Thursday 28 July 2011

History repeating itself?

The macro-economics of August 2011 looks much the same as August 1971, but have we learnt anything about the markets over the past forty years?

Following the 1929 Crash and the consequent world-wide Depression governments around the world had devalued their currencies in order to make their products more competitive in foreign markets. These ‘beggar-thy-neighbour’ policies created a deflationary spiral that magnified the effects of the Crash. In 1944 the Allied powers met at Bretton–Woods, in New Hampshire, and agreed to fix the gold price of the main currencies, the US$ was fixed to gold at $35/oz, while other currencies were pegged to the dollar with the pound sterling being set at $4.03. Bretton–Woods also established the International Monetary Fund and World Bank.

By the late 1960s the Bretton–Woods system was beginning to creak as the Germans and Japanese exported to the Americans,while the U.S. poured money into th e war in Vietnam. As gold was sucked out of the U.S. the system began to look untenable. In 1971, foreign governments demanded that the U.S. honour its “promise to pay” and convert their dollar notes into gold, in July Switzerland converted $ 50 million into gold. There was an arbitrage, buy gold with dollars and then sell the gold for Deutsche Marks. On August 15, 1971 the U.S. President, Nixon, responded to these activities by abandoning the gold-standard, the “promise to pay”. Bretton Woods collapsed and foreign exchange rates stopped being

As a consequence of the collapse of the Bretton–Woods system of exchange rates central banks  were forced to change the interest rates more frequently. In simplistic terms, the level of interest rates has two effects. If rates are low people will borrow from banks, who will create money for the economy and this may generate inflation which devalues a currency. If interest rates are high, and the currency stable, foreign investors will like to deposit their spare cash in banks paying the high rates of interest, raising demand for the currency. After 1972 interest rate policy became a key lever that governments had to control their economies. In the 27 years between 1945 and autumn 1972, when Bretton–Woods collapsed, the Bank of England changed its lending rate 43 times, in the 27 years after 1972, it changed them 223 times, about every 45 days. Finance had moved from a world of deterministic control to one of stochastic control, and people had to think more carefully about controlling their financial risks.

Business responded to this change in the economic environment by returning to the derivatives markets, using them to provide the tools to hedge the risks, whether as a borrower or a lender, of the fluctuating the interest rates. In the same year that Bretton-Woods collapsed, Nixon appointed William Casey, a spy and tax lawyer, as director of the Securities and Exchange Commission (SEC) and the path for the the derivatives exchanges was opened. A currency future had been created in New York in 1970, but had foundered. However when, on May 16, 1972, the Merc began trading futures on seven currencies the market for FX risk management was there and the Merc was rescued from the doldrums of the  1960s.

While futures or forward contracts, firm agreements to buy or sell an asset at a fixed price in the  future, existed in an ethical and legal limbo, option contracts, contracts that gave the holder the right, but not the obligation, to trade were closer to the devil. As late as the 1960s officials of the SEC had compared options to thalidomide and marijuana and claimed that there had never been a case of market manipulation that did not involve options [MacKenzie2008, p 149]. Casey, and the SEC, cleared the Chicago Board of Options Exchange and it opened on April 26, 1973. Within days, the Journal of Political Economy, the house journal of the Chicago economists, published a paper, The Pricing of Options and Corporate Liabilities by Myron Scholes and Fischer Black.

The CBOT launched the first interest rate derivative in 1975, where the underlying was linked to  mortgages, in 1976 the Merc introduced a future on 30-day U.S. Government Treasury bills, and CBOT launched a future on 30-year U.S. Treasury bonds in 1978. The London International Financial Futures Exchange opened in 1982 and in 1984 the equivalent of a stock–market index for interest rates, the London Interbank Offered Rate, LIBOR, began to be published, and futures, known, confusingly, as Eurodollar futures, began to be traded on the Merc based on this index.

It was not only the capital markets that were transformed in the 1970s. Up until 1973 the price  of oil was set by the Railroad Commission of Texas, who controlled the oil production in Texas, and hence the oil price in the U.S., which as the world’s main oil consumer, effectively set the world price. Following the collapse of Bretton–Woods, the U.S. dollar’s value fell and as a consequence, the real income non-U.S. oil producers fell, and the Organisation of Oil Producing and Exporting Companies, OPEC, began to price their oil in gold and agree production quotas, setting the global–price. In 1973 the Middle-Eastern members of OPEC imposed an embargo on the west, following the defeat of the Syrian–Egyptian attack on Israel, and cut production, forcing the price of oil up. This, in-turn, prompted the development of alternative oil–provinces, notably the North Sea between the U.K. and Norway, which had been
previously un-economic. When this extra production hit the market, in the 1980s, just as demand fell, as consumers cut back consumption in response to higher-prices, and Iran and Iraq exceeded their quotas to fund their war (1980–1988), prices collapsed along with OPEC’s cohesiveness. In 1985 OPEC’s price-setting mechanism was abandoned, and another key economic input became a stochastic process, and in response, in 1988, the London based International Petroleum Exchange introduced the Brent oil futures  contract. 

