LTCM: The Failure of Financial Mathematics

Opinion Pieces>LTCM: The Failure of Financial Mathematics

From 1994 until 1998, the most exciting hedge fund in the world was undoubtedly Long Term Capital Management (LTCM). It appeared out of nowhere and in less than three years it had over $100 billion in assets under management, with annual returns of 40%. Its founder was former Salomon Brothers trader John Meriwether, and its board of directors included Nobel-prize winning economists Myron Scholes and Robert Merton, as well as the Vice-Chairman of the Federal Reserve, David Mullins. Investors were clamouring to hand over the $10 million required to get into the fund, certain that the pedigree of its management would make it infallible. But in 1998 its brush with bankruptcy almost caused a global financial crisis.


Before starting LTCM, Meriwether had gained recognition in the financial industry for pioneering the idea of fixed-income arbitrage. This investment strategy exploits the pricing differences in fixed-income securities, such as bonds, and is executed by buying a security in one market for immediate resale at a higher price in another market. In hedge fund management, the strategy usually involves identifying a pair of similar securities, where one security is priced below the price that is perceived by the market to be the normal price and the other is priced above the perceived normal price. The under-priced security is purchased by the trader whilst the over-priced security is sold short. When the prices revert back to the perceived normal price, the trade is liquidated for a profit. Opportunities for executing this trading strategy are difficult to detect and must usually be acted on immediately.

Meriwether headed up the arbitrage team at Salomon Brothers, which developed mathematical models to predict market prices and identify outliers. These models would facilitate the strategic purchase and sale of bonds with prices that deviated from the perceived norm, producing a profit when the prices reverted back to their perceived norm. The team was highly successful and bond arbitrage trading began to gain traction across the financial industry. However, in 1991, a bond trader by the name of Paul Mozer, who worked under Meriwether, was caught trying to corner the Treasury bond auction market by submitting fraudulent bids. As a result of the scandal, Meriwether was fined $50 000 by the Securities and Exchange Commission for failing to supervise his subordinates and was forced to resign from Salomon. Unperturbed, Meriwether pulled together a dream team of financial experts and established LTCM.

The company launched in 1994 with seed capital of $1.25 billion and the firm’s profits rose rapidly for the next three years. LTCM was notoriously secretive about its strategies and the quantitative models that were driving them, and it scattered trades between banks to prevent any one of them gaining enough information to track its movements. And none of its investors minded too much – as long as the profits were rolling in.

With its team of economic masterminds at the helm, LTCM reported impressive annual returns of 43% in 1995 and 41% in 1996, after management had taken its cut in fees. On the back of its successes, LTCM quickly started to expand its scope, venturing out of the realm of fixed-income arbitrage and into the substantially riskier domain of equity and bonds arbitrage, which involved investing heavily in foreign currencies and bonds. LTCM’s investment strategy was based on detecting and exploiting opportunities in markets that were often overlooked by others – but these were generally small and required large-sized investments in order to make a profit. LTCM therefore became increasingly leveraged. At the beginning of 1998, the firm held $129 billion in assets with an equity figure of $4.72 billion – a leverage ratio of 27:1. To put this in perspective, when Lehman Brothers failed it had a leverage ratio of about 31:1.

The first signs of trouble for LTCM came in July 1997, when Thailand defaulted on its foreign debt and the Thai baht collapsed, causing a domino effect across the economies of east Asia. International stocks plummeted as volatility in the US market began to increase and investors turned to Treasury bonds for security. Then, in August 1998, Russia devalued the ruble, defaulted on domestic debt and issued a moratorium on repayment of foreign debt. The US stock market dropped by 20% and European markets fell by 35%, and the flight to Treasury bonds escalated, causing long-term interest rates to fall. LTCM lost $553 million in one day. Within the following month it lost almost $2 billion.

