Transcript Citigroup’s HPD Model Based Credit Portfolio Optimization

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
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Objective
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Lag on the part of Rating agencies to reflect timely default info
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Merton Models VS Citigroup’s Hybrid Probability Of Default Model to
analyze client portfolios
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Loans VS Cash bonds &CDS
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Overall Value addition to Citigroup’s Business and Strategy
and establish Norms for Relative Value of loans
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Sample Loan Portfolio Analysis(Symphony Asset Management (Client)
and Harbor Portfolio for the desk
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Miscellaneous
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Summary
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)
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
The Debt-Equity
Relationship - Intuition Bond-EquityFormalism
Intuition
Relation: Dynamics and Pricing
Firm’s asset value process
Normally distributed future value
of the firm at time T
dV A t
  dt   A dBt
VAt
Dynamics:
Initial value of firm at time t = 0

N δ  σ
 e
T 
VE  V A N δ  σ A T
Solve:
σE 
V0
VA
VE
A
 rT
K N(δ )
A
VE: Market Capitalization (Price x Shares Outstanding)
Value of firm’s
assets at time t
Using:
E: Implied/Historical Equity Volatility
K: Computed using Balance Sheet Data
Region
of
Default
Default Boundary
t0
Some Limitations
Default Point
T
Time
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Source: Citigroup
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
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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,
liquidity, market presence and management
are contained in equity prices
Attempt to model profitability, liquidity, market
presence and management explicitly
Risk Component
Descriptor
Risk Component
Leverage
Debt Term Structure
Capital
Structure
Market
Information
Profitability
Stock Volatility
Equity Price
Return on Assets
Return on Equity
Liquidity
Available Capital
Access to Credit
Market
Presence
Firm Size
Level of Competition
Management
Quality
Market
Information
Earnings Restatements
Bad Press
Credit Rating
Interest Rates
f(x1,x2,…xn)
Probability of Default
Descriptor
Stock Volatility
Equity Price
Traded Volume
Credit Spreads
Profitability
Return on Assets
Return on Equity
Liquidity
Available Capital
Access to Credit
Capital
Structure
Leverage
Debt Capacity
Debt Term Structure
Market
Presence
Firm Size
Level of Competition
Management
Quality
Earnings Restatements
Bad Press
Credit Rating
f(x1,x2,…xn)
Probability of Default
Industry Averages, Interest Rates,
Macroeconomic Variables, etc;
Source: Citigroup
Loans VS Cash bonds &CDS
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Loans are mostly floating RATE
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Funded/Unfunded(Credit-Card
Mechanics)
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Shorter Maturity(~6yrs)
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Are not liquid and hence very difficult
to obtain market prices.
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Secured and Senior Debt and have
higher recovery values in case of a
default
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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
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Involves manually mapping these names
on a company by company basis and it
might mean doing all nighters on
weekends!!!!
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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 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
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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
Intercept
X Variable 1
X Variable 2
X Variable 3
Coefficients
Standard Error
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
1.81612E-39
0.164275962
8.54785E-08
Portfolio Analysis-1
Portfolio Analysis-2
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
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RELIANCE RES INC WTS
KB HOME SR SUB NT
STANDARD PACIFIC CORP SR NT
0.405
-0.562
-0.462
-1.067
-1.882
-0.968
-1.425
-0.079
0.389
0.774
1.582
1.617
• Deteriorating Credits
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VANGUARD HEALTH TERM LOAN
EMMIS COMMUNICATIONS TERM LOAN
SMURFIT CAPITAL FUNDING CORP
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 Corporate Bond Strategy Group
Outline
• For Each Sector :
OAS=a+b*OAD+c*Rating2
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)
• 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 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
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!
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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.