The Failure of Long-Term Capital Management

Ludwig Chincarini* Bank for International Settlements

Banking Department CH-4002 Basel, Switzerland.

Work Phone: 41-61-280-8045. email: 106167.3663@compuserve.com

ludwig_ chincarini@alum.mit.edu.

October 8, 1998

Abstract

The recent collapse of the brilliant hedge fund, Long-Term Capital Management, has caused a lot of concern in the financial community. The quants are saddened by the limits of critical thinking and some of the non-quants are claiming that LTCM is just like the rest of them. This article describes the type of trading LTCM may have been doing and shows analytically what may have gone wrong in August, 1998. It formalizes much of the jitter in the papers in order to understand how a sophisticated system could fail, despite not having any major bets in any one market.

*The opinions expressed are personal and do not reflect the views of the BIS or central banks.

1 INTRODUCTION 1

"U.S. Federal Reserve Seeks a Rescue for Long-Term Capital Management. "-Wall Street Journal

1 Introduction

This Wall Street Journal headline probably shocked more people than any other headline about a

failing investment institution. The reason is clear: humans need superheroes. LTCM was the closest

anyone has ever come to creating a financial investor super-human. It consists of talented Salomon

traders and analysts mostly who came from the renowned Massachusetts lnsitute of Technology. In

fact, two of the firm's principles were Nobel laureates in financial economics. Merton and Scholes

were experts in derivatives, tax arbitrage, portfolio investments, and even a wider area of finance.

More than the incredible credentials of its staff, the LTCM partners were former members of the

very successful Salomon Bond Arbitrage group. This success continued from February, 1994 to

August, 1998 at LTCM with consistently above average returns and low volatility. For quantitative

types, LTCM represented the potentials of critical thinking. They could create order out of chaos.

In fact, many LTCM or MIT derivatives started their own hedge funds in the last few years. For

example, Convergence Asset Management and a company formed from the group of the Goldman

Sachs Asset Management team. Many other of these hedge funds also opened up shop.1 Even for

non-quantitative types, there was a mix of jealousy and admiration. With the annoucement that

LTCM was in dire straights, a reaction of disbelief was soon overwhelmed by confusement. The

non-quantitative people urked a smile of content and said "I told you so." In fact, one trader said

"Let's stop the pretense that these guys were good at all. .. their returns sucked." He goes on to

state that LTCM were " ... clowns ... " He also claims that " ... these guys had a massive bet on Russia,

just massive." This paper will try to evaluate the truth of statements like these. The quantitative

types reacted more solemnly. They were also dissatisfied with LTCM, but for a different reason.

They lost their super-human. Super-man was defeated. It brought us back to the stone-age; back

to the realization that financial markets might really be random walks; that flipping a coin might

do one just as well as anything else. The collapse was sudden. By August 1, 1998, the firm's equity

stood at $4.1 billion, by September 1, 1998 it dropped to $ 2.3 billion, and over the next 21 days

the fund's equity dropped to $ 600 million {85 % of the equity wiped out in 54 days).

2 THE UNVEILING OF LONG-TERM CAPITAL 2

In the next section, we will specifically focus on the death of our superhero. We will try to

understand what leads everyone to mortality in the financial markets.

2 The Unveiling of Long-Term Capital

One way to rationalize the fall of sohpisticated players, like LTCM, is to examine the financial

environment and show that ex-ante, LTCM was leveraged on quite low-risk positions due to the

statistical diversification of strategies. One must also show that these sound and stable statistical

relationships broke down after August 1, 1998 (or around there) due to the Russian crisis and

particularly hurt the ex-ante low-risk trades of LTCM, which, combined with leverage, brought

them to bust.

Below, I attempt to create a rather simplistic example of how LTCM could have rationally

failed. In reality, their trades are extremely sophisticated designed by the most brilliant people

in finance. Nevertheless, the line of reasoning presented should illustrate what went wrong with

LTCM.

A The Losing Trades

" ... the market knew something that our formula didn't know. "-Fischer Black, 1973

In order to untangle the truths and myths about LTCM, one must have some idea of what

kinds of trades they were making. Unfortunately, their trades are confidential information. I will

try to conjecture at to what kinds of trades they may have had using the reports in the press,

John Meriwether's (CEO of LTCM) letter to investors, and financial variable anomalies in July

and August. Even if these aren't the actual trades that lost money for them, I hope to provide an

illustration of what could have gone wrong at LTCM. The types of trades they may have had are

primarily relative value or liquidity trades. Other trades include trades on SWAP spreads in core­

Europe and the U.K., Latin America trades, corporate spread trades, mortgages (Denmark and

elsewhere), European convergence trades, U.S. bond liquidity or flattening trades, and equity-bond

volatility arbitrage trades.

