Applications of CDO Modeling Techniques in Credit Portfolio Management

Transcription

1 Applications of CDO Modeling Techniques in Credit Portfolio Management Christian Bluhm Credit Portfolio Management (CKR) Credit Suisse, Zurich Date: October 12, 2006 Slide

2 Agenda* Credit portfolio management in a nutshell CDO modeling techniques Applications in credit portfolio management * This talk reflects the personal view of the author and does not necessarily represent the opinion of Credit Suisse Date: October 12, 2006 Slide 2

3 Agenda* Credit portfolio management in a nutshell - The never ending cycle of measurement and management - The centrol role of credit risk modeling - Uncertainties in models and parameters/calibration CDO modeling techniques Applications in credit portfolio management * This talk reflects the personal view of the author and does not necessarily represent the opinion of Credit Suisse Date: October 12, 2006 Slide 3

4 Credit portfolio management in a nutshell Credit portfolio management is a core competence of modern sophisticated banks Measurement of credit risks and performance Management of credit risks (short & long) Measurement-driven action Reference Portfolio Originator Super Senior CDS Swap Premium Proceeds SPV CDS Protection Notes Payments Super Senior Swap AAA.. BBB Re-measurement Junior Swap Interest / Principal Proceeds Junior Swap Collateral Reflecting the business Tailor-made/adequately Overall target: Optimization of the risk/return profile of the bank s credit portfolio Approach: Enabling full transparency and control over all short and long credit positions Date: October 12, 2006 Slide 4

5 The central role of credit risk modeling Application of credit risk models appear in three key areas* Credit risk management Credit risk measurement (single client and (sub)portfolio level) Limit setting (at various levels and w.r.t. various credit risk measures) Economic and regulatory capital allocation and steering Credit portfolio management Active credit portfolio steering (main lever: RAP**) Hedging (securitizations, baskets, credit default swaps, etc.) Improvement of capital velocity and capital efficiency Reduction of P&L volatility and concentrations Front office needs Sophistication in credit risk pricing and evaluation Structuring of credit transactions (e.g., in the bank's CDO group) Financial engineering of tailor-made credit products for clients of the bank * Separation between the three fields of application depends on the particular organizational/governance setup of the bank ** RAP: risk-adjusted pricing/determination of credit risk premium Date: October 12, 2006 Slide 5

6 Credit risk modelers deal with uncertainties General situation: Data still can be considered as a scarce resource Insufficient data requires expert-based judgements Expert-based judgements are not an absolute truth Different experts arrive at different judgements Therefore, Solution spaces are more serious than point estimates Adequate communication of model outcomes matters Industry benchmarking is important (e.g., correlations) Simple but meaningful models are superior to complex models requiring more sophisticated calibrations Data situation often is more challenging than modeling Overall "space of outcomes" Likely range of solutions - illustrative - Transparent communication of problem solution space Date: October 12, 2006 Slide 6

7 Agenda* Credit portfolio management in a nutshell CDO modeling techniques - Warming-up: basic credit risk modeling - Dependence measurement and management (diversification) - Capital structure and subordination (leverage) - Implied correlations (compound, base, rating agency tranching-implied) - Hedging and risk measures Applications in credit portfolio management * This talk reflects the personal view of the author and does not necessarily represent the opinion of Credit Suisse Date: October 12, 2006 Slide 7

8 Warming-up: basic credit risk modeling (1/5) Date: October 12, 2006 Slide 8

9 Warming-up: basic credit risk modeling (2/5) General dependence driver Date: October 12, 2006 Slide 9

10 Warming-up: basic credit risk modeling (3/5) Linear dependence driver Date: October 12, 2006 Slide 10

11 Warming-up: basic credit risk modeling (4/5) Reflects dependence structure of portfolio Can depend on default drivers Date: October 12, 2006 Slide 11

12 Warming-up: basic credit risk modeling (5/5) General dependence driver Date: October 12, 2006 Slide 12

13 Copula example Simulation of default times with different copula functions Example (continuing): Asset A: 100 bps PD Asset B: 50 bps PD PD term structures based on NHCTMC* approach * Non-homogeneous continuous-time Markov chains; see References (4) Source: References (3) Date: October 12, 2006 Slide 13

14 Dependence measurement and management - example Second-to-default likelihood = JDP (joint default probability) Source: References (3) Date: October 12, 2006 Slide 14

15 Copula function impact on 2nd-to-default likelihoods Source: References (3) Date: October 12, 2006 Slide 15

16 Standard dependence measure: correlation (1/2) Source: References (3) CWI: credit worthiness index (latent variable model); see Slide for a simple example Date: October 12, 2006 Slide 16

17 Standard dependence measure: correlation (2/2) Source: References (3) CWI: credit worthiness index (latent variable model); see Slide for a simple example Date: October 12, 2006 Slide 17

18 Diversification benefit: Gaussian copula example Source: References (3) Return asset A: 170 bps Return asset B: 110 bps Weight w=1: asset A only Weight w=0: asset B only Mix for 0<w<1 Risk x-axis: portfolio UL (std.dev.) Return y-axix: portfolio return/margin Date: October 12, 2006 Slide 18

