Tuesday, 23 June 2015

Does the hidden hand need to hold a stake in society?

As the father of a four year old daughter, I have been to the cinema to see the the Disney film, Tinkerbell and the Pirate Fairy.  When I took my daughter to the cinema I had taken an mp3 player as I anticipated I would need a diversion, however I became engrossed in the film.

The film tells the story of how a 'fairy scientist', Zarina,  undertook an experiment, which went wrong.  In response, Zarina left the fairy kingdom, taking pixie dust, and got involved with the young Captain Hook.  Hook had convinced Zarina that they were a team, but in fact the pirate was using the fairy so that he could use Zarina's knowledge of pixie dust to get his ship to fly in order that he could become the most powerful pirate. Eventually, other fairies, led by Tinkerbell, rescued Zarina, by showing who her friends really were, and she was bought back into the fairy-fold.

I saw the film around the time I spoke at the Circling the square: Research, politics, media and impact conference last year and there was coverage of the idea that U.S. high tech firms were considering going 'off-shore' so that they would escape regulation.  On the face of it, there seemed to be a connection between Captain Hook and the Seasteading Institute or Andreessen Horowitz.

These thoughts returned to me while reading Albert Hirschman's The Passions and the Interests: Political Arguments for Capitalism before Its Triumph on the advice of @tcspears.  From the back-cover
In this volume, Albert Hirschman reconstructs the intellectual climate of the seventeenth and eighteenth centuries to illuminate the intricate ideological transformation that occurred, wherein the pursuit of material interests - so long condemned as the deadly sin of avarice - was assigned the role of containing the unruly and destructive passions of man. Hirschman here offers a new interpretation for the rise of capitalism, one that emphasizes the continuities between old and new, in contrast to the assumption of a sharp break that is a common feature of both Marxian and Weberian thinking.
Hirschman begins his story with Machiavelli and highlights the following paragraph in Chapter 15 of The Prince
But since it is my [Machiavelli's] object to write what shall be useful to whosoever understands it, it seems to me better to follow the real truth of things than an imaginary view of them. For many Republics and Princedoms have been imagined that were never seen or known to exist in reality. And the manner in which we live, and that in which we ought to live, are things so wide asunder, that he who quits the one to betake himself to the other is more likely to destroy than to save himself; since any one who would act up to a perfect standard of goodness in everything, must be ruined among so many who are not good. It is essential, therefore, for a Prince who desires to maintain his position, to have learned how to be other than good, and to use or not to use his goodness as necessity requires.
In 1532 Machiavelli appears to be making precisely the same point as behavioural economists make today, it beggars the question: what progress have we made in almost 500 years?

 Hirschman identifies this passage as the start of the 'fact-value dichotomy' that features in Hobbes, Spinoza, Rousseau and, most famously (for English speakers?) in Hume. It reminded me that during the Enlightenment, when the consensus was on the dominance of the passions,  today  the fact-value dichotomy is invoked to ensure policy is guided by positivist, 'rational', arguments.

Before the nineteenth century the view was that humans, as they really are, are governed by their passions (in particular, lust, the excessive passion for love; pride, the excessive passion for honour, and avarice, the excessive passion for wealth) and during the seventeenth century there was discussion of how a damaging passion can be harnessed by another passion: a person sublimates their adulterous lust by their desire to be honoured.

Hirschman notes that these thought processes originate in political theory, where the entity in question is the state, but they become applied to individuals, or in the case of Mandeville, how a skilled politician should be able to harness the passions of the people to the benefit of the state.  In particular, Mandeville identifies how personal avarice can be used to temper the other passions.

In Hirschman's account 'Interests' become the main tamers of passions and by the nineteenth century they are equated with wealth, due mainly to Adam Smith  and from this point individual profit maximisation emerges as a virtue that results in public good. Interests guide the hidden hand.

Hirschman notes that the noun 'interest' is difficult, and this is covered in the current edition of the Oxford English dictionary:
There is much that is obscure in the history of this word, first as to the adoption of Latin interest as a noun, and secondly as to the history of the Old French sense ‘damage, loss’. No other sense is recorded in French until the 16th cent. As this was not the 15th cent. sense of English interess(e), it is curious that the form of the French word should have affected the English. The relations between the sense-development in French and English in 16–17th cent. are also far from clear.
The main meaning of the word 'interest' is
 1. The relation of being objectively concerned in something, by having a right or title to, a claim upon, or a share in.
  a. The fact or relation of being legally concerned; legal concern in a thing; esp. right or title to property, or to some of the uses or benefits pertaining to property;  
with the earliest example coming from 1450 "Noon of youre Liege peple hafuyng interest, right or title, of or in ony of the premisses." and in 1478 we have "He neuer knywe..þat I hadde any clayme or entrest in the maner off Heylesdon.".

Relevant to our discussion is the second definition
 2.a. The relation of being concerned or affected in respect of advantage or detriment; esp. an advantageous relation of this kind.
with a 1533 use "Without interest we commit sinne, seeyng peyne commyng withall."  This is significant as it highlights the role of interests in repressing sin.
 b. That which is to or for the advantage of any one; good, benefit, profit, advantage.
with a 1579 example "Caried with ambicious respectes touching their interests and desires particular."

The OED places the financial meaning as secondary, but older:
II. Senses related to medieval Latin interesse, as used by Matthew Paris a1259, and frequently from 13th c. (see Du Cange), in the phrase damna et interesse, in French legal phraseology dommages et intérêts, the indemnity due to any one for the damage and prejudice done to him. Cf. Old French interest (1290 in Godef.) in sense ‘damage’, also recompense for damage done or caused, ‘damages’. In sense 10   French interest (now intérêt) occurs in Rabelais, 1535.
9.a. Injury, detriment. 
 9.b. Compensation for injury, ‘damages’. (French dommages et intérêts medieval Latin damna et interesse.) Obs. rare.
and the examples are two hundred years older than the common meaning:  1259 Propter usuras, pœnas,et Interesse, or 1274   Tam super principali, quam super custibus, dampnis, et interesse refundendis

