ESTIMATING CONSERVATIVE LOSS GIVEN DEFAULT

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					         ESTIMATING CONSERVATIVE LOSS GIVEN
                      DEFAULT

                           Gabriele Sabatoa,# and Markus M. Schmid b

                       a
                           Group Risk Management, ABN AMRO, Gustav Mahlerlaan 10,
                                 1000 EA Amsterdam, The Netherlands
               b
                   Swiss Institute of Banking and Finance, University of St. Gallen, CH-9000
                                        St. Gallen, Switzerland




                                                 Abstract


        The new Basel Capital Accord (Basel II) is going to be embedded in the risk
management practices at many financial institutions shortly, but the academic and financial
world are still discussing about several topics related to the new capital adequacy rules. One
of the most important and prominent examples among these topics is the link between loss
given default (LGD) and the economic cycle. If this link exists, which is suggested by an
extensive literature, the Vasicek model used in the Basel Accord does not take into account
systematic correlation between probability of default (PD) and LGD and, to compensate for
this deficiency, downturn LGD estimates are required to be used as an input to the model.
However, often banks lack an extensive LGD data history covering a full economic cycle
especially for retail assets. In this paper, we propose a simple and realistic solution that can
be adopted in order to derive conservative estimates of LGD. Using data covering a set of
retail loans (secured and unsecured), we investigate the relation between LGD and the credit
cycle over the available period. In contrast to the extensive literature on the topic, our results
show that when ultimate recoveries are used, the linkage between LGD and the credit cycle
is often insignificant (e.g. for two out of three retail asset classes). This implies that the
conservatism required by the supervisory authorities should not always be added to LGD
estimates used to estimate banks’ capital requirements.



JEL classification: G21; G28
Keywords: Loss given default; Basel II; Bank capital requirements; Credit risk




________________________________
#
 Corresponding author.
Group Risk Management, ABN AMRO, Gustav Mahlerlaan 10, 1000EA Amsterdam, The
Netherlands. Tel.: +31-651399907; E-mail address: gabriele.sabato@nl.abnamro.com.
    1. Introduction


       The Basel II Framework Document issued by the Basel Committee in June
2006 requires banks to use estimates of Loss Given Default (LGD) that reflect
“economic downturn conditions” in order to be compliant with the Advanced
Internal Rating Based (A-IRB) requirements. The Framework Document describes
approaches to quantify these “downturn LGDs” in general terms, but deliberately
leaves specific details of the quantification process for supervisors to develop in
collaboration with the banking industry. The requirement that IRB banks use
economic-downturn LGD is intended to ensure that Pillar I capital requirements
properly reflect material systematic volatility in credit losses over time.1 To the
extent that recovery rates on defaulted exposures may be lower during economic
downturn conditions than during "normal" conditions, a capital rule aimed at
guaranteeing sufficient capital to cover realized losses during adverse circumstances
should reflect this tendency.
       Many academic papers (e.g., Izvorsky, 1997; Altman et al., 2005; Covitz and
Han, 2005; Acharya et al., 2007) have demonstrated that negative economic cycles
and high default periods carry with them higher loss-given-default expectations than
if the probability of default (PD) and recovery rate variables were considered
stochastic but independent. However, at the same time, these studies rarely use data
about ultimate recoveries (i.e., the total amount recovered after a sufficiently long
recovery period typically set equal to one or two years) and were never applied to
retail portfolios. The recoveries considered in these studies were generally the ones
that occur during the days immediately after the default event. However, banks need
to use ultimate recoveries when estimating LGD for regulatory capital purposes and
this can lead to significantly different conclusions than those reported in prior
studies.2
1
  The Basel Capital Accord (2006) is divided into three Pillars. Pillar I describes how to calculate
banks’ minimum capital requirements. Pillar II provides the key principles of the supervisory review
process that should insure that banks have adequate capital to support all the risks in their business
and use better risk management techniques to monitor and manage these risks. Pillar III defines a set
of disclosure requirements for banks which will allow market participants to have a more complete
picture of the capital adequacy of the institutions.
2
  LGD is equal to (1- recovery rate).
       Criteria for the quantification of LGD are described in paragraph 468 of the
Framework Document.3 These criteria specify that LGD cannot be less than the
long-run default-weighted average loss given default calculated based on the
average economic loss of all observed defaults within the data source for that type of
facility or pool.4 In addition, a bank must take into account the potential for the LGD
of the facility/pool to be higher than the default-weighted average during a period
when credit losses are substantially higher than average. However, it is also stated
that for certain types of exposures, loss severities may not exhibit such cyclical
variability and LGD estimates may not differ materially (or possibly at all) from the
long-run default-weighted average.
       In the Accord (paragraph 468), three generic methodologies to estimate
downturn LGD are presented:
      • averages of loss severities observed during periods of high credit losses;
      • forecasts based on appropriately conservative assumptions;
      • other similar methods.