2 THE UNVEILING OF LONG-TERM CAPITAL 3

B Recreating the Trades

It is certainly true that any type of spread trades or European convergence trades did poorly

in August, 1998. Flattening trades in the United States also did poorly in July, August, and

September, 1998. A few unhedged cross-currency money market trades also did poorly in August,

1998. Credit spread trades did horribly in August and September, as did U.K. SWAP trades in

the U.K. versus core-Europe. Emerging market investments did poorly in August, 1998. With any

form of leverage, these poor returns were enormously magnified. I constructed a few trades of the

type they may have had.1

The first trade is an equity-bond arbitrage, whereby one purchases the equity index and shorts

the bond index in some predetermined ratio.2 This trade is not really a relative-value trade.

The second trade is a uncovered interest rate parity (UIP) type of trade. It focuses on the

biasedness of forward exchange rates. In particular, this trade considers two countries, the U.S.

and Germany and borrows in the currency whose one-month rate is lower and investing or lending

in the higher rate currency unhedged. This is a zero-investment strategy.

The third type of trade is a U.S. liquidity or flattening trade. It orginates from the arbitrage

of the liquidity premium that might exist on the U.S. curve. In particular, the trade consists of

purchasing the long end of the curve and shorting the short-end of the curve, duration neutral. It

is also a zero-investment strategy, where the excess funds are placed in cash.

The fourth type of trade is a European convergence trade between Italy and Germany. The

trade involves purchasing Italy in the 1-3 year maturity area and shorting Deutschemark in the 1-3

year area, again duration neutral and a zero-investment strategy as well.

An aggregation of these strategies is also constructed and entitled the Fund. The Optimal

Fund is a fund using optimal weightings to minimize the historical variance, pre-August, 1998. All

strategy profits and returns are computed with and without leverage. These results are contained

in table 1.

These illustrate that many leveraged strategies of the type LTCM may have had performed

poorly in August and September, 1998. However, anyone can make bad trades. This is only the

1Unfortunately, I left out a many deal of trades that would have been interesting, such as a UK SWAP versus core-Europe SWAP trades. Anyway, these trades are merely examples of what could have been traded by LTCM.

2Many have claimed that LTCM may have shorted volatility on the equity market. While it is true that this type of trade lost gravely in August, I cannot find a combination of it that profits in the earlier period, so I left it out. If they did have short on the volatility of the equity market, it must have been beneficial combined with some other types of trades.

2 THE UNVEILING OF LONG-TERM CAPITAL 4

first part of the explanation. When other firms fail, one can usually point to one or two huge bets

that went bad. However, did LTCM make huge bets as some people claim or cane we explain their

failure despite having, ex-ante, a very sophisticated and diversified fund? In the next section, we

show how a firm with sophisticated and diversified strategies with very low risk could have gone

bust in this period.

C The Failure of the Magic Wand

"I supposed it takes maturity to know that models are to be used but never believed. "-Henri Theil,

renowned econometrician

In order to show that LTCM was ex-ante rational, one must show that ex-ante the trading

strategies were all risky, but not risky together. This assumes that LTCM has a collection of

sophisticated trading strategies, say 100, and that they choose the strategies such that the collective

risk is close to zero, but with a positive expected return. They then leverage immensely to increase

the return of this almost riskless collective strategy. This is what I believe is the secret or the magic

wand of a firm like LTCM. Providing a two trading strategy example might be useful. With two

risky trading strategies, the expected return and variance is:

E(Rp) = /-lp = aJ.tx + (1 -a )J.ty

<T; = a 2<T; + (1- a)2<T; + 2a(1- a)Pxy<Tx<Ty

(1)

(2)

where a is the weight placed in asset x, 1 -a is placed in asset y, J.lx and /-ly are the means of

strategy x and strategy y respectively, <T; and <T~ are the variances of strategy x and strategy y

respectively, and Pxy is the correlation between the two strategies. One can choose the a to provide

the lowest risk for the portfolio by differentiating the variance equation (equation 2 with respect to

a. The minimum variance a is:

(3)

If one chooses two trading strategies that are perfectly negatively correlated (i.e. Pxy = -1),

one has a riskless portfolio with a positive return. The more general case is a portfolio of n trading

strategies. Assuming that each strategy has similar variance, <T 2, and any pair of strategies have the

2 THE UNVEILING OF LONG-TERM CAPITAL 5

same correlation coefficient, p, and assuming all strategies equally weighted, the portfolio variance

is:

