Value at Risk and LTCM: A cautionary tale of reductive bias

In the year 1994, an all-star team  was assembled. Two intelligent quants from academia, the former head of the bond group at the Saloman brothers, a former Fed-reserve chairman, an ex-Harvard professor and a bunch of former Salamon traders formed a firm called Long Term Capital Management, attracting some of the big banks like Merrill Lynch, Julius Baer and UBS, with a minimum investment size of $10 million. They had a dream run over the next few years, with an investment made in March 1994 becoming over four times its value in 4 years.

With the funds net capital swelling to $6.7 billion by August 1997, they piled on debt financed assets of $126.4 billion. Think about what this implies – they were leveraged at a ratio of 19:1. Why did this not bother them? Their models told them there was no risk involved, where they were pursuing hundreds of trading strategies with a total of 7600 different positions. They reasoned that their positions were uncorrelated, and all of them could not go wrong simultaneously.

Long Term Capital Management was effectively making money by exploiting price discrepancies in global markets. Their biggest bet made use of the Black-Scholes formula for option pricing, where they were selling long-dated options in the American and European markets. This meant that other people could exercise those options if there was a large volatility in stock prices, and the pricing in 1998 implied an abnormal volatility of 22-23% per year, whereas their models told them the volatility would resemble something like the recent average of 10-13%. The firm had no emerging market exposure, and they soon started thinking that since they were well below their target risk level of an annual variation of 20% of assets, they should take more risks. They were lulled into a sense of security by a fact that their Value at Risk models (Read this post by Krishna over at Tyroinvestor for an explanation of how VaR works) told them it would take a ten sigma event for the firm to lose all its capital, a probability they calculated at 1 in 10*24. For a while, there was calm before the storm.

In May 1998, equity markets dipped and volatility went up instead of down. The higher it went, the more LTCM lost money, losing 6.7% and 10.1% in two months, and the firm’s leverage ballooned to 31:1. It was just the beginning however. On August 17th, 1998, on the back of political upheaval, declining oil revenue and failed privatization, the Russian financial system collapsed and the government defaulted on its debt. A contagion effect spread through global markets, causing stock markets globally to plunge and volatility to spike to 45% at the peak. The brain-trust at LTCM predicted that the firm was unlikely to lose more than $45 million in a day. On Friday, August 21st, it lost $550 million, 15% of its capital, further driving the leverage up to 42:1. By the end of the month, the firm was down 44% and had lost $1.8 billion

The fall of LTCM
Pride comes before the fall

In the end, in order to avoid a full-scale panic, the Federal Reserve brokered a $3.625 billion bailout by 14 banks from Wall Street, and the 16 partners were left with a mere $30 million between them. It was one of the greatest implosions in the history of capital management, and one whose lessons echo today.

Lessons from LTCM

LTCM was an example of the danger of reductive bias, which means that they were oversimplifying a complex model. The equations they were using were based on an uncomplicated, stable environment but applied in a complex, dynamic one. In back-testing, LTCM observed that over the prior five years, the correlation between its diverse investments  was less than 10%, and they assumed that correlations could rise at most to 30%. However, when the financial crisis of 1998 hit, the correlations soared to 70%. Taleb was particularly derisive of correlation, saying that “Anything that relies on correlation is charlatanism”, and echoing the trader adage that the only thing that goes up in a bear market is correlation. It was also a  failure to consider the fat-tail events that can throw a wrench into elegant models filled with all sorts of greek symbols, compounded by their greed in using excessive leverage.

The philosopher George Santayana once said –“Those who cannot remember the past are condemned to repeat it”.  The lessons of LTCM were not learned by Wall Street leading to yet another perfectly avoidable crisis in 2008-2009 (and I fear not the last). However, that is a story for another day.

References and additional reading

(1) The Ascent of Money by Niall Ferguson

(2) Thinking Twice: Harnessing the Power of Counterintuition by Michael Mauboussin

(3) When Genius Failed: The Rise and Fall of Long Term Capital Management by Roger Lowenstein

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