Relative Value Trading Opportunities in Portfolios Of Credits

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Relative Value Trading Opportunities in
Portfolios Of Credits

• Raghunath Ganugapati (Newt)
• University Of Wisconsin-Madison
• Doctoral Candidate in Particle Physics

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Agenda

• Introduction to CDOS
• Types of CDOs and the burgeoning Markets
• Structuring of CDOS 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.
• Citigroups HPD model , KMVs Recovery Rate
  model ,Prepayment model (using transition matrix)
  and application to analyzing relative value of
  Collateralized Loan obligations on leveraged
  loans.
• Miscellaneous

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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.
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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

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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

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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).

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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)

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Corporate Bond Spreads

• Expected Loss accounts for small fraction of
  spread
• Role of Taxes
• Liquidity Premium
• Risk Premium
• Non-Diversifiable nature of unexpected losses in
  Credit Risk vs
• symmetry of Equity Returns
• e) How far can we go? Synthetic Arbitrage CDOS

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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.

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Relative Value of CLOS (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)

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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
  Citigroups 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