      The first proposal seems to be the easiest one to implement, when data is
available. The problem is that LGD data is generally sparse and there is very limited
industry experience with regard to LGD estimates. Downturn LGD estimation based
on historical data is currently not possible for many banks because of the short time
periods available (e.g., less than 3 years) or for the lack of an economic downturn
during the available period.
       In general, concerns have been raised by banks about how to identify and
define an economic downturn.5 Bruche and Gonzalez-Aguado (2006) compare credit
downturns and recession periods and show that the credit cycle is related to, but
distinct from the macroeconomic cycle. This important result explains why previous
studies (e.g., Altman et al., 2005; Gaspar and Slinko, 2005) have found that
macroeconomic variables explain only a small portion in the variation of recovery



3
  We explain the process used to estimate the default weighted average LGD in Appendix A.
4
  The Basel Capital Accord requires retail assets to be rated for PD and LGD by pool and not at
facility level.
5
  See for example Risk Management Association (September 2005).
rates and suggests that banks should not rely exclusively on macroeconomic
variables to estimate downturn LGD.
      The lack of clear guidelines on this topic can lead to very different approaches
being implemented across banks and countries, and significant effects on the level of
capital requirements. As many authors have shown (e.g., Saurina and Trucharte,
2004; Altman and Sabato, 2005), Basel II Advanced-IRB capital requirements are
highly sensible to LGD values in particular for retail asset classes. For this reason, a
specific monitoring task has been assigned to the national supervisors in order to
ensure a certain level of consistency in each country.6
      The second proposal gives banks the possibility to estimate downturn LGD
using forecasts based on appropriately conservative assumptions. This can be
considered as an appropriate solution when historical data is not available. However,
the lack of data also affects the ability of financial institutions to forecast LGD.
Linking forecasts to conservative assumptions makes this suggested methodology
very similar to stress testing, where future forecasts are only based on assumptions
on likely economic scenarios.
      The contribution of this study is twofold. First, we analyze the link between
recovery rates and the credit cycle for retail assets over a period of almost four
years. Differently from most of the available studies on this topic, we calculate LGD
using ultimate recoveries observed one year after the default event and we analyze
them at regulatory asset class level (such as prescribed by Basel II).7 In contrast with
the existing literature, we find that the adverse dependencies between default rates
and recovery rates are insignificant for two out of three asset classes ("small and
medium sized enterprises retail asset class" and "qualified revolving exposures"). As
such, we show that in many cases banks will not be obliged to calculate and apply
conservative LGD parameters to estimate their capital requirements.
      Second, we investigate the issue of estimating conservative LGD for retail
exposures and propose a solution for the common lack of retail recoveries data to

6
  We are aware of several central banks applying consistent methodologies to estimate downturn
LGD at country level. However, these methodologies may differ quite significantly between
countries. Considering the relevant impact of LGD on bank capital requirements, we believe that
these differences may cause competitive advantages for banks as Hannan and Pilloff (2004) suggest.
7
  See Basel Committee on Banking Supervision (2005).
cover a full credit cycle (including an economic downturn). Specifically, considering
the significant impact of a collateral on the LGD value, two different techniques are
proposed for secured and unsecured exposures. First, we stress the value of the
collateral and the cure rate in order to find the expected increase of the LGD in a
downturn period. Second, we use the existing correlation between default rates and
recovery rates, if any, to quantify the amount of conservatism to be added to the
LGD during a period of significantly above-average default rates (i.e., downturn
period). Finally, we test both approaches on data of the retail portfolio of a large
international bank in order to underscore our conjectures empirically.
      The remainder of the study is structured as follows. Section 2 provides an
overview of the existing literature on the linkage between recovery rates and the
economic cycle. In Section 3, we present our approach for unsecured and secured
exposures, respectively. In Section 4, we draw our conclusions.



