Quantitative Management of Credit Portfolios vs. Bond Market Indices

1. Quantitative Management of Credit Portfolios vs. Bond Market Indices PRMIA NY New Frontiers in Credit Risk August 14, 2002 Lev Dynkin

2. Multi-factor Risk Model

3. Model Basics The return of any bond can be decomposed as a sum of systematic and non-systematic returns:

4. Quantifying Portfolio Risk � Sample Risk Factors

5. 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

6. 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.

7. Risk & Return of Investment-GradeBonds after Distress

8. 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 <80% of par.

14. Sufficient Diversification in Credit Portfolios

15. Sufficient Diversification in Credit Portfolios Source: Lehman�s historical index data 8/88�12/01 Divide the corporate index into 36 groups: 3 quality (Aaa/Aa, A, Baa) by 4 sector (Yankee, Utility, Financial and Industrial) by 3 duration (0�4, 4�7, 7+) Identify downgraded bonds based on above grouping (Downgrade from A1 to A3 doesn�t 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:

16. Underperformance Due to Downgrades 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

17. The Optimal Portfolio100 bonds, $1 Billion

18. 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

19. What is �Too Much� Diversification? {CRSRVCES}\E_MEDIA\PROJECTS\6200\6225_00\6225_AUX\6225B.XLS!SLIDE{CRSRVCES}\E_MEDIA\PROJECTS\6200\6225_00\6225_AUX\6225B.XLS!SLIDE