J Bus Ethics (2015) 129:599–611 DOI 10.1007/s10551-014-2193-9
Quantitative Method in Finance: From Detachment to Ethical Engagement Jason West
Received: 12 December 2013 / Accepted: 11 April 2014 / Published online: 29 April 2014 Ó Springer Science+Business Media Dordrecht 2014
Abstract Quantitative analysts or ‘‘Quants’’ are a source of competitive advantage for financial institutions. They occupy the relatively powerful but often misunderstood role of modeling, structuring, and pricing complex financial instruments in the capital markets. But Quants often function in a discipline free from ethical burdens. Models used to price complex instruments are usually beyond the mathematical understanding of financial sector participants who rely heavily on the integrity of the Quant who built them. Although there has been some attempt to cover the ethics of mathematics applied to the capital markets, designing a set of rules to guide the ethical behavior of Quants cannot be made explicit and remains inexpressible. Because Quants generally experience a sense of detachment from moral obligation, there is a growing need to convert moral detachment into engagement. Our framework is indebted to key elements of Wittgenstein’s practical ethics philosophy and Rawls’ justice principle. The burden of balancing justice as fairness as defined by Rawls with the inability to explicitly articulate ethical rules as defined by Wittgenstein must fall to the Quant. We propose that the threshold delineating the barrier between ethical detachment and engagement can only be defined by the Quants themselves. It is their moral duty to disclose their level of ethical engagement when their models are put into practice. Keywords Quantitative finance Moral engagement Rawls Wittgenstein Mathematical models
J. West (&) Department of Accounting, Finance and Economics, Griffith Business School, Griffith University, Nathan, QLD 4111, Australia e-mail:
[email protected]
Introduction Once the domain of oddballs and out-of-work physicists, quantitative financial analysts or ‘‘Quants’’ continue their inexorable march into the trading rooms of banks, hedge funds and commodity trading houses. This has become an increasingly mainstream pattern. Greater task specialization by these institutions has motivated the development of more complex yet narrowly defined roles more often demanding superior acumen in, and knowledge of, mathematics. Their tasks are no longer limited to the traditional roles in finance of pricing derivatives and monitoring complex portfolio exposures but now canvass the development of algorithmic and high-frequency trading strategies, statistical arbitrage and dynamic portfolio optimization. The migration of physicists and mathematicians to the applied world of mathematical finance enshrined in the 2004 publication of Emanuel Derman’s fine autobiography My Life as a Quant: Reflections on Physics and Finance. Derman (2004) and his contemporaries (Burton G. Malkiel, Robert Merton, Espen Gaarder Haug, Nassim Nicholas Taleb, and others) comment on many aspects of their profession but all tend to converge when they delineate between theories and models as applied to the capital markets. Science defines a theory as a consistent and robust framework to test a falsifiable hypothesis about some characteristic or of a particular phenomenon. Theories that become widely accepted are those that can be defined and quantified to a tractable degree of accuracy, and in some cases they are even useful. After rigorous testing and peerreview, the theories then form the basis of models which can be used to help describe and anticipate features, behaviors and characteristics. An example of this is in the field of finance the so-called theory of arbitrage which
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underpins the law of one price and forms the basis of many models used in asset pricing. Hayek once pointed out that in physical science the macroscopic constructions are certain while the microscopic concepts, at the atomic level, are abstractions. But in economics, he argues, individuals are certain and the ‘‘economy’’ is the abstraction (Derman 2004). Many scholars, including Derman, Taleb, Sornette, and others passionately advocate that financial models are a merely caricature of the capital markets they seek to represent. Their applicability is necessarily limited by the sheer volume of factors that fail to comply with assumed behavior. Financial theories and their models cannot begin to imitate their counterparts in hard science and are, and may never be, as immutable as, say, the laws of thermodynamics. Financial models attempt to compare behaviors to something else that can be manipulated, but in doing so they simplify and underestimate observed activities and reduce the applicability of the model to unobserved behavior. To paraphrase Derman, these theories help us understand what something is while models help explain to use what something is like. And in many aspects of hard finance, the most popular models do a poor job of it. Often Quants possess a great deal of intellectual horsepower but their contribution to finance is undermined by a failure to appreciate the not inconsiderable moral obligations of their actions. Indeed in many instances, the decisions made by Quants are so far removed from the consequences of their actions that ethical guidelines and their moral obligations are rarely confronted. Quants, as gatekeepers of financial models, need to not only need to understand this difference but must also be able to quantify and explain it. In many cases stretching from the South Sea Bubble to the Government bailout of AIG, they have arguably failed. While bankers take the blame for losses incurred during financial crises, not only the more recent ones but also all throughout history, in contemporary capital markets it is the Quants who are increasingly taking the blame for failing to educate the bankers to understand the key difference between what constitutes a reliable theory and a relatively unreliable financial model. The difference between a theory and a model is no longer merely philosophical; it is an identifiable, quantifiable but perhaps subtle contrast that escapes comprehensive ethical reasoning. The ethical duty of Quants, however, should, to some degree, be to adequately define where this difference lies. If this task cannot be reliably performed, then Quants should justifiably be relieved of their ethical obligations and they be relegated to the role of a computing engine devoid of soul and independent thought.
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Are Quants and statisticians responsible for financial market aberrations that fail to match their model or does this fall upon people in the social sciences who apply statistical methods without understanding them? The greatly increased complexity of the structure of financial instruments in the 1980s stimulated the need for a dedicated mathematical approach to security pricing, particularly in the area of derivatives and other contingent-claim instruments. The need to use mathematical techniques, computing technology and data manipulation to solve complex problems in asset pricing, construct trading strategies, and automate risk management grew in intensity. Indeed, the banking regulators themselves specifically require financial institutions to make extensive use of quantitative methods in measure theory and stochastic simulation to evaluate their financial exposure each and every trading day. Specialization in financial mathematics is required for the manipulation of complex derivatives. A deep understanding of the mathematics involved can be beyond the grasp of most bank executives, Board directors and regulators. Financiers and traders, who are subject to significant ethics oversight and professional codes of conduct, rely heavily on the Quants to create and maintain complex mathematical models. But it is seldom recognized that Quants who implement these actions hold positions of great responsibility that can vastly exceed what their job title suggests, and that there is no underlying code of conduct helping guide behavior other than that which is adhered to by bankers in general. As such, the Quants are left to operate in an ethical vacuum. The practice of quantitative finance rarely strays from mathematical principles or the search for computational efficiency but explicit and tangible rules that define their role, beyond very basic internal bank compliance training, usually goes unchecked. Quants are, by their nature, measure-focused individuals who operate best when behavioral limits are well-defined and quantifiable, no matter how complex. But converting many of the moral subtleties and ambiguities in ethical principles into quantifiable codes appears impossible. In this discussion we, therefore, explore the moral obligations of Quants as a profession and offer a broad framework in which their moral actions recognize the point beyond which they should recognize the need to consider the principles of justice as fairness that stems from social principles and links ethical theory with practice. We encounter a suite of practical and meaningful ethical principles developed in response to philosophical investigations into the ethics of science, ranging from Wittgenstein to Rawls. Our aim is to offer an outlet for Quants to articulate their ethical duty and guide behaviors which may help lend stability to financial markets.