2 0"2 (n-1) 2 O" =- + -- PO"

P n n (4)

Thus, with a large number of these trading strategies, we can elliminate all risk, even if the

average correlation is zero. This might be the concept behind a firm like LTCM.3

For illustration purposes, let's suppose that LTCM has roughly 50 types of trades on at any given

moment. We also suppose, that all trades had roughly the same variance and mean (p = 0.0057

and O" = 0.04). Let's also assume an average risk-free rate of 6 % or 0.0048 per month. Suppose

that LTCM had actually identified these 50 trades with zero correlation among all of them. We also

consider the case of leverage on the profits and risks. Because the mean returns of these "low risk"

strategies is very low, leverage is needed provide an outstanding return on equity.2 The resulting

VaR and possible losses for different p are given in table 2.

The case of particular interest is the 30 times leveraged case. The leveraged case could produce

mean returns on the order of 40 % per annum.3 If one believes that the trading strategies are

distinctly uncorrelated from each other whatever the state of the world, then LTCM wasn't really

taking that much risk. However, if a break-down occurred in these correlations across strategies

making them on average, from 0 to 0.2, one has the potential for losses of $ 3. 78 billion. A crisis

occurred and in actual fact, LTCM lost $ 3.5 billion. This is the risk that was difficult to foresee.

The assumption is that one's estimate of the correlation of the various trading strategies is robust.

Using history or even judging by a mere large quantity of these strategies, one could allow for

a slight change in correlations. In August, with the Russian default on government debt and the

flight to quality, presumably the correlation between strategies changed dramatically (in a way

never witnessed). In LTCM's case, I imagine they changed to be very positively correlated.

Below, I have computed how the correlations changed even in my simple collection of portfolio

strategies. One can see from tables 3 and 4 that the correlations imcreased dramatically post­

August, 1998. In fact, the average correlation between strategies rose from 0.078 to 0.372; a change

of 0.294).

This section attempted to explain the LTCM losses given a group of sophisticated people inact-

30ne may find this too simple explanation for LTCM's failure. However, one must realize that the art is not in the concept, but in the picking of such a group of strategies such as to obtain an average correlation of zero.

3 PAPERBOY DIDN'T DELIVER 6

ing quasi-arbitrage strategies. Meriwether claims that 80 % of the losses were due to these type of

trades, while there was another 20% that were outright bets.4 We have shown that with a leverage

factor of 30, even seemingly uncorrelated strategies could have produced the LTCM collapse. With

20 % of the strategies being outright bets, the LTCM collapse is even more plausible.

3 Paperboy Didn't Deliver

The story that I have depicted above is one of many ways to interpret the LTCM disaster. 5 However,

I find it hard to believe that with so many keen practioners, they weren't worried about the state

of the world. Did they not have a clue that a world recession might be on its way? I find it hard to

believe that with all the jitter in the press about a world recession that they did not reduce their

risks or make the case for possible changes, including changes in correlation. Did the paperboy not

deliver? On the other hand, we do not know what kinds of trades LTCM had on. Perhaps there

was no case in history or even logically imaginable that would have made the average correlation

shoot-up across strategies. Perhaps LTCM did contemplate a default on Russia and the contingent

correlations in that case. However, they somehow underestimated the indirect effects of Russia.

4 LTCM Babies and p

One possible explanation of the rapid change in the correlation across strategies in the growth is

arbitrageurs. If indeed the world has liquidity premiums or other price discrepancies to arbitrage,

there is only so much money that can chase arbitrage opportunities. Over the last few years, how­

ever, many quantitative types with similar ideas to LTCM have emerged. The world is saturated

with arbitrageurs. LTCM may not have estimated the effect that this could have on the stable rela­

tionships across strategies when other players were placing the same types of trades. In particular, a

shock to the market, like Russia6 , could lead to a trigger effect, where all of the LTCM babies began

closing positions. The fear that others may close, led to more closing. In the end, a self-fulfilling

crisis emerged. Thus, perhaps the correlation across strategies drastically changed, because there

were too many LTCM babies playing the same game. LTCM must have underestimated this effect.

Granted, it's very hard to estimate what impact more players can have.7

5 INVESTORS CAN STILL SMILE 7

5 Investors Can Still Smile

Despite LTCM's unbelievable collapse, investors in the fund did not go home empty handed.8 In

the end, LTCM investors made a profit in a noble way. Investors that gave $10 million in 1994

would have received $18.2 million at the end of 1997. The remaining interest in the fund would

have been worth $10 million, but about 90% of that has been wiped out. That translates into an

annualized return of 14 %. The performance of the S&P500 over this same period was 20 % per

annum and bonds (3-5 years maturity index) returned 7.35 % per annum. Investor's in LTCM did

not walk home empty handed, despite the collapse.