Behind Black Monday, the failures of LTCM and The Equitable and the Credit Crisis of 2007–2008 is the fact that the financial world became stochastic in the aftermath of the collapse of Bretton–Woods,. The derivative markets did not spontaneously appear, they developed in response to the increased uncertainty in key economic drivers.

The world of 1980 was very different to that between 1918 and 1970 when exchange, rates,  interest  rates and commodity prices were being controlled by the great and the good. One view might be that the  abandonment of Bretton–Woods had lead to the chaos of 1970s stagflation, another is that Bretton–Woods shattered under the strains of trying to confine the economy to a specific path. The derivative markets emerged in response to freeing the economy, the deterministic  policies created impossible stresses in the global economy, and derivatives enabled risk–management in the resulting uncertainty.

The derivative markets were fundamentally different from the stock-markets, where decisions were made based on an investor’s judgement of the market fundamentals, and the core skills where in understanding economics and a company’s balance sheet, finance. The derivative markets were concerned with comparing the price differences between similar assets across different markets. It was not about the study of objects, but the relations between objects, and the derivative markets needed mathematical skills. In the aftermath of Black Monday significant numbers of applied mathematicians, physicists and engineers began working in the derivative markets, the ‘quants’ had  arrived.

The events of August 2011 are not so different to those of August 1971, but then again these  events are not so different to those of the 1690s!

Trading in stocks did not take off in England until after the Glorious Revolution of 1688. It is  often assumed that this was because, as Geoffrey Poitras puts it, “William III was accompanied by an influx of Dutch persons and practises”. However a market does not create itself and, according to Anne Murphy, a historian who has worked as a currency trader, the root cause of the explosion of stock-market trading, and the accompanying boom, was the Nine Years War [Murphy2009, p 10–14], [Poitras2000, pp 281–285]. Murphy points to a contemporary account written by John Houghton in 1694
a great many Stocks have arisen since the war with France; for Trade being obstructed at Sea; few that had money were willing it should lie idle [Murphy2009, quoting on p 12]
It was not just the shortage of opportunities to participate in regular trade that stimulated the  boom. England had grown wealthy under Charles II and alongside the increase in wealth was a growth in the financial services industry, involving life insurance and annuities, general insurance and the trade in the shares of the handful of joint-stock companies that existed at the time, such as the East India, Hudson Bay and Royal Africa [Murphy2009, p 12–19]. Evidence of this growth in financial services is provided by the 1673 Act of Common Council that looked to put an end to “usurious contracts, false Chevelance, and other crafty deceits” [Murphy2009, p 83].

The additional risks of sea trade resulting from the war with France, and the actions of privateers  meant that merchants looked for domestic investment opportunities and the number of joint-stock companies exploded, and with more companies came a more active stock market. John Houghton describes how the market worked
The manner of managing Trade is this; the Monied Man goes amongst the Brokers  (which are chiefly upon the Exchange [Alley], and at Jonathan’s Coffee House [the origins of the London Stock Exchange], sometimes at Garraway’s and at some other Coffee Houses) and asks how Stocks go? and upon Information, bids the Broker to buy or sell so many Shares of such and such Stocks if he can, at such  and such Prizes [Poitras2000, quoting on p 288].
Brokers put buyers and sellers in touch with each other, for a commission but without actually  taking possession of any asset. Alongside the monied men and brokers were the stock-jobbers or dealers, the speculators, providing liquidity in the market and trying to turn a profit from their trading. This dual-system, separating brokers from stock-jobbers, existed in London up until the ‘Big Bang’ of 1987.

In 1719 Daniel Defoe published Robinson Crusoe and wrote an article The Anatomy of Exchange  Alley in which he described stockjobbing as
a trade founded in fraud, born of deceit, and nourished by trick, cheat, wheedle,  forgeries, falsehoods, and all sorts of delusions; coining false news, this way good, this way bad; whispering imaginary terrors, frights hopes, expectations, and then preying upon the weakness of those whose imaginations they have wrought upon [Poitras2000, quoted in p 290]
An observation, mentioned by Defoe but more explicitly stated by Thomas Mortimer in 1761, concerned  the type of person involved in stockjobbing. Mortimer makes the point that there are three types of stock-jobber, firstly foreigners, secondly gentry, merchants and tradesmen, and finally, and “by far the greatest number”, people
with very little, and often, no property at all in the funds, who job in them on  credit, and transact more business in several government securities in one hour, without having a shilling of property in any of them, than the real proprietors of thousand transact in several years. [Poitras2000, quoted in p 291]
It was not only stocks that were being traded in the first half of the 1690s. Murphy estimates  that around 40% of the trades between 1692 and 1695 were in stock options, that were being traded in order to manage the risks of stock trading. [Murphy2009, p 24–30] Evidence of the widespread use of options comes in 1720 when Colley Cibber, who would become Poet Laureate in 1730,, wrote a play, The Refusal (‘The Option’), describing the action in Exchange  Alley
There you’ll see a duke dangling after a director; here a peer and ‘prentice haggling  for an eighth; there a Jew and a parson making up the differences; there a young woman of quality buying bears of a Quaker; and there an old one selling refusals to a lieutenant of grenadiers [Ackroyd2001, p 308]
Clearly, in 1720 the public were familiar with the trading of derivatives, pretty much everyone was  involved, and social, religious and political differences were forgotten in the markets.