Quantitative Method in Finance
Mathematical Finance: A Confused History The history of mathematical finance as understood by scholars usually starts with the The´orie de la Spe´culation published 1900 by Louis Bachelier (Bachelier 1900). However, earlier work by Thiele in Copenhagen created the first known model that introduced randomness into the analysis of time series’ (Thiele 1880). The approach of this early radical research borrowed from the principles of Brownian motion to model asset prices as stochastic processes. At the time their efforts gained little attention in academia and even less from finance practitioners and were not influential for many decades. Indeed a gap of over a half a century ensued before the portfolio-selection work of Markowitz (1952) and Sharpe (1963) formally married mathematics with the ‘‘black art’’ of investment management. The lack of broadly acknowledged formal literature in finance over this period implies that the level of sophistication in financial markets may have proceeded at a glacial pace until Markowitz’s great revelation in the 1950s. A deeper look at the literature developed over this period, however, reveals the opposite. Indeed the building blocks of capital market theory and asset valuation were developed long before Markowitz’s seminal paper. Concepts such as the immeasurability of utility, insurable risks, the mathematical treatment of economic theory that assumes functions are continuous throughout, positive, strictly monotonic, differentiable, etc., and assumptions on general equilibrium were developed by economists and mathematicians during these decades (Nelson 1904; Knight 1921, 1930; Williams 1938; Hicks 1931, 1939). Economists struggled to interpret capital market behavior using the rigorous application of scientific method for theory formulation to model expectations. Much of the work on capital markets and asset valuation seemed to try and wedge as much of what was observed or what was conventional wisdom into the existing economic theory as possible, which had the predictable outcome of rarely capturing much of the more subtle and random elements that comprise real capital markets. Once the applicability of standard economic theory reached its limit, a brief revolution in the way assets were viewed, rather than as individuals but as part of a portfolio, demanded more rigorous and uniquely defined mathematical principles. While this mini-revolution in perspective leapfrogged the problems inherent in the economic interpretation of value, it still largely relied on the building blocks that led to its development. This period was not without significant advances in other branches of inquiry that have led to complex mathematical structures since made available to solve contemporary problems in capital markets. This included the work of Norbert Weiner to capitalize on Brownian motion for
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constructing stochastic processes (Itoˆ 1951), Andrey Kolmogorov’s development of theory of stochastic integration (Kolmogorov 1931), Wolfgang Doeblin’s1 work on Markov chains and Markov processes (Levy 1955; Bru and Yor 2002) and Kiyosi Itoˆ who made significant advances in solving stochastic integration problems (Itoˆ 1944). While these and other key advances have contributed to capital market and valuation theory, they were developed in fields of inquiry initially unrelated to finance. Within the more orthodox sphere of financial research, the later work of Samuelson and Merton (1974) allowed one-period discrete-time models to be replaced by continuous time, Brownian-motion models and the quadratic utility function implicit in mean–variance optimization was replaced by more general increasing, concave utility functions. Arguably the major revolution in mathematical finance came with the work of Fischer Black and Myron Scholes along with fundamental contributions by Robert C. Merton, who created the notion of a self-financing replicating portfolio for the construction of a mathematical relationship that allowed for the closed-form pricing of contingent claims (Black and Scholes 1973; Merton 1973). While its applicability in practice is perhaps more limited than first envisaged, it nevertheless serves as the basis upon which much of contemporary mathematical finance is built, although the extent of their real influence on practitioners is disputed in Haug and Taleb (2011). Much more sophisticated, though not necessarily better, mathematical tools have since been derived. These include multi-factor models, parametric copulas, and elements of extreme value theory. Some of these models, by necessity, have cross-fertilized ideas among insurance and actuarial research, operations research, monetary economic theory and population health. As much as traditional bankers reject the notion, quantitative analysts have greatly altered the financial landscape in terms of new approaches to asset pricing, trading strategies, and computational efficiency.
Pathways to Entry as a Determinant of Ethics Some institutions view their quantitative teams as a dynamic resource shaping the strategy of the business. Others use their Quants as a secondary line of support, acting as a safety net to focus on the capture of gross errors 1
Doeblin’s framework of stochastic processes with continuous paths was consistent with Kolmogorov’s analytic theory for Markov processes but he was drafted to go to the front during World War II. To avoid sharing his ideas with the Nazis Doeblin first burned his notes and committed suicide. Some of his notes, however, were kept safe by the National Academy of Science of France. The academy safe was opened in May 2000 and it was then that the extent of his work became apparent (Jarrow and Protter 2004).
