenomena on a case-by-case basis. Only after all other possible explanations have been asserted to be inadequate will the church assume divine intervention and declare the miracle worthy of veneration by their followers. The church does not, however, enjoin belief in any extra-Scriptural miracle as an article of faith or as necessary for salvation.

Thomas Aquinas, a prominent Doctor of the Church, divided miracles into three types in his Summa contra Gentiles:

Things that are at times divinely accomplished, apart from the generally established order in things, are customarily called miracles; for we admire with some astonishment a certain event when we observe the effect but do not know its cause. And since one and the same cause is at times known to some people and unknown to others, the result is that of several who see an effect at the same time, some are moved to admiring astonishment, while others are not. For instance, the astronomer is not astonished when he sees an eclipse of the sun, for he knows its cause, but the person who is ignorant of this science must be amazed, for he ignores the cause. And so, a certain event is wondrous to one person, but not so to another. So, a thing that has a completely hidden cause is wondrous in an unqualified way, and this the name, miracle, suggests; namely, what is of itself filled with admirable wonder, not simply in relation to one person or another. Now, absolutely speaking, the cause hidden from every man is God. In fact, we proved above that no man in the present state of life can grasp His essence intellectually. Therefore, those things must properly be called miraculous which are done by divine power apart from the order generally followed in things.

Now, there are various degrees and orders of these miracles. Indeed, the highest rank among miracles is held by those events in which something is done by God which nature never could do. For example, that two bodies should be coincident; that the sun reverse its course, or stand still; that the sea open up and offer a way through which people may pass. And even among these an order may be observed. For the greater the things that God does are, and the more they are removed from the capacity of nature, the greater the miracle is. Thus, it is more miraculous for the sun to reverse its course than for the sea to be divided.

Then, the second degree among miracles is held by those events in which God does something which nature can do, but not in this order. It is a work of nature for an animal to live, to see, and to walk; but for it to live after death, to see after becoming blind, to walk after paralysis of the limbs, this nature cannot do—but God at times does such works miraculously. Even among this degree of miracles a gradation is evident, according as what is done is more removed from the capacity of nature.

Now, the third degree of miracles occurs when God does what is usually done by the working of nature, but without the operation of the principles of nature. For example, a person may be cured by divine power from a fever which could be cured naturally, and it may rain independently of the working of the principles of nature.

Evangelicalism

For a majority of Evangelical Christians, biblicism ensures that the miracles described in the Bible are still relevant and may be present in the life of the believer. Healings, academic or professional successes, the birth of a child after several attempts, the end of an addiction, etc., would be tangible examples of God's intervention with the faith and prayer, by the Holy Spirit. In the 1980s, the neo-charismatic movement re-emphasized miracles and faith healing. In certain churches, a special place is thus reserved for faith healings with laying on of hands during worship services or for campaigns evangelization. Faith healing or divine healing is considered to be an inheritance of Jesus acquired by his death and resurrection.

Hinduism

In Hinduism, miracles are focused on episodes of liberation of the spirit. A key example is the revelation of Krishna to Arjuna, wherein Krishna persuades Arjuna to rejoin the battle against his cousins by briefly and miraculously giving Arjuna the power to see the true scope of the Universe, and its sustainment within Krishna, which requires divine vision. This is a typical situation in Hindu mythology wherein "wondrous acts are performed for the purpose of bringing spiritual liberation to those who witness or read about them."

Hindu sages have criticized both expectation and reliance on miracles as cheats, situations where people have sought to earn a benefit without doing the work necessary to merit it. Miracles continue to be occasionally reported in the practice of Hinduism, with an example of a miracle modernly reported in Hinduism being the Hindu milk miracle of September 1995, with additional occurrences in 2006 and 2010, wherein statues of certain Hindu deities were seen to drink milk offered to them. The scientific explanation for the incident, attested by Indian academics, was that the material was wicked from the offering bowls by capillary action.

Islam

In the Quran, a miracle can be defined as a supernatural intervention in the life of human beings. According to this definition, miracles are present "in a threefold sense: in sacred history, in connection with Muhammad himself and in relation to revelation". The Quran does not use the technical Arabic word for miracle (Muʿd̲j̲iza) literally meaning "that by means of which [the Prophet] confounds, overwhelms, his opponents". It rather uses the term 'Ayah' (literally meaning sign). The term Ayah is used in the Quran in the above-mentioned threefold sense: it refers to the "verses" of the Quran (believed to be the divine speech in human language; presented by Muhammad as his chief miracle); as well as to miracles of it and the signs (particularly those of creation).

