Hedging A Loan Portfolio Using Index Products

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Hedging A Loan Portfolio Using Index Products

• Greg Hopper
• Goldman Sachs

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Overview

• Assume hypothetical high yield loan portfolio
• How do we develop a quantitatively-based strategy
  for hedging the loan portfolio?
• We focus specifically on problem of using a high
  yield index to hedge

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How Do We Develop A Quantitative Hedging Strategy?

• A quantitative credit hedging strategy is not a
  black box model that we use blindly
• Rather, a quantitative credit hedging strategy is
  the art of combining empirical analysis, credit
  judgment, scenario analysis, and pricing
  technology
• It is an art rather than a science because there
  is not necessarily any right answer or procedure

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Hypothetical Portfolio

• 100 high yield commitments, 0 funded
• 54 of loan names are present in the high yield
  index that we will use for hedging
• we may do similar analysis on portfolios that
  have different compositions
• we use this particular assumption to illustrate
  the method of analysis, not to argue for any
  particular conclusions
• Problem given that we have decided to spend a
  certain amount on a hedging budget, how should
  best hedge?
• - we may formulate the problem in different
  ways, depending on the particular business
  situation

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Quantitative Methodology For Pricing

• Must choose pricing models for commitments,
  default swaps, options on default swaps, and
  tranches
• We choose to use simple pricing models for speed
  of computation, since in the simulation models,
  prices have to be evaluated many times
• Important to understand how limitations of
  pricing models affects the analysis

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Pricing Models

• Loan pricing model
• - treat funded part of loan like bond and
  unfunded part like short default swap
• - assume that high yield loan has higher
  recovery
• - assume that covenants prevent full draw in
  default
• - we ignore option to draw and prepay loan
• CDS pricing model
• Standard model with simplified calibration of
  risk-neutral default probabilities for
  computational speed
• Option on CDS pricing model
• Blacks model with simplified calibration of
  risk-neutral default probabilities for
  computational speed
• Tranche model
• Base copula model
• Semi-analytic pricing for computational speed
• Probably most important to speed up tranche
  pricing, since it is slowest pricing model

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Simulation Models For Credit Portfolio Analyis

• Need to simulate many spread scenarios to
  evaluate properties of hedged portfolios
• Standard simulation models are not very useful
• Correlation problematic in standard models, but
  is central to question of hedging with indices
• Typical econometrically-based models do not
  easily allow incorporation of credit judgment
• Scenarios that result from econometric or risk
  neutral models are not interpretable
• We want to build a model that allows very
  flexible what-if and stress testing analysis, in
  order to superimpose credit judgment on empirical
  analysis
• Automatic Scenario Generation (ASG) given some
  specific credit judgments coupled with empirical
  analysis, ASG model can generate thousands of
  self-consistent scenarios

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Properties of Hedging Instruments

• We must understand the features of the hedging
  instruments in order to understand, interpret,
  and formulate the credit scenarios

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CDS on High Yield Index vs. Option on CDS on Same
Index

• Note prices are approximate, based on simplified
  pricing models

• Assume that we have an annual 10 million
  hedging budget
• We adjust notional of option and default swap so
  that we spend 10 million on either instrument
  annually
• Although our motivation for using the
  out-of-the-money option may to gain leverage, the
  very high implied vol limits the options upside
  relative to its initial price, making the default
  swap more attractive in rising spread
  environments
• Advantage of option downside limited in falling
  spread environments
• We must look carefully at the implied vol of out
  of the money options mezz tranches may be more
  effective in gaining leverage and limiting
  downside

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Mezz Tranche on High Yield Index

• Price 10 - 15 tranche as difference between
  0-15 equity tranche and 0-10 equity tranche
• High yield index modeled after CDX3
• Points paid upfront
• Prices include upfront payment

0-10 base correlation
0-15 base correlation
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Mezz Tranche on High Yield Index With 40 Higher
Spreads

• Price 10 - 15 tranche as difference between
  0-15 equity tranche and 0-10 equity tranche
• High yield index modeled after CDX3
• Points paid upfront
• Prices include upfront payment

0-10 base correlation
0-15 base correlation

• Correlation smile risk can be significant
• Analogous risk of the default swap option is
  spread vol, although correlation smile risk is
  inherently more complicated
• Must include correlation smile in scenario model

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Hedging Loan Portfolio Using Default Swaps or
Mezz Tranche

• For this example, we have 900K annual hedging
  budget
• We purchase mezz tranche on high yield index
  with 600 bps running
• Have 100 high yield 0 funded commitments
• 52 of names in loan portfolio are present in
  the index

• Alternatively, we hedge with default swaps
• For each name that is also in the index, we
  hedge with a name-specific default swap
• For the remaining names, we hedge with default
  swaps on the index

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Scenario Analysis

• To simplify analysis, we look at a very limited
  number of scenarios to clarify issues
• Scenarios will focus on average differences in
  movements between names in the index versus the
  idiosyncratic names
• ASG models will generate more nuanced and
  complex scenarios

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Spread Widening Scenario Index Names Widen More
Than Idiosyncratic Names

• Index name spreads up 40 while idiosyncratic
  name spreads up 25
• Not surprisingly, tranche on index provides
  greater protection

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Spread Widening Scenario Idiosyncratic Names
Widen More Than Index Names

• Index name spreads up 25 while idiosyncratic
  name spreads up 40
• In this case, tranche on index provides
  comparable protection to default swaps because
  tranche leveraged
• If we put high probability or weight on spread
  blowout in the near term, tranche may be superior
  in a wide range of correlation circumstances
• If we care more about widening scenarios, may
  not be so important to understand exact nature of
  correlation between index and idiosyncratic names

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Spread Tightening Scenario Idiosyncratic Names
Tighten Less Than Index Names

• Index name spreads down 30 while idiosyncratic
  name spreads down 20
• In this case, leverage of tranche works against
  us, accentuating loss

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Benign Spread Scenario What Is The Effect Of
Time Decay?

• Spreads dont change but 1 year passes
• Tranche hedge loses much more because of time
  decay
• Important to include time in scenarios

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Spread Widening Scenario What Is The Effect Of
Time Decay?

• Index name spreads up 40 while idiosyncratic
  name spreads up 25
• One year has passed
• Although index spreads move up more, favoring
  the tranche, the tranche hedge gains are
  mitigated by the time decay

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Spread Widening Scenario What Is The Effect Of
Time Decay and Implied Correlation Risk?
36 Implied Correlation
25 Implied Correlation

• Index name spreads up 40 while idiosyncratic
  name spreads up 25
• One year has passed
• Although index spreads move up more, favoring
  the tranche, the tranche hedge gains are
  mitigated by the time decay and the decline in
  implied correlation

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How Does Choice of Pricing Models Affect Analysis?

• Ignored optionality when pricing commitments
• This will not be a serious problem if we are
  more focused on larger spread moves
• However, if we are focused on much smaller
  moves, then this approximation may affect our
  conclusions

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Quantitative Credit Hedging Strategy Is Iterative
Fundamental and Macro Credit Judgment
Statistical Analysis
Choose Pricing Models
Choose Characteristics of Scenarios
Choose Hedging Instruments
Formulate Problem Best Risk Return Tradeoff
Given Hedging Budget? Hedge All Risk?
What-If Scenario Analysis or ASG Model