6 The Bailout

"What's true for the Gods, isn't true for the cows. "-Rudiger Dornbusch

Despite the traditional stance of laissez-faire from government institutions, this policy seems to

have been abandoned in the LTCM case. The Federal Reserve Bank organized a meeting of banks

to inject cash into the fund. Fourteen to sixteen comrnerical and investment banks pumped $3.5

billion into the troubled firm. The Fed was not actually involved in bailing out LTCM. However,

its interest brought criticism from many. Paul Volker, former Fed Chairman, criticized the Fed for

its actions. Jim Glasman of Chase Securities Inc. said that "The Fed doesn't care a whit about

Long-Term Capital..." but about the disruptiveness an LTCM failure could bring to the markets.

Peter Bakstansky, senior vice president of the New York Fed, defended the Fed's actions because

" ... the Fed has concerns about the good working of the market place, large risk exposure, and the

potential disruption of payments ... " Despite the many good reasons for helping out LTCM, many

people do not like the implications. One trader stated "How many easings did Wall Street have

to negotiate for them chip in money for LTCM?" Nevertheless, the flow of funds did occur. The

banks that injected funds into LTCM now own 90% of the fund. The partners might own 1/3 of

the remaining 10 % or 3.33 % of the firm.

The LTCM debacle will bring up a whole host of issues for regulators. At the present time, the

Federal reserve had no regulatory authority over hedge funds. One area of examination will have

to be how to access credit risk of institutions like LTCM. Another issue will be to find ways to

adequately measure the risk inherit in banks that use derivatives and leverage. Finally, the whole

7 THE DREAM TEAM'S FUTURE 8

issue of whether it was a failure of the current system or a case of " ... greed overcoming prudence." as

Paul Volker, former Fed Chairman, stated. Banks may have ignored standard procedure because

they trusted in the invincibility of LTCM. In other words, will the benefits of regulating banks

or hedge funds be more important than the benefits of allowing for a free market system? At a

minimum, should leverage be regulated?

7 The Dream Team's Future

The future of LTCM depends upon whether or not the funds injected can meet all the margin calls

and other needs until the illquid positions become profitable again, if at all. Suppose all of the

trades that they own become profitable once the "crisis" ends. Then we will witness LTCM coming

out of a deep hole. The other situation is that the crisis worsens and their illiquid investments

remain so for a further period of time. Either way, the returns on LTCM for the next few years

do not look promising. I personally think that the firm will survive and be strong again if it can

endure the waiting time needed for these trades to become liquid again. John Meriwether may

have the last word: "LTCM will emerge a stronger and better firm." 9

8 Conclusion and Lessons

The brief analysis performed in this paper was intended to show how a firm with a solid and

sophisticated framework could fail so dramatically, despite not having risked everything on one big

bet. In fact, the failure of LTCM is explained by a world that drastically changed in mid-August,

1998. We have conjectured that one of the reasons for LTCM's failure to detect this and for the

dramatic change in average correlation across strategies was due to a saturation of LTCM-type firms

(LTCM babies). This study also shows that claims that LTCM had a massive bet on Russia or

claims of "stupidity" aren't warranted. I have shown that even without altering the basic principles

that have given them so much success, they would have failed dramatically. Finally, the returns of

14 % per annum to investors of LTCM were still reasonable despite their collapse.

Some lessons from the fall of LTCM are worth mentioning. For one, risk management in really

risky situations is difficult. People like to say that VaR is bad or that stress testing was not done.

But VaR is merely a tool to understand future distributions, just as is stress testing. At a certain

point, one is committed to stress testing the unimaginable. Secondly, perhaps funds and banks

8 CONCLUSION AND LESSONS 9

should be extra cautious in times of crises. The world has experienced a lot of shake up in the

last year, with Asia and then Russia. Thirdly, we should not forget the importance of arbitrageurs

in supplying liquidity to markets. In these volatile times, with arbitrageurs going under, we are

learning how important their role may really be. But I think the most important lesson from the the

LTCM failure is that it has reminded us all of the nature of taking risks in, at times, unpredictable

markets. As William Sharpe said, " ... there's no reason to expect reward just for bearing risk."