To defend the possibility of miracles and God's omnipotence against the encroachment of the independent secondary causes, some medieval Muslim theologians such as Al-Ghazali rejected the idea of cause and effect in essence, but accepted it as something that facilitates humankind's investigation and comprehension of natural processes. They argued that the nature was composed of uniform atoms that were "re-created" at every instant by God. Thus, if the soil was to fall, God would have to create and re-create the accident of heaviness for as long as the soil was to fall. For Muslim theologians, the laws of nature were only the customary sequence of apparent causes: customs of God.

Sufi biographical literature records claims of miraculous accounts of men and women. The miraculous prowess of the Sufi holy men includes firasa (clairvoyance), the ability to disappear from sight, to become completely invisible and practice buruz (exteriorization). The holy men reportedly tame wild beasts and traverse long distances in a very short time span. They could also produce food and rain in seasons of drought, heal the sick and help barren women conceive.

Judaism

Descriptions of miracles (Hebrew Ness, נס) appear in the Tanakh. Examples include prophets, such as Elijah who performed miracles like the raising of a widow's dead son (1 Kings 17:17–24) and Elisha whose miracles include multiplying the poor widow's jar of oil (2 Kings 4:1–7) and restoring to life the son of the woman of Shunem (2 Kings 4:18–37). The Torah describes many miracles related to Moses during his time as a prophet and the Exodus of the Israelites. Parting the Red Sea, and facilitating the Plagues of Egypt are among the most famous.

During the first century BCE, a variety of religious movements and splinter groups developed amongst the Jews in Judea. A number of individuals claimed to be miracle workers in the tradition of Moses, Elijah, and Elisha, the Jewish prophets. The Talmud provides some examples of such Jewish miracle workers, one of whom is Honi HaM'agel, who was famous for his ability to successfully pray for rain.

There are people who obscure all miracles by explaining them in terms of the laws of nature. When these heretics who do not believe in miracles disappear and faith increases in the world, then the Mashiach will come. For the essence of the Redemption primarily depends on this – that is, on faith.

Most Chasidic communities are rife with tales of miracles that follow a yechidut, a spiritual audience with a tzadik: barren women become pregnant, cancer tumors shrink, wayward children become pious. Many Hasidim claim that miracles can take place in merit of partaking of the shirayim (the leftovers from the rebbe's meal), such as miraculous healing or blessings of wealth or piety.

Criticism

Thomas Paine, one of the Founding Fathers of the American Revolution, wrote "All the tales of miracles, with which the Old and New Testament are filled, are fit only for impostors to preach and fools to believe."

Thomas Jefferson, principal author of the Declaration of Independence of the United States, edited a version of the Bible in which he removed sections of the New Testament containing supernatural aspects as well as perceived misinterpretations he believed had been added by the Four Evangelists. Jefferson wrote, "The establishment of the innocent and genuine character of this benevolent moralist, and the rescuing it from the imputation of imposture, which has resulted from artificial systems, [footnote: e.g. The immaculate conception of Jesus, his deification, the creation of the world by him, his miraculous powers, his resurrection and visible ascension, his corporeal presence in the Eucharist, the Trinity; original sin, atonement, regeneration, election, orders of Hierarchy, etc. —T.J.] invented by ultra-Christian sects, unauthorized by a single word ever uttered by him, is a most desirable object, and one to which Priestley has successfully devoted his labors and learning."

American Revolutionary War patriot Ethan Allen wrote, "In those parts of the world where learning and science have prevailed, miracles have ceased; but in those parts of it as are barbarous and ignorant, miracles are still in vogue."

Robert Ingersoll wrote, "Not 20 people were convinced by the reported miracles of Christ, and yet people of the nineteenth century were coolly asked to be convinced on hearsay by miracles which those who are supposed to have seen them refused to credit."

Elbert Hubbard, American writer, publisher, artist, and philosopher, wrote "A miracle is an event described by those to whom it was told by people who did not see it."

Biologist Richard Dawkins has criticised the belief in miracles as a subversion of Occam's razor.

Mathematician Charles Hermite, in a discourse upon the world of mathematical truths and the physical world, stated that "The synthesis of the two is revealed partially in the marvellous correspondence between abstract mathematics on the one hand and all the branches of physics on the other".

