Structured finance in the twelfth century

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 [MacCulloch, 2009, 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 Sylla, 1996, p 73]. So a lender could charge interest to compensate for a loss, but they could not make a gain by lending [Kaye, 1998, 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 Sylla, 1996, Chapter 1], [Mauss, 1924 (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 Sylla, 1996, 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 [Poitras, 2000, 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 [Poitras, 2000, p 43], [Homer and Sylla, 1996, 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 [Swan, 1999, p 100], who, for a reason not well understood, “showed a strange insensitivity to ecclesiastical and social censure” [Poitras, 2000, 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 [Poitras, 2000, p 87]. 

A census originated in the feudal societies as an “obligation to pay an annual return from fruitful property”[Homer and Sylla, 1996, p 75, quoting Noonan], [Poitras, 2000, 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 Sylla, 1996, pp 75–76], [Poitras, 2000, pp 31–33]. Censii issued by governments, usually linked to specific tax revenues, became known as rentes [Poitras, 2006, 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 [Poitras, 2000, 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 5∕22 = 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. [Poitras, 2000, 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 [Usher, 1934]). 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.

References

   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 http://www.jstor.org/stable/2245435.

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 No. 928 or 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

Greedy, or desperate, bankers

I am completely bemused.

This morning I hear Robert Peston (the BBC's Business Correspondent) arguing the case of the airline industry, that maybe the scientific advice is too conservative and maybe airplanes could fly through the ash cloaud.

The point is that airplanes have been shown to fall out o f the sky if they fly through ash. Clearly not all planes do this but some will. An airline, facing bankruptcy will be risk seeking and so is going to be comfortable about losing a plane or two, may happen, may not but being grounded will result in failure.

What the airlines will do is force their customers to make a choice - to fly or not to fly. Customers with tickets will be faced with an impossible decision. Do I risk death or risk losing the airfare? This is an unfair choice to put on the public.

Above all, I cannot believe that Peston has not learned the lesson of the credit crisis. Businesses will take unacceptable risks to remain in business, and typically it is the public who end up bearing those risk. Banks and regulators ignored the advice of scientists, if we allow the airlines to ignore the advice, we deserve extinction.

The whole of western science is based on financial maths

A historian Joel Kaye has written widely on the development of science in medieval Europe. In Economy and Nature in the Fourteenth Century he presents a thesis that

In broad terms, the conceptual landscape that emerged in the fourteenth century resulted from a striking shift in the models derived to represent order and activity in the natural world: from a static world of numbered points and perfections to a dynamic world of ever-changing values conceived as continua in expansion and contraction; from a mathematics of arithmetical addition to a mathematics of geometrical multiplication, newly accepting of the approximate and the probable; from a world of fixed and absolute values to a shifting, relational world in which values were understood to be determined relative to changing perspectives and conditions; and from a philosophy focused on essences and perfections to one dominated by questions of quantification and measurement in respect to motion and change. Each of these new directions proved to be of great importance to the future of scientific thought.

Mathematics, Economics and Decision Making

The 2009 Alan Tayler Lecture was delivered by Prof Lord Desai of the London School of Economics and Political Science at the University of Oxford on 30 November.

I did not attend the lecture, but I understand that Lord Desai called for economists to use more sophisticated modeling techniques - i.e. not to rely on single-factor linear models when trying to understand the economy. Makes sense to me.

I shall try and get a copy of the talk.

I also recently attended a talk by Prof Lord Skidelsky who was talking about Keynes, and publicising his book Keynes: The Return of the Master. A key point made by Skidelsky was Keynes belief in "irreducible uncertainty". From the perspective of maths, there is nothing controversial in Keynes is position, the Fundamental Theorem of Asset Pricing, in noting that there are infintely many martingale measure in an incomplet market, makes the same point. As a Russian mathematician has pointed out to me, when economists talk about "rational expectations", ask them under which measure they are calculating the expectation.

Culture clash?

The FSSC report Graduate Skills and Recruitment in The City has the following quotes (p 45) from a graduate recruitment manager at an investment bank

“Sales managers prefer graduates who are academic, with some interest in finance but more social skills with extra-curricular activities e.g. being the Head of the rugby/cricket club. They’re less fussy on the degree subject, but quite fussy in terms of the university they have attended – Oxford, Cambridge, LSE, Imperial.

The [derivatives] trading/research side is much more focussed on the technical. Many of our senior managers are from French universities, with experience of engineering schools and écoles polytechniques in France. They look for expertise in engineering, maths, qualitative [quantitative?] finance. They like Oxford, Cambridge, Warwick”.