The stock market boom that started in the late 1680s had gone bust by the middle of the next decade. At the time it was popular to blame stock-jobbers for destabilising the economy by either ramping worthless stock or undermining a going concern (depending on your point of view) [Murphy2009, p 33], while, more fundamentally, the stock market was attacked for turning “men away from honest and beneficial trades” [Murphy2009, p 68]. More rational explanations were that many of the joint-stock companies were mis-managed and the government’s need for cash sucked funds out of the market, causing prices to collapse [Murphy2009, p 35].

Anyone born before 1970, unless they have actually worked in the markets, find it difficult to  understand the changes in the financial environment that had occurred after the collapse of Bretton–Woods. Derivatives would not start appearing on undergraduate courses in universities until the mid 1990s, and even then, for many of the lecturers in economics and finance educated in the post-war deterministic economies, they would be unfamiliar beasts. This meant that at the turn of the century there was a dire shortage of people with the skills to understand the complex world of derivatives [Tett2009, p 68], which required a unique grasp of financial theory, market practises, applied mathematics, probability and

At the same time, some banks chose business managers as their chief executives, such as Fred  Goodwin at the Royal Bank of Scotland or Andy Hornby at Halifax–Bank of Scotland, rather than ‘bankers’ bought up on the basic process, and the uncertainties, of converting credit into cash. The consequence of this was that some banks focused on efficient profit generation, the allocation of scarce resources, at the expense of monitoring the risks of their activities, managing an uncertain world. This manifested itself by firms buying in expertise, in the form of ‘black–box’ software systems to value the CDOs combined with external (or internal) consultants for advice. Some banks were not only out–sourcing their call centres, but their brains as well.

In the lead–up to the Crisis of 2007–2008, RBS sponsored sports-stars to the tune of 200  million pounds, in the same period they invested nothing in mathematics. J.P. Morgan was different, they developed, in–house, Value at Risk, CreditMetrics and employed David Li as he thought about using copulas to price CDOs. The quants that that they employed were able to develop these tools because they had a deep understanding of the markets and mathematics, and critically, how and where the mathematical models were weak and needed to be augmented. Not only did J.P. Morgan recognise the need for these skills, a feature shared by all the serious investment banks, but in disseminating their models they advertised that their expertise was a fundamental component of “first class banking in a first class  way”.

The benefit of J.P. Morgan’s approach is described by Gillian Tett in her account of the Credit Crisis, Fool’s Gold. The background is it is 2005–2006 and J.P. Morgan’s shareholders are putting  the bank’s managers under intense pressure to mimic the revenues being reported by other  investment banks, who were actively investing in CDOs of MBS.
[The J.P. Morgan chief executive] made it clear that he wanted a mortgage  production line, so Winters had duly asked his staff to re–examine how to create a profitable business selling mortgage–based CDOs.
When they crunched the numbers, though, they ran into a problem. “There doesn’t seem to be a way to make money on these structures,” Brian Zeitlin, one of the bankers who worked in the CDO division reported. …
Reluctantly, Winters told the J.P. Morgan management should not open the spigots on its pipeline after all. The decision was greatly frustrating, though. The other banks were pushing JPMorgan Chase further and further down the league tables  largely due to the bonanza  from their mortgage pipelines. So were they just ignoring the risks? Or had they found some alchemy that made the economics of their
machines work? [Tett2009, pp 148–151]
The J.P. Morgan quants had taken the prices the traders were observing in the market and  reverse engineered them, just like they did with the Black–Scholes pricing formula, extracting the key parameter, ρ. When they told the traders that the basis of the prices in the market was ρ = 0.3, the traders could not believe it. A correlation of ρ = 0.3 implies that there is only a small linkage between defaults, reflecting the fact that if BP went bust it did not mean that Tesco would follow suite. But anyone who had seen an economic downturn would be familiar with whole streets being derelict, the correlation of mortgage defaults was unknown, but not insignificant.

There is another aspect to the approach taken by the banks that weathered the storms  of 2007–2008. While there is frequently the claim that the Credit Crisis was a global phenomenon, it was not. Asian banks were unaffected and British and American banks suffered far more than French or German banks. The explanation that banks were not as involved as RBS or Merrill Lynch is not a satisfactory answer (BNP Paribas, SocGen and Deutsche Bank were all heavily involved in credit derivatives. [FCIC2011, Fig  20.4, for example]). U.S. bankers have been known to suggest that the non Anglo-Saxon banks played fast and loose with accounting rules, not declaring their losses on credit derivatives. The response to this criticism from French mathematicians is typically Gallic, and Cartesian, “They thought the models were wrong before August 2007, they were  certain they were wrong after August 2007, so why should they post losses that they were certain were wrong.”. This point was highlighted by a quote that appeared in The  Economist magazine, in January 2008 in relation to a fraud at the French bank, SocGen
In common with other French banks, SocGen was also thought by many to take  an overly mathematical approach to risk. “ ‘It may work in practice but does it work in theory?’ is the stereotype of a French bank,” says one industry consultant. (‘No Defense’, The Economist, 31 January 2008.)