Baden Powell, an English mathematician and Church of England priest, stated that if God is a lawgiver, then a "miracle" would break the lawful edicts that had been issued at Creation. Therefore, a belief in miracles would be entirely atheistic.

Black swan theory

From Wikipedia, the free encyclopedia
 
A black swan (Cygnus atratus) in Australia

The black swan theory or theory of black swan events is a metaphor that describes an event that comes as a surprise, has a major effect, and is often inappropriately rationalized after the fact with the benefit of hindsight. The term is based on an ancient saying that presumed black swans did not exist – a saying that became reinterpreted to teach a different lesson after they were discovered in Australia.

The theory was developed by Nassim Nicholas Taleb, starting in 2001, to explain:

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

Taleb's "black swan theory" refers only to unexpected events of large magnitude and consequence and their dominant role in history. Such events, considered extreme outliers, collectively play vastly larger roles than regular occurrences. More technically, in the scientific monograph "Silent Risk", Taleb mathematically defines the black swan problem as "stemming from the use of degenerate metaprobability".

Background

The phrase "black swan" derives from a Latin expression; its oldest known occurrence is from the 2nd-century Roman poet Juvenal's characterization in his Satire VI of something being "rara avis in terris nigroque simillima cygno" ("a rare bird in the lands and very much like a black swan"). When the phrase was coined, the black swan was presumed not to exist. The importance of the metaphor 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 logic of any system of thought, 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 presumption that all swans 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.

However, in 1697, Dutch explorers led by Willem de Vlamingh became the first Europeans to see black swans, in Western Australia. The term subsequently metamorphosed to connote the idea that a perceived impossibility might later be disproven. Taleb notes that in the 19th century, John Stuart Mill used the black swan logical fallacy as a new term to identify falsification.

Black swan events were discussed by Nassim Nicholas Taleb in his 2001 book Fooled By Randomness, which concerned financial events. His 2007 book The Black Swan extended the metaphor to events outside of financial markets. 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, the personal computer, World War I, the dissolution of the Soviet Union, and the September 11, 2001 attacks as examples of black swan events.

Taleb asserts:

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

First, it is an outlier, 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

Based on the author's criteria:

  1. The event is a surprise (to the observer).
  2. The event has a major effect.
  3. After the first recorded instance of the event, it is rationalized by hindsight, as if it could have been expected; that is, the relevant data were available but unaccounted for in risk mitigation programs. The same is true for the personal perception by individuals.

According to Taleb, as it was expected with great certainty that a global pandemic would eventually take place, the COVID-19 pandemic is not a black swan, but is considered to be a white swan; such an event has a major effect, but is compatible with statistical properties.

Coping with black swans

The practical aim of Taleb's book is not to attempt to predict events which are unpredictable, but to build robustness against negative events while still exploiting positive events. Taleb contends that banks and trading firms are very vulnerable to hazardous black swan events and are exposed to unpredictable losses. On the subject of business, and quantitative finance in particular, Taleb critiques the widespread use of the normal distribution model employed in financial engineering, calling it a Great Intellectual Fraud. Taleb elaborates the robustness concept as a central topic of his later book, Antifragile: Things That Gain From Disorder.

In 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 because these are not visible in past samples and therefore require a strong a priori (extrapolating) theory; accordingly, predictions of events depend more and more on theories when their probability is small. In the "fourth quadrant", knowledge is uncertain and consequences are large, requiring more robustness.

According to Taleb, thinkers who came before him who dealt with the notion of the improbable (such as Hume, Mill, and Popper) focused on the problem of induction in logic, specifically, that of drawing general conclusions from specific observations. The central and unique attribute of Taleb's black swan event is that it is high-profile. 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.

One problem, labeled the ludic fallacy 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 may be predicted by extrapolating from variations in statistics based on past observations, especially when these statistics are presumed to represent samples from a normal distribution. These concerns often are highly relevant in financial markets, where major players sometimes assume normal distributions when using value at risk models, although market returns typically have fat tail distributions.

Taleb said:

I don't particularly care about the usual. If you want to get an idea of a friend's temperament, ethics, and personal elegance, you need to look at him under the tests of severe circumstances, not under the regular rosy glow of daily life. Can you assess the danger a criminal poses by examining only what he does on an ordinary day? Can we understand health without considering wild diseases and epidemics? Indeed the normal is often irrelevant. Almost everything in social life is produced by rare but consequential shocks and jumps; all the while almost everything studied about social life focuses on the 'normal,' particularly with 'bell curve' methods of inference that tell you close to nothing. Why? Because the bell curve ignores large deviations, cannot handle them, yet makes us confident that we have tamed uncertainty. Its nickname in this book is GIF, Great Intellectual Fraud.

