Getting you there.
Capita selecta in LGD modelling Luc Hoegaerts Seminar KULeuven 11/12/2008
Luc Hoegaerts | Central risk management - Model Development | 14/10/2008 | 1
Outline
1. LGD is a credit risk component 2. Essential for specific and global risk measures 3. When is an obligor at default? 4. What is considered as loss? 5. Measuring LGD 6. Estimating LGD: making choices 7. Estimating LGD: inference 8. Drivers of LGD 9. Variance of LGD 10. VARLGD approaches 11. Downturn LGD 12. A benchmark as global fundament for LGD models 13. Example: corporate lending LGD 14. Example: credit cards LGD 15. Other examples 16. Concluding remarks Luc Hoegaerts | Central risk management - Model Development | 14/10/2008 | 2
1. LGD is a credit risk component Credit Risk is the risk that a borrower will be unable to pay back his debt. For any individual contract, the future loss (over a certain horizon) is random, i.e. unknown in advance. In default models, such loss is commonly broken down in 3 factors: 1. Exposure-At-Default (EAD): amount at risk at the point of default, maximal (monetary) amount of loss on risk i, given that default occurs. 2. Loss-Given-Default (LGD) : degree of security of risk i, expected percentage of the EAD that will be lost, given that default occurs 3. Probability of Default (PD): likeliness of default over e.g. 1 year. EAD and LGD constitute the severity side of the loss, PD the frequency aspect. A certain loss is expected, which represents a cost side of providing credit, and the volatility of this expected loss indicates a risk side of it. Luc Hoegaerts | Central risk management - Model Development | 14/10/2008 | 3
2. Essential for specific and global risk measures • For a single position, assuming stochastic default probability PDi and LGDi, and that LGD’s are independent, we have a mean and volatility for the individual loss:
ELi = EADi PDi LGDi
ULi = EADi
2 2 σ LGDi PDi + μ LGDi PDi (1 − PDi )
number of occurences
• A bank can quantify its portfolio credit risk through the measurement of the expectation and variability of the portfolio credit loss. A bank must hold capital to protect against the volatility, such that it covers the minimal potential loss amount suffered in the 3 worst loss cases when considering 10,000 portfolio loss events (each time over 1 year).
Loss Distribution EL: Expected Loss UL: Unexpected Loss Ecap: Economic capital
UL
• Loss correlation
ρ ijL ≤ ρ ijD
EL ECap
mean
LOSS
[Euro]
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VaR = 99.97% quantile
3. When is an obligor at default? “A default is considered to have occurred with regard to a particular obligor when one or more of the following events has taken place*: (a)It is determined that the obligor is unlikely to pay its debt obligations (principal, interest, or fees) in full; (b) A credit loss event associated with any obligation of the obligor, such as charge-off, specific provision, or distressed restructuring involving the forgiveness or postponement of principal, interest, or fees; (c) The obligor is past due more than 90 days on any credit obligation; or (d) The obligor has filed for bankruptcy or similar protection from creditors.” Often differences between definitions of agencies, banks and third parties. * Section III.F, §146 in Basel Committee on Banking Supervision (2001c). Luc Hoegaerts | Central risk management - Model Development | 14/10/2008 | 5
4. What is considered as loss? When a customer defaults, the bank does not generally lose the full amount of debt outstanding as it is possible that the borrower might recover and resume payments, or that a recovery will be made against the firms assets or securities held against the loan. LGD captures the total economic value of a loss as a percent of EAD. It is the complement to the recovery rate against the EAD: (LGD=1-recovery). Principle Loss
• Principal: the amount of the original loan which is neither repaid nor recovered • Interest: the amount of interest which is due but not received
Interest Exposure At Default
Economic Loss
Expenses Repaid Recovery Recovery Security
• Expenses: workout and legal costs incurred in the bank’s attempt to recover loss
LGD = Economic Loss / Exposure at D efault Luc Hoegaerts | Central risk management - Model Development | 14/10/2008 | 6
5. Measuring LGD 1.Work-out: Financials can often collect information electronically during the recovery process, which facilitates bookkeeping of the full historical cashflow/cost structure, up till a charge-off on the books. This can be a very detailed measurement, but also debatable in terms of proper valuation. 2.Market: Agencies rely typically on observations from defaulted marketable instruments, which properly represent the market’s expected present value of recovery, but liquidity is required to obtain enough defaults. 3.Implied market: In trading rooms, credit models are based on credit spreads, which implies already a recovery value. Sophisticated modelling can back out this component, but often it leads to underestimates. Thus, depending on data availability, one may record LGD by different approaches, which have each their pros and cons, positioned between two ends of a spectrum: on an accounting basis (as a physical, actual value) or on a pricing basis (as a risk-neutral, market value). Luc Hoegaerts | Central risk management - Model Development | 14/10/2008 | 7
