The investment partnership Long-Term Capital Management was set up in 1993 by John Meriwether, previously a successful bond trader and then senior manager at the US investment bank, Salomon Brothers. Meriwether recruited to LTCM, from Salomon and elsewhere, an impressive team of experienced traders and specialists in mathematical finance. Much of its trading was with leading banks, and it largely avoided risky ‘emerging markets’, preferring well-established ones such as those in government bonds of the leading industrial nations. The fund avoided speculation based on hunches. It built carefully researched mathematical models of the markets in which it traded, and invested in a way designed to achieve insulation from market movements, seeking small pricing anomalies from which it could profit. Although it had to borrow large amounts and commit money on a large scale to make an adequate return from these anomalies, LTCM scrupulously measured and controlled the risks it was taking.
From the start of trading in 1994 until the spring of 1998 it was strikingly successful, but unusually adverse market conditions that summer (following Russia’s devaluation of the rouble and partial default on its rouble-denominated debt) pushed LTCM close to bankruptcy by late September. As its difficulties grew, the Federal Reserve Bank feared the consequences for already nervous capital markets of a sudden forced liquidation of the fund’s large commitments, and therefore co-ordinated LTCM’s $3.6 billion recapitalisation by a consortium of American and European banks. The consortium has now recovered and indeed made a profit on this investment, and the fund is being wound up. No public money was spent on the recapitalisation, and – a small number of rich individual investors aside – the losses fell to wealthy institutions well able to absorb them, and to LTCM’s partners and employees.
Material, then, for a business school case study, but no more? Although André Perold of Harvard has produced such a study, exemplary in its measured tone (unfortunately, it is not yet publicly available), the answer seems to be no. In the autumn of 1998, LTCM’s distress provoked a torrent of comment, followed by a series of reports by bodies such as the President’s Working Group on Financial Markets. More than a year later, the story still commands attention: it has recently been the subject of a BBC Horizon programme (a re-edited version was shown on US public television in February) and Inventing Money,a book by Nicholas Dunbar, an editor of Risk magazine. Some of the discussion has been pure Schadenfreude, focusing on the presence among LTCM’s partners of the 1997 Nobel laureates in economics, Robert C. Merton and Myron Scholes. The Horizon programme on the work of Merton and Scholes used the LTCM episode to create an exciting, but distorted and misleading, story. Even Dunbar’s generally informative book is marred by some gratuitous swipes at those involved. Paradoxically, the pervasive belittling of individuals minimises the interest of the episode. If LTCM’s partners and employees had been greedy gamblers, or naive, inexperienced traders, its problems would have been predictable and of little interest. But they were neither: top Wall Street professionals held, and in many cases still hold, LTCM’s partners in the highest esteem.
In the early 1970s Merton and Scholes were responsible (with their colleague, the late Fischer Black) for the single most important breakthrough in the modern mathematical theory of finance. This concerned the apparently esoteric problem of the pricing of options – that is, contracts that give one the right (with no obligation) to purchase (‘call’) or sell (‘put’) an asset such as a block of shares at a given price on a given future date or during a given period. It is a technically demanding problem, and one to which the 20th century’s most distinguished mathematical economist, Paul Samuelson, had failed to find an entirely satisfactory solution.
Black, Scholes and Merton’s solution to the problem was far-reaching, but their basic idea was simple and elegant. They showed how to construct a ‘replicating portfolio’: a continuously adjusted set of investments in both the underlying asset and government bonds or cash that would have exactly the same pattern of returns as an option. In an efficient market, the price of the option has to equal the cost of the replicating portfolio. If those prices diverge, there is risk-free profit to be made by buying the cheaper and selling the dearer of the two, and as arbitrageurs (market participants who exploit discrepancies between the prices of equivalent assets) do this, their purchases raise the cheaper price and their sales lower the more expensive one. Thus arbitrage eliminates any divergence between the price of the option and the cost of the replicating portfolio.
Black, Scholes and Merton’s full analyses were more complex than this account might suggest. It is important to understand that constructing what traders call a ‘position’ may involve not buying an asset but ‘short selling’ it: that is, borrowing it, selling it, and later repurchasing and returning it, a perfectly normal sequence in the financial markets. More profoundly, the construction of the replicating portfolio depends on the assumption that returns on the underlying asset follow what Black and Scholes called ‘a random walk in continuous time’: a chance process with specific, well-defined mathematical characteristics. Previous research had shown that the random walk model gave a surprisingly good description of share price changes, and (largely independently) probability theorists, above all the Japanese mathematician Kiyosi Itô, had developed a sophisticated, rigorous calculus applicable to continuous-time random walks. It is an appealing irony that the Itô calculus, which (following its introduction into finance theory by Robert C. Merton) has become a key aspect of the mathematical foundations of modern American capitalism, was developed in part during the American bombing of Japan in the Second World War.