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that may generate unacceptable risk exposures. No two institutions attribute equal importance to the role of financial mathematics in their businesses. However, paradoxically they all attribute an equally high importance to technology and this is, in fact, where most Quants come in handy. The lack of convention in how best to exploit mathematics for financial gain is perhaps the primary source of blurry ethical boundaries applied by practitioners in the capital markets. To many, mathematics is seen by some as the universal solution to almost all financial matters. To others, it is seen as a blunt tool, in essence a hammer on an eternal search for a nail to strike in the form of an unresolved economic anomaly. Quants generally enter the banking arena via one of two paths, each possessing its own set of ethical norms. The first path is well beaten by seasoned mathematicians, physicists, or engineers with practical experience in stochastic processes and other advanced forms of mathematics useful in financial settings. These veterans, in many cases, are able to directly adapt their knowledge to the more economically lucrative domain of finance. The relative lack of ethical guidelines in the Quant profession has motivated the more ‘‘seasoned’’ Quants to merely adapt and apply the ethical principles that guided their previous research careers (physics, chemistry, engineering, etc.) to the finance domain. The different mix of ethical principles underlying many of these fields has thus resulted in a mishmash of moral ideas applied across the spectrum of financial mathematics. The second path of entry to the profession has been forged by newly minted Quants, armed with a coursework degree in mathematical finance, often the product of a career change motivated by salary, autonomy and the universality of employment opportunities. However, few encounter perspectives that challenge their understanding of business ethics principles, either formally or informally. These individuals graduate and enter the capital markets without a robust moral reference point upon which to ply their new trade and are, therefore, at greatest risk of failing to question their ethical obligations. So in the absence of codes of conduct, the seasoned veterans apply the ethical principles that guided their prior careers while the newer Quants lack a well-calibrated moral compass and appear to have no obligation beyond their relatively minor legal duties to act with ‘‘reasonable care.’’ The latter are at greatest risk of breaching basic business ethics principles. The growth in the use of mathematical finance is naturally accompanied by a growth in the number of scholars designing and delivering dedicated courses for aspiring Quants. Mathematical finance courses have sprouted in business schools across all continents. But the newer mathematical finance courses have adapted physics, mathematics, and statistics techniques to the study
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of finance such that students from non-mathematical backgrounds emerge with a relatively narrow view of mathematics, one that is based only on applications directly applicable in finance. These tend to ignore broader mathematical concepts and tools which may prove useful when the circumstances surrounding a particular problem become very uncertain. Current university curricula has chosen a limited suite of concepts borrowed from mathematics, statistics, and computer science largely based on existing popular research approaches to security valuation (Wilmott 2000). This may be an important contributing factor that ultimately limits the capability of newly minted Quants to confidently develop unorthodox and alternative solutions to common financial problems, and can ultimately lead to overconfidence in models that precipitates the misapplication of theory into practice. One problem with the development of financial mathematics curricula at tertiary institutions is that mathematical finance tends to sit between academic chairs and never on any one of them. The study of mathematical finance has, by necessity, transformed a loose collection of mathematical constructs in such areas as stochastic optimal control, portfolio optimization and derivative pricing into a set of structured principles that address specific mathematical approaches to valuation and risk. A study by West (2012) reported that quantitative finance programs have generally adopted a one-size fits all approach to program delivery. The study of ethics in these programs is conspicuous by its absence. Rigid compliance with the existing limited suite of mathematical tools used for financial applications coupled with the almost mechanical application of popular mathematical methods may undermine the ability for the profession to evolve with the market itself. Independence of Theory Ardalan (2004) suggests that observed behavior in the financial market is not independent of financial theory. This idea draws upon the functionalist paradigm of Burrell and Morgan (1979). Ardalan suggests that the functionalist paradigm has become dominant in mathematical finance. The implication of the functionalist paradigm is that since a growing number of graduates in financial mathematics are steadily influencing financial markets, the caliber and quality of their education which defines their perceptions, attitudes, beliefs, and behaviors will in turn directly influence the practice of quantitative finance. This approach to quantitative finance is rooted in the tradition of economic positivism. Financial theory itself struggles to elevate critical thought on ethics to the same standard that it is applied in other professions, such as medicine. And as the level of complexity increases, the consideration of moral obligations tends to decline. Empirical research by West
Quantitative Method in Finance
(2012) suggests that homogeneity in mathematical finance education and scholarship as well as the similarity in the practice of mathematical finance among financial institutions lends great support to Ardalan’s thesis. In any case, some scholars argue that there is no such thing as a robust financial ‘‘theory’’ and that the use of mathematics to offer explanatory power to finance depends entirely on the use of models (Derman 2004; Haug and Taleb 2011). Of course, models are vulnerable to assumption, naivety, optimism, approximation, redundancy, and inconsistency. They must be calibrated, stress tested and in some cases automated without constant supervision. We now turn our analysis to the ethical obligations of mathematical finance as practiced by its main protagonists—the Quants.
Ethics: The current Quant Perspective Fiduciary Mediator or Idiot Savant? The treatment of ethics specific to the behavior and responsibilities of Quants has not been comprehensively addressed through extant discourse, although excellent coverage of the ethical principles underpinning strands of mathematical finance such as high-frequency trading (Angel and McCabe 2013), market efficiency (Shefrin and Statman 1993) and derivative instruments (Raines and Leathers 1994) have been granted detailed analysis. While these scholars addressed elements of ethical constructs underlying computerized trading, they avoided constructs surrounding the quantitative task itself. Robert W. McGee came closer by examining aspects of the effect of insider trading on market efficiency using mathematical finance principles (McGee 2007) which leveraged off the work of Engelen and Van Liedekerke (2007). These contributions are useful and guide our initial analysis of the ethical constructs underpinning the banking profession as a whole. The role of the Quant is often viewed as a discipline free from ethical burdens. Quants can typically occupy unique, relatively powerful but often misunderstood positions in financial institutions. One of their primary roles is to price and model often complex derivative securities that are used for hedging or proprietary trading. Models used to price such instruments are usually beyond the mathematical understanding of the average financial accountant and even most senior executives, who rely heavily on the integrity of the Quant who built them. For instance, the number of open positions in various derivatives within a single institution can number in the hundreds of thousands and the aggregate notional value in the many billions, often well beyond a bank’s entire equity capital. This role falls to the risk management Quants to perform not only accurately, but
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also in a timely fashion so that the following day’s trading can commence. Valuing the aggregate position of the bank’s exposure in itself is fraught with danger as crosscorrelations in positions can cause non-intuitive value shifts across the portfolio. Scaling this effect many times over across an economy consisting of many banks and other risk-taking institutions and the vast complexity of the whole financial system soon becomes apparent. The complexity manifests itself in unexpected ways. The recent financial crisis, and indeed all previous crises, highlights the role that insufficient knowledge and application of mathematics plays in finance. Simply blaming mathematicians for not anticipating the effects of this complex interaction of factors is futile. In most cases their responsibility does not match their authority over such matters. Unlike banking regulators, Quants are not charged with any responsibility to extend their knowledge of the risks to the institution that they represent to the wider economy. Apportioning blame to Quants for excessive risk exposure across the economy is like blaming the weather man for a devastating tornado that flattens a town. While some financial services firms are merely sellers of financial products and therefore only subject to the ordinary standards of trade practices, most sell products to consumers and companies as fiduciary agents and are, therefore, subject to the principles of ethics and law underlying trust relations. Quants are seen as subordinate to sales. After all, sales are where the rubber hits the road for most profit seeking institutions. But the responsibility of Quants to consider product complexity and the level of client sophistication is not apparent. Other abusive sales practices and poor quality financial products raise further ethical problems, particularly for individual investors as opposed to wholesale investors. This was explored in Frederick and Hoffman (1990). One of the main ethical issues in financial services concerns not only the risk but the also suitability of a product for a client. Only the elements specifically related to risk are addressed through the legally-mandated product disclosure process; appropriateness is harder to define. The obfuscation of information has resulted in successful litigation against institutions that failed to consider the financial sophistication of their clients and the relative suitability of the product they were sold. The first high-profile example of this was the 1996 out of court settlement between Procter and Gamble and Bankers Trust for a complex floating-rate swap structure. The Bankers Trust Quants who structured this instrument knew the true level of risk of the product which was based on relative changes in the interest rate yield curve, but failed to disclose the extent of such risks to Procter and Gamble. There have been other high-profile instances since, including the Federal Home Loan Mortgage Corporation (Freddie Mac) who was found to have understated its earnings in 2000–2002 (OFHEO 2003).
