Two Women and a Duck - a Pragmatic case against HFT

This is the last of four articles on the role of reciprocity in financial economics.  It develops the case for taking a Pragmatic perspective when trying to understand contemporary finance.

I have presented the case that the essence of the FTAP isreciprocity, alternatively Justice and equality in exchange, colloquially fairness. The pre-history of mathematical probability lies in Olivi’s examination of commercial exchange in the context of Aristotle’s Ethics. The subsequent emergence of the topic is in the seventeenth century analysis of contracts in the context of ‘fair’ pricing. In the twentieth century Ramsey provides the ‘Dutch book’ argument, which can be viewed as the ‘Golden Rule’ of reciprocity. However, under theinfluence of a strong fact/value dichotomy that was established in the nineteenth century, the moral injunction not to engage in turpe lucrum, through the practice of arbitrage, becomes highly technical, and ethically neutral, and in the process the essence of reciprocity in the FTAP becomes obscured.

This argument associates the FTAP with the experimental results of the ‘Ultimatum Game’, an important anomaly for neo-classical economics [38]. The game involves two participants and a sum of money. The first player proposes how to share the money with the second participant. The division is made only if the second participant accepts the split, if the first player’s proposal is rejected neither participant receives anything. The key result is that if the money is not split ‘fairly’ (approximately equally) then the second player rejects the offer. This contradicts the assumption that people are rational utility maximising agents, since if they were the second player would accept any positive payment. Research has shown that chimpanzees are rational maximisers while the willingness of the second player to accept an offer is dependent on age and culture. Older people from societies where exchange plays a significant role are more likely to demand a fairer split of the pot than young children or adults from isolated communities ([30], [20], [21], [24]). Fair exchange appears to be learnt behaviour developed in a social context and is fundamental to human society and distinguishes the sapient member of a civitas from the sentient animals. The Ultimatum Game provides observational evidence that reciprocity is, or at least should be, a fundamental concept for financial economics.

We have shown the key role that the FTAP plays in the dominant paradigm of financial economics, involving CAPM (Markowitz portfolio selection), the Efficient Markets Hypothesis (martingales), the use of stochastic calculus and incomplete markets. At first sight one might assume that this paradigm associated with utility maximisation, but on closer reflection the key components are not.

Markowitz portfolio theory explicitly observes that portfolio managers are not (expected) utility maximisers, as they diversify, and offers the hypothesis that a desire for reward is tempered by a fear of uncertainty ([26], see also [35, p 432]). Markowitz’s theory was developed into the CAPM by Sharpe while similar models were developed independently by Treynor, Lintner and Mossin. These models conclude that all investors should hold the same portfolio, their individual risk-reward objectives are satisfied by the weighting of this ‘index portfolio’ in comparison to riskless cash in the bank, a point on the capital market line. The slope of the CML is the market price of risk, which is an important parameter in arbitrage arguments. Significantly, as MacKenzie [25, pp 86—87] observes, Markowitz portfolio selection and CAPM are prescriptive, not descriptive theories; just as medieval merchants were told what was licit by the Scholastics, so, in the 1980s, asset managers were being told what is ‘rational’ by academics.

Merton had initially attempted to provide an alternative to Markowitz based on utility maximisation employing stochastic calculus. He was only able to resolve the problem by employing the hedging arguments of Black and Scholes, and in doing so built a model that was based on the absence of arbitrage, free of turpe-lucrum. The opening paragraph of Black and Scholes includes the prescriptive statement that “it should not be possible to make sure profits”, a statement explicit in the Efficient Markets Hypothesis and in employing an Arrow security in the context of the Law of One Price.

Based on these observations, we conject that the whole paradigm for financial economics, not just the FTAP, is built on the principle of balanced reciprocity. In order to explore this conjecture we shall examine the relationship between commerce and themes in Pragmatic philosophy. Specifically, we highlight Robert Brandom’s position that there is

a pragmatist conception of norms — a notion of primitive correctnesses of performance implicit in practice that precludes and are presupposed by their explicit formulation in rules and principles. [5, p 21]

The argument that we have presented is that reciprocity is implicit in the practice of commerce (e.g. [22]) and this norm becomes explicit in Virtue Ethics and then in the early conceptions of mathematical probability.

