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Transcript of 1 Assessing Alternative Assumptions on Default Risk Capital in the Trading Book Gary Dunn: UK...
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Assessing Alternative Assumptions on Default Risk Capital in the Trading Book
Gary Dunn: UK Financial Services AuthorityMichael Gibson: Federal Reserve Board
Gloria Ikosi: Federal Deposit Insurance CorporationJonathan Jones: Office of Thrift Supervision
Charles Monet: US Securities and Exchange CommissionMichael Sullivan: Office of the Comptroller of the Currency
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Disclaimer
• The views presented here are solely those of the authors and do not necessarily represent those of the institutions with which they are affiliated.
• The model presented is for discussion purposes only to illustrate certain elements of the issue and is neither endorsed nor prescribed by any agency.
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Motivation for the study
• Basel 2 requires firms to model incremental default risk in the trading book
• AIG Trading Book Working Group is discussing guidelines for models of default risk in the trading book
• People are interested in knowing the effects of different modeling choices
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Outline of the talk
• A model of default risk
• How to quantify the benefit of liquidity?
• Three test portfolios
• Results
• Key findings
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A model of default risk
• Single-period Gaussian copula– Similar to A-IRB, reflects concentration
• 99.9 percentile VaR
• Correlation parameter = 10%, 20%, 30%
• Fixed recovery = 40%
• “Constant level of risk” incorporated by scaling up short-horizon PD
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Liquidity and capital horizons
• Liquidity horizon represents the frequency at which the portfolio is rebalanced to a target level of risk (or rating).
• Capital horizon represents the time period over which default events are measured.
• We consider 1 month, 3 months, 12 months for both LH and CH.
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How to quantify the benefit of liquidity?
• What PD to use in the model?
• Two sources of data– Moody’s default database
• Directly compute default rates at various liquidity horizons
– MKMV July 2004 study• Compute “surprise default” ratio at 1-month
liquidity horizon using MKMV EDFs
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Constant position vs. constant risk for a Ba credit
0.00%
0.20%
0.40%
0.60%
0.80%
1.00%
1.20%
1.40%
1 2 3 4 5 6 7 8 9 10 11 12
Capital horizon or holding period (months)
PD
Constant position Constant risk (1-month liquidity horizon)
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Constant position vs. constant risk for a Caa-C credit
0%
5%
10%
15%
20%
25%
30%
35%
1 2 3 4 5 6 7 8 9 10 11 12
Capital horizon or holding period (months)
PD
Constant position Constant risk (1-month liquidity horizon)
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Constant position vs. constant risk for a Ba credit
0.00%
0.20%
0.40%
0.60%
0.80%
1.00%
1.20%
1.40%
1 2 3 4 5 6 7 8 9 10 11 12
Capital horizon or holding period (months)
PD
Constant position Constant risk (1-month liquidity horizon)
PD scaling factor = 0.34 = B/A
A = 1.30%
B = 0.44%
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PD scaling factors
Rating Moody’s MKMV
All IG .18 .16
Ba .34 .23
B .60 .35
Caa-C 1.30 1.92
(shown for a 1-month liquidity horizon and a 1-year capital horizon)
PD scaling factor =PD with rebalancing
Buy-and-hold PD
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Three test portfolios
Portfolio Portfolio Description
Long Only 87 exposures, 70% IG, 30% HY
Long Bias Same long positions; add short positions; 60% long and 40% short
Long Bias with Lumps
Same dollar value of long positions by rating category; same short positions; 3 concentrated credits: one BBB, one BB, and one B
Note: All portfolios have the same A-IRB capital requirement.
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Results (Moody’s, corr.=0.2)
CH
Liquidity horizon (months)
1 3 12 1 3 12 1 3 12
Long only Long biasLong bias with lumps
1 21 18 39
3 33 36 27 30 48 51
12 69 81 99 45 51 60 68 78 92
(See Appendix for full results).
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Key findings
• Model suggests lower capital than A-IRB• Short positions reduce default risk• Liquidity alone reduces default risk by 20-
40 percent with monthly rebalancing• Reducing capital horizon from 1 year to 3
months reduces default risk by 30-50 percent
• Could not compare with Specific Risk Add-ons without a more realistic portfolio
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Appendix – Details of all scenarios
• In the tables below, the reported values indicate the 99.9% downside loss over the capital horizon, net of recoveries. The liquidity horizon is denoted by LH.
