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Citigroup’s HPD Model Based Portfolio Optimization (Loans/Corporate Bonds) Raghunath Ganugapati (Newt) Associate Summer Internship(Citigroup) 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

Outline • Objective • Lag on the part of Rating agencies to reflect timely 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

Objective • To improve the Portfolios of Corporate Loans for the Risk adjusted Return(spread 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 been investigated!!!! • To develop Loan Portfolio Analytics by Calculating one year expected Loss Distributions on a Customer Portfolio using (Copula Techniques)

Rating agencies (e. g. Standard & Poor’s and Moody’s ) assign credit rankings and 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. OAS deviation from the rating Agency Ratings Months From Ratings Change

Merton’s Debt-Equity Model - Dynamics Intuition Formalism Some Limitations • By how much does Merton’s Debt-Equity Model - Dynamics Intuition Formalism Some Limitations • By how much does the business value exceed the debt? How uncertain is the future business value? Asset Value – Default Point = DD Asset * Vol Distance To Default • • 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 highgrade and short-maturity bonds Difficult to implement and maintain

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

Loans VS Cash bonds &CDS • Loans are mostly floating RATE • Funded/Unfunded(Credit-Card Mechanics) Loans VS Cash bonds &CDS • Loans are mostly floating RATE • Funded/Unfunded(Credit-Card Mechanics) • Shorter Maturity(~6 yrs) • Are not liquid and hence very difficult to obtain market prices. • Secured and Senior Debt and have higher recovery values in case of a default • 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!!!! • Have a high prepayment risk and little difference in spread in absolute terms

Value Addition of Leveraged-Loans • Syndicated banks to non-investment grade borrowers ( senior secured 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 noninvestment 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)

Norms for Relative Value of loans • • • HPD (probability of default) (1) 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 loge 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?

Regression Coefficients t Stat P-value 6. 585561757 0. 023837525 -0. 041828294 -0. 037377914 0. Regression Coefficients t Stat P-value 6. 585561757 0. 023837525 -0. 041828294 -0. 037377914 0. 128681429 0. 001784569 0. 030066168 0. 006960784 51. 17725072 13. 35758039 -1. 391208037 -5. 369785205 0 1. 81612 E-39 0. 164275962 8. 54785 E-08 Intercept X Variable 1 X Variable 2 X Variable 3 Standard Error

Portfolio Analysis-1 Portfolio Analysis-1

Portfolio Analysis-2 Portfolio Analysis-2

Copula Based Loss Distribution Probability of the loss • An Inter and Intra Industry Copula Based Loss Distribution Probability of the loss • 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 Loss Percentage

Credit Momentum • Improving Credits • • • RELIANCE RES INC WTS KB HOME Credit Momentum • Improving Credits • • • RELIANCE RES INC WTS KB HOME SR SUB NT STANDARD PACIFIC CORP SR NT 0. 405 -1. 067 -0. 562 -1. 882 -0. 462 -0. 968 • Deteriorating Credits • • • VANGUARD HEALTH TERM LOAN EMMIS COMMUNICATIONS TERM LOAN SMURFIT CAPITAL FUNDING CORP -1. 425 -0. 079 0. 389 0. 774 1. 582 1. 617

Loan Optimizer • Look at Relative Value and Credit Momentum • Buy the undervalued 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

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

Outline • For Each Sector : OAS=a+b*OAD+c*Rating 2 OAS is regressed on Duration and 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

Discussion • Adding HPD information would improve the fit (5 year default point used) 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.

Miscellaneous • I have worked on putting together a desk portfolio along similar lines 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

Summary • I have studied a universe of loans and have built a database 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

 • A big Thank you! • To Citibank • • Dennis Adler, Shuguang • 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.