The ‘primitive correctnesses’ of commercial practices was recognised by Aristotle when he investigated the nature of Justice in the context of commerce and then by Olivi when he looked favourably on merchants. It is exhibited in the doux-commerce thesis, compare Fourcade and Healey’s contemporary description of the thesis

Commerce teaches ethics mainly through its communicative dimension, that is, by promoting conversations among equals and exchange between strangers. [14, p 287]

with Putnam’s description of Habermas’ communicative action based on

the norm of sincerity, the norm of truth-telling, and the norm of asserting only what is rationally warranted ...[and] is contrasted with manipulation. [34, pp 113-114]

There are practices (that should be) implicit in commerce that make it an exemplar of communicative action.

A further expression of markets as centres of communication is manifested in the Asian description of a market as “Two women and a duck”, which immediately brings to mind Donald Davidson’s argument that knowledge is not the product of a bipartite conversations but a tripartite relationship between two speakers and their shared environment (e.g. [12]). The essence of the proverb is that if two women, who are characterised as talkative, and a duck come together, eventually the value of the duck will be determined—knowledge is created. Replacing the negotiation between market agents with an algorithm that delivers a theoretical price replaces ‘knowledge’, generated through communication, with dogma. The problem with the performativity that Donald MacKenzie is concerned with [25] is one of monism. In employing pricing algorithms, the markets cannot perform to something that comes close to ‘true belief’, which can only be identified through communication between sapient humans. This is an almost trivial observation to (successful) market participants (e.g. [37], [4], [13, especially Ch 12]), but difficult to appreciate by spectators who seek to attain ‘objective’ knowledge of markets from a distance.

To appreciate the relevance to financial crises of the position that ‘true belief’ is about establishing coherence through myriad triangulations centred on an asset rather than relying on a theoretical model, consider the comment made by Parliamentary Commission on Banking Standards

Excessive complexity in the major banks is not restricted to organisational structure. The fuelling of the financial crisis by misguided risk models was not simply the consequence of some mathematicians getting their equations wrong. It was the result of ignorance, coupled with excessive faith in the application of mathematical precision, by senior management and by regulators. Many of the elements of this problem remain. [32, para. 93, v. II]

Mathematicians understood the limitations of their models, which they communicated. The problem was that these concerns were not appreciated by policy makers, within an institution, nationally or globally, who appear to have succumbed to the indubitable authority of mathematics [32, para. 60—61, v. II]. Stephen Krasner observes [27] that academics can help policy makers in two respects: “Provide empirical evidence about what has happened, and offer a conceptual framework through which to understand it.” A significant issue with the highly technical mathematical models employed in finance is that they lack a “conceptual framework” that non-specialists can understand. This means that policy makers, whether within or without banks, cannot ascertain the limitations of mathematical models that inform their decision making. Pragmatism provides the philosophical basis for a conceptual framework that acknowledges both the usefulness and the fallibility of mathematics in finance.

The significance of these issues to the FTAP is captured in a text by Rama Cont and Peter Tankov addressing pricing in markets with discontinuous prices

Unless the martingale measure is a by-product of a hedging approach, the price given by such martingale measures is not related to the cost of a hedging strategy therefore the meaning of such ‘prices’ is not clear. [10, 10.5.2]

If the hedging argument cannot be employed, as in the markets studied by Cont and Tankov, there is no conceptual framework supporting the prices obtained from the FTAP. This lack of meaning can be interpreted as a consequence of the strict fact/value dichotomy in contemporary mathematics that came with the eclipse of Poincaré’s Intuitionism by Hilbert’s Formalism and Bourbaki’s Rationalism [39]. The practical problem of supporting the social norms of market exchange has been replaced by a theoretical problem of developing formal models of markets. These models then legitimate the actions of agents in the market without having to make reference to explicitly normative values.