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A. Pairwise Asset Correlation of 0.1 Moody’s Intra-Year PDs
Long Only Long Bias Long Bias w/Lumps
Capital horizon
LH=1 mo
LH=3 mo
LH=1 yr
LH=1 mo
LH=3 mo
LH=1 yr
LH=1 mo
LH=3 mo
LH=1 yr
1 mo. 15 15 36 3 mo. 24 27 21 24 48 51 1 year 51 54 69 39 42 51 61 67 85
MKMV Intra-Year PDs Long Only Long Bias Long Bias
w/Lumps
Capital horizon
LH=1 mo
LH=3 mo
LH=1 yr
LH=1 mo
LH=3 mo
LH=1 yr
LH=1 mo
LH=3 mo
LH=1 yr
1 mo. 15 12 36 3 mo. 21 N/A 18 N/A 45 N/A 1 year 44 N/A 69 33 N/A 51 57 N/A 85
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B. Pairwise Asset Correlation of 0.2 Moody’s Intra-Year PDs
Long Only Long Bias Long Bias w/Lumps
Capital horizon
LH=1 mo
LH=3 mo
LH=1 yr
LH=1 mo
LH=3 mo
LH=1 yr
LH=1 mo
LH=3 mo
LH=1 yr
1 mo. 21 18 39 3 mo. 33 36 27 30 48 51 1 year 69 81 99 45 51 60 68 78 92
MKMV Intra-Year PDs Long Only Long Bias Long Bias
w/Lumps
Capital horizon
LH=1 mo
LH=3 mo
LH=1 yr
LH=1 mo
LH=3 mo
LH=1 yr
LH=1 mo
LH=3 mo
LH=1 yr
1 mo. 18 15 36 3 mo. 30 N/A 21 N/A 45 N/A 1 year 60 N/A 99 36 N/A 60 62 N/A 92
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C. Pairwise Asset Correlation of 0.3 Moody’s Intra-Year PDs
Long Only Long Bias Long Bias w/Lumps
Capital horizon
LH=1 mo
LH=3 mo
LH=1 yr
LH=1 mo
LH=3 mo
LH=1 yr
LH=1 mo
LH=3 mo
LH=1 yr
1 mo. 27 21 39 3 mo. 45 51 30 36 51 55 1 year 90 104 134 51 60 71 70 84 94
MKMV Intra-Year PDs Long Only Long Bias Long Bias
w/Lumps
Capital horizon
LH=1 mo
LH=3 mo
LH=1 yr
LH=1 mo
LH=3 mo
LH=1 yr
LH=1 mo
LH=3 mo
LH=1 yr
1 mo. 24 18 36 3 mo. 39 N/A 27 N/A 48 N/A 1 year 75 N/A 134 42 N/A 71 65 N/A 94
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Appendix – Details of portfolios
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Long only
Rating Value Number Size
AAA 180 9 20
AA 240 12 20
A 300 15 20
BBB 225 15 15
BB 225 15 15
B 150 15 10
CCC 30 6 5
Total $1,350 87 $15.5
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Long bias
Long positions Short positions
Rating Net Value
Dollar Value
# of Positions
Position Size
Dollar Value
# of Positions
Position Size
AAA 60 180 9 20 -120 6 -20
AA 80 240 12 20 -160 8 -20
A 100 300 15 20 -200 10 -20
BBB 75 225 15 15 -150 10 -15
BB 75 225 15 15 -150 10 -15
B 50 150 15 10 -100 10 -10
CCC 10 30 6 5 -20 4 -5
Total $450 $1,350 87 $15.5 -$900 58 -$15.5
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Long bias with lumps
Total Long
Long Lumps
Remaining Long Positions Short positions
Rating Net Value
Dollar Value
Dollar Value
Dollar Value
# of Positions
Position Size
Dollar Value
# of Positions
Position Size
AAA 60 180 180 9 20 -120 6 -20
AA 80 240 240 12 20 -160 8 -20
A 100 300 300 15 20 -200 10 -20
BBB 75 225 100 125 14 8.9 -150 10 -15
BB 75 225 80 145 14 10.4 -150 10 -15
B 50 150 60 90 14 6.4 -100 10 -10
CCC 10 30 30 5 5 -20 4 -5
Total $450 $1,350 $240 $1,110 84 $13.2 -$900 58 -$15.5