and the penultimate meaning is the technical, financial, meaning
10. a. Money paid for the use of money lent (the principal), or for forbearance of a debt, according to a fixed ratio (rate per cent.).
In medieval Latin interesse (Interest) differed from usura (Usury) in that the latter was avowedly a charge for the use of money, which was forbidden by the Canon Law; whereas originally ‘interesse refers to the compensation which under the Roman Law, was due by the debtor who had made default. The measure of compensation was id quod interest, the difference between the creditor's position in consequence of the debtor's laches and the position which might reasonably have been anticipated as the direct consequence of the debtor's fulfilment of his obligation’. This compensation was always permissible when it could be shown that such loss had really arisen (damnum emergens). At a later period, lucrum cessans—loss of profit through inability to reinvest—was also recognized as giving a claim to interesse; both cases appear to be included in the formula damna et interesse. The interesse was originally a fixed sum specified in the contract; but a percentage reckoned periodically, so as to correspond to the creditor's loss, was afterwards substituted (as sometimes in England in the first half of the 13th cent.). Interest in the modern sense was first sanctioned by law (though apparently under cover of the mediæval theory) by 37 Hen. VIII, c. 9 (see quot. 1545); this statute was repealed in 1552, but re-enacted in 1571.
1529   King Henry VIII Instr. Orator Rome,   Which money..shalbe truely repayde with interesse.
1545   Act 37 Hen. VIII c. 9 §3   Be it also enacted..that no person or persons..by way or meane of any corrupte bargayne, loone, eschaunge, chevisaunce, shifte, interest of any wares..accepte or take, in lucre or gaynes, for the forbearinge or givinge daye of payment of one hole yere of and for his or their money..above the sume of tenne poundes in the hundred.
Originally interest was the charge a debtor had to pay a creditor for non-repayment, it was a compensation payment.  In the Middle Ages, this damnum emergens became lucrum cessans, a payment from the borrower to the lender in compensation for the loss of investment opportunities available to the lender.  Over time interest came to indicate "a right or title to, a claim upon, or a share in" something.

It is here that I see the crux, interests imply a stake suggesting that the hidden hand will only work if an individual has a stake in society.
One aspect of Hirschman's account that had me thinking is that the implication was there is an internal dialogue taking place within individuals, there was no reference to the external, cultural pressures, on an individual.

The reason I thought about this is that when faced with a moral decision, I am not concious of sublimating one passion with another, rather I am concious of peer-pressure, what my friends and family might think of me.  I guess in the framework that Hirschman presents this would be covered by 'honour', and maybe  explicitly highlighting the fear of shame, a feature of Calvinism, might not be well received by an 'Enlightened' audience.  Another explanation could be that the likes of Montesquieu, Hume and Smith took it as given that an individual is a part of the society that they will improve by pursuing their personal interests.  None the less, it struck me that if the individual is set adrift from their society and culture, their morals are likely to be compromised (anyone who has experienced working as an ex patriate might be familiar with this phenomenon; I witnessed it working in Abu Dhabi in the 1990s, where adultery was the norm amongst westerners, not the exception).  This to me is a the heart of The Pirate Fairy, and a central risk of Seasteading.

One character whom one might expect to appear in Hirschman's account, but does not, is Hugo Grotius.  Grotius is widely regarded as setting the foundations of international relations in the modern era and Hedley Bull describes a contemporary interpretation of Grotius' theory of 'international society' as
A society of states (or international society) exists when a group of states, conscious of certain common interests and common values, form a society in the sense that they conceive themselves to be bound by a common set of rules in their relations with one another, and share in the working of common institutions. If states today form an international society . . . this is because, recognising certain common interests and perhaps some common values, they regard themselves as bound by certain rules in their dealings with one another, such as that they should respect one another's claims to independence, that they should honour agreements into which they enter, and that they should be subject to certain limitations in exercising force against one another. 
On the basis of Hirschman's claim that during the seventeenth and eighteenth centuries, philosophers adapted state-craft to individual behaviour, I think we can gain insight into the role of interests in guiding the hidden hand by replacing 'state' with 'individual' in the above quotation.

My intuition is that if people become alienated from society then we can't rely on their self-interest promoting the well-being of society, as proposed by Smith and others.  When Zarina becomes alienated from the other fairies she loses here good judgement.  Whether Seasteaders can construct a 'new Jerusalem', as the puritan immigrants to north America set out to do in the seventeenth century, remains to be seen.  But I am doubtful: the 'founding fathers' had a definite moral compass that bound them together, not an infantile desire to do as they see best justified by their personal wealth.

Mark Carney's recent Mansion House speech touches on some of these issues.  For example, when Carney argues that
The Bank of England’s general approach was consistent with the attitude of FICC markets, which historically relied heavily on informal codes and understandings. That informality was well suited to an earlier age. But as markets innovated and grew, it proved wanting. 
can the "informality was well suited to an earlier age" be interpreted as that when the City was less 'global', and market participants closer to each other, they shared 'common interests' which become diluted as traders become separated and potentially alienated (as in the case of Zarina).

Carney goes on to argue that "Real markets are resilient, fair and effective. They maintain their social licence." and "Real markets don’t just happen; they depend on the quality of market infrastructure."  Developing these themes, he highlights the final report the Fair and Effective Markets Review, noting that
Firms’ systems of internal governance and control that were incapable of asserting the interests of firms – let alone the wider market – over those of close-knit trading staff;
highlighting how market participants must share common interests that transcend the local interests of trading cliques.   Carney goes on to observe that the result was
All these factors contributed to an ethical drift. Unethical behaviour went unchecked, proliferated and eventually became the norm. Too many participants neither felt responsible for the system nor recognised the full impact of their actions. For too many, the City stopped at its gates, though its influence extended far beyond. 
I am fairly sure that these comments are relevant as much to those advocating Seasteading as Fixed Income, Currencies and Commodity traders cast adrift from broader society.

Saturday, 6 June 2015

Finance and Mathematics: where is the ethical malaise?

This is a draft of an article that has been accepted by The Mathematical Intelligencer and offers an argument very similar to Romer's 'mathiness' argument as discussed in my previous post.

Discussions of the role of mathematics in finance appearing in The Mathematical Intelligencer can be split into two classes. Marc Rogalski [26] and Jonathan Korman [18] capture a widespread fury at a collapse in commercial ethics while Ivar Ekeland [6] and Peter Haggstrom [13] offer economic facts. The conclusions of Rogalski and Korman can be summarised as that mathematicians should spurn the financial world; Haggstrom and Ekeland point to technocratic solutions, characterised by better regulation. I do not buy into the argument that the problems of finance can be solved by regulations, it is, as both the U.K. and U.S. governments have identified1, an ethical problem. But I also do not think it is virtuous for mathematicians to spurn finance, so I am not completely aligned with Rogalski or Korman. My position is that mathematicians should be forthright in presenting financial mathematics as a discipline centred on the concept of justice, making it explicit that successful finance must be moral finance.