 2. Review of the literature

      In the standard rating-based credit risk model developed by Gupton, Finger
and Bhatia (1997), it is assumed that recoveries on defaulted exposures are random
outcomes, independent of the default event. A similar independence assumption is
made in the models of Jarrow et al. (1997), Kijima and Komoribayashi (1998) and in
the Vasicek model (Vasicek, 2002) used in the new Basel Accord. However, if
realizations of recoveries are low exactly at times when many firms default, the
assumption that recoveries are independent of default rates or constant would result
in an underestimation of credit risk.
      There has been increasing support in the empirical literature that both PD and LGD
are correlated. Frye (2000) shows that during recessions recovery is about one third
lower than during expansions. In his study, he examines data on U.S. corporate bonds
and finds significant synchrony between default and recovery. Frye applies a subjective
10% increase on default rates and uses a previously developed regression model to
estimate recovery rates. Results show that recovery falls by 25% in absolute terms from
its normal-year average. However, it is worth to remember that these results are obtained
using recoveries measured few days after the default and not ultimate recoveries.
      Hu and Perraudin (2002) analyze the dependence between recovery rates and
default rates using Moody’s historical bond market data between 1971 and 2000.
Recovery rates are defined as the ratio of the market value of the bonds to the unpaid
principal, one month after default, averaged across the bonds that default in a given
quarter. Default rates are defined as the fraction of bonds that default in a quarter to
the number of bonds rated at the start of the quarter. Having filtered the recovery
data to allow for variation over time in the pool of borrowers rated by Moody’s, they
study simple measures of correlation between aggregate quarterly default and
average recovery rates. These correlation measures suggest that recoveries tend to be
low when default rates are high. Their study concludes that typical correlations for
post 1982 quarters are -22%. If the period 1971-2000 is considered, typical
correlations are -19%. Again, it is important to note that this study is not based on
ultimate recoveries.
      Altman et al. (2005) argue that the markets for defaulted securities have limited
capacity (i.e., the demand for these securities is not perfectly elastic as standard asset
pricing theory would suggest). Specifically, when the supply of defaulted securities is
high, they trade at lower prices. If recovery is measured as the price of a defaulted
security as a fraction of par (as is standard practice when ultimate recoveries are not
used), then of course this would reduce recoveries in times characterized by large default
rates. Consistently, when regressing recovery rates on the aggregate default rate as an
indicator of the aggregate supply of defaulted bonds, the authors find a negative
relationship. However, when macroeconomic variables such as GDP growth, for
example, are added as additional explanatory variables, they exhibit low explanatory
power for the recovery rates.
      In a recent study, Acharya et al. (2007) use data on defaulted firms in the U.S.
over the period 1982-1999 to investigate whether industry-wide distress affects
creditor recoveries. They show that creditors of defaulted firms recover significantly
lower amounts in present-value terms when the industry of defaulted firms is in
distress. In line with Shleifer and Vishny (1992), they show that creditors recover
less if the industry is in distress and non-defaulted firms in the industry are illiquid
(“fire sales” effect), particularly if the industry is characterized by assets that are
specific (i.e., not easily redeployable by other industries) and if the debt is
collateralized by such specific assets. Acharya et al. (2007) use the prices of
defaulted securities at the time of emergence from default or bankruptcy discounted
up to the time of default to measure recoveries. This definition of recoveries is
closer to the one of ultimate recoveries, but the interval between the default and the
recoveries’ measurement is still too small on average to consider them as ultimate
recoveries.



 3. Conservative LGD estimates


 3.1 Economic Downturn definition

      As outlined in Section 2, we have found that the definition of economic
downturn may vary quite substantially from study to study. The most helpful source
in order to identify an appropriate definition of downturn conditions is Basel
Committee on Banking Supervision (2005). This document helps banks to interpret
paragraph 468 of the Basel Accord and describes the process that should be
followed in order to asses the effects, if any, of economic downturn conditions on
recovery rates. The first step describes how to identify appropriate downturn
conditions.
      Characteristics of economic downturns are different for retail and non-retail
exposures. Wholesale portfolios are more strictly linked to the macroeconomic cycle
than retail portfolios, but the credit cycle is related to, but distinct from the
macroeconomic cycle (e.g., Bruche and Gonzalez-Aguado, 2006). Accordingly,
periods of negative GDP and elevated unemployment rates can help to identify
downturn conditions, but the effect on recoveries can be lagged.
      We believe that the best approach to identify a downturn period for retail
exposures is the one based on observed historical default rates. Periods in which
observed historical default rates have been elevated can be associated with a
downturn period for the specific portfolio. However, we see two major issues with
this approach:
     • which aggregation level for the exposures should be used (asset class,
        product, pool) and,
     • which default rates should be classified as significantly above “normal” or
        average.

       The answer to the first question is provided in Basel Committee on Banking
Supervision (2005) where it is stated that at a minimum, the bank should identify
separate downturn conditions for each supervisory asset class.8 However, it is also
pointed out that a greater granularity in defining downturn conditions should result
in more conservative LGD estimates. Indeed, the bank may identify downturn
conditions at a more granular level if such an approach is more risk sensitive.
       Possible solutions to the second issue are not addressed in Basel Committee on
Banking Supervision (2005). Therefore, the bank needs to set internal policies to
ensure a common definition of downturn conditions for each retail portfolio across
the different business units. The minimum length of the period, in which observed
default rates are higher than the mean rate, and the minimum distance from the mean
required as to consider an observed default rate as “significantly high”, should be
clearly defined.


    3.2 Methodologies to estimate conservative LGD

       The academic and financial world have paid special attention to
methodologies for calculating downturn LGD estimates during the last years. The
central question is how to calculate a downturn LGD when data of an economic
downturn is not available. A number of solutions with large differences in the level
of complexity have been proposed. However, the first issue to be addressed is
whether it is really necessary to estimate a downturn LGD or whether the long-run
default-weighted average LGD is sufficient.