Black, Scholes and Merton’s work has become fundamental to modern financial markets – and not just because options are now far more important products than when their articles on pricing were published in 1973. Their work also provided a new way of thinking about risk, and suggested a method for pricing and controlling the risk in a wide variety of financial products: find the replicating portfolio of more basic assets, and use that both to hedge (that is, offset) the risk of the product and to price it rationally. For example, the method helps investment banks to ‘buy’ risk from institutional clients (by selling them products that offset risk) and ‘sell’ it to others, such as corporations with different vulnerabilities or speculators with an appetite for the large profits that can accrue from risky assets. A massive global industry in financial derivatives has emerged over the last thirty years (its 1997 turnover was estimated by the Financial Times, admittedly using extremely dubious measurements, as the equivalent of more than $60,000 for every human being), and important aspects of it would not be possible without the mathematical techniques that have developed on the foundations laid by Black, Scholes and Merton.
Scholes’s and Merton’s involvement in LTCM has led commentators to ask whether the company’s failure reveals basic errors in the assumptions underpinning their work with Black on option pricing. Dunbar, for example, says that these assumptions are ‘flawed’ – a common conclusion in discussions of LTCM. If Dunbar and the others are correct it would be a matter of real import, given how central these techniques have become to the global financial system. But the extent of the technical dependence of LTCM’s trading on Black-Scholes-Merton reasoning is unclear until there is more information in the public domain – and to ask whether the assumptions of this reasoning are true or false is to pose a misleading question in any case.
Consider the similarities and differences between physics and finance. There is a generic resemblance between much of modern finance theory and mathematical physics. The Black-Scholes-Merton pricing equation is a form of what is known in physics as the heat or diffusion equation, which describes phenomena such as the flow of heat. The random walk model of share price changes appears in physics as Brownian motion, the movement of particles subject to minute, random collisions. Yet there is a crucial difference: finance inhabits the world of what the sociologist Barry Barnes calls ‘social-kind’ terms, not natural-kind terms. We do not ordinarily imagine that the flow of heat along a metal bar is affected by our beliefs about that flow. In finance, however, we cannot make the same presumption. Finance theory describes a world of human institutions, human beliefs and human actions. To the extent to which that theory is believed and acted on, it becomes part of the world it describes.
This (scarcely novel) observation is usually taken as a criticism of finance theory, but it is nothing of the kind. Its implication is not that the assumptions of that theory are false, but that their truth is a historical, context-dependent matter. Black, Scholes and Merton’s basic option pricing theory rests, for example, not just on the random walk model of price changes, but on the assumption that the replicating portfolio can be revised continuously by buying or selling assets (thereby maintaining a perfect hedge against the risks of the option) without incurring transaction costs. In 1973 that was indeed a flawed assumption: stock market transactions were expensive, and option traders could not do what they now can, almost instantly hedge by pressing a few keys on the hand-held computers they use to manage transactions, price options and measure risks. Over the decades since 1973, the assumptions of the possibility of continuous, cost-free revision of a portfolio, and of knowledgable arbitrageurs able to exploit (and thus eliminate) even small price anomalies, have become more, not less, realistic.
Modern finance theory is itself part of the process that has made those assumptions more realistic. For example, ‘index tracker’ funds (one of the most popular products of the theoretical and statistical work that preceded that of Black, Scholes and Merton) seem to have played a part in driving down the cost of share trading. More generally, the availability of a systematic methodology for pricing financial products makes it easier to introduce them, to hedge the risks involved and to identify arbitrage opportunities. The trading activity that results increases the volume and liquidity of the financial markets: hedging by traders on the Chicago Board Options Exchange, for example, forms a significant part of the volume of trading on the New York Stock Exchange. Larger, more liquid markets make it easier and cheaper to buy and sell financial assets, and so the continuous revisability of portfolios becomes a more realistic approximation to reality.
The key general point was made fifty years ago, not by an economist, but by a sociologist, Robert K. Merton, father of the finance theorist: beliefs about social institutions are a constitutive part of those institutions, not simply an external description of them. Merton’s first example – in retrospect a poignant one – of what he called ‘self-fulfilling prophecy’ was a run on a bank: a rumour that a bank is about to fail causes depositors to seek to withdraw their funds, making what was actually a sound financial institution unsound.