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Ethical Interpretation of Mathematical Models
Ethics: A proposed Approach for Quants
The responsibility for Quants to properly consider the full implications of model limitations has considerable bearing on firm performance. Lapses in quantitative model integrity can easily be misinterpreted as earnings manipulation. It has been well established in the literature that market forces make it difficult to create sustained levels of wealth through earnings manipulation (Danielson and Lipton 2010). Karpoff et al. (2008) showed that firms caught manipulating earnings results typically suffer harsh treatment by investors resulting in an average stock price decline of over 30 %, with over 65 % of this decline attributed to reputation effects. Witness the stock price decline of Freddie Mac by 31 % over 2001–2003 from revalued portfolios. Tighter reins have been placed on some, but not all, quant teams as a result. Unfortunately the usual approach to combat ambiguity in fiduciary disclosure responsibilities is regulation. Federal legislation such as Sarbanes–Oxley (SOX) Act attempts to encourage prudential financial management through public disclosures which includes a special provision for the forfeiture of profit or bonuses based on financial statements that later need to be re-stated (Beggs and Dean 2007). But it is difficult to see how more regulation, particularly through SOX and other new measures like the Dodd-Frank derivative reform bill can adequately address unethical practices instituted by the practices of Quants. Regulations that attempt to do this are usually impotent anyway. The efficacy of the models themselves also raises interesting dilemmas. For instance, no two mathematical models used for pricing options will value a derivative the same. The difference in interest rate derivative valuation using a one-factor or a three-factor model is substantial, but it does not necessarily mean the values derived from the simpler one-factor model are less relevant—they simply assume the input from changes is due to fewer factors. Models with more factors are more complex, but not necessarily more representative of reality. Parsimonious models offer advantages in computation time, broader understanding of the model limitations among management and simpler risk management processes. But is a parsimonious model ethically superior to a more complex and probably more accurate model? Quants tread a fine line to establish models that are, to paraphrase Einstein, simple enough but no simpler. Within this context the responsibility rests on the Quants to get the balance right between model completeness and parsimony. This area has been canvassed in the regulation ethics literature that evaluates the trade-off between fairness and efficiency (Boatright 1996, 2010; Shefrin and Statman 1993). But we wish to go one step further and define the line that, when crossed, violates the notions of equality, integrity, and justice.
Borrowing from Philosophy
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Questioning ethics in mathematical reasoning is a good place to start for devising a governing code. One of the more eloquent investigations into the ethical convictions underlying mathematical principles was devised by Wittgenstein. Wittgenstein’s philosophy of logic and mathematics depicts mathematics as a human creation that lays claims to truth, objectivity and necessity, while providing a basis for some form of ethical realism. His belief that reflection on mathematical practice will lend insight into the nature of ethics has gained a hold in subsequent philosophical investigations into mathematics and ethics. Plato argued that training in mathematics was important preparation for our ascent toward perception of the Form of the Good. In mathematics, according to him, we come to perceive that which is universal, immutable and abstract, which is supposed to be relevantly similar to perception of the Good. In Principia Ethica (1903), G. E. Moore, the founder of modern ethical philosophy, agreed with the perspective underlying Kantian ethics that moral reasoning cannot search among psychology and the social sciences to locate ethical principles, because those disciplines yield only causal links and fail to generate a basis for moral justification. To establish a normative ‘‘ought’’ by way of facts is to commit a basic error of logic. Moore calls this the naturalistic fallacy. John Rawls, in A Theory of Justice (1971) offered the suggestion that justice be defined as fairness, to be accepted as an intrinsic good. He argued that this is the imperative we would follow if we had no starting information about our own future status in life. But in making such a suggestion Rawls offered no evidence that justiceas-fairness is consistent with human nature, hence practicable as a principle for the construction of ethical guidelines. A key structural weakness with Rawls’s justice as fairness doctrine is that no one can reliably agree on what is fair. A related weakness is that Rawls would allow force to be used against consenting adults who are engaged in nonrights-violating activity under certain circumstances. Johnson (2012) sided with Rawls in identifying that the fundamental theorem of asset pricing with the ethical statement that equality is a sufficient and necessary criterion for justice. A consequence of this assertion is that it highlights the importance of ethics and social cohesion when society faces uncertainty, rather than scarcity. Johnson goes on to suggest that when an individual is faced with scarcity, decisions based on maximizing utility, the dominant method in neo-classical economics, may be optimal, however, when society is faced with uncertainty, ethics and social cohesion become paramount.
