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					May 2008

Estimation of the Loss Given Default (LGD)
– Retail Portfolio


  Eurobanking 2008 - Maribor
  Agnès Cuenot (agnes.cuenot@cnce.caisse-epargne.fr)
               Agenda

              Concept
              Methodology of estimation
              Results (just for illustration)
              Margin of conservatism
              Costs
              Conclusion




Eurobanking 2008 – LGD on retail portfolio
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               Introduction

              LGD: one of the three parameters (PD, LGD, EAD) in IRB approach for retail
                   >    Unexpected Loss and Minimum capital reserve required proportional to LGD

              Pragmatic approach
                   >    Just a calculation method
                   >    Neither statistical segmentation nor model
                                    In the underlying Merton model of Basel 2 formulas, only E(LGD) is expected.
                                     An individual estimation of LGD is not required.
                   >    Use of the historical data available
                   >    For retail portfolio




Eurobanking 2008 – LGD on retail portfolio
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               Concept

              Definitions
                   (DIRECTIVE 2006/48/EC, 14 June 2006, article 4)


                   >    „loss‟ means economic loss, including material discount effects, and material
                        direct and indirect costs associated with collecting on the instrument;

                   >    „loss given default (LGD)‟ means the ratio of the loss on an exposure due to the
                        default of a counterparty to the amount outstanding at default;



                                                            Loss
                                             LGD 
                                                     Exposure At Default


Eurobanking 2008 – LGD on retail portfolio
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               Concept

              Calculation
                   >    Basic loss : = EAD (exposure at default)
                               – recoveries (all over the period of default)
                               + increases of exposure (all over the period of default)
                   >    Economic loss: add discount effects and costs (human resources…)
                   >    Increases include
                                    drawing after default (not in the CCF parameter)
                                    costs




Eurobanking 2008 – LGD on retail portfolio
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               Concept

              Calculation

                                              R    *
                                                     j    C*
                                                            j             R* 
                                                                                      Rj
                                                                                                    C* 
                                                                                                                  Cj
                  LGD*  1 
                                             j 0
                                                                     cs
                                                                            j
                                                                                  1  r  j         j
                                                                                                              1  r  j
                                                    EAD

                                    where j >=0, at default, j=0 :
                                    EAD = exposure at default
                                    C*j = increases of period j, converted to current value (at default) with rate r.
                                    R*j = recoveries of period j, converted to current value (at default) with rate r.
                                    cs indirect costs (% of exposure) – set, same for all exposures




Eurobanking 2008 – LGD on retail portfolio
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               Concept

              Illustration on a theoretical case (overdraft on a bank account):
                                              May 2004      August 2005       December 2005   March 2006
                                                                                                              Time
                                  - 100
                                 - 130

                                                                                New            Loss: 130
                                 - 300
                                                                           withdrawal: - 30
                            Balance
                                             Default     Recovery: + 200


                   > Basic Loss = Exposure at default – recovery flow + increase flow                      LGDbasic= 43.3%
                                     = 300 – 200 + 30 = 130
                   > Discount effects (rate: 15%)
                     “Discounted” loss = EAD – converted to current value recovery flow                    LGDdiscounted= 50.7%
                                    + converted to current value increase flow
                                    = 300 – (200/1.15) + (30/1.15) = 300 – 174 + 26 = 152
                   > Indirect costs : 10 € for mail, 3% of EAD
                                                                                                           LGDfinal= 53.7%

                   >    Add a margin of conservatism if necessary
Eurobanking 2008 – LGD on retail portfolio
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               Concept

              Illustration on real data:

                   >    1st example – mortgage, default in December 2004, loss in January 2005


                            Current date             Unpaid amount              Capital         Recovery Flux Increase
                                                                                          Flux de                        Flux de Loss
                          Date Arrêté                Montant Impayé       CRD             recouvrement d'aggravation     pertes
                                   December 2004
                                        01-déc-04              17446                 0               0              0               0
                                     January 2005
                                        01-janv-05                    0              0               0              0           17446



