Tuesday 20 March 2018

The Golden Rule

There are two versions of the Golden Rule. The standard is “ Do to others what you want them to do to you” and appears in most developed religions. Colloquially it is “Those that have the gold, make the rules”.

Someone raised this distinction on my work in financial ethics by asking “Are you saying participants in financial markets should be benevolent in how they price instruments?” They answer rhetorically with the observation that the reality is that the markets are motivated by greed and fear with leading market participants acting in a ‘brutish’ manner that motivates the rest to conform. On this basis, ethics needs to be ‘realistic’ in referencing the ‘facts on the ground’ and accommodate human nature. Faced with this reality, you can try to ensure the regulator is of good character (‘superiorly prudent’ to use Adam Smith’s language) and might be able to improve the functioning of markets.

My correspondent referred me to the Menian Dialogue in Thucydides History of the Peloponnesian War as an example of ‘realism’.

This was interesting to me. While I don’t know the full context and Thucydides’ intent, I am confident that there is a widely held view that the behaviour of the Athenian negotiators was an example of hubris; the Menian negotiator even notes that the gods would be on their side. The subsequent defeat of Athens was therefore nemesis. My justification was that hubris/nemesis was a central theme of Greek classical culture along with the idea that a human can never be so sure as to be certain. The Athenian’s were confident that they could sack Menos without fear of reprisal; they were wrong, and I understand the Athenians surrendered to Sparta because they were concerned about the precedent they had set at Menos. Note that there is an important financial connection: the term Romans used for interest was poine the spirit that accompanies Nemesis.

A related topic is this Stoic problem:

A grain merchant from Alexandria arrives at Rhodes, which is gripped by famine.  The merchant knows that other merchants are following him with plentiful supplies of grain, though the town’s inhabitants do not know this.  How should the merchant price the grain he has? 

Cicero, in De Officiis, had argued that the merchant should charge a lower price based on the knowledge of the coming relief. Thomas Aquinas disagreed; the merchant may think that there are more grain shipments on the way, but they do not know. Hence the ‘reality’ of the market prices in Rhodes could be employed. The Franciscans took a different approach, Pierre Jean Olivi, argued that the metaphysical probability of more grain arriving in Rhodes, had a certain reality, which Aquinas was ignoring by focusing on the ‘physical’ reality of the prices being offered in the market. Olivi observed that

The judgement of the value of a thing in exchange seldom or never can be made except through conjecture or probable opinion, and not so precisely, or as if understood and measured by one invisible point, but rather as a fitting latitude within which the diverse judgements of men will differ in estimation.

Olivi realised that market exchange was about equating expectations, not accepting concrete valuations agreed by property owners.  This was a major development over the Pythagorean approach of fixing the relationship between an object and a number.  Olivi regarded uncertain events ‒ such as more grain deliveries, lost ships, or defaults on debts ‒ as influencing prices and so fair exchange had to be based on the sharing and interpretation of information.  This meant that chance could be quantified, and there is a consensus that this observation is the genesis of the idea of mathematical probability.

Changing tack a bit to the issue of ‘power’. I have recently been looking at Beowulf. Beowulf is a rare example of pre-Christian northern European myth and raises the question, why did it survive? One explanation is that it highlighted the transitory nature of human power and so was useful story that Christian missionaries could use in emphasising the transcendent nature of divine power. The Norse myth of Ragnarok has similarly survived and similarly describes the temporality of power (the ‘Muspille’ interpretation). There is a similar structure in the relationship between the Illiad and Odyssey. Anger, honour and power motivate the Illiad whereas Odysseus personifies intelligence (cunning) and a desire to return to domesticity. To me, all these myths emphasise that society has to evolve away from one based the ‘reality of power’ to one based on the application of intelligence. The pragmatic explanation is that a society based on rational reflection and discourse is better able to respond to uncertainty; this is why democratic societies thrive.

These thoughts develop something I touch upon in my book is that there is a train of thought linking Thucydides, Hobbes, Descartes, Spinoza and through to Nietzsche and Schmidt that focuses on the reality of power that I reject. The problem, as I see it, is finance is fundamentally concerned with uncertainty. This means that one day you might clearly perceive what is in your best interests (Athens' subjugation of Melos) but you misunderstood, resulting in catastrophe. This is the pragmatic line, which emerged with Pierce's rejection of Cartesian certainties that he saw at the root of the US Civil War. Cheryl Misak's Truth, Politics and Morality informs me that the antidote is deliberative and I give a series of examples in my book about how (well functioning) markets undermine power. On this basis, I take a pragmatic position on ethics, i.e. culture is an environment in which practices that “work” evolve and these become habituated (the approximate origin of the Greek root of ‘ethics’, the Latin root of ‘morals’). For example, if a society wants to grow its population, contraception and abortion become immoral; if a society wants to limit population growth, they become legitimate.

