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Maximizing Risk and Uncertainty in a Changing World

Notes on Volatility in Cultures of Finance

One of the most remarkable contemporary developments has been the rise of what might be called a “politics of volatility” in which volatility is deliberately produced to take advantage of the uncertainty it creates. Its current embodiment is Donald Trump. Like the efficient market that he embraces, in the primaries, election, and the current transition period, Trump randomly processes and responds to current flows of information in ways that are designed to surprise and unbalance his opponents. As a self-purported master of “decision making under uncertainty,” he openly espouses a strategy of foregoing directional policies to produce volatility, out of which he will “make great deals”; his tactics of non-directionality to maximize uncertainty are reminiscent of randomized strategies in zero-sum games. At the same time, he pictured Hillary Clinton as captured by directional policies of the Obama and Clinton administrations and neither robust nor resilient enough to deal with a changing world defined by the risks and uncertainties of trade and terrorism.

What produced the current politics of volatility? Its genealogy will turn out to go back to the early 1970s, to the origin of derivative finance and the Rawls-Nozick debates that set the parameters for contemporary neoliberalism. The immediate backdrop are the black-swan events of 9/11 and the Great Recession of 2008, which continue to infuse the present campaign with overtones of risk, uncertainty, and volatility that wrap themselves around the contrasting images of Trump as charismatic deal maker and Clinton as the rational risk manager. But Clinton’s image as a neoliberal risk manager reminds us of a longer history out of which the politics of volatility emerges. The fiscal crisis of 2007-2008 was preceded by a 25-year period known as the “Great Moderation,” in which reduced volatility became the focus of economic policy discussions. The combination of neoliberal deregulation and new forms of risk management introduced by financial derivatives were seen as reducing the “macro-economic volatility” of business cycles to historic lows. With the prudent risk manager as model, the reduction of volatility was seen as a triumph of free-market ideology and financial technology.

The Great Moderation was coeval with the rise of both finance and neoliberalism, perhaps best signaled by Robert Rubin’s hiring of Fischer Black at Goldman Sachs in 1984. Rubin was a partner at Goldman Sachs and the head of its Equities Division and would become President Bill Clinton’s Secretary of the Treasury in 1995. Black was the co-discoverer of the Black-Scholes options pricing formula, which is at the heart of modern finance. Rubin hired Black to introduce new forms of quantitative risk management into trading and investment banking, a move that would catalyze the exponential growth of a deregulated derivative finance that Alan Greenspan would advocate.

The long arc of neoliberal deregulation can be traced back from Barack Obama and Bill Clinton to Ronald Reagan and Margaret Thatcher, overlapping the Great Moderation and the 20-year term of its overseer Greenspan as chairman of the Federal Reserve from 1987 to 2006. The results are dramatic as finance increases its share of US corporate profits from less than 10% in 1980 to more than 40% in 2005, thereby inaugurating a transvaluation of values among “the best and the brightest” as finance and investment banking increasingly become the professions to which graduates of elite universities aspire. According to Thomas Piketty’s data, the mid-1980s ascent of derivative finance is also the time when inequality begins to spike upward.

On October 23, 2008, in his humbling testimony to the Government Oversight Committee of the House of Representatives shortly after the crash, Greenspan acknowledged what many critics of derivative finance had suspected: that derivative finance was sustained by an “ideology” that melded a neoliberal commitment to free markets with faith in the financial technology of risk management.

I do have an ideology. My judgment is that free competitive markets are by far the unrivaled way to organize economies. We have tried regulation, none meaningfully worked…In recent decades a vast risk management and pricing system has evolved combining the best insights of mathematicians and finance experts, supported by major advances in computer and communications technology. A Nobel Prize was awarded for the discovery of the pricing model that underpins much of the advance in derivatives markets. This modern risk management paradigm held sway for decades. The whole intellectual edifice, however, collapsed in the summer of last year…I found…[a] flaw in the model that I perceived is the critical functioning structure that defines how the world works, so to speak.

Greenspan’s invocation of the Black-Scholes options pricing model extends the genealogy of volatility back to the early 1970s, when the Black-Scholes equation was first published in 1973. It was a time of great economic volatility — the end of Bretton Woods, which set currencies free to circulate, the Arab Oil Crisis, hyperinflation, a global stock market crash, as well as the founding of the Chicago Options Exchange. The rise of global volatility and huge pools of oil-produced speculative capital fueled the demand for new financial instruments to store and hedge wealth; the result was the exponential growth of derivatives.

