Long Term Capital Management (LTCM) was a large hedge fund that collapsed in 1998 due to significant losses from its investment strategies. LTCM took on extremely high leverage based on models that assumed risk premiums and volatility levels would revert to historical averages. However, the Russian financial crisis and other events caused unprecedented increases in risk premiums and volatility. This led to major losses that overwhelmed LTCM's capital. The Federal Reserve orchestrated a bailout to rescue LTCM's major investors and prevent broader financial fallout. The LTCM collapse demonstrated the dangers of relying on assumptions in models without proper stress testing or margin requirements regardless of reputation.

1. System Collapse:
The case of Long Term Capital
Management (LTCM)
Duc Anh Nguyen
Advanced Quant Env Analysis
Professor Kenneth Mulder

2. Brief Outline/Info
• System Collapse: Financial disaster (The case of LTCM)
Long Term Capital Management (LTCM) is one of the most well-known
case of financial collapse. Collapsed in the late 1990s and need bail out form
Federal Reserve to save its major investors. LTCM’s investors include large
investment banks UBS, Morgan Stanley, Banker Trust, Merrill Lynch, etc
• Key Facts
 The collapse is not caused by moral hazard.
 Unexpected market movement is the main reason causing collapse
 Although the firm’s managers are the best scholars and experienced
traders in field, Model Risks are hard to detect and avoid.

3. About Long Term Capital Management
(LTCM)
• One of the largest (Star) hedge fund at that time:
 Founded in 1994, go bankrupt in 2000
 $1.28 trillion off-balance sheet worth of Asset Under Management (AUM)
• Stellar performance: 21% first year, 43% second year, 41% third year
• Key people:
 John W. Meriwether (founder – Famous Wall Street Bond trader)
 Myron S. Scholes and Robert C. Merton (shared 1997 Nobel Prize in
Economic Sciences for discovery of Black-Schole model)
 David Mullins (later become vice chairman of the Federal Reserve)
Due to the reputation of its managers, LTCM was able to raise impressive
funds in very short period

4. Definition (1)
• Hedge Funds: Closed-End Funds, Only very high net-worth individual or
Institution can invest (typically 1 Million minimum), highly unregulated
• Margin Requirement: The amount of capital must be deposited by a
investor as a proportion of the current market value of the securities.
• Margin Call: Investor must deposit additional money or securities to
maintain margin requirement if their investing position worst off due to
change in value of security.
• Risk Premium (or Credit Spread): The Difference between Risky and
Risk-free Market Rate. (= Rate Risky – Rate Risk Free)
• Volatility: Can be understood as Standard deviation of security values in
certain time-frame.

5. LTCM’s Failure Key Factors
• Taking highly leveraged positions
 Due to LTMC’s reputation, most banks waive the margin requirement for
LTMC transaction of securities, taking long/short positions.
LTMC was able to take a more leveraged trading position
• LTCM Investment Strategy
 Relative value Arbitrage based on Credit spread & Equity Volatility
Seeks to take advantage of price differentials between related financial instruments, such as
stocks and bonds, by simultaneously buying and selling the different securities
• Model Risk, LTMC’s Risk & Return Assumption
 Assume that risk premium (the difference in yield between risky and risk-
free securities) tended to revert to historical level.
 Assume that volatility of equity options tended to revert to long-term
historical level.

6. Definition (2)
• Call option: the buyer of the option have a right but not obligation to buy
the security at a specific Strike Price X0.
 Buyer payoff = Max(0, St –X0) – Option price
 Seller payoff = -Max(0,St –X0) + Option price
• Put Option: the buyer of the option have a right but not obligation to sell
the security at a specific Strike Price X0 .
 Buyer payoff = Max(0, Xo –St) – Option price
 Seller payoff = -Max(0,X0 –St) + Option price
• Interest Rate Swap: An agreement between two parties where one stream
of future interest payments is exchanged for another based on a specified
principal amount. Interest rate swaps often exchange a fixed payment for a
floating payment that is linked to an interest rate (most often the LIBOR)