8
  For retail exposures, supervisory asset classes are the following three: residential mortgages,
qualified revolving exposures, and other retail exposures.
      Basel Committee on Banking Supervision (2005) states that the LGD
estimates may be based on long-run default-weighted average loss rates if no
material adverse dependencies between default rates and recovery rates have been
identified. Hence, downturn LGD has to be estimated only for portfolios (or asset
classes) for which a significant correlation between default rates and recovery rates
has been found. Consequently, at the outset possible adverse dependencies (i.e., high
negative correlation) between default rates and recovery rates have to be identified.
While the appropriate significance level of the correlations may be open to
discussion, it is conventional to consider a correlation higher than (+/-) 10% to be
significant.
      Once the asset classes for which downturn LGD needs to be estimated are
identified, the next step is to choose the methodology to be used for calculating
LGD estimates which are consistent with downturn conditions. The existing
literature offers some guidance on how to address this problem. An interesting
example of a very simplistic technique is proposed in the “Advanced Capital
Adequacy Framework”.9 Although the U.S. agencies encourage banks to develop
internal LGD estimates compliant with what is required by the Advanced IRB
approach, they are aware that it may be difficult for banks to produce internal
estimates of LGD that are sufficient for risk-based capital purposes. The main
reason is that LGD data is sparse and there is very limited industry experience with
incorporating downturn conditions into LGD estimates. Accordingly, the agencies
suggest a linear supervisory mapping function that should be used by banks to
transform their long-run default-weighted average LGD into downturn LGD. The
proposed function leads to a higher correction in the value of downturn LGD, the
lower the value of LGD, and is defined as follows (see Figure 1):


      DLGD=0.08+0.92*ELGD
      where:
        DLGD= downturn LGD
        ELGD= long-run default-weighted average LGD

9
 Document published on the 5th of September 2006 and available on the Federal Reserve website
(www.federalreserve.org).
      While this approach provides a very simple solution for banks to calculate
downturn LGD, the adjustment is very crude as there is only one formula for each
asset class or facility.



  Figure 1. Expected versus Downturn LGD
  This figure shows the relationship between expected and downturn LGD as based on the
  formula proposed in the “Advanced Capital Adequacy Framework”. On the x-axis, the expected
  LGD (i.e., long-run default-weighted average LGD) is shown. On the y-axis, the Downturn
  LGD is calculated as DLGD= 0.08+(0.92*ELGD).

                               Expected vs. Downturn LGD

            100%
             90%
             80%
             70%
             60%
     DLGD




             50%
             40%
             30%                                                   ELGD         DLGD
             20%
             10%
              0%
                   0%   10%   20%   30%   40%   50%    60%   70%   80%    90%   100%

                                                ELGD




            An alternative approach is proposed by Miu and Ozdemir (2005). They
analyze the possibility of estimating downturn LGD by incorporating the observed
correlation between PD and LGD. In this way, they correct the actual LGD
estimates by adding a cyclical ingredient. Their study shows that even at a moderate
level of the PD/LGD-correlation, the average LGD increases by about 37%. It is
important to point out that they find a lower mark-up for secured loans than for
unsecured.
     3.3 Estimating conservative LGD: our approach

         3.3.1    Unsecured exposures

         For unsecured exposures, taking into account the approach presented by Miu
and Ozdemir (2005), we propose to stress test historical average default rates (PD)
for each supervisory asset class (or product) and calculate the shift during the
stressed scenario. Then, using the correlation to correct the estimated default rate
shift, we can calculate the shift that LGD would experience during a period of
higher default rates (economic downturn). The underlying idea is that if we can
observe how PD and LGD move together (by estimating their historical correlation),
we can predict the effect that an increase in default rates would have on LGD.
Accordingly, if a negative correlation is found, there will be no need to estimate a
downturn value for the loss given default.
         We are aware that the correlation between PD and LGD is likely to be higher
during downturn periods. However, lacking appropriate data, we neglect the
potential effect that downturn periods may have on the PD/LGD-correlation. This
shortcoming of our dataset is mitigated by the fact that retail products have a low
correlation with the business cycle.
         We use data on retail loans over the period from July 2002 to March 2007 and
calculate default rates (PD) and LGD for 12 one-year periods. For each consecutive
period, we have 9 months overlapping with the previous period (see Table 1).10


     Table 1. Consecutive observation periods
     This table shows the consecutive observation periods that have been used to estimate PD and
     LGD. In order to have more observations, for each consecutive period there are 9 months
     overlapping with the previous period. The data cover the period from July 2002 to April 2006.
                                    From                       To
             Period1                1 July 2002                30 June 2003
             Period2                1 October 2002             30 September 2003
             Period3                1 January 2003             31 December 2003
             Period4                1 April 2003               31 March 2004
             Period5                1 July 2003                30 June 2004
             Period6                1 October 2003             30 September 2004
             Period7                1 January 2004             31 December 2004
             Period8                1 April 2004               31 March 2005
             Period9                1 July 2004                30 June 2005
             Period10               1 October 2004             30 September 2005
             Period11               1 January 2005             31 December 2005
             Period12               1 April 2005               31 March 2006


10
     We choose this approach in order increase the number of observations for our statistical analysis.
          For each period, the default rate (PD) is given by the number of clients
defaulted during the selected 12 months divided by the total number of clients over
the same period. The LGD for the same period is calculated by comparing the
accrued losses one year after the default for each contract defaulted in the selected
period with the outstanding balance at the default. Hence, our last observation period
ends in March 2006 in order to end up with a one-year period to observe the actual
loss (March 2007).11
          If default rates and recovery rates are correlated, we expect to observe a higher
LGD in the periods with higher default rates and the opposite. We calculate the
correlation between the PD and LGD observations over the 12 available periods. In
addition, we calculate the average PD and standard deviation during the complete
time interval (about four years). Then, we stress the PD to estimate the percentage
increase that would be experienced during a stressed scenario. We define this
percentage as PD stressing factor. We estimate the LGD stressing factor by
multiplying the PD stressing factor by the PD/LGD correlation:

                               n          
                               ∑ PD / n  + σ
                                      i      n
     PDStres sin g Factor   = i =1        
                                                                                       (1)
                                    n
                                    ∑ PD / n
                                         i
                                  i =1

          where n is the number of observations and σ is the standard deviation of the
observed default rates. Hence, the PD stressing factor is equal to the average PD
plus one standard deviation divided by the average PD. The LGD stressing factor is
obtained by multiplying the PD stressing factor by the correlation between PD and
LGD (ρPD/LGD):


       LGD Stres sin g Factor = PDStres sin g Factor * ρ PD / LGD                      (2)




11
     See Appendix A for more details on LGD estimation.
      Although this analysis can be also conducted at the product level, we suggest
to analyze correlations at asset class level in order to apply a uniformly consistent
approach per each asset class.12 However, we split the “Other Retail” asset class
(ORE) between private individuals (ORE-PI) and small and medium sized
enterprises (ORE-SME), considering the significant difference in the risk profile of
these clients.
      The results of the analysis show a high and positive correlation of 0.77 for
ORE-PI and a negative correlation for ORE-SME (-0.12) as well as Qualified
Revolving Exposures (QRE) (-0.84), suggesting that the latter two classes do not
need a downturn LGD (see Figure 2).
      Applying the approach described before and using a stress scenario with one
standard deviation added to the mean, we find a PD stressing factor of 33%. This
factor needs to be multiplied by 0.77 (PD/LGD correlation for the ORE-PI asset
class) in order to calculate the LGD stressing factor (26%). Finally, we find an
average increase in the one-year LGD for the entire class of 17%.13 This factor
should be added to each one-year product LGD within the ORE-PI class in order to
calculate the product/pool level downturn LGD.
      To avoid the possibility of getting a LGD higher than 100% and to ensure a
larger increase for lower LGDs (where the biggest shift can be expected in case of a
downturn), we propose the following formula:

      DLGD= ASAC+[(100-ASAC)*ELGD]                                                             (3)
        where:
        DLGD= downturn LGD
        ASAC= average expected LGD increase for the asset class
        ELGD= long-run defaulted weighted average per pool

This formula for the selected ORE-PI portfolio equals:

        DLGD= 0.17+ (0.83*ELGD)



12
  This solution is the one recommended by the Basel Committee (2005).
13
  The LGD stressing factor (26%) has to be applied to the average LGD of the asset class (67%) in
order to calculate the specific LGD mark-up to be added (17%).
Figure 2. PD and LGD correlation per asset class
This figure shows the PD and LGD distribution over the 12 consecutive periods that have been used
for the analysis. The graphs present the retail asset classes, i.e., Other retail (divided into PI and
SME) and Qualified revolving exposures.


                         Other Retail Exposures - PI                                                                          Other Retail Exposures - SME
                                                                       0.8                                                                               PD                LGD
                               PD                 LGD
                                                                                                                                                                                      0.9
                                                                       0.75


                                                                       0.7                                                                                                            0.85




                                                                                 LGD




                                                                                                                                                                                             LGD
   PD




                                                                                                    PD
                                                                       0.65
                                                                                                                                                                                      0.8

                                                                       0.6

                                                                                                                                                                                      0.75
                                                                       0.55


                                                                       0.5                                                                                                            0.7
         1     2    3     4    5    6    7    8    9    10   11   12                                     1       2        3        4         5      6    7    8   9   10    11   12

                                   Periods                                                                                                         Periods



                                                             Qualified Revolving Exposures

                                                                                           PD                    LGD
                                                                                                                                            0.9



                                                                                                                                            0.85



                                                                                                                                                   LGD
                                              PD




                                                                                                                                            0.8




                                                                                                                                            0.75




                                                                                                                                            0.7
                                                    1   2    3    4          5         6        7    8       9       10       11       12

                                                                                 Periods




  Figure 3. Expected versus Downturn LGD for ORE-PI asset class
  This figure shows the relation between the expected and the downturn LGD based on the
  formula proposed in this paper for the analyzed ORE-PI asset class. On the x-axis, the expected
  LGD (i.e., long-run default-weighted average LGD) of the ORE-PI is shown. On the y-axis, the
  Downturn LGD for the ORE-PI asset class is calculated as DLGD= 0.17 + (0.83*ELGD).
                                                    Expected vs. Downturn LGD

               100%
                   90%
                   80%
                   70%
                   60%
         L D
        DG




                   50%
                   40%
                   30%                                                                                                                 ELGD                   DLGD
                   20%
                   10%
                   0%
                              0%        10%       20%    30%       40%                 50%           60%             70%               80%           90%      100%

                                                                                   ELGD
       Figure 3 shows that the downturn LGD distribution resulting from this
approach looks similar to the one proposed by the US regulator. However, in
contrast to the approach proposed in the “Advanced Capital Adequacy Framework”,
our approach relies on empirical analyses and provides a different formula for each
asset class or facility. Moreover, our approach allows banks to re-estimate
periodically the DLGD formula in order to incorporate changes in the credit cycle
and the resulting effects on the PD/LGD-correlation or the standard deviation of the
PD.