But volatility was not restricted to the economic domain. As Ulrich Beck’s Risk Society: Toward a New Modernity and David Harvey’s The Condition of Postmodernity have pointed out, the early 1970s was also a time of great social transformation — the rise of “risk society” and “ postmodernity” in response to fundamental changes in capitalist modernity. Although they give alternative accounts of the rise of “reflexive modernity” and postmodernity, they now appear to be more complementary than competing. With the hindsight of our genealogy of volatility, Beck, along with the sociologist Anthony Giddens, can now be seen as placing Frank Knight’s distinction between risk and uncertainty at the heart of the development of modernity but without an explicit account of its role in the economic processes that bring about risk society. Harvey’s work, however, makes an internal connection between finance capitalism and postmodernity, but it does not investigate the role of risk and uncertainty in the development of finance, especially the role of derivatives.

Both Beck and Harvey agree that changes in capitalism in the early 1970s led to significant cultural transformations in modernity, which for Beck is the development of reflexive modernity and for Harvey postmodernism. Yet despite their different emphases, each can be seen as highlighting something that the other overlooks. Beck deepens Harvey’s account by pointing to the crucial role that risk and uncertainty play in finance capitalism, whereas Harvey describes fundamental changes in capitalist production (flexible accumulation and the resultant time-space compression) that will give birth to both postmodernism and risk society. Combining these accounts, we find the key factor is the role of risk and uncertainty in the financialization of capital. But if we probe further into the development of contemporary finance, we discover that the key discovery in derivative finance is not simply new ways for managing risk and uncertainty, but the isolation and pricing of volatility. It is the discovery of volatility in the form of the Black-Scholes option pricing formula that gives birth to derivative finance.

The Black-Scholes option pricing formula became the foundation for modern finance because it showed how to “replicate” one financial asset from another — it became the principle of innovation in modern finance by showing how, for example, an option might be constructed out of stocks and a riskless bond — by pricing volatility. An unexpected feature of the Black-Scholes formula is that it makes no mention of the expected return of the underlying asset — the key variable is its volatility. Portfolio theory is concerned with balancing risk and return, but the internal mechanism of Black-Scholes effectively neutralizes (via “delta-hedging”) directional risk to access and price volatility. Derivative finance thus rests upon first distinguishing volatility from directional risk then isolating and pricing it.

At the core of derivative finance is the Black-Scholes model for pricing options, which is still used more than 40 years after its initial discovery to price trillions of dollars of derivatives on a daily basis. At the heart of the model is the idea of “dynamic replication,” which is a way of continuously deriving an unknown asset price (that of the option) from the behavior of a better-known asset (the stock). This “replication” would become the principle of innovation for derivatives and other financial instruments and was the major reason for the explosive development of derivative finance.

The Black-Scholes formula is a partial differential equation, which can be solved by inputting the strike price and expiration date of the option, the price and volatility of the stock, and the risk-free interest rate. The only unknown variable is the volatility of the stock; there is no mention of the expected return of the stock, which surprised many analysts who were looking for a solution to the options pricing problem. In fact, the internal mechanics of the model involve hedging out or neutralizing directional risk. As the price of the stock changes, the market maker dynamically readjusts the hedge to maintain a risk-free position — to access or price volatility (and the option), the model gets rid of directional risk.

The discovery of volatility is at the core of derivative finance. Dynamic replication becomes the way to invent new financial instruments out of old ways — it is the principle of innovation in finance — and the separation of directionality from volatility is at the heart of the breakthrough of Black-Scholes and derivative finance. The derivative makes explicit an aspect of volatility that is difficult to capture because volatility and directional-risk are confounded in the notions of change and movement.

In finance, asset prices can move up or down; the uncertainty around these moves creates a “directional” sense of risk. The volatility of an asset is the randomness in the asset price and the magnitude of change independent of its direction. Volatility is calculated by determining the mean of the price movements and then squaring the difference between the mean and each price used in calculating the mean. The squaring is to ensure that positive and negative movements do not simply cancel each other out. The traditional measure of volatility is the standard deviation, which is the square root of the sum of the squared differences.

Volatility is thus a measure of the spread of price changes, their magnitude of difference from the mean, norm, or average. But all that we can observe are the price changes and movements — the volatility has to be inferred by some way that differentiates it from movements. This can be approximated by computing an historical average. Doing so, however, produces a paradox because volatility is not an historical quantity, but rather, as the quantitative finance researcher Paul Wilmott noted, an instantaneous one.

