Diapositiva 1

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CreditPortfolioViewTM

• 
  
  IMEF
  (2006-2007), Risk Management
• 
  
  
  Dr. Tasca Paolo, June 2007
• 1. Introduction.
• Wilson T. (1997) articles describe a new
  practical method that can provide answers to the
  following main
• questions, by tabulating the exact loss
  distribution from correlated credit events
• What is the risk of a given portfolio?
• How do different macroec. scenarios (at regional
  an ind. sector level) affect the portfolios risk
  profile?
• What is the effect of changing the portfolio mix?
• How could risk-based pricing at individual
  contract and portfolio levels be influenced by
  the level of expected losses and credit risk
  capital?
• 2. What is CreditPortfolioView (CPV) ?
• Developed on 1997 by Thomas Wilson (on behalf of
  McKinsey Company), CPV is a instrument able to
• measure the portfolios credit risk modelling the
  relationship between the cycles of the economy
  and the credit
• risk. CPV is a discrete time multi-period model
  where default probabilities are conditional on
  the macro
• variables which to a large extent drive the
  credit cycle in the economy.
• 3. Differences from other approaches.

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• 3) The tabulated loss distribution are
  conditional on the current state of the economy,
  rather than being based
• on unconditional or n-years averages that do not
  reflect portfolios true current risk. Specific
  country and
• industry influences are recognised on the basis
  of empirical relationship.
• 4. The logic behind CPV.
• The logic behind CPV follows this two step
  approach. Firstly there is a split of the
  customers-portfolio in
• function of the geo-industry belonging of the
  counterparts. And secondly there is a simulation
  of the joint
• distribution of Probability of Default (DP) and
  credit migration conditionally to the values
  assumed by
• macroeconomic indices considered particularly
  significant to estimate the credit merit.
• This logic takes inspiration from the realization
  of 5 stylized facts
• Diversification helps to reduce loss uncertainty,
  all else being equal.
• There exist sostantial loss uncertainty for even
  the most diversified portfolios.
• The PDs are strongly influenced by the tendency
  of economic cycle. These macroeconomic factors
  also influence in the same way the probability of
  credit migration. In other words, credit cycles
  follow business cycles closely.
• The influence of the macroeconomic factors apply
  not only to each stand-alone country, but also to
  different sectors inside the considered Country.
• Different sectors react in different ways to a
  change in the tendency of economic cycle. CPV is
  a flexible instrument. Beside the fact that some
  macroeconomic factors are directly input by CPV
  (i.e. rate of GDP growth, rate of unemployment,
  etc..). Any other macroeconomic factors
  considered particularly important to influence
  the credit rating of the counterparts, can be
  input in the model by the user.
• 5. How to derive the portfolio loss distribution
  with this multifactor systemic risk model ?

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• Generally are taken into consideration, three
  states of the world
• Economic expansion characterized by a GDP growth
• Economic average characterized by a GDP growth
  equal to zero
• Economic recession characterized by a GDP
  reduction
• 5.2 Determine the conditional probability of
  default for each segments
• Based on this state of the economy, it will be
  calculated the average speculative default rate
  for each
• country/industry segment. It is necessary to
  assign to each scenario a probability of
  realization, in order to
• develop at the end an unconditional loss
  distribution by convolution. All the counterparts
  in portfolio, are
• subdivided in clusters which represent different
  industry segments or regional areas. By means of
  a mapping
• process, each cluster is declared dependent on a
  set of macroeconomic factors. Obviously different
  clusters
• can be dependent on the same macroeconomic
  factor. The dependence on the same macroeconomic
  factors
• and/or the correlation between different factors
  are able to explain the correlation between the
  counterparts
• coming from different clusters. The initial
  hypothesis, to develop the model, is to express
  for each j-cluster,
• the DP of the counterparts using a Logit
  functional form as follow

