TimetoDefault : Life Cycles, Global and Industry Cycle Impacts

1
Time-to-Default Life Cycles, Global and
Industry Cycle Impacts

• Fabien Couderc, Olivier Renault
• European Investment Review Annual Conference, 9
  September 2004
• PhD Student, FAME University of Geneva
• Associate Fellow, FERC, Warwick Business
  School.
• Research sponsored by Standard Poors Risk
  Solutions

2
Motivations

• Academic efforts have concentrated on credit
  pricing (which relies on risk neutral
  probability) and far less on credit risk
  management.
• What can we tell about default probability under
  the physical measure ?
• Traditional models, i.e. structural (firm-value
  based) and reduced-form models, have shown some
  limitations. Mixed approaches appear promising.
• This suggests the use of a factor driven duration
  model.
• Current works try to enhance models introducing
  dependence structures in large portfolios and
  complex derivatives (e.g. CDOs).
• Modelling firm-specific variables is
  insufficient.

3
Motivations (2)

• Most studies only factor in the effect of current
  economic conditions.
• Can we provide a more thorough analysis of the
  determinants of default probability ?
• Despite numerous academic and practitioners
  studies some issues remain outstanding
• What are the links between the default cycle and
  the global business cycle ?
• Do firms life cycles provide additional
  information ?
• Is the industry instrumental in explaining
  default probability ?

4
Overview of paper

• We study durations to default for different types
  of risk classes through simple non-parametric,
  semi-parametric and parametric models
• We analyse the potential drivers of default
  intensities (probabilities of default in the very
  short run)
• We show how they may be factored in a model.

Definition of intensities considering a
counting process initially null when the
firm enters in a risk class and which jumps to
one when the firm defaults, the intensity at
time u, is the expected probability to
jump between u and udu under the whole
knowledge on the process right before u.
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Ratings Data

• Database Standard Poors CreditPro database
  recording rating events from 1/1/1981 to
  12/31/2003
• Main Statistics
• Around 33044 events on 10439 issuers
• 25 different grades
• 13 industrial groups
• 93 countries
• 3/4 US firms
• 1386 defaults and default rates range from 3 to
  29 across industries
• All firms do not enter in the observed pool at
  the same time
• Presence of left-truncation (degenerate form)
• Some firms are leaving the default process for
  several reasons mergers, acquisitions, end of
  activities without failure,
• Presence of right-censoring (NR rating)

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A first look at times to default
Our non-parametric estimator of the default
intensity relies on gamma kernels
represents the so-called risk set and
includes all kinds of censoring.
Intensities are estimated by calculating a
weighted average of default rates. The weights
are determined by the choice of kernel. b (the
bandwidth) controls the degree of smoothness of
the estimator.
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Behaviour of Times-to-Default Results
IG and NIG intensities up to the last observations
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Behaviour of Times-to-Default Results (2)

• Presence of humps is a recurrent feature.
• Starting macro-economic conditions matter over
  the whole life of firms.
• Junk issuers (B and CCC) exhibit downward sloping
  patterns whereas others are upward sloping.
• Rating momentum effects but in the long run
  upgraded issuers present higher probabilities of
  default.

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Potential Default Determinants

• Macro-economic factors retained and expected
  impacts on intensities
• Stock market indicators
• Return on SP500 current, short and mid term
  component, impact
• Volatility of SP500 returns impact
• Interest rates long term economic indicator,
  current costs, / impact
• US 10yr. treasury yield
• Slope of the US term structure
• Economic growth indicators impact
• Real GDP Growth
• Des. Industrial production growth
• CPI growth
• Personal income growth

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Potential Default Determinants (2)

• Credit Cycle Information
• BBB yield long term forecast, current costs,
  / impact
• BBB spread current, short and mid term
  component, impact
• BBB-AAA spread same as BBB spread
• Net treasury issues Macro indicator and
  potential crowding out effect.
• Money lending (M2-M1) impact
• Rating agencies information pure default
  process indicators
• Upgrade and downgrade ratios on Investment Grades
  (IG, SP)
• Upgrade and downgrade ratios on Speculative
  Grades (NIG, SP)
• Some of the above variables are highly correlated
  which deteriorates statistical
• significance on the full set. Univariate studies
  bring a lot of information. PCA
• analysis show that most of the variation in
  default intensities is explained by 4 to 6
• significant underlying factors.

