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**LTCM’s Analysis of Risk Management**

February 28, 2002 Frank Burke Larry Kissko Gurkan Salk Heather King

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**Agenda LTCM Background Swap Spread Trading Strategy Project Analysis**

Comparison/measurement of LTCM’s Risk Assessment Discussion on return and spread distribution, calculated implied std deviation Estimate of LTCM’s Value-At-Risk Proxy Tests Take-aways

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LTCM Background August 21, 1998, fund lost $550m mostly from swaps spreads and equity volatility bets. LTCM believed this event would occur 1 in every 800 trillion years (or an 8.3 std dev move). Swap spreads shot up from 60 bps to 80 bps intraday vs. an average daily move of 2 bps LTCM’s swap position represented 2.4% of global swap market in December 1997 Leverage ratios varied from 28:1 to a high of 55:1 in late 1998

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**LTCM Trading Strategy We focused on of one of LTCM’s biggest trades:**

Swap Spread Relative Value Trade Swap spread – difference between the fixed rate on a fixed-for-floating swap and the yield on a coupon-bearing Treasury bond of comparable maturity Speculative strategy that spread would converge to its historical mean Long swap/short the treasuries (in 1998) Crisis: Aug 21, spreads spiked 21 bps intra-day

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**Swap Spread Frequency: “the bet”**

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**Project Analysis Parametric VAR – assumes normal distribution**

Historical VAR – based on actual data distribution Proxy search – difficult to find a strong correlation BAA- 10 year treasury AAA- 10 year treasury MBS - 10 year treasury Forecasted daily variance Value At Risk – defined as the expected maximum loss over a target horizon within a given confidence interval

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**Swap Returns Distribution (thru 7/98)**

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**.16% = 4 observations over 10 year period**

Analytic Results Risk analysis LTCM Satchmo Return distribution Normal Curve Non-normal: w/Kurtosis & fat tails 99.7% confidence interval [- 6.07%, %] from the mean return 0.01% [ %, %] from the mean return 0.01% Implied Daily Std. deviation 2.03% 3.46% Value at Risk (VAR) - estimated $60M $95.2M Probability of Aug 21 event 10-13 Or % .16% = 4 observations over 10 year period

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**Value at Risk (VAR) Principal measure of risk at LTCM**

LTCM parametric VAR measure Capital (assume $1b) x daily std dev of returns (.02) x std dev of required confidence interval (3 = 99.85% 1-tail) $1.0b x 2% x 3 = $60,000,000 Our historical VAR measure $ 1.0b x % = $95,238,000

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Take-Away Thoughts VAR not necessarily suspect – correct inputs are critical Cannot blindly apply normal distribution Dig into your data If data is not complete consider: Developing a risk proxy Assuming fatter tails in distribution (Student’s T curve)

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Appendix - charts August 21, 2002

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Appendix - charts

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Appendix - charts

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Appendix - charts

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Appendix - charts

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**References Jorion, P., 2000 Risk Management Lessons from LTCM**

Kolman, Joe, 1999, “LTCM Speaks”, Derivatives Strategy (April) p.12-17 Lewis, Michael, 1999, “How the Egg-Heads Cracked” New York Times Magazine, January 24, p 24-77 Anonymous, 1998, “Too Clever By Half”, The Economist Magazine, November 14 Whaley, Robert, 2001, “Derivatives” Class Presentation Scholes, Myron, 2000, “Crisis and Risk Management- The Near Crash of 1998”, AEA Papers and Proceedings Vol 90 No. 2, May. Bloomberg – Swap spread data

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