      3.3.2    Secured exposures

       For secured exposures, our approach takes into account the two main drivers
(i.e., cure rate and collateral value) that are expected to affect the LGD during a
downturn period. We test this approach on a Dutch mortgage portfolio using a
sample of approximately 90,000 currently open mortgage contracts.14 In order to
divide our sample into risk-homogeneous pools, we use the Loan To Value (LTV)
variable that is calculated and available for each contract.15 Moreover, we have data
on the indexed execution value of the collateral, the exposure, and the current LGD
segment.
       We define the cure rate as the number of defaulted clients (i.e., over 90 days
past due) that pay back their debt divided by the total number of clients in default
over a one year period. The cure rate is expected to decrease during a downturn and
consequently the average LGD to increase.
       After performing a sensitivity analysis with different stressing factors
(between 5% and 50 %), we apply a subjective stressing factor (10%) to the cure
rate excluding the selected percentage (10%) of self-cure clients from the
development sample.16 We perform this stress testing analysis per LTV band as
shown in Table 2.

14
   We exclude the government fully guaranteed loans from the sample.
15
   The Loan To Value variable is calculated by dividing the loan by the value of the house. The
higher the LTV, the riskier the mortgage is considered (i.e., the higher PD and LGD).
16
   The cure rate stressing factor can also be obtained empirically by analyzing the relation between
PD and cure rate. In our limited database, we were unable to uncover the expected negative
correlation between PD and cure rate. Therefore, we have tested different subjective stressing factors
between 5% and 50% and we have selected the most appropriate one (10%) based on our
expectations.
                    In order to stress test the collateral value, we calculate the yearly average
      growth rate and standard deviation of the NVM (Dutch Union of Real Estate
      Brokers) house-price index over the past 38 years (1968-2005). The growth rates are
      displayed in Figure 4.


      Table 2. Cure rate stress testing per LTV band
      This table shows the cure rate and LGD value per LTV band before and after applying the chosen
      10% stressing factor. The first and third columns report the cure rate per LTV band before and after
      applying the 10% stressing factor. The second and fourth columns report the LGDs.
                                                                                                               A c tu a l                                   S tr e s s e d s itu a tio n




                                                                                    A c tu a l C u re                                           S tre s s e d C u re                         S tre s s e d
                                                                                          ra te                          A c tu a l L G D              R a te                                   LG D
           ltv   > 1 .2 5                                                                   4   4   %                      1 8 .3 2 %                           3   9    %                    1 9 .7 4 %
           ltv   < = 1 .2   5      a   n   d      lt v      >   1   .1   6                  4   8   %                      1 4 .7 9 %                           4   4    %                    1 6 .1 8 %
           ltv   < = 1 .1   6      a   n   d      lt v      >   1   .0   7                  5   5   %                      1 1 .5 2 %                           4   9    %                    1 2 .9 0 %
           ltv   < = 1 .0   7      a   n   d      lt v      >   1   .0   0                  5   8   %                       8 .8 1 %                            5   2    %                    1 0 .0 1 %
           ltv   < = 1 .0   0      a   n   d      lt v      >   0   .8   3                  6   5   %                       4 .6 5 %                            5   9    %                     5 .5 2 %
           ltv   < = 0 .8   3      a   n   d      lt v      >   0   .6   7                  7   2   %                       1 .3 1 %                            6   5    %                     1 .6 4 %
           ltv   < = 0 .6   7      a   n   d      lt v      >   0   .4   4                  7   7   %                       1 .1 3 %                            6   9    %                     1 .5 0 %
           ltv   < = 0 .4   4      a   n   d      lt v      >   0   .2   4                  7   4   %                       1 .2 1 %                            6   7    %                     1 .5 6 %
           ltv   < = 0 .2   4                                                               7   2   %                       3 .1 5 %                            6   5    %                     3 .9 8 %
           A v   e ra g e                                                                                                   5 .4 1 %                                                           6 .2 0 %




            Figure 4. Growth rates of the Dutch house price index over the past 38 years
            (1968-2005)
            This figure shows the growth rate of the house price index over the past 38 years (1968-2005) in
            the Netherlands. The data source is the Dutch Union of Real Estate Brokers.

                 50,00%
                                                                                                                                                       Average             6,37 %
                                                                                                                                                       Standard Deviation 9.32 %
                 40,00%


                 30,00%


                 20,00%
Growth %




                 10,00%


                  0,00%
                            1969

                                           1971

                                                     1973

                                                                1975

                                                                             1977

                                                                                     1979

                                                                                            1981

                                                                                                        1983

                                                                                                                  1985

                                                                                                                           1987

                                                                                                                                  1989

                                                                                                                                         1991

                                                                                                                                                1993

                                                                                                                                                         1995

                                                                                                                                                                        1997

                                                                                                                                                                               1999

                                                                                                                                                                                      2001

                                                                                                                                                                                              2003

                                                                                                                                                                                                     2005




                 -10,00%


                 -20,00%
                                                                                                                          Year
      Using the observed average growth rate (6.37%) and standard deviation
(9.32%), we create six stress test scenarios. Assuming that house prices follow a
normal distribution, we assign to each scenario its expected probability. For each
stress scenario, we calculate the expected house prices growth rate as:


      Expected Growth Rate= Average growth rate- X*standard deviation                           (4)


      where X depends on how severe the economic downturn is expected to be
(e.g., between 0.5 and 3). The results from this analysis are reported in Table 3.