On the specific issue of benevolence, I introduce the idea of charity in commerce through Shakespeare's The Merchant of Venice, which I present as an argument against "iron laws" and in favour of "merciful judgement"; that is don't trust the model but use judgement. I describe how British finance was built on Quaker institutions that had charity/benevolence as a keystone and there are numerous accounts of how they were able to prosper in a very uncertain environment because they put great store in charity, reciprocity and sincerity. Finally I describe the collapse of LTCM as being a consequence of a lack of charity. LTCM believed it was impregnable (like Athens) and so did not feel the need to act charitably. The account of their failure I use is they got the structuring of a fax wrong ("We need more money because the markets are in turmoil and there are lots of opportunities" instead of "There are lots of opportunities because the market is in turmoil, do you want to invest?") and in the resulting run they had no reliable friends.

Financial crises, I believe, can be characterised as representing a paradigm change, where an old ‘reality’ is replaced by a new reality. In order to inhibit the development of crises, people need to be doubtful of their circumstances and there need to be ways to allow opinions to change slowly without a (mathematical) catastrophe. There is the example of how the powers who created the Bretton Woods system could not conceive of the eclipsing of British and French power by German and Japanese economic might in the 1960s. J. P. Morgan doubted the profitability of CDO of MBS and so investigated the apparent reality and survived the crisis of 2007-2009; I think J.P. Morgan was like Odysseus where as Lehmans was more Achilles.

In my book, I try and bring these themes together by addressing the issue of voluntary slavery. Consequentialst/utilitarian ethics cannot reject voluntary slavery coherently, and so cannot reject slavery. The ‘reality of power’ cannot reject slavery. Deontological ethics, like Kant’s, can reject slavery. Pragmatic ethics rejects slavery on the basis that any rational opinion might be valid in solving a problem/prompting a gradual change in opinion. Since slaves are silenced from giving opinions, therefore slavery cannot be tolerated.

I believe my approach is coherent with Adam Smith, mainly because Smith worked within the Aristotelean framework. In the Theory of Moral Sentiments I note that Smith compares ‘prudence’ with ‘superior prudence’ as

Prudence, in short, when directed merely to the care of the health, of the fortune, and of the rank and reputation of the individual, though it is regarded as a most respectable and even, in some degree, as an amiable and agreeable quality, yet it never is considered as one, either of the most endearing, or of the most ennobling of the virtues. It commands a certain cold esteem, but seems not entitled to any very ardent love or admiration.

Wise and judicious conduct, when directed to greater and nobler purposes than the care of the health, the fortune, the rank and reputation of the individual, is frequently and very properly called prudence. We talk of the prudence of the great general, of the great statesman, of the great legislator. Prudence is, in all these cases, combined with many greater and more splendid virtues, with valour, with extensive and strong benevolence, with a sacred regard to the rules of justice, and all these supported by a proper degree of self-command. This superior prudence, when carried to the highest degree of perfection, necessarily supposes the art, the talent, and the habit or disposition of acting with the most perfect propriety in every possible circumstance and situation. It necessarily supposes the utmost perfection of all the intellectual and of all the moral virtues. It is the best head joined to the best heart. It is the most perfect wisdom combined with the most perfect virtue. It constitutes very nearly the character of the Academical or Peripatetic sage, as the inferior prudence does that of the Epicurean.

For Aristotle, reciprocity was a component of justice. Justice, itself, was, according to Plato, the virtue that ensures a functionally differentiated system, such as a society, works well. Therefore, my treating markets as centres of communicative action, governed by reciprocity, sincerity and charity, fits within Smith’s framework of ‘superior prudence’ as well as classical conceptions of the relationship between the polis and the individual, since the ideas are rooted in classical theory.

Friday 2 March 2018

Mathematical Finance

I wrote this piece for the National Institute for Economic and Social Research's Rebuilding Macroeconomics project.
There are three types of mathematicians: those that can count and those that can’t. This aphorism challenges the public perception of mathematics as being concerned with calculation and is liked by mathematicians because it enables them to highlight what mathematics is concerned with, which is identifying and describing relationships between objects.

A more sophisticated misunderstanding relates to the way mathematics is conducted. The error originates in how mathematicians present their work, as starting with definitions and assumptions from which ever more complex theorems are deduced. This is the convention that Euclid established in his Elements of Geometry and led Kant to believe that synthetic a priori knowledge was possible. Euclid actually started with Pythagoras’ Theorem, and all the other geometric ‘rules’ that had emerged out of practice, and broke them into their constituent parts until he identified the elements of geometry. It was only having completed this analysis did he then reconstruct geometry in a systematic way in The Elements. Today the consensus within mathematics is that the discipline is analytic, from observations, not synthetic, outside of mathematics there persists a belief in the power of pure deductive, synthetic a priori reasoning.

Physical sciences are in tune with what mathematicians do. This is exemplified by Newton who gathered observations on the planets and invented calculus to interpret the data. On this basis he concluded that momentum was being conserved and deduced the gravitational law. The key idea originating with Newton is that momentum is an invariant in a dynamic system. This is understood most clearly when presented using calculus, the mathematics Newton invented. Since Newton, all significant advances in physics have been associated with the identification of an invariant (momentum, energy, increase in entropy, speed of light) and inventing clear and succinct ways of describing objects (mathematics) that re-presents nature based on an invariant.