                                                                  0
                                 LGDwithout indirectcosts  1         100 %
                                                                17446




Eurobanking 2008 – LGD on retail portfolio
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               Concept

              Illustration on real data :
                   >    2nd example – Mortgage, default in October 2003, last recovery in March 2004
                                    Discount rate : 7.5% (1 year), or 0.6% (1 month)
                                                                                           Flux de        Flux            Flux de
                            Current date
                           Date Arrêté                Unpaid amount
                                                      Montant Impayé       CRD   Capital         Recovery d'aggravation
                                                                                           recouvrement        Increase   pertes Loss
                                         01-oct-03
                                     October 2003                45444                 0              0               0                 0
                                   November 2003
                                        01-nov-03                45570                 0              0             126                 0
                                   December 2003
                                        01-déc-03                45570                 0              0               0                 0
                                     January 2004
                                        01-janv-04               45570                 0              0               0                 0
                                    February 2004
                                         01-févr-04              25570                 0          20000               0                 0
                                      March 2004
                                       01-mars-04                      0               0          25570               0                 0



                                                                             20000              25570            126
                                                                                                           
                                   LGDwithout indirect costs        1
                                                                        1.006 4 1.006 5                     1.006
                                                                                               45444

                                                                            44218 1226
                                                                   1                  3%
                                                                            45444 45444
Eurobanking 2008 – LGD on retail portfolio
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               Methodology

               Conversion to current value: choice of the rate
                   >    Not detailed in Basel 2 Framework
                   >    Choice of Group: real interest rate of the loan
                                    Coherence with IFRS
                   >    Conversion with a monthly step

              Horizon
                   >    Recovery observed on 10 years
                   >    All recovery flows coming after 10 years are considered as lost




Eurobanking 2008 – LGD on retail portfolio
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               Methodology

              Practical calculation – individual level
                   >    Division in 10 years of recovery
                                    Year 0 = 12 months following default
                                    Year 1 = 13 to 24 months following default
                                    …
                                    Year 9 = 108 to 120 months following default
                   >    Look at every period j, from 0 to 9 years, of
                                    Recovery flows, converted to current value (Rj*)
                                    Increase flows, converted to current value (Cj*)
                                    Amount still to recover at the beginning of period j (RRj*)
                                          – At default, j=0 and RR0 = EAD
                                          – After default            RRj = RRj-1 – R*j-1 + C*j-1
                                    marginal rate of recovery, on period j
                                          – j = (R*j - C*j) / RRj-1

                   >    Calculation of a rate of no recovery at 10 years (Kaplan-Meier estimator)

                                                                                   1   
                                                                                    9
                                       LGD  Rate of no recovery10 years                    j
                                                                                   j 0
Eurobanking 2008 – LGD on retail portfolio
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               Methodology

              Aggregation of flows – Vintage matrix
                   >    By category of product and by generation of default
                   >    construction of matrix giving the dynamic of recoveries for each generation of
                        default (A generation groups all loans or overdrafts in default at the same time, year,
                        quarter or month)
                                          0-1             1-2           2-3              3-4           4-5           5-6
         Génération     EAD
                                   R       C    P    R     C    P   R    C     P     R    C    P   R    C    P   R    C    P
             N-5
             N-4
             N-3
             N-2
             N-1
              N



                                      Still to recover              RR j  RR j 1  R*1  C*1 where RR0  EAD
                                                                                       j      j


                                       Marginal rate                       R*  C *
                               
                                                                    j 
                                                                            j     j

                                                                              RR j
                                      LGD                          LGD   1   j 
                                                                              j 0

Eurobanking 2008 – LGD on retail portfolio
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               Methodology

              Truncated and censored data


                            Truncated left           Default                                      End of default   Censored right


                       Default           End of default        Default                                                    End of default


                          Default                                                      End of default
                                                                                                                             Time
                                                                         Observation


                   >    The oldest generations aren‟t observed since default => left truncation
                   >    The youngest generations are still in default and not closed => right censoring
                   >    They take part to the calculation while they are observed




Eurobanking 2008 – LGD on retail portfolio
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               Methodology

