System Collapse: The case of Long Term Capital

Management (LTCM)

Duc Anh Nguyen

Advanced Quant Env Analysis

Professor Kenneth Mulder

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.

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

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.

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.

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 sellthe 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)

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

Definition (4)

• Bond Price and Market Interest Rate

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 decreaseover 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

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

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

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)

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

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

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.

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

Thanks~