Quantitative Management of Credit Portfolios vs' Bond Market Indices

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Quantitative Management of Credit Portfolios vs.
Bond Market Indices
Confidential

• PRMIA NY
• New Frontiers in Credit Risk
• August 14, 2002
• Lev Dynkin

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Multi-factor Risk Model
Confidential
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Model Basics

• The return of any bond can be decomposed as a sum
  of systematic and non-systematic returns

where xi value of risk factor i (a market event
which affects returns of an entire market
segment) fbi exposure of bond b to factor i
(factor loading) eb nonsystematic return on
bond b (issuer and individual issue effects)
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Quantifying Portfolio Risk Sample Risk Factors
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Time-Decay vs. Equal Weighting

• Time-decay produces better estimates when
  volatility has a predictable component.
• Equal weighting produces more efficient estimates
  if volatility is not predictable.
• Predictability of return volatility depends on
  the time interval strong predictability at daily
  frequencies but weak at monthly.
• Risk Model currently uses equal weighting for
  estimating factor covariance and idiosyncratic
  volatilities.
• Recent rise in security-specific risk

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Global Risk Model Combination of Regional
Models or a Coarser View of Risk

• Globalization of credit spread and even yield
  curve movement
• Sharp rise in security specific risk in local
  markets divergence between different credit
  sectors
• Combining U.S., Euro, Sterling and JGB Risk
  Models produces a large number of factors, some
  with short history
• Statistical remedies exist, but reduce confidence
  in covariances
• Coarser partitions of each credit universe means
  aggregation of industries with low correlation,
  and thus loss of information.
• A macro view of global risk creates potential
  inconsistencies with regional risk models for a
  single currency portfolio.

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Risk Return of Investment-GradeBonds after
Distress
Confidential
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Definition of a Distressed Bond

• We define a distressed investment-grade bond as
• Rated Baa3 or higher
• Fixed coupon
• OAS to US Treasuries of 400bp or more and
• Dollar price lt80 of par.

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Identifying distressed bonds
 
distressed amount (par)
as of issues outstanding
credit index   Vintage Year
1990 50 9,381 1.70 1991
14 1,953 0.32 1992 1
75 0.01 1994 1
245 0.04 1995 5 900
0.13 1996 1 100
0.01 1998 29 6,984
0.64 1999 10 2,375 0.20
2000 139 36,797 2.62
2001 54 18,166
1.02 Jun 2002 68
48,875 2.65
  total 372  

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For a distressed bond, duration is not a good
measure of price sensitivity
JCP - 2000
price vol. 12 months after distress
month price vol. 12 months prior to
distress month
For distressed bonds, a better measure of
relative exposure vs. the index is market value
percentage.
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24-month Cumulative Excess Returns vs. Treasuries
1990
2002
Generally very positive, but not since 01/ 2001

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Subsequent Excess Returns (vs. UST) of
investment-grade bonds after distress
  distressed
24-month issues
excess return vs. UST  
Vintage Year 1990 50 28.28
1991 14 40.94 1998
29 19.33 1999 10
10.69 2000 139
8.35 2001 54
-23.08 Jun 2002 68
-24.21 Years prior 2001 250 16.56
Years since 2001 122 -23.71
All Years 372 3.35  

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Cliff Price of distressed bonds

12-Month Cumulative Excess Returns sorted by
Distress Price
Prior 2001
Since 2001
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Sufficient Diversification in Credit Portfolios
Confidential
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Sufficient Diversification in Credit Portfolios

• Source Lehmans historical index data 8/8812/01
• Divide the corporate index into 36 groups 3
  quality (Aaa/Aa, A, Baa) by 4 sector (Yankee,
  Utility, Financial and Industrial) by 3 duration
  (04, 47, 7)
• Identify downgraded bonds based on above grouping
  (Downgrade from A1 to A3 doesnt count)
• For each downgraded bond calculate
  underperformance ? relative to its peer group for
  each of the 12 months before downgrade
• Multiply by probability q of a downgrade to
  produce expected loss vs peer group

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Underperformance Due to Downgrades
Average Monthly Underperformance Due to
Downgrade8/88 12/01

• Loss of value due to a downgrade occurs over a
  few prior months. Depending on the initial credit
  quality losses could stretch over 2 months for
  AAA-AA up to 8 months for BAA
• The variability of the magnitude of the loss
  (i.e., Standard deviation) is very significant

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The Optimal Portfolio100 bonds, 1 Billion
Worst case underperformance of corp. index due to
downgrades (with 95 confidence, assuming normal
dist) -48 bp The ratio of the optimal position
sizes (or lot sizes) for different quality
ratings should be Aa-AaaABaa 941
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Downgrade Risk vs. Other Non-Systematic Risk

• The risk of downgrades is not the only source of
  idiosyncratic risk
• Stable-rated bonds experience natural spread
  volatility
• Including natural spread volatility produces
  idiosyncratic risk less differentiated by quality
  compared to downgrade risk alone

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What is Too Much Diversification?