Quantitative Method in Finance
Mathematics can construct robust models of absolute objectivity, to yield truths independent of the arbitrary and subjective judgments of individuals. However, arguments for ethical relativism arising from the mere fact that ethical principles are held by people, and are not checkable by measurement or scientific observation, face the objection that mathematical truths do not have their objectivity impugned by similar considerations. From the Manhattan Project to Manhattan These ethical constructs are not novel, nor are they the exclusive domain of the professional era of business and corporate finance. The pursuit of scientific understanding has always sought to define appropriate ethical boundaries. While financial mathematics may not strictly be regarded by many as a strand of science, it does borrow tools and techniques, not to mention scientists themselves, to add scientific method to its arsenal. Famously, J. Robert Oppenheimer confronted the morality of science as slave to political and military purposes during his management of the Manhattan Project. Physicists working on the project often voiced their reservations about the morality of their work, but Oppenheimer dampened dissent and curbed their misgivings by arguing the ethics of their project in the context of a brutal war with Japan and Germany. He maintained that atomic bombs would make fear a permanent feature of ordinary life and that they might in fact end future wars. A naive but common line of thinking among scientists at the time was that national governments would surrender much of their sovereignty to the United Nations, leading to world peace (Cassidy 2009). Scientists in many endeavors often claim that it is beyond their moral remit to question political or military means and ends, and places the burden of moral authority on other men ‘‘qualified’’ to settle such matters. Up to a point, some form of moral detachment from the immediate task at hand is often a key feature of scientific roles. In Oppenheimer’s case, he projected a deliberate detachment which stemmed from his conviction, at least initially, that to deliver the atomic weapon was an exclusive priority, while the subsequent use of the weapon remained the concern of statesmen and statesmen alone. Acquiescence of direct responsibility stemmed from the absence of a scientifically derived link between the development of the weapon and its use. Recently scholars have attributed the feeling of reduced moral responsibility as being more of a product of the prevailing cultural norms of the time rather than of a particular sensibility or judgment (Cassidy 2009). But the need for a moral detachment was a view shared by influential past and present public policy figures. Vannevar Bush was head of the US Office of Scientific Research and Development (OSRD) during World War II
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and was responsible for almost all wartime military R&D, including the Manhattan Project. He was of the contrary view to Oppenheimer that the role of scientists should devolve from enlightened keepers of cultural ideals toward being mere technicians of physical processes. Public policy figures since this era have voiced their view that leading scientific minds are no longer equal partners with military and political statesmen, but are merely tools available to a bureaucratic hierarchy. Thomas Edison famously claimed that he ‘‘can hire a mathematician but a mathematician cannot hire me.’’ The urge to displace technicians toward the sidelines of scientific insight, as if they were merely hired hands, has continued through to modern times, and pervades all industrial endeavors. The disestablishment of science from morality in the era of the Manhattan Project has percolated through to recent behaviors in finance and banking circles, where, after all, a great number of trained scientists now operate. But crucially, the moral detachment has historically occurred up to a point. Where this point is remains the key conjecture of our discussion because firm ethical guidelines have failed to materialize in prior inquiry into this issue. The existence of the ‘‘point’’ can best be illustrated through the use of an example. At the cessation of war in the fall of 1945, another influential scientist Edward Teller was pressing for immediate development of the hydrogen bomb. This was to be known as the ‘‘Super.’’ Oppenheimer emerged from his self-imposed moral detachment in response to development plans to attest that ‘‘I neither can nor will do so.’’ Oppenheimer regarded the Super as a genocidal weapon with the only conceivable purpose to destroy civilian populations in large numbers. The use of H-bombs in war would result in annihilation. He joined Enrico Fermi and other eminent physicists in lobbying Roosevelt’s former vice-president Henry Wallace to stop H-bomb development ‘‘because we should prefer defeat in war to victory obtained at the expense of the enormous human disaster that would be caused by its determined use’’ (Cassidy 2009). But the Atomic Energy Commissioner (AEC) Lewis Strauss did not agree, joining Teller in favor of a ‘‘quantum jump’’ in the lethal capacity of that nation’s nuclear stockpile; they wanted H-bombs as fast as they could be built. For a time, Oppenheimer’s counsel prevailed in the AEC but by 1949, even though the Commission narrowly voted not to develop the Super, President Truman overrode the Commission’s decision, and the Super project was approved. Oppenheimer, along with many of his scientific colleagues, withdrew from public life and surrendered their claim to help address urgent matters of public policy from any sense of moral obligation. For many years science was relegated to the academic sidelines and scientists reduced to mere technicians in the service of political men. With
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Oppenheimer’s subsequent defrocking at the hands of anticommunists, scientists gradually became aware that in the future they could serve the state only as experts on narrow scientific issues (Bird and Sherwin 2006). While it is natural enough that the individuals who designed the weapons should have some say in how best to use or not use them, intellectual pride may see that individuals gifted in one sphere of thought should imagine themselves equally gifted in others. In reality they are not. The complex moral arguments used to justify the development of nuclear weapons are an important aspect to consider because it was an era of such rapid change that the progress of ethical debate significantly lagged scientific advancement. These circumstances are remarkably similar to the situation that Quants and financial markets find themselves in today, albeit arguably a lot less dramatic. The loose similarity between genuine weapons of mass destruction and nascent financial weapons of mass destruction reinforces parallels in the moral obligations of their chief technicians. The record not only of Oppenheimer’s own divided mind but also other leading scientists of the era including Einstein, Fermi and Szilard shows that technical expertise is something very different from moral prudence. That a scientist may be a superb technician and even possess an acute sensibility does not necessarily make them a public philosopher or statesman. The suppression of moral questioning breached a threshold which invigorated a need to question underlying objectives, from the particular viewpoint of the technician. The trouble was, that by then there were many technicians who could easily fill the void should morality inhibit the participation of scientists. Defining and Refining the ‘‘Point’’ In the nuclear development program, ethical questioning remained somewhat detached up to a point. It would seem that this ‘‘point’’ or threshold would need a better definition in order to serve as a reliable guideline to be followed in any practical sense. The point must be as universal in its definition as in its derivation and it should not matter whether its application is in finance, medicine, social policy or war. Highlighting the need to discover this ‘‘point’’ may help through the use of a practical example. Take mortgage backed securities used in financial markets for securitizing liabilities (packaging securities into more easily consumable investments containing narrowly defined risk-return profiles). The day to day life of a Quant designing and packaging mortgages into such instruments is quite far removed from the actual beneficiaries of those mortgages by so many levels that any attempt to personalize the relationship is likely to be met with indifference. The disassociation manifests itself into various axiomatic
