A SURVEY ON DEFAULT TIMES AS A TOOL FOR PORTFOLIO MANAGEMENT

Transcription

1 A SURVEY ON DEFAULT TIMES AS A TOOL FOR PORTFOLIO MANAGEMENT RISK DAY, ETH ZURICH, OCTOBER 15, 2004 Dr. Christian Bluhm Head Credit Suisse, Zurich christian.bluhm@credit-suisse.com

2 AGENDA INTRODUCTION SINGLE-NAME DEFAULT TIMES DEFAULT TIMES FROM A PORTFOLIO'S PERSPECTIVE APPLICATIONS ACTIVE PORTFOLIO MANAGEMENT STRUCTURED CREDIT PRODUCTS STRUCTURED CREDIT RISK HEDGING WRAP-UP OF FINDINGS / Christian Bluhm Slide 2

3 AGENDA INTRODUCTION SINGLE-NAME DEFAULT TIMES DEFAULT TIMES FROM A PORTFOLIO'S PERSPECTIVE APPLICATIONS ACTIVE PORTFOLIO MANAGEMENT STRUCTURED CREDIT PRODUCTS STRUCTURED CREDIT RISK HEDGING WRAP-UP OF FINDINGS / Christian Bluhm Slide 3

4 THE EARLY TIMES OF CREDIT RISK MODELLING... First "off-the-shelf"-models in the market: Frequency CreditMetrics (RMG) ~ 1997 Portfolio Manager (Moody's KMV) ~ 1987* CreditRisk+ (CSFP) ~ 1997 Credit Portfolio View (McK) ~ 1997 Clear model target setting: Quantification of expected and unexpected loss of a credit portfolio Understanding the portfolio decomposition Loss [%] of Exposure EL = mean value of loss distribution E(R)C = [quantile - EL] or expected shortfall Expected Loss [ACP] Economic (Risk) Capital [ERC] Applications: Capital buffers, loss reserves, capital allocation, portfolio steering, limit setting, etc. * 1987 was the release date of some seminal work by O. A. Vasicek; however, KMV corporation has its hour of birth several years earlier than / Christian Bluhm Slide 4

5 TODAY BANKS HAVE A MORE DYNAMIC POINT OF VIEW Today credit risk modelling* is more "dynamic": Li (default baskets) ~ 2000 Finger (stochastic default rate models) ~ 2000 Schmidt & Ward (default baskets) ~ 2002 single-name τ Rating time (semi-annually) B & Overbeck (semi-analytic DTs) ~ 2003 Clear model target setting: Still quantification of expected and unexpected loss of a credit portfolio, but also Understanding of the timing of defaults Evaluation of structured credit products Financial engineering of credit-linked products portfolio view Recovery Single credit risks are combined by a "copula function" (Gaussian or Student-t or...) time (semi-annually) Implementation: [term structure of default probabilities] [one or more copula functions] * The four mentioned contributions are just a very small subset of the rich literature on credit risk modelling and default times of recent years / Christian Bluhm Slide 5

6 AGENDA INTRODUCTION SINGLE-NAME DEFAULT TIMES DEFAULT TIMES FROM A PORTFOLIO'S PERSPECTIVE APPLICATIONS ACTIVE PORTFOLIO MANAGEMENT STRUCTURED CREDIT PRODUCTS STRUCTURED CREDIT RISK HEDGING WRAP-UP OF FINDINGS / Christian Bluhm Slide 6

7 SINGLE-NAME CREDIT RISK "Credit risk is the risk that a change in the credit quality of a counterparty will affect the value of a bank's position. Default, whereby a counterparty is unwilling or unable to fulfill its contractual obligations, is the extreme case; however, banks are also exposed to the risk that the counterparty might be downgraded by a rating agency." (Source: Crouhy, Galai and Mark: Risk Management, McGraw-Hill (2001) Quantification: downgrade risk default risk Source: B and Overbeck: An Introduction to CDO Modelling and Applications; in: D. Shimko, Credit Risk, RISK Books (2004) / Christian Bluhm Slide 7

8 DEFAULT PROBABILITIES OVER TIME - EXAMPLE (1/3) / Christian Bluhm Slide 8

9 DEFAULT PROBABILITIES OVER TIME - EXAMPLE (2/3) Q-matrix best-matching the given one-year migration matrix: Source: B and Overbeck Error M - Exp(Q) is at basispoint level / Christian Bluhm Slide 9