The bankers at J.P. Morgan, along with French risk–managers, kept in mind Hume’s observation  that “it is never contradictory to deny matter of fact”. Bankers, like all scientists, must use their intellect and constantly ask themselves the questions ‘why’ and ‘how’ to give them the foresight not to act recklessly.

The common thread linking financial crises since Bretton-Woods, Black Monday, the Equitable,  the super–portfolio that bought down LTCM, the tech–bubble of 2000 and the Credit Crisis was not the collapse of Bretton–Woods but the adoption of standardised approaches to finance. Had the majority of traders, bankers and regulators thought like mathematicians, or French risk managers, and asked themselves, in a Cartesian manner, “how do I know what I think I know is true?”, then the crises might have been avoided. Banning speculative trading in deriviatives is simplistic, and not the answer.


P. Ackroyd. London: The Biography. Vintage, 2001.

FCIC. The Financial Crisis Inquiry Report. Technical report, The National Commission
on the Causes of the Financial and Economic Crisis in the United States, 2011.

D. MacKenzie. An Engine, Not a Camera: How Financial Models Shape Markets. The
MIT Press, 2008.

A. L. Murphy. The Origins of English Financial Markets. Cambridge University Press,

G. Poitras. The Early History of Financial Economics, 1478–1776. Edward Elgar, 2000.

G. Tett. Fools’ Gold. Little Brown, 2009.

Monday 25 July 2011

Why magic? Why gold?

Wordle: why magic, why gold

Someone has asked me why this blog is Magic, maths and money.
In 1902 two sociologists, Marcel Mauss and Henri Hubert wrote ‘Outline of a general theory of magic’ where they identified that
The magician is a person who, through his gifts, his experience or through revelation, understands nature and natures …Owing to the fact that magicians came to concern themselves with contagion, harmonies, oppositions, they stumbled across the idea of causality, which is no longer mystical even when it involves properties which are no way experimental [Mauss and Hubert, 1902 (2001), pp 94–95]
The origins of magic in primitive societies is the idea that there is some sort of causal link between a ritual and a phenomenon and as such, the individual can control nature, making it less unpredictable.

Recently, the history of science has identified one of the motivations for scientists in Europe during the sixteenth and seventeenth centuries was a desire to find hidden mechanisms of cause and effect, mechanism that they could then employ to control the universe [Dear, 2001, p 52], [Henry, 2008, Chapters 5], [Hall, 1962, p 159]. The belief that these hidden mechanisms actually existed was inspired by what would now be considered as magical beliefs [Dear, 2001, p 25], [Henry, 2008, Chapter 4] and as the historian of science, John Henry, puts it
The history of magic since the the eighteenth century has been the history of what was left to the tradition after major elements of natural magic had been absorbed into natural philosophy. [Henry, 2008, p 57]
 By their very nature, these mechanisms were uncommon and had to be discovered and the process of exploration in the world was replicated by experimentation in the laboratory.

In the ‘general theory of magic’ book, Mauss and Hubert distinguish magic and science by observing that magic is based on belief in a set of rituals [Mauss and Hubert, 1902 (2001), p 114]. A person will only consult a magician if they have faith in the actions that the magician will perform. Science is not based on belief in its theorems, the equivalent of magic’s rituals, but on a belief in the process by which science is created. Science is a process that creates rituals, not simply a collection of rituals. This is a subtle point, but the effect is that magic is necessarily static, a contemporary astrologer would have more authority if they claimed to be experts in ancient knowledge. On the other hand, science is necessarily dynamic, we trust modern science’s explanations of the universe more than those of the Babylonians.

While magic and science are distinguished by static or dynamic belief, Mauss and Hubert distinguish magic and religion by hidden and open belief
Where religious rites are performed openly, in full public view, magical rites are carried out in secret. …and even if the magician has to work in public he makes an attempt to dissemble: his gestures become furtive and his words indistinct. [Mauss and Hubert, 1902 (2001), p 29]
The suggestion is, for science to be reputable and maintain a divide with magic, it needs to be carried  out, like religion, in the open. As soon as either science or religion takes place out of the public arena, they risk degenerating into magic.

The choice of the word ‘magic’ is to highlight that financial mathematics needs to be a process  of developing and refining theories, not simply of adopting sets of rituals (like pricing assets using risk neutral valuation), and that it needs to be conducted in a public forum. The public should be familiar with the “equations that blow up Wall Street” before the explosions.

This might seem a little metaphysical, non-scientific, but then isn’t this why financial  mathematics is not just interesting. For example, with concerns of a U.S. default, the price of gold keeps climbing – but why gold?

Around 4,000 years ago, people started making ornaments out of electrum (an alloy of gold and silver), copper and gold [Diamond, 1998, pp 362–363], metals found naturally (i.e. without processing) in nature. Metals have an almost unique, natural, physical property; they reflect light. The only other material that stone-age humans would have come across that reflected light would have been water, so to these people gold would appear to combine the essence of both water and the sun, the basis of life [Betz, 1995], [Landes, 1999, pp 70–73]. Imagine the awe that humans would have felt the first time they spotted a nugget of gold sparkling in a river bed, here was an object that seemed to captured and store life-giving sunlight, the ‘tears of the Sun’ as the Incas said. In the medieval period, European alchemists believed that metals were produced by some mechanism involving rays from different ‘planets’: gold from the Sun, silver from the Moon, mercury from Mercury, copper from Venus, iron from Mars, tin from Jupiter and lead from Saturn.