During the Financial Crisis of 2007-2009 I was the U.K. Research Council's ‘Academic Fellow' in Financial Mathematics, meaning my background is, like Ekeland and Haggestrom, that of a financial mathematics ‘insider'. In this role I was expected to explain the discipline I represented to U.K. policy makers, both in government and in the media. As I attempted to meet these expectations I took an unconventional step for a mathematician and started looking into the origins of mathematical probability, both technically and the cultural context. I noticed that in solving the Problem of Points, in 1654, Pascal and Fermat were pricing a derivative contract on a binomial tree, and their solution would today be recognised as the Cox-Ross-Rubinstein option pricing model, published in 1978. There was a difference between the 1654 and 1978 models, CRR give a methodology for identifying the branch probabilities on the tree, Pascal and Fermat assume they are a half. This raised the question: how did Pascal and Fermat conceive the probabilities they used?

The answer came, initially, in some work the historian Edith Dudley Sylla did in the process of translating the Ars Conjectandi. Sylla observes that
equity among associates or partners rather than probabilities in the sense of relative frequencies provided the foundation for the earliest mathematical probability theory.[28, p 13]
and that
the foundations (...) [were] not chance (frequentist probability), but rather sors (expectation) in so far as it was involved in implicit contracts and the just treatment of partners.[28, p 28]

Intrigued by this point, I followed the path of mathematical probability from the origins of western mathematics in Fibonacci's text on financial mathematics, the Liber Abaci, to contemporary mathematics' Fundamental Theorem of Asset Pricing. The Fundamental Theorem is a consequence of Black and Scholes' paper on pricing options [2] that is based on the arbitrage argument, which originates in Aristotle's discussion of justice in commercial exchange in Nicomachean Ethics and features in the Liber Abaci. The novelty of contemporary financial mathematics is not in the techniques used, or the products traded2, but in the fact that, today, mathematicians approach the problem of one of ‘positive' science, not ‘normative' ethics. For example, Black and Scholes opens with the observation that “it should not be possible to make sure profits”3, appealing to a consequentialist argument that if you get your price wrong4 someone will bankrupt you, where as medieval merchants were conscious of the Catholic Church's injunction that a riskless profit was turpe lucrum (filthy money).

Back in 2009, at the start of this journey, I took a position similar to Ekeland: there are economic laws that “outweigh the puny might of mathematicians” and the solution is in the hands of regulators. Today I have a darker view of the role of mathematics in the markets.

European science is often distinguished from other cultures' science by the fact that it is mathematicised and there is an argument, first offered in 19345 but developed more recently [1217], that this came out of Aristotle's examination of ethics in commerce. Justice in exchange is distinguished from distributive and restorative justice by Aristotle as being characterised by equality, “there is no giving in exchange”, it is a reciprocal arrangement essential in binding society together and for social cohesion [17, p 51; 3, 1133a15-30]. It is notable that Aristotle approached this ethical problem mathematically, since he rarely applied mathematics to the physical world elsewhere [12, p 75; 4, p 13; 3, 1094b15-28]. On this basis, the medieval Scholastic scholars realised that money was a universal measure, up until then Hellenic thought (including Islamic scholarship of the time) had considered different physical properties, such as time and space, to be ‘incommensurable' - it was impossible to represent momentum, mass x length/time, mathematically - and it was this property of money as a universal measure that enabled the development of modern physics based on mathematics [417]. To appreciate the point, Copernicus wrote on money before he wrote on the planets; Stevin, founder of the influential Dutch Mathematical School, was a financier; the financier Gresham endowed the first chair of mathematics in England and laid the foundations for the Royal Society. Recently, Bernard Bru has explained the significance of Bachelier's experience of stock-markets in the development of Kolmogorov's ideas on probability [30, pp 20-21]. The close relationship between mathematics and finance is born out of the fact that finance is concerned with relations, measured as prices, between objects. Finance informs mathematics on measurement and uncertainty while mathematics is critical to finance because we cannot perform experiments in the economy. It might not be possible to divorce the two disciplines, even if we wanted to.

The classicist Richard Seaford offers some insight into this account when he goes into the roots of western thought and argues that Greek philosophy, including democracy and mathematics, are a consequence of Archaic Greece's use of money [27]. He notes that other ancient civilisations were based on centralised re-distribution, where as pre-Socratic Greek society was based on exchange, reliant on a conception of equality and reciprocity. He suggests that when the Pythagoreans assigned a number to every object, they were, in fact, pricing the object.

The view that finance is socially corrosive is more novel than the practices of finance. One way of approaching Shakespeare's The Merchant of Venice is as a study of the four natures of love - erotic, familial, friendship and the highest form of love - charity/caritas/agapi - and Shakespeare personifies charity in the form of Antonio, the merchant of Venice. Throughout the seventeenth and eighteenth century, commerce was considered a civilising influence, in The Rights of Man (1792) Thomas Paine writes “commerce is a pacific system, operating to cordialise mankind” following a path laid by Montesquieu, Hume, Condorcet and Adam Smith [158].

After the Industrial Revolution, these attitudes all but disappeared and today it would be inconceivable to personify Christian love in the form of a merchant. An explanation for this cultural shift can be found in Dialectic of Enlightenment [1] where it is argued that the Enlightenment led to the objectification of nature and its mathematisation, which in turn leads to ‘instrumental mindsets' that look to optimally achieve predetermined ends in the context of an underlying need to control external events. Where as during the seventeenth and eighteenth centuries public spaces emerged, the public sphere, which facilitated rational discussion that sought the truth in support of the public good, through the nineteenth century, mass circulation mechanisms came to dominate the public sphere and these were controlled by private interests. As a consequence, the public became consumers of information rather than creators of a consensus through engagement with information [11].