In making this observation and by considering the implications of believing that the FTAP is an expression of reciprocity, we are employing the ‘Pragmatic maxim’ and are making a commitment to real-life experiences. Another, more direct, consequence of associating the FTAP with reciprocity is related to the EMH. Miyazaki observes [29, p 404] that speculation by arbitrageurs has been legitimised as ensuring that markets are efficient. The EMH is based on the axiom that the market price is determined by the balance between supply and demand, and so an increase in trading facilitates the convergence to equilibrium. If this axiom is replaced by the axiom of reciprocity, the justification for speculative activity in support of efficient markets disappears. In fact, the axiom of reciprocity would de-legitimise ‘true’ arbitrage opportunities, as being unfair. This would not necessarily make the activities of actual market arbitrageurs illicit, since there are rarely strategies that are without the risk of a loss, however, it would place more emphasis on the risks of speculation and inhibit the hubris that has been associated with the prelude to the recent Crisis.

These points raise the question of the legitimacy of speculation in the markets. In an attempt to understand this issue Gabrielle and Reuven Brenner identify the three types of market participant. ‘Investors’ are preoccupied with future scarcity and so defer income. Because uncertainty exposes the investor to the risk of loss, investors wish to minimise uncertainty at the cost of potential profits, this is the basis of classical investment theory. ‘Gamblers’ will bet on an outcome taking odds that have been agreed on by society, such as with a sporting bet or in a casino, and relates to de Moivre’s and Montmort’s ‘taming of chance’. ‘Speculators’ bet on a mis-calculation of the odds quoted by society and the reason why speculators are regarded as socially questionable is that they have opinions that are explicitly at odds with the consensus: they are practitioners who rebel against a theoretical ‘Truth’ ([6, p 91], [4, p 394]). This is captured in Arjun Appadurai’s argument that the leading agents in modern finance

believe in their capacity to channel the workings of chance to win in the games dominated by cultures of control ...[they] are not those who wish to “tame chance” but those who wish to use chance to animate the otherwise deterministic play of risk [quantifiable uncertainty]”. [1, p 533-534]

In the context of Pragmatism, financial speculators embody pluralism, a concept essential to Pragmatic thinking (e.g. [33], [2], [3, Ch 2]) and an antidote to the problem of radical uncertainty.

Appadurai was motivated to study finance by Marcel Mauss’ essay Le Don (‘The Gift’), exploring the moral force behind reciprocity in primitive and archaic societies and goes on to say that the contemporary financial speculator is “betting on the obligation of return” [1, p 535], and this is the fundamental axiom of contemporary finance. David Graeber also recognises the fundamental position reciprocity has in finance [17], but where as Appadurai recognises the importance of reciprocity in the presence of uncertainty, Graeber essentially ignores uncertainty in his analysis that ends with the conclusion that “we don’t ‘all’ have to pay our debts” [17, p 391]. In advocating that reciprocity need not be honoured, Graeber is not just challenging contemporary capitalism but also the foundations of the civitas, based on equality and reciprocity [16, p 235].

The origins of Graeber’s argument are in the first half of the nineteenth century. In 1836 John Stuart Mill defined political economy as being

concerned with [man] solely as a being who desires to possess wealth, and who is capable of judging of the comparative efficacy of means for obtaining that end. [28]

In Principles of Political Economy of 1848 Mill defended Thomas Malthus’ An Essay on the Principle of Population, which focused on scarcity. Mill was writing at a time when Europe was struck by the Cholera pandemic of 1829—1851 and the famines of 1845—1851 and while Lord Tennyson was describing nature as “red in tooth and claw”. At this time, society’s fear of uncertainty seems to have been replaced by a fear of scarcity (e.g. [23]), and these standards of objectivity dominated economic thought through the twentieth century. Almost a hundred years after Mill, Lionel Robbins defined economics as “the science which studies human behaviour as a relationship between ends and scarce means which have alternative uses”.