Table 3. Stress testing scenarios for house prices growth in the Netherlands
The first column of the table reports the multiplier of the observed standard deviation (9.32%), the
second column the expected growth in house prices, and the third column the expected probability
associated with each scenario under the assumption of normally distributed house prices.
 S c e n a r io       O b s e r v e d v a r ia t io n       G ro w th %        P r o b a b ilit y
 A v e ra g e         (n o n e )                                   6 .3 7 %           5 0 .0 0 %
 D o w n tu rn    1   d o w n 0 .5                                 1 .7 1 %           6 9 .1 5 %
 D o w n tu rn    2   d o w n 1 .0                                -2 .9 5 %           8 4 .1 3 %
 D o w n tu rn    3   d o w n 1 .5                                -7 .6 1 %           9 3 .3 2 %
 D o w n tu rn    4   d o w n 2 .0                             - 1 2 .2 7 %           9 7 .7 2 %
 D o w n tu rn    5   d o w n 2 .5                             - 1 6 .9 3 %           9 9 .3 8 %
 D o w n tu rn    6   d o w n 3 .0                             - 2 1 .5 9 %           9 9 .8 7 %



      During an economic downturn the value of the collateral (i.e., real estate prices
in this case) is likely to decrease.17 If the value of the collateral decreases, the LTV
will increase and, at the portfolio level, a certain number of clients will migrate to a
higher LTV band (see Table 4). Therefore, by observing the migration in the LTV
distribution associated with the simulated stress scenario, we can calculate the new
stressed average LGD. We define this as “migration effect”.




Table 4. Migration effect per LTV band

17
   The severity of the decrease in the real estate price may be based on a subjective decision or
estimated empirically based on historical data. In this case, we chose the scenario with the house
prices growth rate as close as possible to the lowest (-11%) observed in the Netherlands in the
previous 40 years (i.e., Downturn 4 with an expected decrease in house prices of 12.27%). We are
aware that this is a very conservative choice.
This table shows the migration effect per LTV band. After having chosen the Downturn 4 scenario,
the -12.27% growth rate is applied to the house prices in each LTV band. As such, the LTV variable
is recalculated per each contract and then each contract is reassigned to the new LTV band. The first
column reports the percentage of the actual population in each LTV band, the second column reports
this percentage figure when the migration of clients into new LTV bands due to shocks in house
prices is accounted for. The third and fourth columns report the actual and stressed LGDs,
respectively.

                                    % P o p u la tio n    % P o p u la tio n                  S tre s s e d
               LTV                     Ac tu a l         a fte r m ig ra tio n    LGD            LGD
ltv > 1 .2 5                             6 .5 6 %             1 4 .2 9 %         1 8 .3 2 %    1 9 .7 4 %
ltv < = 1 .2 5 a n d ltv > 1 .1 6        4 .1 7 %              5 .4 6 %          1 4 .7 9 %    1 6 .1 8 %
ltv < = 1 .1 6 a n d ltv > 1 .0 7        5 .3 6 %              5 .4 8 %          1 1 .5 2 %    1 2 .9 0 %
ltv < = 1 .0 7 a n d ltv > 1 .0 0        4 .7 6 %              3 .7 8 %          8 .8 1 %      1 0 .0 1 %
ltv < = 1 .0 0 a n d ltv > 0 .8 3       1 1 .1 4 %             9 .7 1 %          4 .6 5 %       5 .5 2 %
ltv < = 0 .8 3 a n d ltv > 0 .6 7       1 1 .6 2 %            1 3 .1 0 %         1 .3 1 %       1 .6 4 %
ltv < = 0 .6 7 a n d ltv > 0 .4 4       2 1 .9 7 %            1 8 .5 7 %         1 .1 3 %       1 .5 0 %
ltv < = 0 .4 4 a n d ltv > 0 .2 4       1 7 .6 3 %            1 5 .4 2 %         1 .2 1 %       1 .5 6 %
ltv < = 0 .2 4                          1 6 .7 8 %            1 4 .2 0 %         3 .1 5 %       3 .9 8 %
             Av e ra g e               1 0 0 .0 0 %           1 0 0 .0 %         4 .5 2 %       6 .6 2 %




        We calculate the final LGD stressing factor by comparing the two average
LGDs presented at the bottom of Table 4 (4.52% and 6.62%). Specifically, we
calculate the LGD stressing factor by dividing the difference between average
stressed and unstressed LGD by the unstressed LGD (i.e., 2.1%/4.52% = 47%). This
LGD stressing factor will be applied to every pool or facility in the secured portfolio
in order to calculate the final downturn LGD as


        Downturn LGD= (1+Z)* average LGD,                                                                   (5)

        where Z is the final LGD stressing factor (i.e., 47% in our study).