One aspect of this process of alienation for the public is the attitude that mathematics is an almost mystical pursuit that can reveal hidden truths, but only for the initiated, a recurring theme in the presentation of mathematics in popular culture. This is nicely captured in a documentary film on the development of the Black-Scholes-Merton equation where the economist Paul Samulelson describes how he ‘discovered' Bachelier's thesis, much as Indiana Jones might discover a magical artefact,
In the early 1950s I was able to locate by chance this unknown book by a French graduate student in 1900 rotting in the library of the University of Paris and when I opened it up it was as if a whole new world was laid out before me.6

This trope might seem benign in the context of popularising mathematics, but when combined with the idea that mathematics is immutable and indubitable, themes of traditional histories and philosophies of mathematics, we are given the impression, to paraphrase William Tait, that
A mathematical proposition is about a certain structure, such as financial markets. It refers to prices and relations among them. If it is true, it is so in virtue of a certain fact about markets. And this fact may obtain even if we do not or cannot know that it does. [29, p 341]

While mathematicians themselves might not make this claim explicitly, mathematics has been used by many to obscure and legitimise financial activity, passing over any consideration of the ethical implications of those activities. Ekeland might see mathematics as ‘puny', but others value its authority and there are too many examples of how mathematics has been employed to prevent democratic oversight of the markets. In their submission to the Parliamentary Commission on Banking Standards in 2013 the Bank of England was highly critical of how some firms have used advanced mathematical techniques to ‘pull the wool' over the eyes of the regulator [22, v. II, para. 89] while U.S. authorities identified that this type of mathematical sleight of hand played a part in the ‘London whale' episode [23, p 14]. The existence of the Gaussian copula as a ‘'truth-teller' of the value of complex debt portfolios played a central role in the Crisis of 2007-2009, justifying the actions of banks, despite its short-comings being known to mathematicians [31219]. In the early 1970s, the Black-Scholes-Merton framework played an important part in legitimising the re-emergence of financial derivatives markets [20, p 158]. As long ago as 1877 a large, corporate, insurer defended their actions in undermining fraternal/mutual insurers to legislators with the argument that
There are certain fundamental rules †which can only be understood by actuaries, and it is impossible for me to go into here [19, p 198]

An antidote to the causes and consequences of ‘instrumental mindsets' identified above is to turn away from the philosophical paradigm of Foundationalism, which sees language as being made up of statements that are either true or false and complex statements are valid if they can be deduced from true primitive statements. This approach is exemplified in the standard mathematical technique of axiom-theorem-proof. An alternative approach is to shift the focus from what language says (true or false) to what it does. Specifically, the function of language is to enable different people to come to a shared understanding and achieve a consensus, this is defined as discourse7 [10]. Because discourse is based on making a claim, the claim being challenged and then justified, to be successful discourse needs to be governed by rules, or norms. The most basic rules are logical and semantic, on top of these are norms governing procedure, such as sincerity, and finally there are norms to ensure that discourse is not subject to coercion or skewed by inequality. This is why reciprocity is central to financial mathematics, it is a norm of market discourse, embedded in the language of mathematics.

Mathematics has not been passive in recent financial crises and I would argue that if mathematicians are not part of the solution, they are part of the problem. For me, the correct response of mathematicians to the financial crises is to work in support of those who wish to redirect finance from regarding markets as competitive arenas to seeing them as centres of cooperative, democratic, discourse8. In this vein I have developed the argument [16] that reciprocity is the central message of financial mathematics and it is one of three norms of market discourse, the others being sincerity and charity. For this case to be coherent I have followed Putnam [25] and abandoned the idea of mathematics being a value-neutral truth-teller, rather it is a means of discourse. This is a significant step if you perceive mathematics as being monogamous with the natural and physical sciences, or even celibate. I believe certain twentieth century mathematicians, such as Poincaré9 [14], Ramsey [5] and Putnam, would have sympathy with the approach I take, particularly in the cases where mathematics is employed in the social and human sciences.

Notes

1In the U.S. Financial Crisis Inquiry Commission’s report of 2011 and the U.K. ‘Changing Banking for Good’ report of 2013.

2Most of these products existed in medieval times, the ‘Triple Contract’ shares the features of ‘structured products’ prominent in the crisis. ‘Mortgage Backed Securities’ were introduced in the U.S. in the late nineteenth century — see [19, Ch 5] for an enlightening account. It is not in the interests of well dressed bankers to tell their clients that what they are charging fat fees for existed before Columbus.

3This is the basis of Ekeland’s argument.

4Ramsey’s ‘Dutch book’ argument, which has been described as a modern version of the ‘Golden Rule’, “Do unto others as you would have them do unto you”, Luke 6:31.

5By the Marxist theoretician Borkenau in The Transition from the Feudal to the Bourgeois World View.

6The programme is ‘The Midas Formula’ also known as ‘The Trillion Dollar Bet’ and is available on YouTube. The relevant section is around 12:20/48:53 minutes. A transcript is available at http://www.bbc.co.uk/science/horizon/1999/midas_script.shtml.

7According to a recent translator of Fibonacci, a key feature of the techniques given in the Liber Abaci was that they enabled ideas to be transmitted and improved upon [7, Introduction].

8An I.M.F. paper on the crisis, Resolution of Banking Crises: The Good the Bad and the Ugly (WP/10/146) reveals that countries with a significant proportion of ‘not for profit’ mutual banks (e.g. Germany, France, Italy) did not require the public bailouts needed in the U.K. and U.S. — finance is not necessarily capitalist.

9Poincaré’s approach is captured in his observation “these two propositions ‘the earth turns round,’ and ‘it is more convenient to suppose that the earth turns round,’ have one and the same meaning” [24, p 91].


References


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Wednesday, 3 June 2015

Mathiness: not just a problem of macro-economics

I was aware of the "mathiness" discussion initiated by the macro-economist Paul Romer, but have only recently read the articles because while the discussion was taking place I was finishing of an article for The Mathematical Intelligencer that presents a remarkably similar argument (noting that mathematicians consider a coffee cup and doughnut to be the same).