Yet the instantaneous or actual volatility of a stock is in real time. It is what traders and market makers feel when they trade a stock or option, the feeling on the basis of which they capture, fix, and freeze when they performatively agree with their counterparties to buy or sell an asset at a fixed price. It is felt as the intensity of change, which is nicely captured in the following description of trading by Elie Ayache, a quant and former options trader, in terms that would also fit a surfer or high-stakes poker player:

Through the dynamic delta-hedging and the anxiety that it generates (Will I execute it right? When to rebalance it, etc.), the market-maker penetrated the market. He penetrated its volatility and he could now feel it in his guts. In a word, he became a dynamic trader. He now understood — not conceptually, but through his senses, through his body — the inexorability of time decay, the pains and joys of convexity.

In this account, we can see the interaction between the quantitative and qualitative sides of volatility. The mathematics of the options pricing model meets the phenomenology of volatility in trading the option; “dynamic delta-hedging” bridges the abstract calculations of volatility and the experience of trading that the market maker feels “in his guts.” The phenomenological experience of volatility is the qualitative side of a whole range of social and cultural activities — the cultural side of the “culture and capital” equation — that also began to appear in the early 1970s. New forms of risk-taking developed out of the volatility created by the decline of Fordist production and the rise of social movements in the 1960s. Out of the ruins of the city came “derivative” movements such as hip-hop, skateboarding, and graffiti as well as a variety of artistic forms all of which converge around the discovery of volatility. Derivatives make explicit what was implicit in the risk-taking practices that developed in the 1970s and 1980s: to access and play with the “upside” of volatility, you have to hedge away, neutralize, or buffer out directional risk.

In addition to the efflorescence of cultural forms associated with both postmodernism and reflexive modernity, the early 1970s also saw two works that would frame the philosophical parameters of neoliberalism: in 1971, John Rawls’s A Theory of Justice Appears and in 1974 the libertarian alternative to distributive justice found in Robert Nozick’s State, Anarchy, and Utopia. Both works draw heavily from The Theory of Games and Economic Behavior by John Von Neumann and Oskar Morgenstern, which is also the basis for modern portfolio theory and is the starting point for modern quantitative finance. The crown jewel of portfolio theory will lead to the capital asset pricing model, which in the hands of Fischer Black and Myron Scholes will result in the Black-Scholes formula for pricing options, undoubtedly the foundation of derivative finance. Michel Foucault’s prescient College de France lectures on neoliberalism would be given in 1977-1978, to be followed by its political implementation by Margaret Thatcher in 1979, Ronald Reagan in 1980, and Bill Clinton in 1992.

We can begin to see a different story emerging with the rise of finance capitalism — the intertwining of derivative finance with the rise of neoliberalism. In the wake of the collapse of the postwar Fordist economy, the late 1960s and early 1970s saw the blighting of cities, civic and political unrest, as well as an explosion of new cultural forms, many of which seemed not to be simply extensions of directional risk-taking, but rather steeped in volatility. Fordist economies emphasized centralized mass production and vertical organization of expertise and decision making. With the development of post-Fordism and flexible accumulation, the centripetal forces oriented toward the center break down, creating centrifugal flows and volatility.

The rise of risk society and postmodern cultural forms is a response to the increased social and economic volatility caused by a variety of factors, ranging from post-Fordist flexible accumulation to student protests and global decolonization movements. In the financial sector, the end of Breton Woods and the Arab Oil Crisis create an unpredicted and unpredictable global volatility that produces huge amounts of speculative capital looking for safe havens. In this context, derivative finance was born, with the Black-Scholes formula as its technical core. The neoliberal deregulation of derivatives and their markets during the Great Moderation will catalyze the unprecedented expansion of derivatives whose notional value will skyrocket in 40 years from tens of millions dollars annually to more than a quadrillion.

Although derivative finance differentiated directional risk from volatility to price it and create financial instruments, the discovery of volatility has been made independently in many different domains. The exploded volatilities of abstract expressionist painters such as Jackson Pollack or de Kooning and the aleatory music of John Cage and Karlheinz Stockhausen are relatively early twentieth century developments but are soon incorporated in other media such as dance as experimentation with volatility becomes increasingly fashionable as an expression and exploration of a new “ postmodern” sensibility. Hip-hop, skateboarding, mixed martial arts can all be seen as movement-based explorations of volatility.