Dichotomies emerge in the aftermath of the Cartesian revolution that aims to remove doubt from philosophy [3, Ch 1]. Theory and practice, subject and object, facts and values, means and ends are all separated. In this environment ex cathedra norms, in particular utility (profit) maximisation, encroach on commercial practice. This is exemplified by the 1950 English court case Buttle v. Sunders ([1950] 2 All ER 193) where it was judged that ‘my word is my bond’ was subordinate to the profit maximisation principle.

In order to set boundaries on commercial behaviour motivated by profit maximisation, particularly when market uncertainty returned after the Nixon shock of 1971, society imposes regulations on practice. As a consequence, two competing ethics, functional Consequential ethics guiding market practices and regulatory Deontological ethics attempting stabilise the system, vie for supremacy. It is in this debilitating competition between two essentially theoretical ethical frameworks that we offer an explanation for the Financial Crisis of 2007-2009: profit maximisation, not speculation, is destabilising in the presence of radical uncertainty and regulation cannot keep up with motivated profit maximisers who can justify their actions through abstract mathematical models that bare little resemblance to actual markets.

This tension is exemplified by the Chartered Financial Analyst (CFA) Institute Standards of Practice Handbook [9], where the primary obligation is to obey the law, where Buttle v Saunders is tempered by the Basel treaties. There is no discussion of how professionals should interact amongst themselves, only how they interact with clients and employers, agents with whom they have a contractual relationship. This suggests that a distinction is being made between the market, populated by analysts, and society as a whole.

An implication of reorienting financial economics to focus on the markets as centres of ‘communicative action’ is that markets could become self-regulating, in the same way that the legal or medical spheres are self-regulated through professions. This is not a ‘libertarian’ argument based on freeing the Consequential ethic from a Deontological brake. Rather it argues that being a market participant entails restricting norms on the agent such as sincerity and truth telling that support knowledge creation, of asset prices, within a broader objective of social cohesion. This immediately calls into question the legitimacy of algorithmic/high-frequency trading that seems an anathema in regard to the principles of communicative action.

The purpose of these four posts has been to explore the ethical character of contemporary financial economics in light of the Financial Crisis of 2007—2008.

By examining the contemporary scholarship on the early development of probability we show that the field emerged in the seventeenth century out of the ethical assessment of commercial contracts. In the following century, the doux-commerce thesis dominated discussion of the morality of markets, emphasising the role markets play in binding society. The ethical aspect of probability theory disappears from mathematics at the start of the nineteenth century as science replaces uncertainty with Laplacian determinism [15] and the self-destructive thesis eclipses doux-commerce. Economics developed on Mill’s premise that the discipline is “concerned with [man] solely as a being who desires to possess wealth” and ‘value—neutrality’ emerges, built on the foundation scientific determinism. It was within this conceptual framework that the Black-Scholes equation was developed.

When a mathematical ‘theory’ to underpin the Black-Scholes-Merton approach, the Fundamental Theorem of Asset Pricing, is developed it relies on Kolmogorov’s abstract probabilities. The essence of this paper is in identifying these ‘martingale measures’ with probabilities that ensure equality in exchange, implicitly imitating the explicitly ethical approach of the early probabilists. This observation is significant in that it provides evidence of ‘oversocialisation’ in a domain traditionally considered ‘undersocialised’.

The argument presented in this post is based on employing the Pragmatic approach that acknowledges the contingency of knowledge. By taking this path we argue that markets should be regarded as centres of ‘communicative action’ governed by Pragmatic norms and that recent financial crises have been as a consequence of a dissonance between market participants working to Consequentialist norms but constrained by Deontological norms. In taking this approach we see a correspondence with Brandom’s semantic pragmatism, firstly because we see the implicit norm of reciprocity being made explicit in probability, and secondly because there is a correspondence between the results of the Ultimatum game, which show humans prefer reciprocity to utility maximisation and animals do not, and Brandom’s distinction between animal sentinence and human sapience. This, in turn, offers a solution to the problems of financial regulation.

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