1. Relative Value Trading Opportunities in Portfolios Of Credits Raghunath Ganugapati (Newt) University Of Wisconsin-Madison Doctoral Candidate in Particle Physics

2. Agenda Introduction to CDO’S Types of CDO’s and the burgeoning Markets Structuring of CDO’S and Probability of Default,Correlation and Recovery Rates Copula Functions to model Default times and Default Correlation. Copula to use? Advanced strategies to make markets using some inconsistencies in pricing mechanism and relative value trading. Citigroup’s HPD model, KMV’s Recovery Rate model,Prepayment model (using transition matrix) and application to analyzing relative value of Collateralized Loan obligations on leveraged loans. Miscellaneous

3. Introduction A collateralized debt obligation (CDO) is an asset backed security (e.g. corporate bonds, MBS, Bank loans or could be synthetic deriving their value from an instrument called credit default swap which is the cost of insuring a corporate or a sovereign or something similar. The funds to purchase the underlying assets (called collateral assets) are obtained from the issuance of debt obligations (tranches) structured to satisfy the demands of various kinds of Investors in segmented markets (say credit and equity) depending on their risk appetite and the difference in pricing. How does tranching create value to fulfill structuring fee and other business risks? Differences in spreads between wholesale markets and retail markets and work done in repackaging (ask a fruit vendor?). Returns in Fixed Income are non-normal unlike equity returns. The iTraxx standardization tranching has not only increased liquidity but allowed credit players to trade different types of risk across the capital structure facilitating the separation of market risk, currency risk etc from credit risk.

4. Issuance and Types  Transaction Balance Sheet and Arbitrage CDO  Securitization Cash and Synthetic CDO  Underlying Asset CLO, CBO, Single Tranche CDO, CDO, CDO2  Funding Funded and Unfunded  Management Static and Managed

5. CDO valuation (Key Inputs) Probability Of Default for different maturities (Snapshot of Credit Curves) Dynamics of probability of default with time (mean reversion, mean reversion level, volatility and possible two state volatility i.e. regime model) (marginal distribution) Default Correlation (Joint Distribution through copula function )(Equity, Mezzanine and Senior Tranches are affected by correlation) Recovery rate in case of default (actually anti correlated with overall level of default, the amount of liquid assets, country in which industry located etc) Risk Appetite

6. Copula Function We take the marginal distributions, each of which describes the way in which a random variable moves “on its own,” and the copula function tells us how they come together to determine the multivariate distribution and hence stitch together these marginals The market standard model is the Gaussian Copula model (David Li) however we know that Gaussian captures only the first two moments. To conquer this desks take a snapshot of correlation and credit curves and using the Gaussian Copula model the default times are simulated, loss distribution obtained and hence pricing done (this is static). An important aspect of Credit Risk is the unexpected losses and risk premiums for the non diversifiable nature of it therefore we should really be concerned about the tails of return distributions. These are also important for regulatory purposes (VaR).

7. Extreme Value Copulas Market defaults tend to be more correlated in a bear market than in a bull market which leads to a skew in the default correlation. Further this default correlation is higher in bear markets for higher rated securities as they are related to the systematic market wide shock more than the lower rated ones which are more related to idiosyncratic risk.These asymmetries are further worsened by the fact that the value of the recovery on the collateral for defaulted entities tend to be lower in a high default environment. An extreme value Copula like the Archimedean Copulas capture tails better and hence the nature of default correlation and recovery in default. What is the right copula function, how should a single correlation number be smeared with right function with different level of dependencies? Depends on market data, for instance one should try to capture the historical correlation structure of various ratings by the level of probability of default and see if we could replicate this also descriptive statistic of fits could help too (See Das and Geng)

8. Corporate Bond Spreads Expected Loss accounts for small fraction of spread a)Role of Taxes b)Liquidity Premium c)Risk Premium d)Non-Diversifiable nature of unexpected losses in Credit Risk vs symmetry of Equity Returns e) How far can we go? Synthetic Arbitrage CDO’S

9. Aggressive Relative Value Trading Strategies  The relative value trading opportunities created because of the business cycle dynamics. Higher rated Fixed Income securities are more default correlated to the economy wide shock as a whole that generates large skewness in return distributions.  Rating agencies are conservative in announcing upgrades/downgrades and investors persistence on these ratings for assessing risks while the market prices the increased/decreased level of risk well before the upgrade/downgrade happens (look at CDS and Equity markets) this generates relative value trading opportunities  Market prices by using a snap shot of credit curves and using static inter and intra indutry correlation, static recovery to get loss distributions we could use information on credit cycles etc to get better value for this numbers to create relative value trades  Recent change in the rating methodology of individual credits by S & P, lowering investment grade default probability and increasing non-investment grade default probability is likely to change the CDO market. Points to be kept in mind in re-evaluating spreads are credit cycles and how these investment grade credits are more related to the systematic factors and hence high correlation with market shocks.

10. Relative Value of CLO’S (At Citigroup) Each Loans Spread is due to a) Probability of Default (HPD model) b) Recovery Value upon default (KMV model) c) Market Risk (Beta Risk) (From moving averages of market prices) d) Prepayment speed (Ratings Transition) (Transition matrix) e) Illiquidity of Leveraged Loans (Size of loans from INTEX) After correcting portfolio of leveraged loans of 13000 names (obtained through INTEX quotes I observed significant amount of Relative value between Loan Credits as a function of rating) The regression was done between log (probability of default), Recovery,Duration, log (Rating) VS log (Spread)

11. Miscellaneous I computed VAR for CLO portfolios of the desk for leveraged loans using a two factor copula and made relative value analysis I have made Relative value Trade recommendations for an Asset Management Firm (client of Citigroup) I have done analysis on corporate bonds using Citigroup’s HPD I have done a sector wide study and the coefficients of regression for fair spread on these sectors to support cross sector asset allocation