10 DEFAULT PROBABILITIES OVER TIME - EXAMPLE (3/3) Source: B and Overbeck / Christian Bluhm Slide 10

11 SINGLE-NAME DEFAULT TIMES / Christian Bluhm Slide 11

12 AGENDA INTRODUCTION SINGLE-NAME DEFAULT TIMES DEFAULT TIMES FROM A PORTFOLIO'S PERSPECTIVE APPLICATIONS ACTIVE PORTFOLIO MANAGEMENT STRUCTURED CREDIT PRODUCTS STRUCTURED CREDIT RISK HEDGING WRAP-UP OF FINDINGS / Christian Bluhm Slide 12

13 PORTFOLIO PERSPECTIVE / Christian Bluhm Slide 13

14 PORTFOLIO PERSPECTIVE - EXAMPLE Firm risk decomposition: Gaussian copula dependency Moody's KMV's Global Correlation Model / Christian Bluhm Slide 14

15 AGENDA INTRODUCTION SINGLE-NAME DEFAULT TIMES DEFAULT TIMES FROM A PORTFOLIO'S PERSPECTIVE APPLICATIONS ACTIVE PORTFOLIO MANAGEMENT STRUCTURED CREDIT PRODUCTS STRUCTURED CREDIT RISK HEDGING WRAP-UP OF FINDINGS / Christian Bluhm Slide 15

16 PORTFOLIO MANAGEMENT STEERS RISK & RETURN deals not only with pure credit risk management but has the mandate to optimize the risk/return profile of the bank s credit portfolio by means of application of various instruments, e.g., - risk-adjusted pricing, - single-name risk buying and selling, e.g., by means of credit derivatives, - portfolio-risk buying and selling, e.g., by means of default baskets and CDOs, - and by framework-generating policies and guidelines. Source: Credit Risk Policy; Credit Suisse, page / Christian Bluhm Slide 16

17 PORTFOLIO MANAGEMENT THINKS 2-DIMENSIONAL Source: B and Mussil: Basket Kreditderivate und Collateralized Debt Obligations als Instrumente des Portfoliomanagements; to appear in: Handbuch Kreditderivate, zweite Auflage, edited by Burghof et al / Christian Bluhm Slide 17

18 RISK TRANSFER - EXAMPLE ("DUO BASKETS") Hedging of joint defaults: Standard: Credit event = payment default on any financial obligation of one asset Duo Baskets: Credit event = 2nd-to-default (both assets default, 2nd default protected) Source: B and Overbeck: Modelling of Collateralized Debt Obligations, Book Manuscript (2003/04) / Christian Bluhm Slide 18

19 N-TH-TO-DEFAULT BASKETS Asset 1 Asset 2 Asset 3 τ 1 τ 2 τ 3 Buy protection on the first, second, third,... default in the basket. Asset m "Basket" Bullet exposure profile No triggers simple mechanism τ m Monte Carlo simulation of the default times of the basket's assets; then: scenario-based cash flow evaluation; full performance check / Christian Bluhm Slide 19

20 N-TH-TO-DEFAULT BASKETS - EXAMPLE Comonotonic approximation of a 1st-to-default distribution Comonotonic approximation of a 2nd-to-default distribution "Comonotonic": One can prove: Application of the comonotonic copula to given marginal default time distributions for a portfolio of credit-risky assets. If the basket can be approximated by a uniform credit curve and a uniform asset correlation, then the comonotonic approximation is exact! Source: B and Overbeck: Comonotonic Default Quote Paths; submitted preprint (2004) / Christian Bluhm Slide 20

21 AGENDA INTRODUCTION SINGLE-NAME DEFAULT TIMES DEFAULT TIMES FROM A PORTFOLIO'S PERSPECTIVE APPLICATIONS ACTIVE PORTFOLIO MANAGEMENT STRUCTURED CREDIT PRODUCTS STRUCTURED CREDIT RISK HEDGING WRAP-UP OF FINDINGS / Christian Bluhm Slide 21

22 WRAP-UP OF FINDINGS Sound portfolio management needs sound tools for credit risk evaluation Such tools should reflect the time dynamics of default event distributions Correlated default times constitute an appropriate tool for measuring defaults over time Challenges are always at the calibration side, not that much at the pure model side / Christian Bluhm Slide 22