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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/
89
11/1
/89
5/1/
90
11/1
/90
5/1/
91
11/1
/91
5/1/
92
11/1
/92
5/1/
93
11/1
/93
5/1/
94
11/1
/94
5/1/
95
11/1
/95
5/1/
96
11/1
/96
5/1/
97
11/1
/97
5/1/
98
11/1
/98
5/1/
99
11/1
/99
5/1/
00
11/1
/00
5/1/
01
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
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