Romer's concern is in the field of economic growth - an area I am unfamiliar with -  but two related statements caught my attention
For the last two decades, growth theory has made no scientific progress  toward a consensus. ... The question posed here is why the methods of science have failed to resolve the disagreement between these two groups.
and, postulating on why science has failed to come to a consensus, Romer offers an explanation as "mathiness"
Like mathematical theory, mathiness uses a mixture of words and symbols, but instead of making tight links, it leaves ample room for slippage between statements in natural versus formal language and between statements with theoretical as opposed to empirical content.
My article for the Intelligencer is titled "Finance and Mathematics: where is the ethical malaise" and was written in response to a series of articles  about the role of mathematics in financial crises.  I begin my piece
Discussions of the role of mathematics in finance appearing in The Mathematical Intelligencer can be split into two classes. Marc Rogalski and Jonathan Korman capture a widespread fury at a collapse in commercial ethics while Ivar Ekeland  and Peter Haggstrom off er economic facts. The conclusions of Rogalski and Korman can be summarised as that mathematicians should spurn the financial world; Haggstrom and Ekeland point to technocratic solutions, characterised by better regulation. I do not buy into the argument that the problems of finance can be solved by regulations, it is, as both the U.K. and U.S. governments have identified, an ethical problem.
I go onto to explain that mathematics has not been neutral in recent financial crises
In their submission to the Parliamentary Commission on Banking Standards in 2013 the Bank of England was highly critical of how some fi rms have used advanced mathematical techniques to 'pull the wool' over the eyes of the regulator [para. 89] while U.S. authorities identified that this type of mathematical sleight of hand played a part in the 'London whale' episode [p 14]. The existence of the Gaussian copula as a 'truth-teller' of the value of complex debt portfolios played a central role in the Crisis of 2007-2009, justifying the actions of banks, despite its short-comings being known to mathematicians. In the early 1970s, the Black-Scholes-Merton framework played an important part in legitimising the re-emergence of financial derivatives markets. As long ago as 1877 a large, corporate, insurer defended their actions in undermining fraternal/mutual insurers to legislators with the argument that
 "There are certain fundamental rules . . . which can only be understood by actuaries, and it is impossible for me to go into here [p 198]"
 In my piece, for the mathematics community, I note that while mathematicians might see these abuses, which I am fairly certain could be ascribed to 'mathiness' as coined by Romer, as being abuses of mathematics, we do bear some responsibility.

Many mathematicians, but probably only a minority, argue that there is an issue with mathematics in that it is often used to obscure rather than enlighten.  Part of this trope is the presentation of mathematics as a mystical key that can unlock hidden truths:













In economics, my favourite example is Samuelson's account of how he 'discovered' Bachelier's thesis, much as Indiana Jones might uncover a magical artefact

video
(From the BBC programme "The Midas Formula/The Trillion dollar Bet")


This all might seem benign in to context of encouraging people to engage with mathematics, but when combined with he dominant philosophical paradigm of Foundationalism and finance, problems emerge.

Foundationalism sees language as being made up of statements that are either true or false and complex statements are valid if they can be deduced from true primitive statements. This approach is exemplified in the standard mathematical technique of axiom-theorem-proof and so arguments presented mathematically are automatically imbued with the quality of 'truth' and so hold authority.

I then give a Habermasian explanation of what happens when mathematics and finance come together.
the Enlightenment led to the objectification of nature and its mathematisation, which in turn leads to 'instrumental mindsets' that look to optimally achieve predetermined ends in the context of an underlying need to control external events. Where as during the seventeenth and eighteenth centuries public spaces emerged, the public sphere, which facilitated rational discussion that sought the truth in support of the public good, through the nineteenth century, mass circulation mechanisms came to dominate the public sphere and these were controlled by private interests. As a consequence, the public became consumers of information rather than creators of a consensus through engagement with information.
Habermas, and Pragmatic philosophy more generally, offer an antidote by switching the emphasis of what language says (whether it is true or false) to what it does
Specifically, the function of language is to enable different people to come to a shared understanding and achieve a consensus, this is de fined as discourse. Because discourse is based on making a claim, the claim being challenged and then justified, to be successful discourse needs to be governed by rules, or norms. The most basic rules are logical and semantic, on top of these are norms governing procedure, such as sincerity, and finally there are norms to ensure that discourse is not subject to coercion or skewed by inequality.
This is the basis of my claim that Reciprocity is a Foundation of Financial Economics.

With regard to the 'mathiness' discussion it is interesting to see that Romer argues the issues are in the collapse of 'economic norms', so are diagnosis and treatment appear aligned.  My criticism of Romer is mild, and it is that he has not presented his case in the context of Pragmatism, which would provide him with a firmer foundation for his case (I recommend Haack and Misak  as bedrocks).

However, I do not see my contribution as calming the criticism there has been for Romer, because my suggestion is the issue is not with one, or another, local mis-understanding but a fundamental issue with the dominant pardigm supporting science.  Economists might disagree on their growth models but they are likely to agree that science is based on Foundationalism.  This said, the problems Romer, and I, identify are pervasive, with science being unable to resolve many problems ranging from finance to climate change.

Thursday, 29 January 2015

A moral case for bank money

Finance is a skeleton that supports the development of a healthy society, not a utility that plumbs the economy together. The justification for this observation is historical. Richard Seaford has argued that the culture that emerged in Greece some two and a half thousand years ago, creating a unique approach to science and democratic politics, was a consequence of a peculiar Greek invention; money, a token that signifies trust between citizens. The flowering of European culture, and the genesis of modern science, in thirteenth century Europe followed, and some argue was a consequence of, a period of rapid monetisation of society that initiated the end of feudalism. Similarly, western Europe’s development accelerated ahead of the rest of the world in the seventeenth century powered by financial innovations in the Netherlands and Britain.

Charles Mackay in his classic comparison of England’s South Sea Bubble and France’s, almost simultaneous, Mississippi Bubble, emphasises the different reactions in France and Britain to the credit bubbles. In the aftermath of the crises, the French inhibited the development of private banks but maintained the autocratic political system, whereas the British reformed the political system and enabled the development of finance. The results of Britain’s Financial Revolution were Agricultural and Industrial Revolutions along with the eclipse of France as a global power. For France, dependent on taxation to fund the state, there was the ultimate collapse of the political system in bloody revolution.

Getting the structure of our financial system right is not a trivial matter.