In ancient Babylon, Egypt and Greece, temples became associated with stores of metals, gold for  the Greeks, silver for the Babylonians and copper for the Egyptians. It seems that these metals had developed a religious significance and become important as temple offerings. Consequently followers  of the religion would look to acquire the metal, to enable them to make an offering, and so the metal became the commodity in the most universal demand. [Pryor, 1985] Athens treasury was in the Temple of Athena, and Jesus cast the money-lenders, exchanging worldly Roman money for divine shekels, out of the Temple.

The earliest tokens used as ‘money’ were not specific weights of a certain metal but roughly cut pieces of metal with an official stamp on them [Ingham, 2004, p 98] – monopoly money as it were.  The emergence of money, in the sense of coins, in Greece coincides with the emergence of mercenary troops, the term ‘soldier’ is derived from the word for a Roman gold coin, solidus. A simple economic model developed, states paid soldiers in gold, who then spent it in the community. The government then recovered the gold by taxing the merchants and innkeepers that the soldiers had paid for food and lodgings. This model would survive and drive colonialism until the modern age. A power, such as Alexander’s Greece, Imperial Rome, Napoleonic France or Industrial Britain, would take control of a region through force of arms. They would then demand tax from the conquered nation, which would have to be paid in currency specified by the coloniser. The conquered nation could only obtain the currency by exchanging their produce for the specified currency. For example, in the 1920s the British taxed Kenya at a rate of about 75% of wages, while the Belgians did not tax the Congo – they relied on forced, rather than ‘free’ wage labour [Ingham, 2004, p 76].

In the 1920’s, John Maynard Keynes became obsessed with the origins of money [Ingham, 2004, p 209, Note 16]. In neo-classical economic analysis, money is a consequence of exchange, and from  money comes banking and then the ‘credit relations’ between borrowers and lenders, pretty much as Aristotle had conceived things. However, at the start of the twentieth century, anthropologists studying primitive societies observed that cultures that had not developed money, tokens to facilitate exchange, none the less, lent and borrowed.

One of the most studied examples of these sorts of systems was that of indigenous people around  Vancouver in North Western Canada. A young man would lend five blankets to an older, richer person, for a year and they would be repaid with ten blankets. A similar situation existed in the  Southwestern Pacific were strings of shells were lent by a young man, sometimes to an unwilling borrower, at very high rates of interest. The value of the shells was was purely ceremonial, they bought entry to the fraternities of adult men [Homer and Sylla, 1996, pp 22–23]. In fact many cultures had systems where by a gift had to be reciprocated by a greater gift in return [Mauss, 1924  (2001)] and it could be disastrous to be given a present, since it would require the return of more han what was given. What these very primitive societies had done was create credit-debit relationships, reciprocity, which played a critical role in gluing society together by creating bonds between  the rich and poor, the old and young. [Sahlins, 1972 (2003], [Mauss, 1924 (2001)]

The anthropologist Marcel Mauss summed up the research in a paper on 1923, ‘An essay on the gift: the form and reason of exchange in archaic societies’
The evolution in economic law has not been from barter to sale, and from cash sale to credit sale. On the one hand, barter has arisen through a system of presents given  and  reciprocated according a time limit. …On the other hand, buying and selling arose in the same waywith the latter according to a fixed time limit, or by cash,  as well as by lending. For we have no evidence that any of the legal systems that have evolved beyond the phase we are describing [primitive society] (in particular, Babylonian law) remained ignorant of the credit process that is known in every archaic society that still survives today. [Mauss, 1924 (2001), pp 46–47]
Keynes knew that he Babylonians had established credit relations. There was a Babylonian  prototype of the Bill of Exchange from a time when the Babylonians did not use coins and in the 1930 Treatise on Money Keynes, like Mauss, argued that money did not, in fact, originate in the market place, rather it was created by the state or community ‘the age of money had succeeded to the age of barter as soon as men had adopted a money of account’ [Keynes, 1971, p 4]. Here, ‘money of account’ is the generally accepted medium by which debts are settled, for example the Babylonians settled debts, typically tax debts or loans from temples, in either grain or an amount of silver, and this medium was defined by the state  and based on trust in credit relations, the state theory of money or money as a ‘social relation’.


O. Betz. Considerations on the real and the symbolic value of gold. In G. Morteani and J. P. Northover, editors, Europe: Mines, Metallurgy and Manufacture, chapter 2, pages 19–28. B. B. Price, 1995.

P. Dear. Revolutionizing the Sciences. Palgrave, 2001.

J. M. Diamond. Guns, Germs and Steel: A short history of everybody for the last 13,000 years. Vintage, 1998.

A.R. Hall. The Scientific Revolution 1500-1800. Longmans, 1962.

J. Henry. The Scientific Revolution and the Origins of Modern Science. Palgrave, 2008.

S. Homer and R. Sylla. A History of Interest Rates. Rutgers University Press, 3rd edition, 1996.

G. Ingham. The Nature of Money. Polity Press, 2004.

J.M. Keynes. The collected writings of John Maynard Keynes. Vol. 5 : Treatise on money 1: The pure theory of money. Macmillian, 1971.