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principles to model outcomes using assumptions like ‘‘house prices never go down’’ or ‘‘the distribution of future mortgage default rates replicate the past.’’ These assertions prey upon the ethical void within the Quant profession. Deliberately setting model assumptions like price floors for assets equal to their book value or blindly applying future default rates to equal historical rates introduces fundamental limitations, and therefore flaws, into a model. A model implies the capacity to account for all important and influential factors that are observed—this condition is violated when unrealistic assumptions are imposed and ultimately contradicts the very notion of ‘‘model.’’ A moral boundary is crossed when model representations fail to reflect reality; in the moral philosophy of Wittgenstein and Rawls, the notion of equality becomes divorced from justice. We will turn to these notions in the next section. Using another example, single-factor stochastic models are used to measure the risk of interest rate exposures. It is well known that the yield curve can only be reliably modeled using multiple factors calibrated against market observations. Using a single-factor model severely limits the representation of positions along the yield curve and if forward rates are sufficiently volatile the estimates are merely guesses at best. But during benign interest rate environments (low volatility) a single-factor model may perform the same or better than multifactor models. The use of a single-factor model in place of the richer multifactor model for the purpose of computational expediency may violate ethical principles. This depends on your perspective. A shareholder seeking a true representation and therefore an implicit understanding of the risk of their investment might prefer a more sophisticated model but perhaps the risk manager who needs a daily estimate might be satisfied with the broad approximation. Quants are caught between competing objectives driven by audience demands; one single method will not satisfy both. And the threshold delineating the two is unclear. While it may be ethically sound to allow for all manner of assumptions to exist so that models can generate a range of sensible and nonsense outcomes, whether an investor can actually understand the implications of these assumptions is doubtful. Disclosing assumptions underlying financial instrument construction and pricing to investors already occurs to some extent, both by statute and by custom. But it is difficult to attribute full responsibility on the model’s designer to adequately represent all possible world states and absorb model deficiencies by presenting all possible scenarios. The risk of reality failing to be reflected in theory would then be transferred to the investor who may not have the tools to anticipate the model’s shortcomings. So given the practical limits of model design and assumption disclosures to ‘‘ordinary’’ investors, a high proportion of the responsibility to cater for model
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inaccuracies should lay with the model’s designer, the Quant. This fact greatly agitates our need to define the ‘‘point’’ at which detachment should convert to engagement; the point where the ethical imperative becomes dominant. To meet their moral obligation, Quants need to know where this ‘‘point’’ is; but how do they identify it? Guidance by Conduct and Deed We need to introduce two elements to help construct the ethical framework relevant to the duties of the Quant: the articulation of rules and guidelines that define the boundary between detachment and engagement, and the underlying imperative that actually defines these rules. We will start with the formulation and articulation of ethical guidelines. Reflecting on the writing of Wittgenstein reveals an interesting perspective of the ethics of mathematics. He argued that although one’s actions are usually guided by rules and also that people generally act in consistent ways, it is of concern that the reasons behind this are not fully understood. He claims that it cannot be made explicit and remains inexpressible. Ultimately, it is about what one does, and not about the reasons that are given, which are redundant and guidance for a systematic approach to moral philosophy will, therefore, always necessarily fail (Wittgenstein 1993). Wittgenstein compared ethical problems with being trapped in a fly-bottle and not knowing one’s way about. Rules act as signposts suggesting a direction, but at its core, the systematic following of rules is so complex and subtle that there is no one correct way to follow such rules. Indeed, he suggested that it is imperative that sometimes we need to make up the rules as we go (Wittgenstein 1921, 1953). This does not mean, however, that one should act in any way one likes. This approach to ethics suggests that interpretation and understanding of rules does not imply how such rules are to be followed because it is the doing of the act that matters, rather than the articulation of the rule (Wittgenstein 1953, 1969; Malcolm 1958). It is almost impossible to articulate a set of rules to guide behaviors. Quants confront this reality almost every day. Wittgenstein likens rule-following to Michael Polanyi’s idea of tacit knowledge, which claims that understandings that enable complex activity and decision making cannot comprehensively be put into words (Wittgenstein 1921, 1993; Arendt 1958). Science, medicine, business and most other pursuits fit this mold. So if rules, guidelines and boundaries cannot be articulated then how are they formed? The capacity to understand moral boundaries need to be learned through observation and emulation or trial and error, and not through explicit instructions. It is essential that novices watch and participate within the safety of a company of experts in a gradual fashion over time. The
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articulation of moral obligations is thus formed over time and the prime adherents are those Quants who operate in a culture that values experience and wisdom over mathematical brilliance. This suggests that the importance of the quantitative function to financial markets cannot be simply left to gifted, yet inexpert mathematicians, whose understanding of the moral boundaries underlying Polyani’s tacit knowledge or Wittgenstein’s fly-bottle is undermined by inexperience. Wittgenstein’s approach suggests a way based on matters of conduct, learned in context through observation and emulation, and performed more or less consistently without being the result of conscious deliberation or strict adherence to rules. The boundary cannot be set based on some transcendental aspiration inexpressible in words (Wittgenstein 1980; Malcolm 1958). Lifting the Veil of Ignorance If the inability to explicitly express ethical guidelines defeats the capacity to articulate rules, what about the formulation and definition of the rules themselves? If we accept that rules cannot be fully described, perhaps it is impossible to comprehensively define the rules themselves, especially when searching for the threshold separating engagement from moral detachment. But there is a way around expressing a set of ethical norms that can still lead to definable ethical qualities that can be used in practice. Rawls’ theory of justice, to a large degree, promised to replace standard ethical theory when it was introduced. Rawls regarded the notion of distributive justice as dealing with ‘‘the way in which the major social institutions distribute fundamental rights and duties and determine the division of advantages from social cooperation’’ (Rawls 1999). He proposed to deduce just distributive arrangements from some assumptions about an ‘‘initial position,’’ in which individuals must choose principles from behind a ‘‘veil of ignorance,’’ which allows them self-interest and knowledge of general facts about human nature, but no knowledge of their initial position in society. This aspect of Rawls’ theory, while important, is less relevant to this discussion than his coverage of the fundamental principles of equality; ‘‘the principles that free and rational persons concerned to further their own interests would accept in an initial position of equality as defining the fundamental terms of their association’’ (Rawls 1958; Barry 1973). Is the nature of the equality of persons in the initial position ethical equality or not? Officially, it is not. The persons in the initial position have self-interest, but their attitude to others is neither benevolent nor envious. The veil of ignorance includes ignorance even about the ‘‘conception of good’’ that one will turn out to have. The appeal of Rawls’s position has proved to be exactly his derivation of just distributions from non-moral postulates.