Alone among the commentators on LTCM, Dunbar notes Merton’s article, but even he does not explore its full significance. To do so, we must free ourselves from the assumption that a self-fulfilling prophecy is necessarily pathological. In some cases it is: Merton gave the example of the racist belief that black workers were strike-breakers, which was used to justify their exclusion from trade unions, and often left them in the position of having to take whatever work was available. In other cases, however – probably the vast majority – self-validating belief is perfectly rational. In the case of money, for example, the widely-shared belief that dollar bills will continue to be exchangeable for goods and services makes them usable for such purchases (that it is beliefs that ultimately constitute money becomes plain when those beliefs become precarious, as in times of social collapse or hyper-inflation). More generally, as Barnes has pointed out, all stable social institutions are underpinned by self-validating beliefs, and that is no criticism of the institutions or the beliefs: it is what constitutes their stability.
As markets and financial institutions change, the relationship between the assumptions of finance theory and ‘reality’ (even in very particular areas) does not remain static: it evolves. The dominant tendency, over the last thirty years, of what Robert C. Merton calls the ‘financial innovation spiral’ has been to increase the truth of finance theory’s typical assumptions. Markets have become more efficient and more liquid, new products have made them more complete, arbitrageurs on the look-out for inefficiencies have become smarter, more thorough and more determined, transaction costs have decreased radically, and the ease with which positions can be adjusted has typically increased considerably.
Within this primary pattern, however, are many secondary complexities: the interconnections of institutions, beliefs and actions do not always promote stability. That, perhaps, is what gave the summer and autumn months of 1998 their dreadful significance for LTCM. The fund’s market positions were varied, but a common theme underlay many of them. Using extensive statistical databases and theoretical reasoning, the firm identified pairs of financial assets the prices of which ought to have been closely related, which should over the long run converge, but which for contingent reasons had diverged: perhaps one was temporarily somewhat easier to trade than the other, and therefore more popular, or perhaps institutions had a particular need for one rather than the other. The fund would then buy the underpriced, less popular asset, and borrow and sell the overpriced, more popular one. The close relation between the two assets would mean that general market changes such as a rise or fall in interest rates would affect the prices of each nearly equally, and long-run convergence between their prices would create a small but low-risk profit for LTCM. The partnership knew perfectly well that over the short and medium term prices might diverge further, but the risks and the consequences of them doing so were carefully calculated by using statistical ‘value-at-risk’ models, which measure the potential losses from adverse market movements and are now used by all the sophisticated players in the financial markets. As Dunbar notes, LTCM also ‘stress-tested’ its trading positions to gauge the effect on them of extreme events not captured by standard statistical models, such as the failure of European Monetary Union or stock exchanges crashing by a third in a day.
The Russian default was just such an extreme event, though one that no one had anticipated: the surprise was not that Russia was in economic trouble, but that it defaulted on debts denominated in roubles, rather than simply printing more money, and also that it temporarily blocked some foreign exchange transactions by Russian banks. LTCM itself had only a minor exposure to events in Russia, but the precise form of Russia’s actions caused significant losses to Western banks. An investment fund called High Risk Opportunities failed, and (quite unfounded) rumours began to circulate that Lehman Brothers, an established investment bank, was also about to do so. Suddenly, market unease turned into self-feeding fear. A ‘flight to quality’ took place, as a host of institutions sought to liquidate investments that were seen as difficult to sell, and potentially higher risk, replacing them with lower risk, more liquid alternatives. Because LTCM’s ‘convergence arbitrage’ generally involved holding the former, and short selling the latter, the result was a substantial market movement against the fund.
Although the evidence is still largely anecdotal, three additional factors seem to have worsened the effect of the flight to quality. The first was the simple fact that it took place in August, when many traders and managers are on holiday and markets tend to be thinner and less liquid than usual. The second factor was that LTCM was by no means the only market participant involved in convergence arbitrage: many of the world’s leading banks, notably Wall Street investment banks, had broadly similar large positions. The third factor was that, as Dunbar points out, these banks employed value-at-risk models not just as LTCM did (to gauge the overall risks faced by the fund), but also as a management tool. By allocating value-at-risk limits to individual traders and trading desks, big institutions prevent the accumulation of over-risky positions while giving traders flexibility within those limits. However, if adverse market movements take positions up to or beyond the limits, the traders involved have no alternative but to try to cut their losses and sell, even if it is an extremely unfavourable time to do so. In August 1998, widespread efforts to liquidate broadly similar positions in roughly the same set of markets seem to have intensified the adverse movements that were the initial problem. Crucially, they also led to greatly enhanced correlations between what historically had been only loosely related markets, across which risk had seemed to be reduced by diversification.