19 Capital structure and subordination Source: References (3) Date: October 12, 2006 Slide 19

20 Loss allocation in different parts of the capital structure Tail losses Source: References (3) First losses; including the expected loss Date: October 12, 2006 Slide 20

21 Example for a simple model: HLPGC* approach (1/2) Tranched loss distribution * Homogeneous large pool Gaussian copula Source: References (3) Date: October 12, 2006 Slide 21

22 Example for a simple model: HLPGC* approach (2/2) * Homogeneous large pool Gaussian copula Date: October 12, 2006 Slide 22

23 Spread leverage illustration typical structure Source: References (3) Date: October 12, 2006 Slide 23

24 Spread leverage illustration simplified example Spread collections from a whole portfolio can be non-linearly distributed to the tranched portfolio Subordination and potential other credit enhancements protect senior note holders Due to credit enhancements, senior note holders require comparably low spreads Loss 100% Loss distribution of CDS portfolio Total average spread: 150 bps Spread leverage 30 bps Return Return on on first first loss loss piece: piece: 1.2% 1.2% / / 5% 5% = = 24% 24% (before (before losses) losses) 5% 0% 120 bps 5% subordinated capital as protection/credit enhancement for (next) senior tranche Date: October 12, 2006 Slide 24

25 Implied compound correlation in STCDOs Source: References (3) See also Reference (1) for a general intro to index tranches Date: October 12, 2006 Slide 25

26 Implied base correlation in STCDOs Source: References (3) Calculation based on References (5) and (6); see also Reference (1) for a general intro to index tranches Date: October 12, 2006 Slide 26 See Slide 21 for

27 Rating agency securitization-implied correlation Portfolio loss distribution BB-tranche Probab[ Loss PF AP BB ] Look up subordinated capital below considered tranche Look up rating of considered tranche Look up default probability of tranche from agency matrix (hitting probab. for target rating) Find correlation parameter in HLPGC* model in order to match model-implied and agency-assigned hitting probability of tranche Portfolio loss AP: attachment point (for BB-tranche) <-> Quantile of loss distribution Match correlation parameter in HLPGC* model for given quantile and level of confidence * Homogeneous Large Pool Gaussian Copula Date: October 12, 2006 Slide 27

28 Hedging in CDOs delta hedging STCDO example: Underlying names: itraxx Europe Series 5 Tranche: 3% - 6% Index spread: 32 bps Tranche spread: 65 bps Index PV01 = -5 Tranche PV01 = -25 Delta = 5 Delta hedging can be expensive: here, we have a negative carry! Source: References (3) Date: October 12, 2006 Slide 28

29 Hedging and risk measures in capital-structured portfolios Tranche delta w.r.t. portfolio spread: Delta quantifies the PV change of an instrument, e.g., a CDO tranche, given a 1 bps spread widening of the underlying Equity tranche delta decreases if the underlying portfolio spread widens Senior tranche delta increases if the underlying portfolio spread widens Mezzanine tranche delta depends on the particular position in the capital structure Tranche gamma w.r.t. portfolio spread: Gamma measures the sensitivity of delta w.r.t. 1 bps spread widening of the underlying Equity tranche gamma is negative because equity tranche delta decreases with wider spreads Senior tranche gamma is positive Because senior tranche delta increases with wider spreads Jump-to-default w.r.t. single names: Jump-to-default as a risk measure refers to the mark-to-market or mark-to-model impact (PV change) on a tranche if a name in the portfolio defaults (scenario analysis; conditional PDs; dependence structure) Gap risk: Gap risk measures the impact of large spread moves (e.g., downgrades on a rating scale) Date: October 12, 2006 Slide 29

30 Agenda* Credit portfolio management in a nutshell CDO modeling techniques Applications in credit portfolio management - Parameter benchmarking for credit risk positions - Tailor-made credit risk insurance strategies - Cost-to-securitize and mark-to-model for credit risk positions - Evaluation and management of hybrid portfolios - bottom-up approach - Developing the market for illiquid credit risks (e.g., SME loans) * This talk reflects the personal view of the author and does not necessarily represent the opinion of Credit Suisse Date: October 12, 2006 Slide 30

31 Securitization-implied correlation benchmarking (1/3) Date: October 12, 2006 Slide 31

32 Securitization-based correlation benchmarking (2/3) Reference portfolio outstanding notional 100% CLO reference portfolio Number of assets: > 2,000 Replenishment period: 5 years Maturity: 7 years Amortization: approximately linear CLO example (illustrative) 5 7 Time Implied correlation Agency tranching implied correlations Remarks: One-factor CWI correlation vs multifactor model and 1-year vs multi-year horizon Applicability to illiquid (sub)portfolios if securitization of comparable pool can be found in the market Date: October 12, 2006 Slide 32