Finance has developed a mathematical theory in the Fundamental Theorem of Asset Pricing that has the same status in mathematical finance as Newton’s Laws have in classical physics. The central principle, analogous to the conservation of momentum, is that of ‘no-arbitrage’. The Fundamental Theorem of Asset Pricing states that if an asset is priced on the principle of no-arbitrage then there is a reciprocal relationship in the exchange. There are at least two ways of understanding this principle. It is a version of Euclid’s ‘First Common Notion’: if A=B and C=B, then A=C. Money takes the role of “B” and arbitrates the value of A relative to C. Alternatively, it is a version of the scholastic argument that a riskless profit is a shameful gain (turpe lucrum).

The no-arbitrage principle is justified through Ramsey’s ‘Dutch Book Argument’ that requires markets are mediated by jobbers (market-makers or dealers in the US) rather than brokers. When a jobber quotes a price, they do not know whether the counter-party is looking to buy or sell at the price. The jobber will quote a price at which they will buy and a higher price at which they will sell. They signify confidence in their quote by having a narrow difference between the prices. If a jobber quotes a price that another trader believes is wrong, the trader will take the quote, immediately moving the market. These jobber-mediated markets are, therefore, essentially discursive. Jobbers are engaged in making assertions as to prices, which are challenged when others take the quote; this is ‘market making’. If the market agrees that a jobber has correctly priced the asset, no trading will take place - silence is consent - and the market dissolves.

Jobbers do not hold assets and prefer trading in financial contracts rather than hold physical assets, they have no commitment to the assets they trade and identify themselves as taking long and short positions rather than buying or selling. While they lack commitment to assets, jobbers must be sincere in their statements, they must believe the quote is right. This means, that in the face of radical uncertainty, a jobber’s price quote is reliable, it can be trusted.

The significance of reciprocity in markets rests on the no-arbitrage principle that can only be justified if exchange is being conducted by jobbers, who will buy and sell at the quoted prices. Markets in economics tend to be based on brokers who bring property owners, one a buyer, one a seller, together. The focus on broker-mediated markets rather than jobber-mediated markets means that the importance of reciprocity in exchange is obscured. The different emphasis is rooted in financial markets being concerned with uncertain futures whereas economic markets are concerned with immediate scarcities.

In modern business, if a manufacturer can sell a product at an enormous profit, creating an arbitrage, they are succeeding. Economic theory argues that in the presence of these excess profits, competitors can come in and the price of the product will fall. This appears to be no different to the situation in a jobber-mediated market: jobbers will bid (buy) at the cost of production and offer (sell) at that cost plus a risk premium, just as manufacturers will do in a competitive broker-mediated market. However, while the ultimate point might be the same for jobber and broker mediated markets, the routes to the point are different. For jobbers, no-arbitrage, and hence reciprocity, are iron laws that must not be breached, ever. In broker-mediated markets, arbitrages are transitory and the ideal is to capture them before they disappear; it is a virtue to break the principle of reciprocity. Prices at which exchange takes place in jobber-mediated markets are always disputed prices, but sincere; in broker-mediated markets, prices are always accepted, if not fair.

Consider some thought experiments. If a manufacturer, making arbitrage profits, was obliged to buy identical goods, manufactured by others, at the prices they themselves quoted, would they quote the same price? If a slum-landlord had to live in the accommodation they rented, would they rent inferior quality accommodation? Public services are often expensive because they are of a quality that the providers would like to receive. These examples highlight the ethical nature of dual-quoting, it imposes the categorical imperative: do unto others as you would have them do unto you.

Financial instability has long been blamed on jobbers, who trade ‘paper’ and lack commitment to material assets, they are 'disinterested'. However, bubbles are a consequence of property owners ‘ramping’ assets and selling them above their intrinsic value. The failure of Long Term Capital Management in 1997 was precipitated by an apparent arbitrage, in the ‘asset swap’ strategy involving rock-solid US government debt, being an illusion. The Credit Crisis was a result of investment banks believing they could construct mortgage backed securities (MBS), out of ‘real’ assets, for less than their worth, not realising the inherent risks because they believed in arbitrages. Investment banks have been fined for selling MBS above their internally recognised value; they were being profit maximisers but insincere. There is evidence that the ‘Bitcoin’ bubble of December 2017 was a consequence of it being easy to buy Bitcoin, but difficult to sell; something not possible in a jobber-mediated market. These are all situations where financial instability originates in a belief that the no-arbitrage principle could be ignored or that prices could be insincere, and so it was possible to earn risk-less profits.

Recognising that the no-arbitrage principle is analogous to Euclid’s First Common Notion means that arbitrageurs should be regarded in the same way as promoters’ perpetual-motion-machines are: mis-guided cranks. It also emphasises that exchange should be reciprocal, it should not involve profiting at another’s expense. Mathematics only works on the basis of Euclid’s First Common Notion; markets only work well on the basis of reciprocity.