LTCM’s Analysis of Risk Management

February 28, 2002

Frank BurkeLarry KisskoGurkan SalkHeather King

LTCM Risk Management

Agenda

1. LTCM Background 2. Swap Spread Trading Strategy 3. 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

4. Take-aways

LTCM Risk Management

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

LTCM Risk Management

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

LTCM Risk Management

Swap Spread Frequency: “the bet”Frequency through 7/31/98

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

16.00%

30 36 42 48 54 60 66 72 78 84 90 96Swap Spread

Freq

uenc

y

August 20, 88 August 21, 88

Upper 95%

LTCM Risk Management

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

LTCM Risk Management

Swap Returns Distribution (thru 7/98)Frequency of Spread Returns through 7/31/98

0

200

400

600

800

1,000

1,200

1,400

1,600

-9.09% -6.71% -4.32% -1.93% 0.45% 2.84% 5.22% 7.61% 9.99% 12.38%Spread % Return

Upper 99.85% based on Normal

Distribution

Upper 99.85% based on actual

distribution

LTCM Risk Management

Analytic Results

Risk analysis LTCM Satchmo

Return distribution

Normal Curve Non-normal: w/Kurtosis & fat tails

99.7% confidence interval

[- 6.07%, + 6.10%] from the mean return 0.01%

[- 10.32%, +10.39%] 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 .00000000001%.16% = 4 observations

over 10 year period

LTCM Risk Management

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 9.5238% = $95,238,000

LTCM Risk Management

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)

LTCM Risk Management

Appendix - chartsChange in Spreads

0

50

100

150

200

250

300

350

400

11/1

/88

5/1/

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/89

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11/1

/01

Spre

ad (i

n bp

s)

Swap Spreads Baa/Treasury Spreads Aaa/Treasury Spreads

August 21, 2002

LTCM Risk Management

Appendix - chartsFrequency through 2/20/2002

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

30 40 50 60 70 80 90 100 110 120 130 140

Swap Spreads

LTCM Risk Management

Appendix - chartsFrequency 7/31/98 - 2/20/02

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

58 64 70 76 82 88 94 100 106 112 118 124 130 136

Swap Spread

LTCM Risk Management

Appendix - chartsFrequency Of Spread Return through 2-20-02

0

200

400

600

800

1,000

1,200

1,400

1,600

% Price change

LTCM Risk Management

Appendix - chartsFrequency of Spread Returns after 7/31/98

0

50

100

150

200

-10.77% -8.35% -5.93% -3.51% -1.09% 1.33% 3.75% 6.17% 8.59% 11.01%

Spread Change

LTCM Risk Management

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