However, these experiments remain relatively local, whereas the discovery of formal techniques to access and manage volatility in derivative finance, especially the Black-Scholes equation, extend “derivative experimentation” to new areas, such as the importation of sabermetrics into baseball, deftly described in Michael Lewis’s Moneyball, or into public policy debates, such as Robert Schiller’s proposals for livelihood and inequality insurance. Over the 40 years since the discovery of Black-Scholes, these various forms of “risking-together” have become more intertwined through their discovery of volatility, which has then led to the use of statistical techniques derived from derivative finance to “slice and dice” and recombine them into new configurations for new functions and purposes.

For the 25 years of the Great Moderation, derivative capitalism produced incredible wealth as the United States moved toward an increasingly finance-based economy. But in 2008, we learned that such wealth was at tremendous social cost. No matter what their theoretical role in “risk management,” neoliberal policies that deregulated and privatized derivatives increased volatilities, which amplified the risks, precarity, and uncertainties borne by societies as a whole. Efficient markets and neoliberalism do not produce the world that they promise.

Social critics often reject the whole financial apparatus of derivative capitalism, pointing to its speculative excess, greed, and social inequality. However, the Great Moderation undoubtedly produced great amounts of new wealth. Yet, questions arise. Was the Great Recession a result of derivatives or their neoliberal deregulation? Is the wealth the problem, or the way it was produced, or perhaps its distribution? Instead of deregulation, could social regulation of derivative finance have resulted in more wealth more equally distributed?

From a Marxist perspective, the wealth produced by derivatives is fictitious, as it is the product of circulation and not labor-based production. Thus, the ontological status of volatility is unclear: its pricing by the Black-Scholes formula makes it a new potential source of wealth, but it inhabits a world of circulation and not production in the classic sense. Yet perhaps the most tantalizing aspect of volatility may be its role in rethinking ethics. The current debate over the ethical status of derivative wealth is framed by left objections to its unequal distribution or free market advocates to its regulation. But the dynamics of options pricing may suggest a possible ethics that is incompatible with both neoliberal considerations of distributive justice and libertarian market freedom.

Both Rawls and Nozick rely on game theory to derive their ethics, which are variations on the type of utility maximization that Von Neumann and Morgenstern axiomatized in their Economic Behavior and the Theory of Games. Harry Markowitz’s portfolio theory, which is the theory behind index funds, also relies on Von Neumann and Morgenstern. The trajectory in finance from expected utility to risk and uncertainty and then volatility is fairly direct. Portfolio theory is the immediate predecessor to the capital asset pricing model from which the Black-Scholes formula is derived.

Nevertheless, there is a radical break between directional risk and volatility in the transition from portfolio theory to Black-Scholes, from stocks to derivatives, that relies on establishing and maintaining non-directionality. This turn to non-directionality via neutralizing directional risks raises the question of what a non-directional ethics would look like — a question originally raised by Nozick in his criticism of Rawls. Can dynamic replication replace decision making under uncertainty as the framework for an ethics of volatility?

Rawls explicitly introduces uncertainty into ethical decision making in form of the original position. In the original position, people does not know what status they will have in society and will therefore choose the “difference principle” — “the higher expectations of those better situated are just if and only if they work as part of a scheme which improves the expectations of the least advantaged members of society” — because they may end up as one of the least advantaged. It would not be rational to allow others to benefit unless it benefited the least advantaged, a group of which one might be a member.

Nozick argued that the difference principle was an end state or patterned principle of justice (it judged the present situation in terms of a preexisting pattern or distribution) and incompatible with an historical-entitlement conception of justice. Even though the difference principle is supposed to apply to an “ongoing and continuing institutional process,” as an end-result principle it remains external to such processes and cannot be what Nozick calls a “current time-slice principle.” As an example of such a process principle, Nozick offers instead his “acquisition, transfer, and rectification” version of Locke’s theory of acquisition.

Markowitz, Rawls, and Nozick all accept the decision-making framework of Von Neumann and Morgenstern. But Black-Scholes develops a version of Nozick’s current time-slice principle in its notion of dynamic replication, a continual real-time adjustment of the delta-hedge to the changing prices of the stock. To get access to and to price volatility, Black-Scholes hedges away directional risk — it maintains a non-directional stance in the face of continual change. Further questions then arise.

Is there an ethical decision-making counterpart to dynamic replication? Is there such a thing as a non-directional ethics? And, as a good Marxist might argue, is the ethics that arises compatible with or critical of the source of wealth in society? What would a non-directional ethics of volatility look like? As a new source of tremendous wealth in an age of increasing inequality, does volatility play a role in contemporary “risk society” similar to that of value in Marx’s time as a site of struggle and a harbinger of changes yet to come?

Ben Lee

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