1. Citigroup’s HPD Model Based Portfolio Optimization (Loans/Corporate Bonds) Raghunath Ganugapati (Newt) Associate Summer Internship(Citigroup) Doctoral Student in Particle Physics and a Masters Student in Quantitative Finance University Of Wisconsin-Madison August 25 -2005

2. Outline Objective Lag on the part of Rating agencies to reflect timely default info Merton Models VS Citigroup’s Hybrid Probability Of Default Model to analyze client portfolios Loans VS Cash bonds &CDS Overall Value addition to Citigroup’s Business and Strategy and establish Norms for Relative Value of loans Sample Loan Portfolio Analysis(Symphony Asset Management (Client) and Harbor Portfolio for the desk Miscellaneous Summary

3. Objective To improve the Portfolios of Corporate Loans for the Risk adjusted Return(spread obtained while reducing the risk by making necessary substitutes to credits This has been Successfully applied in the past for Cash Bonds and CDS but loans have never ever been investigated!!!! To develop Loan Portfolio Analytics by Calculating one year expected Loss Distributions on a Customer Portfolio using (Copula Techniques)

4. Rating agencies (e.g. Standard & Poor’s and Moody’s ) assign credit rankings and are designed to provide an estimate of the likelihood that a credit will default. Rating Agencies Are Often Slow to React to Credit Events in an effort to provide clear signals to the market. The graph at the right shows monthly average spread deviations (in bp) from target rating category means vs. time to ratings change. It appears that investors react to changes in credit quality at least six months prior to ratings downgrades and even earlier prior to upgrades. Agency Ratings Months From Ratings Change OAS deviation from the rating

5. Merton’s Debt-Equity Model - Dynamics IntuitionFormalism By how much does the business value exceed the debt? How uncertain is the future business value? Asset Value–Default Point Asset * Vol = DD Distance To Default Some Limitations Default occurs only if boundary is crossed No option to refinance in distress Bond prices play no role in estimating the value of the firm Under predicts spreads for both high- grade and short-maturity bonds Difficult to implement and maintain

6. Merton-Type Models vs. Hybrid Models Merton Models Assume all information about profitability, liquidity, market presence and management are contained in equity prices Hybrid Models Attempt to model profitability, liquidity, market presence and management explicitly Source: Citigroup

7. Loans VS Cash bonds &CDS Loans are mostly floating RATE Shorter Maturity(~6yrs) Secured and Senior Debt and have higher recovery values in case of a default Have a high prepayment risk and little difference in spread in absolute terms Funded/Unfunded(Credit-Card Mechanics) Are not liquid and hence very difficult to obtain market prices. No loan CUSIP identifiers and Loan names are often random combination of “English” alphabet(if lucky!!) and should be mapped to Loan Prices and Citigroup’s HPD ID Involves manually mapping these names on a company by company basis and it might mean doing all nighters on weekends!!!!

8. Value Addition of Leveraged-Loans Syndicated banks to non-investment grade borrowers ( senior secured debt having high recovery) and a surprising result is that these are greater in terms of outstanding amount to non- investment grade bonds and consistent returns through time are guaranteed through structural protection. Low volatility and low correlation to other asset classes. Dominated by a few players and good investment for capital preservation. Middle market portfolios offer consistent returns with low volatility then large corporations Overall Desk Risk Management and distribution capabilities taking strategic advantage of distribution capabilities in place CLO Trading and Sales Loans VS Bonds VS CDS(Cap Arb,requires confidence in the models)

9. Norms for Relative Value of loans HPD (probability of default) (1) Recovery Values(2) Weighted Average Life(3) ((Coupon+Libor)/Market Price) as proxy (4) This might in some sense partly account for the prepayment and other optionality We Regress the sum of the log e of the quantities 1,2,3 with 4 and compute the standardized residual of each loan relative to the regression to do rich cheap analysis Why use log?

10. CoefficientsStandard Errort StatP-value Intercept6.5855617570.12868142951.177250720 X Variable 10.0238375250.00178456913.357580391.81612E-39 X Variable 2-0.0418282940.030066168-1.3912080370.164275962 X Variable 3-0.0373779140.006960784-5.3697852058.54785E-08 Regression

11. Portfolio Analysis-1

12. Portfolio Analysis-2

13. Copula Based Loss Distribution An Inter and Intra Industry Correlation of 0.15 and 0.3 was used and a Gaussian Copula two factor model is used.Could compute VAR from this for Risk Management if it was a desk portfolio Probability of the loss Loss Percentage

14. Credit Momentum Improving Credits RELIANCE RES INC WTS 0.405-1.067 KB HOME SR SUB NT -0.562-1.882 STANDARD PACIFIC CORP SR NT -0.462-0.968 Deteriorating Credits VANGUARD HEALTH TERM LOAN -1.425 0.774 EMMIS COMMUNICATIONS TERM LOAN -0.079 1.582 SMURFIT CAPITAL FUNDING CORP 0.389 1.617

15. Loan Optimizer Look at Relative Value and Credit Momentum Buy the undervalued Loan and sell the Overvalued Loan all else same,collect the spread and go home! Pick a loan in the same industry,same duration,comparable rating,comparable recovery and any other guidelines set by customer while working on his portfolio while making substitutions to get more return for the same amount if risk

16. Improving Citigroup Relative Value Model for Corporate Bonds Raghunath Ganugapati For Dennis Adler and Corporate Bond Strategy Group

17. Outline For Each Sector : OAS=a+b*OAD+c*Rating 2 OAS is regressed on Duration and Rating only Problem: As we discussed Ratings are coarse measure of Credit Risk and rating agencies lag in time. I am working on adding the default probability to do Rich/Cheap Analysis Into production mechanism so that this can be used on a routine basis

18. Discussion Adding HPD information would improve the fit (5 year default point used) Improvement significant for Industrials where we have maximum default data I have got the code in good shape and it can be used to do Rich/Cheap Analysis for corporate bonds Code computes how much a bond is Rich/Cheap relative to old model and adding KMV and HPD information as well.

19. Miscellaneous I have worked on putting together a desk portfolio along similar lines and whenever we could not map an ID we infer an average HPD based on rating. Further I also worked on other portfolios for a week when an Associate and Analyst Were on Vacations During the earlier weeks of my internship I have studied in great length about a study done on EDF to forecast future default using Archimedean Copulas,This gives insights into Pricing Credit Derivatives and other correlation products and we could do similar studies on HPD

20. Summary I have studied a universe of loans and have built a database for loan analytics and used to to optimize a client portfolio to get better return for lesser amount of risk. I have Computed a 1 year loss distribution for the clients portfolio Built the necessary infrastructure to do rich/cheap analysis on leverage high yield loans and this will be useful for both our clients and Desk Risk Management people I have worked on testing the necessary infrastructure to produce a production level code for corporate bond Rich/Cheap analysis adding default probability as an additional parameter

21. A big Thank you! To Citibank Dennis Adler, Shuguang Mao, Hiedy Kim, Steve Conyers Terry Benzschawel Justin Jiang Henry Fok Ji Hoon Ryu Shelli Faber Speakers at our Seminars My Co-interns and everyone who helped me me in this forge.