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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