        Using formula (5), banks will be able to calculate the appropriate conservatism
to be added to each product/pool LGD. As expected, we find the level of
conservatism to be higher for secured products where a possible shock to the
collateral values is likely to have significant effects on the ultimate recoveries.
 4. Conclusions


      In this study, we analyze the issue of estimating a conservative loss given
default for retail assets as prescribed by the new Basel Capital Accord. Banks that
will implement the Advanced IRB approach will need to estimate a downturn LGD
to calculate their regulatory capital. However, we have found that a commonly
accepted methodology to estimate the appropriate conservatism to be added to the
average LGD is still lacking.
      In terms of contribution to the literature, and to the best of the authors’
knowledge, this is the first paper to analyze the link between recoveries and the
credit cycle for retail assets, to investigate the issue of estimating conservative LGD
for retail exposures and to propose a solution for the common lack of retail
recoveries data to cover a full credit cycle (including an economic downturn).
      We update the existing literature in two ways. First, we analyze the link
between recovery rates and the credit cycle for retail assets over a period of almost
four years. Differently from most of the available studies on this topic, we calculate
LGD using ultimate recoveries observed one year after the default event and we
analyze them at regulatory asset class level. In contrast with the existing literature,
we find that the adverse dependencies between default rates and recovery rates are
not present in all asset classes. As such, our results suggest that in several cases
banks will not be obliged to calculate and apply conservative LGD parameters to
estimate their capital requirements.
      Second, we investigate the issue of estimating conservative LGD for retail
exposures and propose a solution for the common lack of retail recoveries data to
cover a full credit cycle (including an economic downturn). Specifically, considering
the significant impact of a collateral on the LGD value, two different techniques are
proposed for secured and unsecured exposures. For the former, we stress the value
of the collateral and the cure rate in order to find the expected increase of the LGD
in a downturn period. For the latter instead, we use the existing correlation between
default rates and recovery rates, if any, to quantify the amount of conservatism to be
added to the LGD during a period of default rates significantly higher than the mean
(i.e., downturn period). Finally, we test both approaches on data of the retail
portfolio of a large international bank in order to underscore our conjectures
empirically.
      The methodology proposed in this paper is based on an empirical analysis and
provides a specific formula for each asset class or facility. Moreover, the proposed
approach allows banks to re-estimate periodically the DLGD formula in order to
incorporate changes in the PD/LGD-correlation and the standard deviation of PD.
     Considering the importance of the LGD in the Basel II Advanced IRB
approach, we believe that banks should pay significant attention to the way they
decide to add conservatism to this important parameter. Approaches to estimate
downturn LGD that are not conservative enough will be rejected by the supervisory
authorities. Approaches that are over-conservative will have a significant negative
impact on bank’s capital requirements and will present a competitive disadvantage
for the adopting banks.
Appendix A: LGD estimation
LGD can be estimated by means of forward-looking statistical models or by long-run
default weighted average LGD.

A long-run default weighted average LGD should be estimated for each pool. Preferably the
estimation takes into account one full economic cycle. For each period considered (month or
year), the number of defaults occurring in that period should be used to weight the final
calculated average.

To determine a long-run default weighted LGD, banks should follow these steps:

    1. Calculate the LGD per exposure facility in the observation period, by dividing the
       Economic Loss by the Exposure at Default

    2. Sum the exposure facility LGD percentages in a pool and divide them by the
       number of defaults in the pool. This is the single-year default-weighted average
       LGD (assuming a 12-month observation period)

    3. Apply Steps 1 and 2 to all years in the economic cycle, with a minimum of 5 years

    4. To obtain the long-run default-weighted average, sum each single-year average
       multiplied by the number of defaults in the specific year divided by the total number
       of defaults in the multi-year period (i.e. default weight).

A numerical example is shown below:
           Facility ID -                  Recoveries      Costs    Economic Loss (EAD           EL/EAD per
                            EAD
            Year X1                      (discounted) (discounted)    -(Rec - Costs))             facility
 Step 1.      AB01             125,000         52,000         12,500                  85,500                 68%
              AB02              95,000         55,000          3,500                  43,500                 46%
              AB03             100,000         40,000          6,000                  66,000                 66%
              AB04             100,000         40,000          6,000                  66,000                 66%
                                                                                                            246%
 Step 2. Single year average
         Default-weighted LGD Year X1 = (1/4 x 68%)+(1/4 x 46%)+(1/4 x 66%)+(1/4 x 66%) =               61.5%

 Step 3. Over year average
                    Year                 Default-weighted LGD          No. Defaults
                    X1                           61.5%                           4
                    X2                           55.4%                           3
                    X3                           61.3%                           5
                    X4                           65.4%                           7
                    X5                           65.2%                           8
                                                                                27
 Step 4. Default-weighted LGD average
                     = (4/27 x 61.5%) + (3/27 x 55.4%) + (5/27 x 61.3%) + (7/27 x 65.4%) + (8/27 x 65.2%)
         Over year weighted average:             62.9%
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