This quote resonated by an interview with a former Lehman's executive published in the Sunday Times on 23 August, Lehman Brothers failures exposed:

"Instead of reviewing the bank’s risk management systems, the executive directors would have ndless meetings discussing the corporate dress code as Fuld was a stickler for appearances. A angerous lack of awareness about the technical financial products the bank was playing with didn’t elp matters."

Most people employed in finance are involved in sales and marketing activity, and so the soft skills needed for these roles are frequently highlighted by employers to the likes of the FSSC and Universities. However, the core of the banks' business is is highly quantitative, to quote from p 14 of the FSSC report:

“…[banks] need high level maths skills because that’s how the bank makes money – vanilla roducts have very little margin.”

The financial innovation (or more accurately, the re-introduction of derivative products into financial markets) since the 1970s has changed the nature of banking, has the culture of banking kept up?

Perhaps a solution is to separate financial institutions into "traditional banks", undertaking lending and M&A activities relying on sales and marketing skills and "speculative banks" specialising in trading, derivatives and risk management. However, this is not the only model. Many manufacturing firms, particularly pharmaceutical and oil companies, are based on core expertise in science and engineering but where the majority of employees are involved in sales and marketing. So it appears the cultures can co-exist.

It's academic

On of my favourite quotes from the credit crisis comes from the 2/02/08 edition of The Economist, the article "No Defense" on fraud issues at Societe General, states

"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."

In response to "Of couples and copulas", Prof Paul Embrects sent the following letter to the FT

Dear Sir
The article "Of couples and copulas", published on 24 April 2009,
suggests that David Li's formula is to blame for the current financial
crisis. For me, this is akin to blaming Einstein's E=mc² formula for
the destruction wreaked by the atomic bomb.

Feeling like a risk manager whose protestations of imminent danger
were ignored, I wish to make clear that many well-respected
academics have pointed out the limitations of the mathematical tools
used in the finance industry, including Li's formula. However, these
warnings were either ignored or dismissed with a desultory
response: "It's academic".

We hope that we are listened to in the future, rather than being
made a convenient scapegoat.

The Royal Society calls for more funding of financial maths

The Royal Society published a report on Science, Technology, Engineering and Maths impact on the service sector. They devote a whole chapter (3) to financial innovation, see Hidden Wealth. The report was covered in the FT.

I was contact by the Royal Society in mid-July, this is (their) summary of what I said:

1. The financial crisis was not a homogeneous events; some institutions did (much) better than thers.

2. The root of the problem is in banks mis-pricing assets. When pricing assets the banks were relying on mathematical models. Some banks had "engineered" their own models, others "bought in" models (either by buying "off the shelf" or by hiring individuals from the innovating banks). Banks who treated models as "black boxes" have done far worse than those that had a reputation or developing their own.

3. Many quants (the majority ?) have a background in physics and engineering (there is a factoid that the majority of engineering graduates from top UK universities go into finance rather than engineering - you could check this. Similarly The City is the largest employer of physics PhDs). They understand deterministic systems but only have a rudimentary understanding of modern probability theory (the majority of maths graduates are in a very similar position, I spoke to a maths teacher who had a degree from Glasgow who told me he had not done probability since he was 16).

4. Financial economics developed in the late twentieth century using relatively straightforward maths. The models it produced are "too simple" (see pp 4-12 in "An Engine, Not a Camera"), but are "elegant".

The physicists / engineers were given a simple framework in which deterministic approaches appeared to give definite results. This approach is related to the "Crash of 87" and "When genius failed" in '98.

5. Throughout the industry a belief emerged that maths, "rocket science" removed risk. In the 1990s, mathematicians began to investigate financial models and re-evaluate them. A more rigorous approach to financial economics revealed the naivety of the assumptions that led to the simple models.

6. Because the financial mathematics community is small and peripheral in British science, it lacks authority , and the theory (from the mathematicians) became disconnected from the practice in industry.

7. In Europe, because they approach probability as a branch of analysis rather than from the perspective of statistics, there seems to have been a better appreciation that simple models that fitted data were inadequate. This is a subtle point. The issue is whether the "quants"
really understand stochastic systems. Does the UK education system (schools to universities) produce the volume of people with (basic to advanced) skills in probability and statistics. There is a view that France & Germany are better at this, as demonstrated by the large number of continental scientists and engineers employed in London banks.

8. The credit crisis provides a tangible example and introduction to a wider problem about our poor understandings of complex and stochastic systems. The concern is that many of the global challenges we face involve these sorts of systems. Is our science up to the task?

9. There is a basic competency issue but also a need to develop new mathematics able to describe what Lord May describes as "ephemeral" systems, but in other areas relating to fundamental maths.