D. S. Landes. The Wealth and Poverty of Nations. Abacus, 1999.

M. Mauss. The Gift: Form and Reason for Exchange in Archaic Societies. (Routledge), 1924 (2001).

M. Mauss and H. Hubert. A General Theory of Magic. (Routledge), 1902 (2001).

F. L. Pryor. The origins of money. Journal of Money, Credit and Banking, 9(3):391–409, 1985.

M. Sahlins. Stone Age Economics. (Routledge), 1972 (2003)

Tuesday 19 July 2011

Structured finance in the twelfth century

Wordle: stuctured finance in 12 cent

From about the twelfth century the Catholic Church began to examine closely the concept of usury, elevating it, without scriptural justification, to a sin equivalent to one of the seven deadly sins [MacCulloch2009, p 369]. 

Usury is sometimes equated with the charging of interest, but by the thirteenth century it was recognised that the two ideas were different. Usury derives from the Latin usura, meaning ‘use’, and referred to the charging of a fee for the use of money. Interest comes from the Latin intereo, meaning ‘to be lost’, and originated, in the Roman legal codes as the compensation someone was paid if they suffered a loss as a result of a contract being broken[Homer and Sylla1996, p 73]. So a lender could charge interest to compensate for a loss, but they could not make a gain by lending [Kaye1998, p 83]. 

It is easier to understand this with a simple example. A farmer lends a cow to their cousin for a year. In the normal course of events, the cow would give birth to a calf and the cousin would gain the benefit of the cow’s milk. At the end of the loan, the farmer could expect the cow and the calf to be returned. The interest rate is 100%, but it is an interest since the farmer, if they had not lent the cow to their cousin, would have expected to end the year with a cow and a calf. Similarly, if the farmer lent out grain, they could expect to get the loan plus a premium on the basis that their cousin planted the grain, he would reap a harvest far greater than the sum lent. 

Another aspect, which was important in the Jewish tradition, but is, in fact, deeply rooted in all societies [Homer and Sylla1996, Chapter 1], [Mauss1924 (2001], was that loans should be made to support members of the community who were in distress, and not for the benefit of the lender [Homer and Sylla1996, p 71]. This approach was taken to maintain the cohesiveness of the community, a distinguishing feature of Judaism, and so the Talmud prohibited the charging of interest within the Jewish community, but allowed a Jew to charge interest to an outsider [Poitras2000, p 77]. 

By the start of the twelfth century different streams of thought, Greek, Roman, Biblical and feudal, came together at a time of great economic growth and the question of where the dividing line between usury and interest lay became one of the most important questions of the age. At the extreme where the ‘manifest usurers’ who were quite content with flouting Christian doctrine. The most well known example of these usurers were the Jews, who were immune from the Church’s sanction of excommunication and were able to take usury outside of their community. 

Pawnbrokers were another class offer manifest usurers. Pawnshops were widely tolerated, and frequently defended by local magnates in retrain for a license fee [Poitras2000, p 43], [Homer and Sylla1996, p 72]. The last group of recognised usurers were the Lombards. Originally from modern day Hungary, they dominated Italy during the Dark Ages and centred around the port of Amalfi, the Lombards produced communities of “remarkably creative and energetic” merchants [Swan1999, p 100], who, for a reason not well understood, “showed a strange insensitivity to ecclesiastical and social censure” [Poitras2000, p 43, quoting de Roover, 1948] and quite happily engaged in usury. Over time, the term ‘lombard’ was used to describe any Christian usurer and today many European cities have a Lombard Street at the heart of the financial district. 

These manifest usurers were beyond the influence of the scholastics, who focused on establishing the legitimacy of various types of related contracts; poena, census, prestiti, societas and, most widely used, the Bill of Exchange

In Roman mythology, Poena was the goddess of punishment who accompanied Invidia (the Latin version of Nemesis), who dealt out retribution for excessive pride, undeserved happiness or good fortune, and the absence of moderation. The word poena became synonymous with a penalty for late payment under the terms of a contract. In the medieval world, this Roman principle evolved into the practice of entering into ‘legitimate’ loan contracts that included the implicit understanding that the borrower would delay payment, by and agreed period, incurring the poena, which could be justified to the clerics as a licit interest payment [Poitras2000, p 87]. 

A census originated in the feudal societies as an “obligation to pay an annual return from fruitful property”[Homer and Sylla1996, p 75, quoting Noonan], [Poitras2000, p 91]. What this means is that the buyer of the census would pay a landowner, for example, for the future production from the land, such as wheat or wine, over a period of time. As economic life in western Europe became based on money transactions rather than barter transactions, censii lost the link to specific produce, cartloads of wheat or barrels of wine. The buyer of the census would accept regular cash payment instead of the actual produce, and this was legitimate in the eyes of the canon lawyers as long as the lump-sum paid buy the buyer ‘equated’ with the value of the ‘fruitful property’ being produced by the seller. 