More generally, decision theory, which is based on a fixed universe or a model of possible outcomes, ignores and minimizes the effect of events that are "outside the model". For instance, a simple model of daily stock market returns may include extreme moves such as Black Monday (1987), but might not model the breakdown of markets following the September 11, 2001 attacks. Consequently, the New York Stock Exchange and Nasdaq exchange remained closed till September 17, 2001, the most protracted shutdown since the Great Depression. A fixed model considers the "known unknowns", but ignores the "unknown unknowns", made famous by a statement of Donald Rumsfeld. The term "unknown unknowns" appeared in a 1982 New Yorker article on the aerospace industry, which cites the example of metal fatigue, the cause of crashes in Comet airliners in the 1950s.

Deterministic chaotic dynamics reproducing the Black Swan Event have been researched in economics. That is in agreement with Taleb's comment regarding some distributions which are not usable with precision, but which are more descriptive, such as the fractal, power law, or scalable distributions and that awareness of these might help to temper expectations. Beyond this, Taleb 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.

Saturday, March 4, 2023

Financial modeling

From Wikipedia, the free encyclopedia

Financial modeling is the task of building an abstract representation (a model) of a real world financial situation. This is a mathematical model designed to represent (a simplified version of) the performance of a financial asset or portfolio of a business, project, or any other investment.

Typically, then, financial modeling is understood to mean an exercise in either asset pricing or corporate finance, of a quantitative nature. It is about translating a set of hypotheses about the behavior of markets or agents into numerical predictions. At the same time, "financial modeling" is a general term that means different things to different users; the reference usually relates either to accounting and corporate finance applications or to quantitative finance applications.

Accounting

In corporate finance and the accounting profession, financial modeling typically entails financial statement forecasting; usually the preparation of detailed company-specific models used for decision making purposes and financial analysis.

Applications include:

To generalize[citation needed] as to the nature of these models: firstly, as they are built around financial statements, calculations and outputs are monthly, quarterly or annual; secondly, the inputs take the form of "assumptions", where the analyst specifies the values that will apply in each period for external / global variables (exchange rates, tax percentage, etc....; may be thought of as the model parameters), and for internal / company specific variables (wages, unit costs, etc....). Correspondingly, both characteristics are reflected (at least implicitly) in the mathematical form of these models: firstly, the models are in discrete time; secondly, they are deterministic. For discussion of the issues that may arise, see below; for discussion as to more sophisticated approaches sometimes employed, see Corporate finance § Quantifying uncertainty and Financial economics § Corporate finance theory.

Modelers are often designated "financial analyst" (and are sometimes referred to (tongue in cheek) as "number crunchers"). Typically, the modeler will have completed an MBA or MSF with (optional) coursework in "financial modeling". Accounting qualifications and finance certifications such as the CIIA and CFA generally do not provide direct or explicit training in modeling. At the same time, numerous commercial training courses are offered, both through universities and privately. For the components and steps of business modeling here, see Outline of finance § Financial modeling; see also Valuation using discounted cash flows § Determine cash flow for each forecast period for further discussion and considerations.

Although purpose-built business software does exist (see also Fundamental Analysis Software), the vast proportion of the market is spreadsheet-based; this is largely since the models are almost always company-specific. Also, analysts will each have their own criteria and methods for financial modeling. Microsoft Excel now has by far the dominant position, having overtaken Lotus 1-2-3 in the 1990s. Spreadsheet-based modelling can have its own problems, and several standardizations and "best practices" have been proposed. "Spreadsheet risk" is increasingly studied and managed; see model audit.

One critique here, is that model outputs, i.e. line items, often inhere "unrealistic implicit assumptions" and "internal inconsistencies". (For example, a forecast for growth in revenue but without corresponding increases in working capital, fixed assets and the associated financing, may imbed unrealistic assumptions about asset turnover, debt level and/or equity financing. See Sustainable growth rate § From a financial perspective.) What is required, but often lacking, is that all key elements are explicitly and consistently forecasted. Related to this, is that modellers often additionally "fail to identify crucial assumptions" relating to inputs, "and to explore what can go wrong". Here, in general, modellers "use point values and simple arithmetic instead of probability distributions and statistical measures" — i.e., as mentioned, the problems are treated as deterministic in nature — and thus calculate a single value for the asset or project, but without providing information on the range, variance and sensitivity of outcomes; see Valuation using discounted cash flows § Determine equity value. A further, more general critique relates to the lack of basic computer programming concepts amongst modelers,  with the result that their models are often poorly structured, and difficult to maintain. (Serious criticism is also directed at the nature of budgeting, and its impact on the organization.)