For many, the sudden end of LTCM’s winning streak came as a shock. But despite its early successes, there were some who had always been critical about the degree to which LTCM’s strategy was reliant on the idea of completely rational markets. The firm’s approach assumed a predictable rate of volatility in bonds – but the reality is that bond prices had displayed unpredictable volatility in the past decade and that changes in prices are also driven by behavioural factors. The devaluation of the ruble and Russia’s subsequent default was beyond the limits of what LTCM had assumed possible, and the risky nature of its highly leveraged investments was exposed. Many have considered this to be something of a once-off event, painting LTCM as a victim of highly surprising movements in the market that nobody could have predicted. However, others have argued that fault can also be found in the firm’s overall business approach. Ron Rimkus – Director of Economics and Alternative Assets at the Chartered Financial Analyst (CFA) Institute – notes that whilst the Russian default did act as a catalyst for a flight to safety by investors, the impact of this on bond yields and arbitrage spreads was not unprecedented, with similar movements having occurred 13 times in the 27 years since the US’s departure from the Gold Standard in 1971. He goes on to question why it was, then, that LTCM and its team of industry experts had failed to guard against market movements that, statistically, had a 48% chance of occurring in any given year, based on historical data.

As LTCM began to engage in more risky trades, the firm made bets on particular outcomes using Value at Risk (VaR) models, stress testing and scenario analysis to gauge risk. LTCM used a VaR measure that it believed was aligned with the US stock market VaR, based on a daily standard deviation of security prices and correlations among all securities owned by the company over the previous 500 trading days, assessed at a 95% confidence interval. However, it was an over-reliance on this model that many commentators have argued led LTCM to disaster, for whilst VaR is a highly useful measure for volatility on a day-to-day basis most of the time – enabling firms to standardise their risk management approach across different portfolios, products and asset classes – it does not effectively capture material risk events.

The VaR models used by the firm did not take long-term historical data into account and were not sensitive to large-scale economic and political changes. Rimkus highlights that LTCM’s VaR calculations predicted that an event such as the Russian default, for example, could only happen once every 6.4 trillion years. Yet, an objective observation of Russia’s political and economic circumstances – including factors such as its high debt levels and widening bond spreads, the pegging of its currency to the US dollar, and declining global oil prices – should have alerted market participants to the fact that risk of a default had been mounting for three years before it occurred. LTCM’s VaR calculations had predicted that the firm could lose no more than $35 million in a day and yet on 21 August 1998, it lost $553 million in a day. VaR assumes randomness in market movements, and the Russian default – and the movements in the market that resulted from it – were anything but random. This is something that LTCM may have realised if it had placed as much emphasis on real-world events and empirical evidence as it did on its mathematical models.

Additionally, what these VaR models had not taken into account was that these events were not independent of one another, which had the effect of magnifying risk, rather than diversifying it. Believing not only that an event such as the Russian default could almost never occur, but also that market volatility would decline during the course of the year, LTCM had made some bold moves in the earlier part of 1998. By late 1998, the firm was in significant trouble – it had lost $4.8 billion and held $400 million in equity with assets totalling about $100 billion, implying a leverage ratio of roughly 250:1. Banks began to worry that if LTCM were to default, all fifty of its counterparties would also find themselves in a dire position. Potentially, if LTCM fell, so would the global financial system through the knock-on effect that would occur if its counterparties failed. The firm was essentially too big to fail – and, thus, the US Federal Reserve brokered a deal with some of the largest Wall Street banks, including Bear Stearns, J.P. Morgan, Lehman Brothers, Merrill Lynch, Morgan Stanley and Goldman Sachs, to save LTCM with a $3.65 billion bailout.

The LTCM crisis revealed just how fragile the modern financial system was. Shortly after LTCM’s failure, the so-called financial dream team disbanded and the financial industry claimed to have learned some valuable lessons about placing too much trust in the predictive power of mathematical models. The LTCM crisis had also clearly illustrated just how interconnected financial markets are – to such a degree that failure in one institution can mean failure for many. Because of this, regulators have often deemed it necessary to intervene in financial markets, but in doing so, they undermine the very basis of a free market system and create moral ambiguity through the idea that there is safety associated with being a large firm in this interconnected world. Just ten years later, in the financial crisis of 2007/2008, many of the salient features of LTCM’s near-failure would be observed again, only this time, on a much larger and more damaging scale.

This article is from the Monocle Quarterly Journal, A Short History of Banking. Visit our "Journals" section to read the full issue.