7. Definition (3)
• LIBOR Rate: London Interbank Offered Rate, is the average interest rate
between banks in the London interbank market. LIBOR is a widely used
short-term interest rate benchmark since it is designed to reflect the cost of
borrowing between some of the world's largest, most reputable banks.
Known as Floating Interest Rate
• Repurchase Agreement (Repo): are transactions in which a borrower
"sells" securities to a lender and agrees to purchase it back for at a specified
price on a later date.
• Difference Between LIBOR and Repo Rate:
 Repos are considered a secured loan (use of collaterals)
 LIBOR is used for unsecured interbank lending

8. Definition (4)
• Bond Price and Market Interest Rate

9. Model Risk! What really happened?
1. Assume risk premium (credit spread) tended to revert to historical level
 Long Interest rate swaps & Short U.S. government bonds at a time
when credit spreads were at historically high levels.
 Credit Spreads: (Rate LIBOR – Rate Repo) is high, and will decrease
over time
 Long position LIBOR Swap payoff:
= Notional Principle x (Rate Fix – Rate LIBOR) x Time Frame
Benefit if LIBOR Rate Decrease
 Short U.S. Government bonds payoff (Enter Repo-Repurchase Agreement):
= Bond Value (at Time Selling) – Bond Value (in the Future).
Benefit if Future Bond Price Decrease Future Repo Rate Increase

10. Make it Simple
• Credit Spreads were historically high:
(Rate LIBOR – Rate Repo) is High
• Model assume that: (Rate LIBOR – Rate Repo) will
Benefit if LIBOR Rate & Repo Rate

11. Model Risk (2)
2. Assume that volatility of equity options tended to revert to long-term
historical level.
 Sold options at historically high implied volatilities
Benefit if actual volatility is lower than the implied volatility

12. Unexpected and Extreme events
• August 1998, Russia defaults on it debts, Russia Interest Rate soaring 200%,
Crushing Value of Ruble
• Brazil devalued its currency
Increase interest rate, risk premium and market volatility unexpectedly
 LTCM lost 44% of its capital in 1 month due to Cash flow crisis
Force to liquidate position to meet margin calls due to sharp divergence
of asset prices.
 Prices in Relative value arbitrage strategy can diverge and create
temporary losses before they ultimately converge.
If LTCM have enough funds to withstand the Cash Flow Crisis, The hedge
fund will ultimately gain profit in the long-term (when prices converge)

13. Lessons Learned - Conclusion
• LTCM Failure Key Factors
 Model Risk (Assumption of risks and returns)
 Lack of Stress Testing in VaR assumption (Value at Risk Model)
• VaR model didn’t not incorporate illiquidity adequately
• Lack of Stress Scenario assessing Market & Credit risk
• Lessons Learned
 Stress scenarios including extreme stresses and interaction between market
& credit risk
 Incorporate liquidity in Financial Models
 Initial margin are always required regardless of the firm’s reputation

14. Definition (5)
• Value at Risk (VaR) Model: measures the potential loss in value of a risky
asset or portfolio over a defined period for a given confidence interval.
 VaR(%) = Expected Return – z(depend on CI chosen) x Volatility (STDVE)
• Can be parametric or non-parametric historical based approach
 Parametric approach limitation: depend on the shape (assumption)
of return distribution
 Non-parametric historical approach limitation: lack of data, past
historical data might not reliable to predict future unexpected market
movement
Both approach can be used by Monte Carlo Simulation

15. Definition (5)
• Value at Risk (VaR) Model: measures the potential loss in value of a risky
asset or portfolio over a defined period for a given confidence interval.

16. References
• Bionic Turtle FRM Part I study materials – Financial Disasters, Book 1
Foundations of Risk Management
• Financial Risk Manager Handbook (6th Edition)
• Steve Allen, Financial Risk Management: A Practitioner’s Guide to Managing
Market and Credit Risk (New York: John Wiley & Sons, 2003). Chapter 4 -
Financial Disasters
• Schweser FRM Exam Part I Book 1 – Financial Disasters

17. Thanks~