One argument gaining support is that the root of recent problems in finance is the private creation of money by banks, and so the solution is to strip banks of this ability. What this would entail is not clear but a core theme is that transactions would involve minted cash (physical or electronic), not bank money. We can visualise the practical consequence of this in little brown envelopes on pay-day containing coins and Bank of England notes. No bank transfers, certainly not in the foreseeable future, meaning no debit cards at the supermarket checkout and the replacement of cyber-crime by good old-fashioned robbery. This makes concrete part of the problem  Martin Wolf identifies when he makes the observation that "The transition to a system in which money creation is separated from financial intermediation would be feasible, albeit complex."   It might prove impossible to get through the Christmas binge, when there is widespread short-term demand for cash.  Could a computer system cope with the funds transfers associated with Black Fridays and Cyber Mondays without the ability to create money? Banks, in this environment, would come to resemble peer-to-peer lending facilitators and the consequence would be that people who have wealth, or are connected to wealthy networks, could buy expensive things, but for the majority it would be harder to get a mortgage.  While this might sound a bit draconian to the British, Germans still have a preference for cash and traditionally live in rented accommodation, having long connected debts (schulden) and guilt (schuld) and, after all, they have done well economically.

Unfortunately it is not certain that German economic success rests on the German preference for cash. An equally plausible explanation is the structure of the German banking system, which, unlike the British and U.S. systems, is not dominated by private profit seeking banks but has a significant sector of not-for-profit, regional, financial institutions. An IMF paper highlights how countries with this type of financial system, including France and Spain, did not require the massive government bailouts that British and U.S. banks did in 2008-2009. Mutuals and public banks create money in the same way as privately owned banks and so preventing banks from creating money seems to be a rather extreme solution when the problem might be elsewhere.

Calls to prevent banks from creating money to ensure financial stability resemble calls to ban the internal combustion engine to prevent climate change. It would clearly go a long way to solving the problem, in theory, but is totally impractical. One group who would like to see the debate on banking reform focus in on money creation are the banks themselves, because they can be confident that if this is where the debate is centred, nothing will change. Most voters need bank credit just as they need cars.

I cannot offer a straightforward alternative to preventing banks, or anyone else, making money. I do have an alternative idea of where the problem lies though. If you read about eighteenth century finance it is striking how engaged people were with financial innovations. Well before the South Sea Bubble Daniel Defoe wrote about the problem of banking

Money has a younger sister, a very useful and officious Servant in Trade ... Her name in our Language is call'd CREDIT… This is a coy Lass ... a most necessary, useful, industrious creature: ... [and] a World of Good People lose her Favour, before they well know her Name; others are courting her all their days to no purpose and can never come into her books. If once she is disoblig'd, she's the most difficult to be Friends again with us … for as once to want her, is entirely to lose her; so once to be free from Need of her, is absolutely to posses her.

Lady Credit was seen as a coy mistress, much as Boethius had perceived Fortuna

I know how Fortune is ever most friendly and alluring to those whom she strives to deceive, until she overwhelms them with grief beyond bearing, by deserting them when least expected

Right up until the mid twentieth century credit was represented in this way, with John Strachey writing

The banks are essentially feminine institutions. They create the new money which sets the wheels of production turning again. But they cannot procreate without a spouse. The newly born money must have a father as well as a mother. Someone must take the active, positive role of borrowing, spending, and employing, or the banks will remain barren.

In this conception commerce is a marriage between credit and opportunity with the objective of producing growth. However, Lady Credit is attractive and, as Defoe observed in 1709, sometimes her relations are not so benign

The first Violence they committed was downright Rape ... these new-fashion'd thieves seiz'd upon her, took her Prisoner, toss'd her in a Blanket, ravish'd her, and in short us'd her barbarously, and had almost murther'd her

If women run the risk of sexual assault, the civilised response is not to lock them away out of harm’s reach, but focus on the perpetrators. The problems of finance are not in creating money but in lending money to unsuitable projects.

Through the nineteenth century science became confident that it had tamed fortuna and a consequence was the mechanisation of finance. Credit was no longer a prize to be wooed but a servant to be controlled. As finance became de-humanised the morality of the Quakers, who established many of Britain's financial institutions, was replaced by the profit maximising principle. In the process, people have become alienated from finance and lost the capacity to make their own financial judgements; we need to employ professionals to plan our future.

I have argued that profit maximisation should not be at the heart of commerce, rather the norms (virtues, if you prefer) of reciprocity, sincerity and charity. In this framework mutual mechanisms, including peer-to-peer and crowdfunding, are as legitimate as profit maximising private banks. I believe the advantage of this approach is that it takes as given that the economy is capricious and beyond the control of wise men observing nature and pulling controls. Preventing banks from creating money reflects a desire to freeze the economy in order to stop it becoming chaotic. This is a forlorn hope, to which the collapse of Bretton-Woods is testimony.

If you feel my claim that reciprocity, sincerity and charity should be, or even could be, at the heart of finance is as absurd as preventing banks creating money I would point you to Shakespeare’s The Merchant of Venice. One reading of the play is as a study of the four classical loves: friendship (philia), affection (storge), romantic (eros) and unconditional (agape/caritas/charity). Shakespeare personified charity in the form of Antonio, the Merchant of Venice; why did he do that?




I wrote this piece, arguing against removing banks' ability to create money,  for Res Publica's Disraeli Room blog in response to a post Money Creation and Society: The beginning of the debate on how money is created

The case I present is not technical but moral,  in the sense of mores/moeurs.  I admire Izabella Kaminska's review of the case to strip banks of their money creation powers, and agree with her analysis of the issues, in particular I support the trilateral monetary system, based on sovereign, bank and private money, that she describes.  Specifically, I like her comment that
A more prudent path [to stripping banks of their ability to create money]might just be encouraging both the central bank and the market to get better at identifying over or under issuance where and when it happens, something which could be made easier if private money’s price signal was detached from the state peg.
This lays the foundation, in part, for presenting a moral case, I don't think the solution to credit bubbles lies in how finance is plumbed together, rather the ethical context under which finance is conducted

A further motivation for presenting a moral case originated in my experience of the Scottish Independence referendum, particularly the dismal performance of Alistair Darling, leader of the unionist campaign, in the final TV debate with the leader of the nationalist campaign, Alex Salmond.  A central issue in the campaign was the currency an independent Scotland would use, and Salmond advocated retaining the pound, controlled by the Bank of England. Darling, as a former Chancellor of the Exchequer had a deep understanding of the technical problems this presented, but Salmond, relying on the public's indifference to these problems and Darling's inability to articulate them, won the debate. 