6. Estimating LGD: making choices The Basel accord leaves 2 options: a standardized approach (using prescribed levels of LGD by product type and rating) or an advanced internal approach, where a bank can employ its own model, meeting certain requirements. Models range from mere look-up tables, linear regression to advanced nonlinear inference techniques (kernel density estimation, trees, neural networks, support vector machines, etc). The wide range of statistical techniques can be applied. LGD needs to be consistently summarized over a horizon and a group of data when it is computed at facility level by averaging over time, EAD weighting, simple average, etc,… as well for reporting on obligor or portfolio level, plus the roll-over (new exposure inflow) might hide trends. LGD should be consistent with PD when it comes to estimation as a pointin-time or through-the-cycle outcome. EAD may be also uncertain (eg in case of credit lines), which complicates the modelling (additional variance due to random EAD). Luc Hoegaerts | Central risk management - Model Development | 14/10/2008 | 8
7. Estimating LGD: inference The target in modelling LGD for a segment is to infer the probability density distribution: ¾Values constrained between 0% - 150% ¾Often bimodal: 2 peaks around 20-30% and 70-80%, depending on securitization or subordination degree ¾Summary statistics move upward in bad economic conditions ¾Commonly fitted with the beta distribution Inference by means of a structural model is more complicated (pre-processing variables, model selection, optimization, etc), but yields explanatory power, allows more accurate prediction, provides refined sensitivity/stress testing options and outperforms the pdf in backtesting. Remark that model choices can affect capital requirements easily by 50% Luc Hoegaerts | Central risk management - Model Development | 14/10/2008 | 9
8. Drivers of LGD Variables that aid segmentation and have explanatory power in modelling LGD: Instrument type: structure of debt (loan, bond, …) Rating: borrowers’ credit quality (junior, subordinate, senior) Collateral: type and amount of securitization (cash, assets or expected proceeds from the work-out of the assets,…) Support: backing by equity capital, subsidiaries, government or other parties Sector/industry status: recovery of sector, global economic indicators Geographic status: recovery of region, local economic indicators Company status: relative seniority, distance to default, restructuring,… Client ancienity, EAD, excess draw, time in recovery state, nr of reminders, marital status, gender, nr of restructurings, salary level, etc… Luc Hoegaerts | Central risk management - Model Development | 14/10/2008 | 10
9. Variance of LGD Many factors influence LGD, which are complementary (low intercorrelation), but also contribute to the variance: VARLGD
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10. VARLGD approaches Convenience leads to adopt external benchmark values per instrument type and seniority (from agencies or academia – eg S&P or Altman studies), in the range 5% to 10%; not considered as part of basel capital, more for economic capital Credit risk and pricing models assume, a posteriori, a parametric family, often based on LGD only, which fixes VARLGD as function of LGD ¾binomial k=1, ¾uniform k=2/3, ¾normal k=π,
VARLGD = LGD * k − LGD
But since skewness is a typical feature of LGD, most models employ ¾beta k=α+β+1 ≈ 4
VARLGD =
LGD * (1 − LGD ) k
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11. Downturn LGD QIS-3 Technical Guidance, paragraph 415 “A bank must estimate a long-run average LGD for each facility. This estimate must be based on the average economic loss of all observed defaults within the data source (referred to…as the default weighted average) and should not, for example, be the average of the average annual loss rates. Since defaults are likely to be clustered during times of economic distress and LGDs may be correlated with default rates, a time-weighted average may materially understate loss severity per occurrence. Thus, it is important that banks utilize default-weighted averages as defined above in computing loss severity estimates. Moreover, for exposures for which LGD estimates are volatile over the economic cycle, the bank must use LGD estimates that are appropriate for an economic downturn if these are more conservative than the long-run average. “
It is generally expected that the LGD will increase when the macroeconomic conditions are worse than on average, as well as PD’s…due to correlation. Typically one estimates an add-on, to be calibrated, with magnitude on the order of several percents. The add-on can be based on the difference between average conditions and worst case conditions in macroeconomic systematic components of the drivers of a structural model. Also changes in GDP, unemployment rate, drop in underlying value of collateral, etc…can serve in the estimation, or indicate how well the dowturn LGD is already implemented. Luc Hoegaerts | Central risk management - Model Development | 14/10/2008 | 13
12. A benchmark as global fundament for LGD models Altman studies derived on bonds provide a basis for conservative LGD estimates for loans at the bank. Typically, for equity or debt, fixed percentages are applied, while for lease or commercial trading, fractions are taken.