              Advantages of the method:
                   >    All observations can take part to the estimation, including when data are
                        censured or truncated
                   >    Marginal rates can easily be “backtested”
                   >    An estimation of LGD depending of age in default can be produced:
                                    After j periods in default:

                                                   LGD j   1   k 
                                                                   k j


              Segmentation
                   >    By category of product, type of guarantee, age in default
                   >    Not a statistical model



Eurobanking 2008 – LGD on retail portfolio
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               Methodology

              Margin of conservatism
                   >    Reasons of adding a margin of conservatism
                                    Lack of robustness (low numbers of data)
                                    Temporal volatility (changing in organization, big amounts…)
                                    Economic cycle (downturn LGD)
                   >    Methods to treat these uncertainties
                                    Bootstrap
                                             – 1000 random draws
                                             – quantile : 95%
                                    Sampling (elimination of 5% of quarterly generations with the better marginal rate)




Eurobanking 2008 – LGD on retail portfolio
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               Methodology

           Bootstrap
                >    Recent method (1979 - B. EFRON) based on data simulation
                >    Sampling with replacement, where sample size is the same as the original
                     dataset. Each sample simulate new “stressed” data.
                >    Estimation of LGD on all these samples
                >    Distribution of empirical statistics, and quantiles giving a confidence interval.




                                                                              40% 45% 50%
                                                                           LGD of Private overdraft


Eurobanking 2008 – LGD on retail portfolio
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               Methodology

              Additional margin
                   >    For approximations done during estimation, intended for disappearing. They can
                        lead to errors in estimation, that is why a margin is added to regulatory margin of
                        conservatism.
                   >    Examples of approximations identified:
                                    Entity bias (estimation on 10 regional banks among 25)
                                    Loss registered in commercial agency, not available in data
                                    Exact Basel default not available in historical data, approximation with other close
                                     notions




Eurobanking 2008 – LGD on retail portfolio
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               Costs

              Costs entered:
                   >    From litigation department
                   >    3 types of costs:
                                    Human resources (70%)
                                    Customers (25%)
                                    Regular costs (5%)
              Methodology:
                   >    Average cost of litigation (by loan)
                   >    Average exposure at default (by loan)
                   >               Weight of indirect costs 
                                                                  Average cost
                                                                Average exposure


              Results (illustration for example)
                                                                       Average cost         Average exposure     Weight of indirect costs
                                     Private                                          100                 4000                      2.5%
                                     Professional                                     150                15000                      1.0%


Eurobanking 2008 – LGD on retail portfolio
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               Results

              Results
                   >    For confidential reasons, the results are changed…

                                                              Before margin of      With margin of        Final estimation (with
                                                              conservatism and   conservatism, without   margin of conservatism
                                                                indirect costs      indirect costs         and indirect costs)

                                             Overdraft              45%             47.3% (+5%)                  48.8%

                       Private               Mortgage               5%              5.5% (+10%)                    8%

                                             Personal loans         25%             26.3% (+5%)                  27.8%

                                             Overdraft              30%             37.5% (+25%)                 38.5%
                       Professional
                                             Loans                  20%              22% (+10%)                   23%




                   >    Big impact of indirect costs and margin of conservatism




Eurobanking 2008 – LGD on retail portfolio
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               Results