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A Logit formulation such that, can be seen as a
multifactor model able to determine the
conditional DP for a specific industry segment of
the economy. The terms of the vector Xj,t, can be
associated to the systemic risk part. Whereas,
the random term ?j,t can be associated to the
specific risk part effecting the sector j. To
model the development of the individual
macroeconomic time series describing the
economys health, Wilson used a set of
auto-regressive equations of order two (AR2).
More precisely it is assumed that the dynamic of
each macroeconomic factor is governed
by Where Xj,i,t is the value of the ith
macroec. variable in the jth segment at time t
ai,j are the three constants to be estimated for
each of the macroeconomic variables. For every
country-industry-segment up to three macro
variables are identified as the most suitable
exogenous factors ej,i,t is the error term
assumed to be iid N(0,sj) Once the
parameters, have been estimated, the error terms
e,j,i,t can be considered as the forecast
surprises for the t-step ahead. Since they are
correlated, it is necessary to estimate the joint
covariance matrix. So, S is the (ji)x(ji)
covariance matrix of macroeconomic variable
forecast errors (?) and segment-specific
speculative default rate shocks (e).
Summarizing, to obtain the speculative default
rate for each country/industry segment we can
introduce the following equation system Where
the vector (ji)lt1 vector of innovations ?
affecting the idiosyncratic risk components for
each segment and the shock e affecting the
macroeconomic variables for each factor, is given
by
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5.3 Computation of transition matrixes for each
cluster j After having simulated the speculative
default rate for each country/industry segment j,
CPV uses these forecasts to build a transaction
matrix (for each segment and for any time
horizon) linked to the state of the world (the
economic cycle), by using the equation Mt
?i1..t M(SDPt/FSDP) where Mt represents the
t-year conditional cumulative rating distribution
for a given future path of the speculative
default rates. M(SDPt/FSDP) is the conditional
one-year rating transition matrix dependent upon
the speculative default rate. SDPt is the
realized speculative default rate and FSDP is the
average speculative default rate. 5.4 Credit
events simulation Using the equation Mt
?i1..t M(SDPt/FSDP) and the simulated
speculative default rates, it is possible to
calculate the rating distribution for any initial
rating at different points in time in the future,
conditional on the simulated macroeconomic cycle
over that time horizon. Given the simulated
default probability distribution for each of the
segments, by rating, it is possible to tabulate
several distribution parameters such as the
expected conditional DP and the maximum possible
DP for each segments. 5.5 Derivation of the
portfolio loss distribution conditional to each
scenario The conditional expected cumulative DP
could represent the conditional expected
portfolio loss rates only under these restrictive
assumptions 1) Diversified portfolio 2) The
actualization factor of the exposure is not
considered 3) The exposure at default is
deterministic and constant for all the time 4)
The recovery rate 0. 5.6. Derivation of the
unconditional portfolio loss distribution 5.6.1
Undiversified portfolios The conditional loss
distribution in the simple two-counterparty (A
and B) is tabulated by recognising the existence
of possible states of the world. And
conditionally to these states there are only four
default cases A defaults, B defaults, A and B
default or neither default. The conditional
probability of each of these loss events for each
state of the economy is calculated by convolution
or aggregating each positions marginal
loss distribution under the assumption of
independence for each state.
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• The implicit assumption underlying the
  calculation of the conditional loss distributions
  is that all default and
• migration correlations are fully determined by
  the systematic risk model.
• So, to tabulate the unconditional portfolio loss
  distribution, it is follow a two step approach
• Tabulate the cond. portfolio loss dist. for each
  state of the world (given that counterparty
  defaults and credit migrations are independent),
  conditional on that state of the world.
• Aggregation of these cond. loss distributions to
  an unconditional loss dist. by recognising that
  each was generated by an independent, random draw
  form the possible states of the world.
• 5.6.2 Diversified portfolios.
• CPV is consistent with a quite large logic, used
  by others uni/multifactors models (eg CAPM), that
  can be
• summarized as follow. It is possible to diversify
  away the idiosyncratic risk, by increasing the
  number of
• counterparties in each segment, leaving only
  systematic risk. As we diversify our holdings
  within a particular
• segment, that segments loss distribution will
  converge to the loss distribution implied by the
  segment index.
• 6. Variable exposures, discounted losses and
  liquid assts.
• The derivation of CPV introduced till now,
  doesnt take into consideration that the risks
  exposure amount can
• change over the time. This fact cannot be
  neglected when the portfolio is composed by
  liquid instruments with
• a value changing continuously. Moreover, till now
  the model does not consider the actualization
  factor of the
• losses. Practically speaking, these limitations
  are not welcome. So it is necessary to introduce
  the
• methodology followed by CPV to take into
  consideration these issues. Considering that, the
  financial value of
• a loss changes according to the time the default
  occurs, to know the real value of a future
  potential loss it is