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Information Impacts Log-Linear Intensities

• Usual duration models are built using technology
  developed for interest rates
• models. Intensities are assumed to follow
  exponential affine combinations of
• explanatory factors Z (GDP growth, interest rates
  etc.)
• Parameters can be estimated in the usual
  likelihood framework. Dynamics of
• factors are assumed to be independent of the
  default process and observed
• monthly.
• We estimate
• Univariate specifications (only one explanatory
  variable),
• Sensitivity with respect to several lags,
• Multivariate specifications from factor groups
  and major indicators.
• Diagnostics can be done through likelihood ratios.

12
Simple Tests of Models Performance

• We study a semi-parametric specification Cox
  type intensities the common
• default probability (baseline) is not necessarily
  constant and estimated non-
• parametrically.
• We can test whether starting conditions and/or
  current conditions are sufficient
• to explain intensities variations according to
  the proportional hazard assumption
• 
  and

In this framework sensitivities to explanatory
factors can be estimated by a partial likelihood
function representing conditional probabilities
of default.
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Simple Tests of Models Performance (2)
Rectangle shows the models we focus in
Stock and bond market information is not always
relevant and delivers very limited explanatory
power (around 25 of the variations of
probabilities). It corresponds to findings of
Collin-Dufresne al. for credit spreads.
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Simple Tests of Models Performance (3)
Still waves non perfect co-cyclicality with
the market cycle
Overestimation over the first years
conservatism
Baseline for intensities driven by stock markets
for BB issuers If the model performs, the blue
line should not deviate from the constant
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Improving Traditional Models Parsimonious
Choices of the Information Set
Arrows show the models we focus in

• The economic cycle exhibits distinct explanatory
  power through the real GDP
• As well as credit cycle information through
  global issuer quality and behaviour of the BBB
  spread.

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Improving Traditional Models Parsimonious
Choices of the Information Set (2)
Non-parametric intensities (black) versus
semi-parametric baselines (blue) and
corresponding means (comparable to the constants
of log-linear models)
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Improving Traditional Models Parsimonious
Choices of the Information Set (3)
Point out strong overestimation of NIG default
probabilities due to a large influence of the
2001 peak of the default cycle models need to
overweigth impacts of stock markets to fit these
high default rates - less pronounced with
additional information
Non-parametric intensities (black) versus
semi-parametric baselines (blue) and
corresponding means (comparable to the constants
of log-linear models)
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Improving Traditional Models Lagged Information

• Lagged information increases likelihood by a
  factor between 2 to 10
• Lagged volatility has higher impact than current
  one,
• As well as past stock market information for
  non-investment issuers.

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Improving Traditional Models Lagged Information
(2)
After 2.5 years, unexplained variations for IG
default probabilities are not significant for the
improved model
Non-parametric intensities (black) versus
semi-parametric baselines (blue) and
corresponding means (comparable to the constants
of log-linear models)
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Improving Traditional Models Industry
Information

• No trivial structural factor to capture
  information relevant to a particular industry
  impacts of industry are often left out.
• Current works try to model persistence phenomena
  through contagion or applying a dependence
  structure on firm specific components.
• What are the real links of causalities we may
  think about the global economy and financial
  markets as a contagion vehicle between industries

• Can industry information provide more insights ?
• Aggregate default processes may provide
  information. We test a log-ACD
• model on durations between two defaults in a
  given industry.
• In this simple setting the intensity of default
  on an industry is inversely proportional to the
  expectation of the future duration until the next
  default.

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Improving Traditional Models Industry
Information (2)
Implied intensity for a firm from the
Telecommunication industry explosition at the
recession starting point
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Improving Traditional Models Industry
Information (3)
Implied intensity for a firm from the Automobile
and Aerospace industry intensities jumped up
before the recession
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The Story

• We showed that the largest part of deformations
  of intensities can be explained by the business
  cycle and financial market cycle.
• However starting conditions should not be ruled
  out from modelling as they potentially affect
  short and mid term intensities of default. In
  particular forward looking macro-economic factors
  bring information on future regime changes of the
  default cycle.
• But the story is not over default cycles are
  determined by other factors.
• Lagged Information improves traditional models (1
  months, 3 years).
• Industry conditions may partially fill remaining
  deficiencies, and should capture leading and
  persistence effects on the default cycle after
  global cycles at lower costs than contagion
  models.