9 TABLES

9 Tables

Table 1: Average Returns from 'Ifading Strategiesa

Period of Estimation Value of$ 4.1 B* Strategy 1994:02-1998:06 1998:07-1998:10 Lev. (0) Lev. {10)

Equity-Bond Arb.6 0.01 -0.07 3.54 0.35 ( 3.51 ) ( -6.03 )

UIP 'Ifadec 0.01 -0.03 3.87 2.06 ( 1.82 ) ( -1.08 )

Liquidity Premium (Flattener)d -0.00 -0.00 4.07 3.84 ( -0.28 ) ( -3.12 )

Convergence 'Ifadee 0.00 -0.00 4.10 4.05 ( 3.50 ) ( -0.12 )

The Fundi 0.02 -0.09 3.38 0.03 ( 4.47) ( -0.12 )

The Optimal Fundg o.o5t -0.00 4.06 L8ot ( 2.25 ) ( -0.12 )

a These strategies were zero-investment simulated strategies from data obtained from the BIS FAME database. b This strategy consisted of ohorting the bond market and going long equities using a hedge ratio to limit the exposure. c This strategy consisted of investing in the U.S. or Germany (unhedged) based on which countries short-term rates were higher. d This strategy played the Hicks' arbitrageur by absorbing the liquidity premium (or a flattening trade). e This strategy was a convergence play on Italian yields versus German yields. f The Fund represents an aggregate of all the strategies simultaneously. 9 The Optimal Fund was constructed using past data and choosing the weights to minimize the fund variance. In fact, the weights on the strategies were (0.028, -0.028, 0.904, 0.078). All individual strategies are zero-investment strategies. Transaction costs are ignored. * These columns represent the value of $4.1 billion from the beginning of August until the end of September. t Represents the actual returns given a leverage of 70 times the capital base on a monthly basis.

10

9 TABLES 11

Table 2: Sensitivity of VaR to Strategy Correlationsa

p=O p = 0.1 p = 0.2 p = 0.5 p=1 a2

p 0.0057 0.1374 0.0186 0.0286 0.04 VaR -0.009 -0.023 -0.031 -0.047 -0.066

Losses from a Position of: $4.1 B -0.038 -0.093 -0.125 -0.193 -0.271

With Leverage: 10 Times 0.383 0.929 1.26 1.93 2.71 20 Times 0.765 1.86 2.52 3.86 5.41 30 Times 1.15 2.79 3.77 5.80 8.12

a VaR is computed at a 95 % confidence interval. Losses are in billions of U.S. dollars.

9 TABLES 12

Table 3: Correlations Among Strategies Pre-August, 1998a

Trade 1 Trade 2 Trade 3 Trade 4 Trade 1 1 0.048 -0.234 0.152 Trade 2 1 0.147 0.351 Trade 3 1 0.005 Trade 4 1

a Correlations were computed from the inception of LTCM in February, 1994 until date indicated.

9 TABLES 13

Table 4: Correlations Among Strategies Post-August, 1998a

Trade 1 Trade 2 Trade 3 Trade 4 Trade 1 1 -0.284 0.333 0.984 Trade 2 1 0.809 -0.107 Trade 3 1 0.497 Trade 4 1

a Correlations were computed from the date indicated until the end of September, 1998.

NOTES 14

Notes 1This may have actually been one of the factors leading to LTCM's collapse. Too many arbitrageurs. 21n fact, theory would say that strategy with almost zero risk should be almost equal to the risk-free rate due to

arbitrageurs. However, we are speaking about the arbitrageur himself, so we can allow for these riskless possibilities. 3This is close to the actual LTCM profits. In 1995 and 1996, the net-of-fee profits were 42% and 35% respectively.

Fees are 2 % flat fee and 25 % of profits. The without leverage returns to equity of LTCM would have been 7 %. Hardly a claim of genius. Hence, leverage was needed to show attractive profits. The leveraged mean returns are: p,~ = ~ L:~=l P,p + (l- 1)~ L:~=l (p,p- TJ ), where l is the leverage factor.

4LTCM's letter to Investors, September 2, 1998. 5 Another story may be that they returned capital to investors and maintained the same level of risk to provide

a higher return on capital. In fact, therefore they didn't have enough capital to cover their risks. However, this is inconsistent with the LTCM quote about not knowing they had so much risk.

6 0ne might ask why the Asian crisis didn't cause a similar effect. Perhaps it was because the Russian default was a much larger event. One may also wonder whether Meriwether's announcement of losses may have actually exacerbated the LTCM collapse.

7LTCM did return funds at the end of 1997 stating that the investment opportunities were more limited. Perhaps they did not realize the extent of the limitation.

8 The press has been particularly harsh to LTCM, giving the impression that investors were wiped out, which is hardly the case.

9 0ne should be aware that he said this before the collapse in his letter to investors on September 2, 1998.

.•.