A common irritant with the Independence Referendum debate was that both parties claimed a vote for them would change everything, but change nothing.  It struck me that the case presented by Positive Money was similar; stripping the bank's of their ability to create money will end the boom and bust cycle, to the benefit of the public, without changing individuals' experience of banking.  The recent Greek election, similarly, centred on the claim that the Greeks can re-negotiate their rescue package, to the benefit of the electorate, without the negative consequences of leaving the Eurozone.  Personally I feel the chance of this turning to tragedy or comedy are about equal, but the most likely outcome will be a yawn: the debt will be re-negotiated, the ECB having had five years to ring-fence the problem.  However, in the context of discussions of bank money it is worth highlighting that the Greek bankruptcy was a consequence of Greek government mis-management, and the austerity was imposed by a troika of public institutions.  Boom and bust is as likely to be caused by public bodies as private banks.

So, my aim in this piece was to side-step the complex technical problems and present a moral argument that might be more accessible to a general audience.

My piece survived on the Res Pubica blog for around two weeks and then was pulled at the request of Ben Dyson, the author of the original piece.  Mr Dyson objected to two 'inaccuracies' in the piece. Since both relate to what might happen if banks are prevented from creating money, and given these are contingent events, I don't think they can, in fact, be described as inaccurate; we have differing opinions. I invited Mr Dyson to engage in public deliberation on the points, through the Disraeli Room blog, but his response was to persuade Res Publica to pull my piece.  An interesting outcome given the claim that the original article was to be the the start of a debate.  What follows, not perfect but an honest attempt to continue the debate, is my original piece. The points of contention were the following in the original,
No bank transfers, certainly not in the foreseeable future, meaning no debit cards at the supermarket checkout and the replacement of cyber-crime by good old-fashioned robbery.  People who have wealth can buy expensive things, but for the majority it would be difficult to get a mortgage and impossible to use a credit card to get through the Christmas binge. While this might sound a bit draconian to the British, Germans still have a preference for cash and live in rented accommodation, having long connected debts (schulden) and guilt (schuld) and, after all, they have done well economically.

which has been clarified in this version.




Thursday, 4 December 2014

Maths and morals, economics and greed

This piece has been posted on the Res Publica think tank Disraeli Room blog.

I recently asked a prominent mathematician who once ran a hedge fund, Doyne Farmer, whether seeking to make a riskless profit was ethical. I don't think he understood the question. Mathematics has always been part of finance but with the re-introduction of derivatives markets in the 1970s and their growth in the nineties, ‘quants’, trained in engineering, physics and mathematics, came to dominate the ‘casino banking’ that is widely criticised. My concern is that the quants are not amenable to questions of morality, and so the problems of finance are going to be difficult to resolve without finding the right way of communicating with the bankers who see themselves as scientists.

I am a mathematician who works on financial problems who became interested in the role of mathematics in the financial crises since 2006. Initially my focus was on explaining why mathematics is so critical to modern banking in response to, for example, the FSA's misplaced assessment, in the Turner Review, that there had been an over-reliance on sophisticated mathematics in the lead up to the crisis (the techniques they discussed were simplistic and not part of mathematics). Subsequent, more authoritative, reviews such as the US Financial Crisis Inquiry Commission and the Parliamentary Commission on Banking Standards removed mathematics from centre stage and replaced it with ethics.

At first sight this re-direction of blame was a relief, but I soon realised it raises a concern: if the problem of finance is one of ethics, what role does mathematics have in its solution? The immediate response is none, but the concern is that if we believe that maths, physics and engineering are concerned with what is, and have nothing to say about what ought to be, we will struggle to convince people trained in the scientific tradition to take commercial corporate morality seriously. The Chartered Institute of Bankers are working on Professional Standards but are struggling to engage with the quants, who operate the casino branch of banking, because the quants believe science is value neutral; it delivers truths beyond morality.

Arguing that ethos and purpose should be placed at the heart of finance misses the point that there is an ethos and purpose at the heart of modern finance. The ethos is based on consequential morality: that an individual seeking a profit has consequential societal benefit, and excesses can be restrained by well-crafted rules. This results in the purpose of finance being any profit within the letter of the law. This ethos presupposes, firstly, that it is possible to calculate consequences and secondly, that restraining regulations can be well crafted. It is a very scientific ethos whose origins can be traced back to Descartes, and comes to us via the British empiricists, Hume and J. S. Mill. It is the ethos that has led to the contemporary study of economics imbuing the student with greed. Many quants would regard the doctrine as being comparable to Darwinian evolution and the Big Bang Theory. This brings to mind Alasdair MacIntyre's ‘disquieting suggestion’ that modern society has completely lost the ability to make moral judgements and I see it as the brick wall that most attempts to reform banking will crash into.

I believe the brick wall can be dismantled relatively easily: by recognising that many of the practices of contemporary finance associated with ‘casino banking’ were widespread before the eighteenth century. Unlike today, they were undertaken in the context not of consequentialist or deontological ethics, but of virtue ethics that focuses on good practice. It might seem surprising that I suggest this is a relatively easy approach. What make it easy is that rather than criticising modern finance on the basis that it is degraded from a mythic golden age of finance, the starting point is the doux-commerce thesis that finance is civilising. Rather than characterising bankers as amoral spivs, they are presented as paragons of rational morality and the approach gives the bankers the opportunity to carry on their activities while, critically, reconstructing their own ethos.  I developed this representation in my paper Reciprocity as a Foundation of Financial Economics.

The hurdle this approach needs to cross is that of the dominant ideologies of markets. The market ideology holds that the market mechanism will deliver optimal solutions to society, while anti-market ideology argues that profits are degrading and markets are destructive. The hurdle can be crossed by ignoring both these ideologies and analysing the role that money and markets have played in forming both Western science and democracy. We need to represent markets as centres of communication and deliberation, not as competitive arenas driven by profit maximisation. The clue is in the word forum, which defined both the market place and the political centre of a Roman city.

Wednesday, 17 September 2014

Hyperbolic (or Simple) Discounting

I was critical of Doyne Farmer in my previous post, and in response I got a message from someone I respect
But I like Farmer's work... solar costs follow Moore's law; and we should value future more (hyperbolic discount rates).
What struck me is that there is an incongruity in associating Moore's Law and Hyperbolic discounting, which I shall explain, and when combined with the first statement points to something more peculiar: do ideas now derive their legitimacy from individuals rather than in relation to each other?