Quantitative finance

In quantitative finance, financial modeling entails the development of a sophisticated mathematical model. Models here deal with asset prices, market movements, portfolio returns and the like. A general distinction is between: "quantitative financial management", models of the financial situation of a large, complex firm; "quantitative asset pricing", models of the returns of different stocks; "financial engineering", models of the price or returns of derivative securities; "quantitative corporate finance", models of the firm's financial decisions.

Relatedly, applications include:

These problems are generally stochastic and continuous in nature, and models here thus require complex algorithms, entailing computer simulation, advanced numerical methods (such as numerical differential equations, numerical linear algebra, dynamic programming) and/or the development of optimization models. The general nature of these problems is discussed under Mathematical finance § History: Q versus P, while specific techniques are listed under Outline of finance § Mathematical tools. For further discussion here see also: Brownian model of financial markets; Martingale pricing; Financial models with long-tailed distributions and volatility clustering; Extreme value theory; Historical simulation (finance).

Modellers are generally referred to as "quants", i.e. quantitative analysts, and typically have advanced (Ph.D. level) backgrounds in quantitative disciplines such as statistics, physics, engineering, computer science, mathematics or operations research. Alternatively, or in addition to their quantitative background, they complete a finance masters with a quantitative orientation, such as the Master of Quantitative Finance, or the more specialized Master of Computational Finance or Master of Financial Engineering; the CQF certificate is increasingly common.

Although spreadsheets are widely used here also (almost always requiring extensive VBA); custom C++, Fortran or Python, or numerical-analysis software such as MATLAB, are often preferred, particularly where stability or speed is a concern. MATLAB is often used at the research or prototyping stage because of its intuitive programming, graphical and debugging tools, but C++/Fortran are preferred for conceptually simple but high computational-cost applications where MATLAB is too slow; Python is increasingly used due to its simplicity, and large standard library / available applications, including QuantLib. Additionally, for many (of the standard) derivative and portfolio applications, commercial software is available, and the choice as to whether the model is to be developed in-house, or whether existing products are to be deployed, will depend on the problem in question. See Quantitative analysis (finance) § Library quantitative analysis.

The complexity of these models may result in incorrect pricing or hedging or both. This Model risk is the subject of ongoing research by finance academics, and is a topic of great, and growing, interest in the risk management arena.

Criticism of the discipline (often preceding the financial crisis of 2007–08 by several years) emphasizes the differences between the mathematical and physical sciences, and finance, and the resultant caution to be applied by modelers, and by traders and risk managers using their models. Notable here are Emanuel Derman and Paul Wilmott, authors of the Financial Modelers' Manifesto. Some go further and question whether the mathematical- and statistical modeling techniques usually applied to finance are at all appropriate (see the assumptions made for options and for portfolios). In fact, these may go so far as to question the "empirical and scientific validity... of modern financial theory". Notable here are Nassim Taleb and Benoit Mandelbrot. See also Mathematical finance § Criticism, Financial economics § Challenges and criticism and Financial engineering § Criticisms.

Competitive modeling

Several financial modeling competitions exist, emphasizing speed and accuracy in modeling. The Microsoft-sponsored ModelOff Financial Modeling World Championships were held annually from 2012 to 2019, with competitions throughout the year and a finals championship in New York or London. After its end in 2020, several other modeling championships have been started, including the Financial Modeling World Cup and Microsoft Excel Collegiate Challenge, also sponsored by Microsoft.

Philosophy of financial modeling

Philosophy of financial modeling is a branch of philosophy concerned with the foundations, methods, and implications of modeling science.

In the philosophy of financial modeling, scholars have more recently begun to question the standardly held assumption that financial modelers seek to represent any "real-world" or actually ongoing investment situation. Instead, it has been suggested that the task of the financial modeler resides in demonstrating the possibility of a transaction in a prospective investment scenario, from a limited base of possibility conditions initially assumed in the model.

Inequality (mathematics)

From Wikipedia, the free encyclopedia https://en.wikipedia.org/wiki/Inequality...