                 Illustration on theoretical data:
                   >    Marginal Recovery Rate on 10 years - Mortgage
                              Marginal       Marginal       Marginal       Marginal       Marginal       Marginal       Marginal       Marginal       Marginal       Marginal
                               rate 0         rate 1         rate 2         rate 3         rate 4         rate 5         rate 6         rate 7         rate 8         rate 9
                   1987   .              .              .              .              .              .              .              .              .              .
                   1988   .              .              .              .              .              .              .              .              .                       2%
                   1989   .              .              .              .              .              .              .              .                       0%             0%
                   1990   .              .              .              .              .              .              .                       0%             3%             1%
                   1991   .              .              .              .              .              .                       1%             1%             5%             1%
                   1992   .              .              .              .              .                       1%             2%             0%             1%             2%
                   1993   .              .              .              .                       3%             5%             3%             1%             1%             1%
                   1994   .              .              .                       3%             7%             4%             1%             1%             1%             2%
                   1995   .              .                       8%            16%             8%             8%             2%             1%             1%             1%
                   1996   .                      44%            12%             6%             6%             3%             3%             0%             1%             1%
                   1997           78%            27%            16%            12%             2%             5%             1%             1%             0% .
                   1998           75%            28%            25%            11%            10%             8%             2%             0% .              .
                   1999           80%            42%            13%            12%            10%             5%             3% .              .              .
                   2000           74%            22%            14%            15%             8%             7% .              .              .              .
                   2001           72%            34%            19%            26%             8% .              .              .              .              .
                   2002           80%            50%            25%            22% .              .              .              .              .              .
                   2003           80%            39%            25% .              .              .              .              .              .              .
                   2004           75%            30% .              .              .              .              .              .              .              .
                   2005           82% .              .              .              .              .              .              .              .              .
    total                         77%            35%            19%            15%             6%             5%             3%             1%             1%             1%
    cumulative "no
                                  23%            15%            12%            10%             9%             9%             9%             9%             8%             8%
    recovery" rate



Eurobanking 2008 – LGD on retail portfolio
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               Results

               Graphic illustration         90%
                                                                        Marginal rate by category par type
                                                                Taux marginaux de recouvrement of productde produit


                                             80%
                                             70%
                                             60%
                                                                                                                              CCE
                                                                                                                               Prof Overdraft
                                             50%
                                                                                                                              CDD
                                                                                                                               Priv Overdraft
                                             40%
                                                                                                                                Personal loan
                                                                                                                              CONSO
                                             30%
                                                                                                                                 Mortgage
                                                                                                                              IMMO
                                             20%
                                                                                                                              PRO Prof loan
                                             10%
                                             0%
                                                    0       1        2     3      4        5       6       7     8   9   10
                                                                           années depuis l'entrée en défaut
                                                                                     Years in default


                                                               Cumulative de of no recovery by category of product
                                                            Taux cumulés ratenon recouvrement par type de produit

                                             100%
                                              90%
                                              80%
                                              70%
                                                                                                                               Prof
                                                                                                                              CCE   Overdraft
                                              60%
                                                                                                                               Priv
                                                                                                                              CDD   Overdraft
                                              50%
                                                                                                                                Personal loan
                                                                                                                              CONSO
                                              40%
                                                                                                                                 Mortgage
                                                                                                                              IMMO
                                              30%
                                                                                                                                  Prof loan
                                              20%                                                                             PRO
                                              10%
                                               0%
                                                    0   2   4    6   8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
                                                                          trimestres depuis l'entrée en défaut
                                                                                  Quarters in default

Eurobanking 2008 – LGD on retail portfolio
                                                                                                                                                21
                Results

               Results by age of default


                                                 0      1     2     3     4     5     6     7      8      9

                              Overdraft        48.8%   70%   85%   90%   92%   95%   98%   99%    100%   100%
                              Mortgage          8%     35%   60%   80%   85%   90%   95%   97%    99%    100%
      Private                 Personal loans   27.8%   40%   55%   70%   80%   87%   91%   95%    98%    100%
                              Overdraft        38.5%   75%   80%   85%   90%   95%   97%   100%   100%   100%
      Professional
                              Loans            23%     55%   70%   75%   80%   85%   90%   96%    98%    100%




Eurobanking 2008 – LGD on retail portfolio
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               Conclusion

              Link with provisions
                   >    For exposures in default (with PD = 100%), comparison between LGD and
                        provisions, with impact on RWA
                   >    For all exposures, comparison between LGD and provisions, with impact on
                        capital
                   >    Interactions with accounts department
              Link with economic capital
                   >    Use of single factor models, like in Basel 2 framework
                   >    LGD still an fundamental parameter
                   >    May be adjusted (margin less conservative)




Eurobanking 2008 – LGD on retail portfolio
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