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The reason why Rawls is able to operate without an assumption of benevolence is that it is replaced by ignorance: the self-interested actor in the initial position is forced to care about all people, because he does not know which of them will be him. As Rawls puts it, ‘‘the combination of mutual disinterest and the veil of ignorance achieves much the same purpose as benevolence’’ (Rawls 1999). Rawls also introduced the notion of the ‘‘difference principle’’ to consider the effect of inequality under a just ethical structure. The difference principle only permits inequalities that work to the advantage of the worst-off. While this can be misinterpreted as trickle-down economics, Rawls reverses the argument by guaranteeing the worst-off a fair deal. Rawls thus compensates for naturallyoccurring inequalities justified on the basis that the ‘‘just’’ choice from a set of Pareto optimal outcomes would be that benefiting the worst-off rather than the best-off (Rawls 1985). We should note here that a contrary view is expressed in Robert Nozick’s work Anarchy, State, and Utopia (1974) where he argues that the distribution of goods is only just if brought about by free exchange among compliant parties from a just starting position, even if large inequalities subsequently emerge from the process (Nozick 1974). This appealed to the idea introduced by Kant that people be treated as ends and not merely as a means to another end and thus challenged the conclusion of Rawls’ second principle of distributive justice. Nozick suggested, as a critique of Rawls and more importantly of utilitarianism, that the inviolability of life deems property rights to be non-negotiable such that individual personal liberty renders state policies of redistribution illegitimate. This is a principle that has emerged supporting libertarian arguments in contemporary politics. The main idea behind Rawls’ ethical construct is that moral principles do not rest on intuition and are not derived from utilitarian principles (or other teleological principle) holding that there is some optimal outcome to be sought and maximized. The theory of justice including the difference principle is proposed as a viable alternative to the more widely-held utilitarian and intuitionist doctrine. Rawls does not seek a radical change in ethical thinking, merely a de-emphasis of utilitarian principles so that principles of justice, allowing for inherent inequality, can be re-established. Aside from the fact that it is impossible to measure utility, a utilitarian would totally ignore rights if the outcome were a positive-sum game. So how does the plight of a mere Quant relate to Rawls’ view of justice and the difference principle? The central element we encounter is fairness derived as a just choice that does not exploit those who are at a natural disadvantage. Under this structure there is no need to integrate
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messy utilitarian ethics or the plurality of first principles from intuitionism into a set of guidelines that serve as rules. Rather, under Rawls’ theory the work of a Quant can readily transition from detachment to moral engagement and vice versa through actions that do not serve an injustice but can simultaneously maintain a position of inequality that seeks to maximize the benefit to the disadvantaged. This guideline is relatively simple and tractable. The practical implementation of this guideline, however, does not come without presenting at least some hurdles. From Detachment to Engagement Ethics as a practice means that individuals engage in a constellation of learned activities, behaviors and skills. The engagement occurs through complex practices by and emulating others who are more skilled, as well as through our own practice of trial and error. It necessarily means making mistakes, and learning from them, deliberation and reflection on what we are doing and why and through creatively responding to new and unexpected situations. The ethical framework we are sketching here is no different. The ranges of situations Quants characterize as ‘‘ethical’’ do not necessarily share any single common feature. Broadly they concern issues of moral definition, but in different senses of that term. They concern activities that express and develop ethical identities, and they do so in different ways. This point is worth emphasizing, because all practices, insofar as they are practices, are never entirely personal and idiosyncratic. They are learned, taught and usually form part of a shared legacy. Enactments of those practices always exist against the background of implicit norms necessary for those practices to be exercised and maintained within a particular context and time frame, and for them to be carried forward and passed on to others over time (Franklin 2004). In this sense it is not an exaggeration to call ethics the practice of practices. Wittgenstein claimed that ethical teaching cannot simply be reduced to training. Our proposed framework, illuminating some of the dimensions of conceiving ethics as a practice, is indebted to key elements of Wittgenstein’s philosophy and Rawls’ justice as fairness principle, though not exclusively. In our view, there can be no ‘‘method’’ of ethical deliberation and no single way in which our ethical agent, the Quant, arrives at a proper course of action. In practice, the process of teaching, learning and refining the practice of ethics cannot be easily separated. The dimensions of such practice operate differently in different circumstances and any effort to quantify the practice of ethics beyond an accounting of the considerations is highly artificial. We propose that the threshold delineating the barrier between ethical detachment and ethical engagement can
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only be defined by the Quants themselves. The burden of balancing the justice as fairness construct and the difference principle with the inability to explicitly articulate a list of rules must fall to the Quant. It is their moral duty to state whether the putative barrier has been crossed when they put their decisions and models into practice. If the barrier between detachment and engagement has not been crossed, it falls upon them to justify ‘‘if not, why not.’’ The burden must be placed on Quants to consider their moral duty and the effects of their decisions. The only individuals capable of knowing where the barrier is, is the Quants themselves. Wittgenstein’s notion of ‘‘learned experience’’ coupled with Rawls’ justice as fairness. Revisiting the example we discussed earlier, assume that a Quant is preparing a model for the construction and pricing of derivatives on residential mortgage backed securities (RMBS) for sale to retail investors. Only the Quant intimately knows the strengths and limits of the model, its assumptions and its sensitivities. An ethically detached Quant could simply construct the model, define limits so that it does not return unpalatable outcomes when unusual economic assumptions are inserted and generate structures and prices that would attract buyers. Disclosing the full range of model assumptions may not help an investor better understand the product’s features. For instance, a Quant could disclose that she used an implicit finite difference method with monthly step sizes over the 30-year life of the security priced on the current yield curve with constant volatility at each tenor and historical default rates. This explanation, while thorough, does not disclose the sensitivities of the model to changes in volatility, default rates, underlying yield curve dynamics or time step selection. Obviously, the Quant would understand these issues, but how far do they go to protect the investor from assuming a risk exposure they cannot afford, or which lies beyond their capacity had they been aware of the model limitations? That is, where is the threshold that separates detachment and indifference from engagement and moral obligation? As we propose above, the threshold can be defined as the point where the action of the Quant does not serve an injustice and can simultaneously maintain a position of inequality that seeks to maximize the benefit to the disadvantaged. But only the Quant will know where this threshold lies. Thus the Quant should disclosure that if their application of theory to practice is morally detached, it is their responsibility to state it as such and declare why. No one else can define this and no set of rules or guidelines can adequately account for the model subtleties. For the Quant designing RMBS derivatives, a feasible disclosure to declare would be that the model used for pricing does not reflect reality because volatility was assumed to be constant and default rates are based on history alone. The level of