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7. Variable recovery rates and country
defaults Till now we have assumed that the
recovery rate (RR) was a known constant dependent
only upon the rating of counterparty. Indeed,
the actual amount that could be recovered in the
event of default is neither constant, nor is it
dependent solely on the rating of the
counterparty. So, a way to model the impact of
random RR is to simulate jointly defaults and
recovery rates. It is necessary first specify a
recovery distribution for each of the relevant
recovery classes. For every simulation of the
systematic risk factor then, it necessary to take
a random draw on this recovery distribution to
tabulate the exposures loss in the event of
default. This technique implicitly assumes that
random RR can be drawn independently from one
another across different macroeconomic scenarios
and counterparts. This assumption doesnt fit
well in the following two cases. First, when we
are tabulating potential losses in the event of
default arising form trading exposure. And
second, for certain asset classes (ie mortgages)
the RR is highly negatively correlated with the
DP. 8. Summary and Conclusions
Risk Type Migration Risk and Default Risk.
Exposure at default Market value/Account
value. Recovery Rate Stochastic. Output
Default probabilities and Portfolio Loss
distribution. Counterparts correlations
Simulating the values of macroec. factors in t1,
the hypothesis of conditional independence
between counterparts permits to obtain the joint
distribution of the random variables which
represent the credit merit of counterparties and
so the portfolio loss distribution conditional to
the factors at time t1. So, the correl.
structure between counterparties is implicit in
the multifactor model describing the migration
and default probabilities. According to this
approach, the empirical correl. between default
rates are due to a changing in the conditional DP
of the single counterparts.
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• Sensibility to the economic cycle The economic
  cycle directly determines the Default
  Probabilities and the
• migration matrices.
• Advantages
• Capacity to trace back the systemic factors
  affecting the portfolio risk profile.
• CPV is particularly suited for macroeconomic
  stress testing as it explicitly models credit
  risk in dependence of macroeconomic variables.
• CPV allows its users many degrees of freedom for
  data entry in such a way to enable them to modify
  diverse model components.
• Disadvantages and limitations
• Likely complex procedure to estimate the
  coefficients ß for each industry segments.
• The derivation process of the conditional
  migration matrix is involved by an uncertain
  confidence level. Sufficient data are needed,
  including reliable default data for each country
  and industry sectors, to calibrate the model.
• Another limitation of the model is the ad-hoc
  procedure to adjust the migration matrix starting
  form an unconditional Markov transition matrix
  calculated using rating agency data, own
  experiences or JP Morgans estimated transition
  matrix. It is not clear that the proposed
  methodology performs better than a simple
  Bayesian model where the revision of the
  transition probabilities would be based on the
  internal expertise accumulated by the credit
  department of the bank, and the internal
  appreciation of where we are in the credit cycle
  given the quality of the banks credit portfolio.
• The market value of most credit instruments
  remain difficult to determine. The idiosyncratic
  nature of most credit instruments, implies that
  they are not easily tradable and that there are
  no current or historical market prices available
  for them. CPV as others Credit risk models, get
  around this lack of information by looking at
  credit ratings.
• Bibliography
• Wilson T. (1997), Portfolio Credit Risk (I),
  Risk Primer, Vol 10, n.9, September
• Wilson T. (1997), Portfolio Credit Risk (II),
  Risk Primer, Vol 10, n.10, October