unsecured
LGD
1) LGD buckets interpolated along the credit quality dimension
rating
2) also splitup according to presence of collateral
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13. Example: corporate lending LGD Obligors are normally managed by risk management of the business. Obligors that cross a limit of the internal rating class system, will go into default mode, and become managed by intensive care and recovery. Loss given loss (LGL) is measured. Most stay in default, but a certain part (say cured = 25%) will return to a normal state, or defaults with full repayment, so a factor (1-cured) is applied, to obtain true LGD In case of collateral (as function of assets), part of the losses can be covered, which introduces a factor (1-coverage), applied to the ‘unsecured’ LGD in emerging countries or in countries with an unfavourable legal environment, a country add-on is calibrated based on expert scores, up to 25% An expert level can override the LGD value based on more specific info, and subsidiaries receive commonly the same LGD as the parent Eventually a floor and ceiling function can be applied Backtesting shows a conservative estimation, high cure rates, less volatilty than for bonds Luc Hoegaerts | Central risk management - Model Development | 14/10/2008 | 15
14. Example: credit cards LGD
Exposure is bucketed according to the clients’ time past due, eg in months of 30 days
The time horizon is sliced in steps, eg months
For each bucket, a transition rate y/x measures the loss of exposure over each time step
exposure b0 b1 b2 b3 b4 b5 b6 b7 b8
t0 x c
t1 u y d
t2 v
The average of rates for a bucket is weighted by total exposure at each time step, over a period of (at least) 5 years LGD is set equal to the multiplication of rates of default buckets b4-b7 Leads to rather conservative estimates, compared to backtesting Typical portfolio: 1 B exposure, 2 M accounts, 0.7% defaults, 15 M loss Luc Hoegaerts | Central risk management - Model Development | 14/10/2008 | 16
t3
t4
15. Other examples Mortgage secured personal loans after default, clients remain about 3Y in recovery. Then part of them end up in recollection, having a high LGD of x%, while others repay having a low LGD of y%. By modelling (by logistic regression ifo a set of drivers) the probability p of ending up in recollection, one determines LGD= p * x + (1-p) * y Cash loans:
100% 90% 80% 70% 60%
LGD
LGD = historical default weighted average loss at default,
50% 40% 30%
around 40 %
20% 10% 0% 0
5
10
15
20
25
months since default
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30
35
16. Concluding remarks ¾Is the modeling effort rewarded? Report results against a simple method, like eg (historical) averaging, to assess the gain. ¾Is the model performing well? Use many different measures: MSE, ROC, power, correlation with actual losses, plot actual versus predicted, actual within variance/confidence intervals, large errors distribution, parameter sensitivity, etc ¾Is VARLGD determined together with the LGD modelling step? Do not separate the two statistics; especially near the boundaries there is a bias introduced, which can eg distort the a posteriori credit risk model, and underestimate ¾Are intra correlation of LGD and inter correlation with PD accounted for (especially unsecured segments)? Eg estimate a downturn LGD by simulating with the credit risk model and reverse engineer a more conservative LGD in function of the LGD
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references
Miu P and B Ozdemir, 2006,Basel requirements of downturn LGD:modeling and estimating probability of default and loss given default correlations, Journal of Credit Risk 2 (2), pages 43–68 Barco, Michael, Credit risk models. Going downturn. Risk, 20 (2007), 8, S. 70 - 75 Renault, Olivier & Scaillet, Olivier, 2004. "On the way to recovery: A nonparametric bias free estimation of recovery rate densities,“ Journal of Banking & Finance, Elsevier, vol. 28(12), pages 29152931,December. Schuermann, Til, 2004, "What Do We Know About Loss Given Default?", Working Paper, Federal Reserve Bank of New York, also in D. Shimko (ed.), Credit Risk Models and Management, 2nd Edition, London, UK, Risk Books, 2006. Greg M. Gupton, 2005. "Advancing Loss Given Default Prediction Models: How the Quiet Have Quickened," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 34(2), pages 185-230, 07 E. Altman, Default Recovery Rates and LGD in Credit Risk Modeling and Practice: An Updated Review of the Literature and Empirical Evidence , 2006
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Getting you there.
Luc Hoegaerts | Central risk management - Model Development | 14/10/2008 | 20