33 Securitization-based correlation benchmarking (3/3) Illustrative example: one-factor vs multi-factor model correlation benchmarking Multif-factor model (5 regions, 10 industries) Distribution of pairwise CWI correlations Frequency Pairwise CWI correlation One-factor CWI correlation in this example is between 7.5% and 8.5%, depending on calculation/matching approach* Source: References (3) * 1st and 2nd moment matching, or JDP matching, or quantile matching, etc Date: October 12, 2006 Slide 33

34 Example: tailor-made credit risk insurance strategies Credit origination strategy Originate loan A with PD p A Originate loan B with PD p B Buy protection on 2nd-to-default event of duo basket with loans A and B As a consquence, either A or B but not A and B (simultaneously) can cause a loss The lower the correlation between A and B, the more efficient the joint default hedging CDO of duo baskets Duo baskets could be pooled again (CDO of 2nd-to-defaults) Protection can be bought based on tranched duo basket portfolio (should be cheap!) Strong reduction of tail risk and concentrations Source: References (3) Date: October 12, 2006 Slide 34

35 Cost-to-securitize and mark-to-model (1/5) Revisiting the CLO example from Slide 32 CLO example (illustrative) Weighted average spread 45 bps + upfront (annual.) Cost of hedging in form of a diversified pool For transaction costs of 45 bps (focussing on liability side spreads only), underlying reference loans' credit risk can be sold in the market in form of a diversified product (CLO) In other words, if we charge 45 bps on average to each loan, we have sufficient hedging budget How can one make this uniform allocation of 45 bps more risk-sensitive w.r.t. underlying names? Date: October 12, 2006 Slide 35

36 Cost-to-securitize and mark-to-model (2/5) Warming-up: expected shortfall contributions in an illustrative sample portfolio Example: 100 reference names Multi-factor model underlying Average rating BB to B Inhomogeneous R-squared ESF contributions of names to ESF w.r.t. 99.9%-quantile Expected shortfall (ESF): ESF = mean L>q 99.9%-quantile Source: References (3) E[ L PF L PF q ] m k 1 E[ L k L PF q ] Date: October 12, 2006 Slide 36

37 Cost-to-securitize and mark-to-model (3/5) Tranche hit contributions as most fundamental tranche risk measure Source: References (3) Date: October 12, 2006 Slide 37

38 Cost-to-securitize and mark-to-model (4/5) Source: References (3) Date: October 12, 2006 Slide 38

39 Cost-to-securitize and mark-to-model (5/5) Cost-to-securitize concept allocates tranche spreads back to underlying reference names Allocation key is a chosen tranche risk measure Aggregation over all tranches for a given reference name provides the cost-to-securitize of that name Source: References (3) Date: October 12, 2006 Slide 39

40 Evaluation and management of hybrid portfolios Source: References (3) Date: October 12, 2006 Slide 40

41 Developing the market for illiquid credit risks Many of the discussed CDO modeling techniques can be seen as portfolio management techniques too Moreover, many techniques work for public, non-public, and illiquid loans Implied correlations help challenging and benchmarking credit risk model parametrizations Cost-to-securitize components can help in pricing framework, working toward a mark-to-model approach in credit risks Clear understanding of positions in the capital structure of credit portfolios help to hedge exactly the risky parts of the portfolio the portfolio manager is uncomfortable with Hedging techniques can be applied to track single assets through the capital structure of a portfolio Leverage and diversification can be exploited for the benefit of risk/return optimization Outlook/hope/vision: Techniques are further developed and standardized More and more banks start to actively trade also formerly illiquid credit risk positions Non-public debt is meaningfully marked-to-market by portfolio managers An active and transparent secondary market is developed for all credit risks, including SME loans Date: October 12, 2006 Slide 41

42 References (1) Amato, J. D., Gyntelberg, J.; CDS Index Tranches and the Pricing of Credit Risk Correlations; BIS Quarterly Review, March (2005) (2) Basel Committee on Banking Supervision; International Convergence of Capital Measurement and Capital Standards; Bank for International Settlements, November (2005) (3) Bluhm, C., Overbeck, L.; Structured Credit Portfolio Analysis, Baskets & CDOs; Chapman & Hall/CRC Financial Mathematics Series, CRC Press, October (2006) (4) Bluhm, C., Overbeck, L.; To Be Markov or Not to Be: Term Structures of Default Probabilities; Working Paper, submitted (2006) (5) JP Morgan; Introducing Base Correlations; Credit Derivatives Strategy, March (2004) (6) O'Kane, D., Livesey, M.; Base Correlation Explained; Lehman Brothers, Fixed Income Quantitative Credit Research, November (2004) (7) Morokoff, W. J.; Simulation of Risk and Return Profiles for Portfolios of CDO Tranches; Proceedings of the 2005 Winter Simulation Conference, edited by M. E. Kuhl, N. M. Steiger, F. B. Armstrong, and J. A. Joines (2005) Date: October 12, 2006 Slide 42

43 Contact Dr. Christian Bluhm Managing Director Head Credit Portfolio Management (CKR) Credit Risk Management Credit Suisse Bleicherweg 33 CH-8070 Zurich Personal website (download of papers, etc.) Date: October 12, 2006 Slide 43

44 Date: October 12, 2006 Slide 44