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quantitative indifference applied in the model should be communicated and made clear. It may not result in a very attractive sounding product pitch, but the Quants have at least asserted their moral obligation and authority to more appropriately explain their involvement and the limits of their capacity. This type of disclosure then affords the investor some level of comfort that the risk is dependent on restrictive assumptions and that the analysis is rudimentary. Using this approach, the Quant has not exploited inequality and such declarations were made in fairness. On the other hand, a Quant who has catered for both the obvious and more subtle assumptions that drive price differences in the model could cross the threshold and become morally engaged by defining the adequacy or otherwise of the product for certain investors, investment styles or trading strategies. A small retail investor looking for a high-yielding product for instance, may be offered a RMBS derivative, which would obviously not be an entirely suitable investment. Instead of the burden of understanding being transferred to the investor, a Quant could assert that the product is unsuitable for retail investors (because of their inability to diversify default rate risk and volatility risk) and even define exactly what type of investor the product would be suitable for. Because the Quant knows the product and its model better than anyone, it is their duty to define its boundaries. While no articulation of rules can supply a threshold definition, avoiding the exploitation of inequality and the notion of fairness serves as the principles under which a Quant has become morally engaged. This is the Oppenheimer moment where concerns over model validity are elevated to highlight the model’s true limitations. We believe that this approach to the detachment-engagement transition will help Quants (with their models) convert the perception of Quants from a position of suspicion at best to one based on wisdom, confidence and integrity.
A Note on Industry Codes of Practice Many scholars would claim that the solution to the lack of ethical considerations in financial markets is to introduce more courses, especially on ethics, and make them mandatory. The current emphasis is on classical ethics which were theories developed without financial engineering in mind (Franklin 2004; Boatright 2010). While such courses would be valuable by developing Quants to reflect on their actions more clearly, they do not address concerns intimately tied to financial engineering practice. Appropriate development in ethics education for Quants is needed to identify points in the decision-making process where ethical questions can arise, and to explain how Quants can protect stakeholders from the costs of unethical behavior.
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In 2013, the CFA Institute commenced a revision of its ethics framework to account for the use of mathematical models in product development and sales. The updated code of conduct requires that advisors should clearly inform clients, on a continual basis, of any significant risks and limitations associated with a particular recommendation or strategy, particularly in the development of financial products and strategies that rely on advanced investment models. The key phrase in this statement is the need to inform ‘‘on a continual basis’’ meaning that the single disclosure usually delivered during the initial offer should be revised and disclosed further as either external conditions change or the instrument itself undergoes substantial variations in value. This definition fits neatly with our discussion on justice as fairness and the need to restrict the exploitation of inequality in the context of quantitative methods. While this code of ethics is not comprehensive, it does at least address the need for greater consideration of the limitations of complex models. Other professional bodies such as the International Association of Financial Engineers, however, do not consider ethics worthy of inclusion in their suggested core body of knowledge. Most economist and actuarial industry bodies are similarly vague on the notion of the application of ethics practices to their profession, particularly in the areas of valuation, pricing and risk management. What this means is that unless a Quant is employed in an area requiring mandatory compliance through accreditation such as in risk management or as part of the regular compliance schedule of a financial institution to meet licensing conditions, in the current environment the chances of a Quant encountering ethics and professional standards, as well as critical thought around their development, are slim. Our discussion above hopes to reverse this position.
Conclusion John von Neumann once said that ‘‘if people do not believe that mathematics is simple, it is only because they do not realize how complicated life is’’ (Alt 1972). The complex and yet subtle mathematics used in the capital markets is pervasive in engineering and science and has emerged from the wilderness of naive reliability. The field of mathematical finance will continue to develop in the future and the existing foundations are probably likely to be replaced by less restrictive mathematical constructs. There are a range of new ideas challenging conventional theory with the common thread being that they use alternative mathematical approaches to classical finance and contain fewer assumptions. Uncertainty will continue to augment randomness in the modeling approach and underlying theories.
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In general, a more ‘‘common sense’’ approach will replace blind reliance on mathematical models, while market incompleteness will be accepted and no longer feared. Mathematical finance is at a critical turning point given that many models used in the past have run their course. One thing for sure, however, is that there is likely to be a major change in direction for future modeling efforts and the fiduciary responsibility to advance the field will increasingly lie with the Quants themselves. Ethical behavior is not comprehensively reinforced through securities legislation and the gap between them suggests that the only way to bridge the two is through a broader approach to ethics in practice. In this discussion, we have confined the treatment of ethics to Quants, but it can be broadly applied across the finance profession. Quants often encounter ethical decisions in which they generally have little experience. This is particularly hazardous given their role as the resident experts on the mathematical models used to measure and manage financial risk. We propose that the threshold delineating the barrier between ethical detachment and ethical engagement be defined by the Quants themselves. The burden of balancing justice as fairness and the associated difference principle with the inability to explicitly articulate a list of rules must fall to the Quant. It is their moral duty to state whether the ethical barrier has been crossed when they put their decisions and models into practice. Such an approach will go some way toward aligning the profession with other specializations in banking and may even help avoid the introduction of even more complex and unnecessary regulation. Acknowledgment I wish to thank the editor and an anonymous reviewer for their valuable comments and inputs.
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