The Moore's Law statement is easier to explain and I assume it comes from this paper (a nice summary was published in Forbes) that investigates the theories
that cost [of production] decreases as a power law of cumulative production [Wright's Law]. An alternative hypothesis is Moore's law, which can be generalized to say that technologies improve exponentially with time.
and that
Our results show that technological progress is forecastable, with the square root of the logarithmic error growing linearly with the forecasting horizon at a typical rate of 2.5% per year. 
I think this final statement exemplifies the gulf between Farmer and myself: he presents technological growth as a matter of (statistical) fact, I see it as one of commercial values (the argument is presented by Deirdre McCloskey, particularly in Bourgeois Dignity).  But this post is not about that.

I suspect the reference to hyperbolic discounting is related to this paper.  Before commenting on Farmer's specific paper I would like to make some comment on the idea of hyperbolic discounting in general.  A hyperbolic discount factor is usually described as follows

f_H(D)=\frac{1}{1+rT}\,

where k is the rate of discounting and D is the maturity (I apologise for the notation I am lifting equation .png from elsewhere to save time).  They are contrasted with exponential discounting factors

f_E(D)=e^{-kD}\,.
The statement the hyperbolic discounting implies valuing the future more is a bit naive.  If we fix k then the decline in the exponential discount factor is faster than decline in the hyperbolic discount factor, but this assumes the k in both equations have equivalent meaning, which is not the case - and my undergraduate actuarial students get annoyed with me when suggest (in the context of discrete time derivative pricing) they are.  If we do not assume the rates are the same, we can see we can choose a rate for the exponential that gives the same discount factor as the hyperbolic:
Exponential discounting does not imply, a priori, that the future is valued less, the discount rate , k, determines how we value the future.

Farmer points out that hyperbolic functions decrease at a lower rate than exponential functions and so in the limit as time approaches infinity, hyperbolic functions will always value the future more than exponential discounting.  Farmer goes on to suggest that in certain cases of hyperbolic discounting "there is an infinite weight on the far future", this is problematic as if decision making placed infinite weight on the far future we would never consume now, but would have resources available at the end of time when the universe dies.  More technically, these discount functions would contravene the 'transversality condition', which originates in classical mechanics.

Classically in finance, a discount factor is given in terms of hyperbolic discount factor and one uses a D-specific value for k, obtained from the yield-curve.  This gets to the heart of the difference between exponential and hyperbolic discounting; in exponential discounting it is usually assumed that the rate k is constant, and the discounting is time-consistent, where as in hyperbolic discounting the rate k is time-dependent.  This is why the exponential discount function is deemed not to fit Thaler's empirical data, because it is assumed k is fixed, independent of D.

However, it should be noted that the whole field of interest rate models in mathematical finance is concerned with relating the exponential discount rate to the yield curve in order to identify the right discount factor, and in such models it is (generally) assumed that the exponential discount rate is time dependent, and usually stochastic.

To me the discussion of hyperbolic discounting is symptomatic of much of behavioural finance, in that it introduces a sophisticated term into finance for something that has been understood for some time.  My first reaction to hyperbolic discounting was "isn't this just simple (as distinct from compound) discounting", this is a naive but none the less not an unreasonable first approximation. I dislike the adoption of the difficult term "hyperbolic" to re-package the idea that the yield-curve observed in experiments is (peculiarly) decreasing (in itself not a trivial concept) as I see it as "mystifying" finance.  I often associate this process with claims that financial theory is novel.  For example Farmer asserts that exponential discounting was "originally posited by Samuelson (1937) and put on an axiomatic foundation by Koopmans (1960)."  It might come as both a surprise, and a disappointment, to Prof Farmer to learn that the number "e" was first identified by James Bernoulli in 1683,a few years before Newton's  Principia, by considering how a bank account grew as the time between interest payments became infinitesimally small, a year later Leibnitz tackled the problem in the abstract  and arrived at the same answer.  In fact, the problem of Brachistochrone curve, a key step in the development of dynamics, makes a related connection between Bernoulli, Leibnitz, Newton and the transversality condition mentioned above.

The issue I have with hyperbolic discounting is similar to the issue I have with"Prospect Theory"; a key insight of which is that utility functions are S-shaped, this was observed by Friedman and Savage in their 1948 paper The Utility Analysis of Choices Involving Risk (Kahneman and Tversky's paper of 1979, Prospect Theory: An Analysis of Decision Under Risk, has 10 times the citations as Friedman and Savage).  I wonder if this is a reflection of the higher status of the natural sciences over the social sciences: when an economist and a statistician make the observation, it is ignored (partially because it makes the optimisation problem hard), if psychologists make similar observations, admittedly armed with experimental data, it is taken seriously.  I have already discussed similar issues I have with "physics imperialism".  There is also the assumption that because when people are presented with the choices in the experiment choose to value future payoffs peculiarly highly, this is in some way "correct".  Mathematics has a long history of debunking "common sense" because it requires careful thinking.  It is peculiar to value distant payoffs more highly because there is the chance that you die waiting (the experiments usually involve cash payoffs to participants, not public goods).

What perplexes me is that, on the one hand Moore's Law, and the exponential growth of technology, is perceived as reasonable, where as on the other, exponential growth of the much simpler process of money in a bank account, is perceived as unreasonable.  Now some might argue that I miss the essential nature of hyperbolic discounting in associating it with interest accrual, but I would claim this is the essential point.

Financial "behaviour" is that interest is compounded, not simple, and so when discounting I suggest it is more coherent to employ exponential discounting with a non-constant discount rate than try and fit a constant hyperbolic discount rate.  I think this is a preferable approach because it emphasises the dynamic (and contingent) nature of discounting, rather than arguing about the "true" model and its seeking its "true" parameters.

Basically I see the role of academics as making things coherent, identifying the relationship between ideas.  I feel this places me outside the norm, where academic success seems to be measured by coming up with new ideas, even if not new and however problematic they are.  What I find worrying is that there appears to be an emergence of a "cult of personality" in science, where by people express an allegiance to an individual who personifies correct thinking, rather than autonomously challenging authority.  Maybe that's just because I have been too close to the Scottish independence referendum campaign recently and am a bit jaded by it all.