Used as management tools, value-at-risk models (intended to describe the market as if it were something external) thus became part of a process that magnified adverse market movements, which reached levels far beyond those anticipated by the models. For example, if Dunbar’s account of LTCM’s risk modelling is correct, the probability of the fund’s August 1998 losses was so low that its occurrence even once in the lifetime of the universe was very unlikely. Furthermore, though the use of such models was perfectly rational at the level of, say, the individual investment bank, it may have helped to produce a collectively irrational outcome. As ‘spreads’ (the difference between prices of related assets) widened, and thus in a certain sense arbitrage opportunities grew more attractive, arbitrageurs did not move into the market, narrowing spreads and restoring ‘normality’. Instead, risk models used as management tools forced potential arbitrageurs to flee, widening spreads and intensifying the problems of those who remained, such as LTCM.
LTCM, however, was constructed so robustly that, though they caused major losses, these problems were not fatal. In September 1998, though, a social process of a different kind got underway, in effect a run on a bank. LTCM’s difficulties became public. On 2 September Meriwether sent a private fax to the company’s investors, describing its difficulties and seeking to raise further capital to exploit what he described (quite reasonably) as attractive arbitrage opportunities. The fax was posted almost immediately on the Internet and seems to have been read as evidence of desperation. The nervousness of the markets crystallised as fear of LTCM’s failure. Almost no one could be persuaded to buy, at any reasonable price, an asset that LTCM was known or believed to hold, because of the concern that the markets were about to be saturated by a fire sale of the fund’s positions. In addition, LTCM’s counterparties – the banks and other institutions that had taken the other side of its trades – tried to protect themselves as much as possible against LTCM’s failure by a mechanism that seems to have sealed the fund’s fate. LTCM had constructed its trades so that solid collateral, typically government bonds, moved backwards and forwards between it and its counterparties as market prices moved in favour of one or the other. Under normal circumstances, when prices were unequivocal, it was an eminently sensible way of controlling risk. But in the fear-chilled, illiquid markets of September 1998, prices lost their character as clear facts. As was in effect their contractual right, LTCM’s counterparties marked against it: that is, they chose prices that were unfavourable to LTCM, seeking to minimise the consequences for their balance-sheets of LTCM’s failure by getting hold of as much of the firm’s collateral as possible. Fearing the failure, they made it inevitable by draining the firm of its remaining capital.
Subsequent events offer an intriguing coda. The episode seems not to have been simply a short-lived market aberration. Despite the general return of confidence following the Federal Reserve’s three interest rate cuts in autumn 1998, spreads have remained stubbornly high (see, for example, the Bank of England’s November 1999 Financial Stability Review). The reasons are complex, but one factor appears to be the wholesale flight of arbitrage capital. LTCM was the most dramatic victim of 1998, but by no means the only institution to be damaged. The proprietary trading activities of many banks also incurred heavy losses, and the leading American investment banks, which suffered substantial falls in their share prices, seem now to have withdrawn from convergence arbitrage almost completely. The absence of arbitrageurs has helped keep spreads wide. Fearing convergence arbitrage to be too risky, market participants have in a sense ensured that it remains so. One important participant, however, believes this implicit consensus to be wrong: LTCM’s founder, John Meriwether. By last December, he had raised the first $250 million of investment for a new venture. His Relative Value Opportunity Fund will perform convergence arbitrage similar to LTCM’s, although it will not take such large positions and will use a risk model revised to take account of the huge, highly correlated, market movements of August 1998. If this new fund shows healthy profits, other participants are likely to return to convergence arbitrage, and spreads will eventually decline again.
LTCM’s fate has provoked some anti-intellectual nonsense. Mathematical finance is part of the infrastructure of the modern world. The techniques developed out of the research of Black, Scholes and Merton continue to work perfectly well in millions of transactions daily, and to abandon them would be unthinkable folly. Yet we must also remember that finance theory describes not a state of nature but a world of human activity, of beliefs and of institutions. Markets, despite their thing-like character, their global reach and their huge volumes, remain social constructs and the feedback loops that constitute them are intricate, knotted and far from completely understood.