Anyone who could became involved in censii. A labourer might sell a census based on the future revenue from their labour, states sold them based on the future revenue from taxes and monopolies, and the Church invested bequests by buying censii [Homer and Sylla1996, pp 75–76], [Poitras2000, pp 31–33]. Censii issued by governments, usually linked to specific tax revenues, became known as rentes [Poitras2006, p 82]. Censii could be ‘temporary’, lasting a few years, or ‘permanent’, until one of the parties died. In today’s terms, temporary censii resemble modern mortgages, permanent censii resemble the ‘annuities’ pensioners live off today. They could be ‘redeemable’, by one or both parties, meaning that the contract could be cancelled. 

The complexity of these innovative contracts meant that they did not have a clear price. For example, a census to supply three cows, every November, for five years had a price that was fairly explicit. But what about a permanent cash census based on someone’s labour? How much was the labour worth each year, and how long would the seller live? 

Prestiti were a development from the rentes created by states. Around the twelfth century the Italian city-states of Venice, Genoa and Florence began to forcefully sell temporary rentes to their rich citizens. By the mid-thirteenth century the different issues of rentes were consolidated into a mons (mountain) and everyone who had been made to buy a rente was given a share, proportionate to their contribution, in the mons. 

Venice created its mons, the monte vecchio, in 1262 and the shares, known as prestiti, entitled the holder to be paid 5%, a year, of the sum they lent, which was written on the prestiti and known as the ‘face value’. While there was no obligation for the states to pay the coupon, the annual payment, there was an expectation that they would if it could be afforded and the mountain itself was paid back as and when funds allowed [Poitras2000, pp35–36]. 

Quickly a market for Prestiti emerged, where holders who needed ready cash would trade them with people who had a surplus of cash and wanted to save. During times of peace and prosperity they had a high price, but during war and uncertainty, they traded at a low price. 

For example, Venetian prestiti traded for their face value around 1340 when the Republic paid off a lot of the mons, but in 1465, during a disastrous war with the Ottoman Turks, they fell to 22% of face. The Florentine prestiti actually had a built in facility where a holder could go to the state and sell them for 28% of their face value, however their market price was never so low as to make this profitable. 

The legitimacy of the prestati was debated by the canon lawyers. On the one hand the coupons, the regular cash payments can be seen as compensation for the forced nature of the original loan. The lender had no choice and so does suffer a loss. However, if a prestiti with a face of 100 ducats was sold for 22 ducats, the buyer would be receiving interest at a rate of 522 = 23%; in what way had this buyer of the prestiti been forced to enter into the contract? An interest payment of 23% in these circumstances seemed to be “asking for more than what was given”. 

Prestiti are important in that are one of the earliest representations of an actively traded financial instrument. The prestiti does not represent bushels of wheat or barrels of oil, it is a contract where by a state promises to pay a specified amount of money. Whether or not the state does pay out on the contract, is unknown and uncertain, hence the value of the contract is also unknown and uncertain. 

The Franciscans, in the fifteenth century, developed the state run mons into the Montes Pietatius (‘mount of piety’). This mons was created by bequests from the wealthy and then the friars would make low interest loans to those not able to borrow money elsewhere. The Montes Pietatius can be seen as a medieval version of micro-finace schemes, now spreading throughout the developing world. 

A Societas was a partnership contract. Originally each partner would put a sum of money into an enterprise and at the end of the activity, the enterprise was capitalised, all its assets sold off and converted into cash, which was divided between the partners in the same proportion as their original investments. For example a group Venetian merchants might form a societas to trade with Caffa, the the trading post on the northern shore of the Black Sea. Pooling their money, they would buy a shipment of manufactured goods and hire a ship to transport the goods, where they, or their agents, would trade the manufactured goods for furs and amber, which they would ship back to Venice and sold. The proceeds from these sales would be shared amongst the partnership. 

A societas was obviously legitimate, and this type of contract still represents the cornerstone of Islamic finance. The agreement was usually created by a close knit group1 meaning that an outsider, a foreigner or a poor entrepreneur, without the right connections would find it difficult to participate in a societas. To get around this barrier, the ‘triple contract’ was created. 

At the heart of the triple contract was a societas between the entrepreneur and an investor, this was the first contract. The second contract would be an insurance contract taken out by the entrepreneur to insure against the loss the investor’s capital. The third contract was another ‘insurance’ contract given to the investor by the entrepreneur, where by the investor surrendered their rights to a share of the profit in exchanged for a fixed payment from the entrepreneur, this payment was guaranteed by the second contract. In effect, the triple contract was a ‘usurious’ loan to the entrepreneur, wrapped up in a complex financial structure to hide its nature from the prying eyes of the Church. [Poitras2000, p38] What is most striking is the similarity between a ‘triple contract’ and the Credit Default Swap. 

All in all, at the start of the thirteenth century western Europe was going through a financial revolution (See also [Usher1934]). The creation and management of the poena, censii, prestiti, societas and Bill of Exchange required complex negotiation and calculation. The merchant would be looking to ensure they did not lose money on a transaction, for the sake of their family, while the Church tried to ensure the contracts were not usurious, for the sake of their souls. 

1If the partners did not know each other, it was an anonymous partnership, and today limited companies are known as S.A., or “anonymous societies” across continental Europe.


