Citigroup

1
Citigroups 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 Citigroups Hybrid Probability
  Of Default Model to analyze client portfolios
• Loans VS Cash bonds CDS
• Overall Value addition to Citigroups 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
Agency Ratings
Rating agencies (e.g. Standard Poors and
Moodys ) 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.
OAS deviation from the rating
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.
Months From Ratings Change
5
Mertons Debt-Equity Model - Dynamics
Intuition
Formalism

• 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

Distance To Default
By how much does
Asset Value

Default Point
the business value
exceed the debt?
DD

How uncertain is
Asset Vol
the future business
value?
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

• 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 Citigroups HPD ID
• Involves manually mapping these names on a
  company by company basis and it might mean doing
  all nighters on weekends!!!!

• 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

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)
• ((CouponLibor)/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?

10
Regression
Coefficients Standard Error t Stat P-value Interc
ept 6.585561757 0.128681429 51.17725072 0 X
Variable 1 0.023837525 0.001784569 13.35758039 1.8
1612E-39 X Variable 2 -0.041828294 0.030066168 -1.
391208037 0.164275962 X Variable
3 -0.037377914 0.006960784 -5.369785205 8.54785E-0
8
 
 
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Portfolio Analysis-1
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Portfolio Analysis-2
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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

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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
• OASabOADcRating2
• 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

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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.