   S. Homer and R. Sylla. A History of Interest Rates. Rutgers University Press, 3rd edition, 1996. 

   J. Kaye. Economy and Nature in the Fourteenth Century. Cambridge University Press, 1998. 

   D. MacCulloch. A History of Christianity. Allen Lane, 2009. 

   M. Mauss. The Gift: Form and Reason for Exchange in Archaic Societies. (Routledge), 1924 (2001). 

   G. Poitras. The Early History of Financial Economics, 1478–1776. Edward Elgar, 2000. 

   G. Poitras. Life annuity valuation. In G. Poitras, editor, Pioneers of Financial Economics: contributions prior to Irving Fisher, pages 79–99. Edward Elgar, 2006. 

   E. J. Swan. Building the Global Market: A 4000 year history of derivatives. Kluwer Law, 1999. 

   A. P. Usher. The origins of banking: The primitive bank of deposit, 1200–1600. The Economic History Review, 4(4):399–428, 1934. URL

Wednesday 13 July 2011

What is financial mathematics

My article "What is Financial Mathematics" was included in the anthology "The Best Writing on Mathematics: 2010".

Following this I have received a number of enquiries about books to read.

Currently, my favourite introductory textbook is Mark Joshi's The Concepts and Practice of Mathematical Finance.  I think it has a good balance of correct theory and practical application.

The canonical text is Steven Shreve's Stochastic Calculus for Finance I and II.

I tell all my students to read Donald MacKenzie's analysis of the use of mathematics in derivative markets, such as An Engine, Not a Camera: How Financial Models Shape Markets and his recent review of the Credit Crisis, The Credit Crisis as a Problem in the Sociology of Knowledge.

Martin Creed

Simon Singh passed my details on to the Fruitmarket Gallery when they contacted him about talking about the work of the artist Martin Creed.  Initially the gallery were interested in a mathematician talking about the concept of zero. 
However, the exhibition was full of works like work image Work No. 928 or work image Work No. 958 and it struck me that the concepts of the discrete vs continuous and limits were much more interesting, and relevant and bought in zero's alter ego, infinity. 

The talk,Much Ado about Nothing’ took place on 13 October 2010.

Back from a blog sabbatical

This blog has been dormant for over a year, a year where I have done more research into the links between science and finance, and I now plan to start posting more regularly.

 In April 2010 the Edinburgh International Science Festival hosted a panel discussion that I organised involving Prof Donald Mackenzie, Dr Gillian Tett and, Ms Terri Duhon.  This is the text of an article published by The Scotsman (3/4/2010) in the lead up to that event, and the joint BMC/BAMC held in Edinburgh at the same time..

On 2 November 2008 the former French Prime Minister, Michel Rocard, was reported in Le Monde as saying that “mathematicians are guilty (unwittingly) of crimes against humanity” in reference to the financial crises that engulfed the world that year. The following March, our own Financial Services Authority, in their review of the financial crisis, listed one of the causes as “a misplaced reliance in sophisticated mathematics”, and pointed their finger at a technique known as Value at Risk (VaR) (see the FT's response at  Maths and markets and my own comment at Maths and the Markets )

A series of events taking place in Edinburgh through April, as part of the Edinburgh International Science Festival and Maths2010, the largest meeting of mathematicians in the UK for five years, will address the question of the role of mathematics in finance, and correct any misconceptions that French premiers and UK regulators might have had – since the FSA have revised their assessment on consideration of the facts.

On April 8 at 11:30, Professor Paul Embrechts, an internationally recognised expert on financial risk management will give a public lecture “Did mathematics really blow up Wall Street”. Paul’s talk will focus on what went wrong; why it went wrong and how, by finance and mathematics working together future crises can be avoided.

The following week, at 8pm on 14 April, Gillian Tett, the Markets Editor at the Financial Times will chair a discussion between Professor Donald Mackenzie, a sociologist at the University of Edinburgh, Terri Duhon, who was involved in the innovation of the financial products traded by the banks and Dr Tim Johnson, a mathematician at Heriot-Watt.

Gillian Tett has emerged as one of the leading authorities of on the credit-crisis, based on her understanding of the activities the banks were involved in, which she describes in her book Fool’s Gold. Donald Mackenzie has been observing the financial markets from his perspective of a sociologist of science and technology for over a decade. He is regarded, both within the industry and by research mathematicians, as having some of the clearest understanding of how and why the mathematics technology failed. Terri Duhon worked for J.P. Morgan when the American investment bank developed the VaR technology and pioneered the use of Collatrorallised Debt Obligations. However, while J.P. Morgan innovated it did not engage in the reckless activities that bought Lehmans down. The key points of Terri’s experience being that not all banks got it wrong and financial innovation is not intrinsically dangerous. Finally Tim Johnson can give insights on the, surprisingly, close relationship between maths and finance and how science can learn as much from finance as finance can learn from mathematics.
Despite the very different backgrounds and perspectives of the panellists, it is likely that there will be some agreement in their conclusions, and like Paul Embrechts’s views, the solution is for mathematicians, social scientists and financiers to work more closely, and also for the public to become more involved in finance, just as society is involved in medical or energy technology.

Gillian Tett mentioned the meeting in here FT column