Default probability and loss severity

Credit scoring’s primary strength is its ability to rank risk. Increasingly, however, lenders have to estimate expected losses (ELs)—and even profits—whether for risk-based pricing or port-folio valuation. The EL is the amount that the lender expects to lose, based upon available data. It is made up of two parts: probability-of-default (PD), which is the risk of non-payment according to some definition; and loss severity, the extent of the loss in the event of default, which is affected by the exposure-at-default (EAD), loss-given-default (LGD), and maturity of the loan (M).

Equation 3.4. Expected loss $EL PD%  $EAD  LGD%  f(M)

Probability-of-default (PD%)—An obligor (borrower) risk rating, which is related to indi-vidual economic and environmental circumstances.

Exposure-at-default ($EAD)—A monetary value related to the outstanding balance, agreed loan limit, the lender’s shadow/target limits, and loan product characteristics.

Loss-given-default (LGD%)—Proportion of the EAD that the lender expects to lose if default occurs, which is heavily influenced by collateral and other security.

Maturity (f (M))—An adjustment that is a function of the remaining loan term or repayment schedule, which applies in the wholesale market for maturities of longer than one year.

Care must be taken here, as there will always be a positive correlation between default prob-ability and loss severity, which is not captured in many models. This is best illustrated by con-sidering an economic downturn, when both increase: (i) as asset values reduce, counterparties are more likely to walk away from them, which results in an increase in both LGD and PD;³ (ii) LGDs increase, because the time frames required to collect, if at all, become longer;

(iii) because the number of defaults are higher, the LGD values will be dominated by those occurring during downturns, which will result in conservative results for capital allocation and pricing calculations; and (iv) EADs may be higher, because lenders are more likely to: (a) take greater advantage of any credit lines currently available; (b) request increases; and/or (c) abuse the facilities. On this last point, there are also contrary tendencies, because lenders relax and tighten their lending policies according to the perceived risk, both for individual borrowers, and during the cycle. This leads to higher EADs during upturns, and for companies perceived as low risk.⁴

Some further comments can be made with respect to some of the individual elements. First, according to Miu and Ozdemir (2005:30) it is common practice to split EAD into drawn EAD_d and undrawn EAD_ucomponents, and the ‘forward-looking dollar amount’ is calculated as EAD d  EAD_d u  EAD_u. The components are calculated for defaulters using aggregated drawn and undrawn values at time of default and one year prior:

EAD_d min (d_T, d_T1)/d_T1, and

EAD_u min (1, max (0, d_T d_T1)/u_T1).

Note that these formulae assume defaulters have—on average—been managed at or within their limits.

Second, there are two primary approaches for LGD estimation: (i) workout, which discounts post-default cash flows; and (ii) market, which uses the market value of a security at time of default. The latter is infeasible for retail portfolios. Third, the final term, f (M), is used to recog-nise the higher risk of longer maturities, and applies mostly to corporate, inter-bank, and sover-eign lending. It is usually dropped, because in most cases: (i) its impact is negligible; (ii) lenders annualise the PD, EAD, and LGD values; and (iii) at least part of it may be already reflected in the EAD and LGD values. For loans with known repayment schedules, M is calculated as the weighted-average time-to-maturity, using the scheduled cash flows. If M cannot be derived, then the termination date of the agreement should be used, as a conservative estimate. M is not used directly in the formula, but is instead used to calculate an adjustment, the ‘f(M)’ (function of maturity) shown in Equation 3.4, which is usually only slightly greater than 100 per cent.

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3 This can be especially difficult for real estate markets, where asset correlations are high. Property owners are prone to jump ship simultaneously, especially when their wage or rental incomes fail to cover loan repayments.

4 See Miu and Ozdemi (2005:32), who also made points (ii) and (iii) (p. 28, fn 25).

Fourth, losses can be split into: (i) the loss of principal; (ii) collections and recovery costs (workout and legal); and (iii) the cost of funds (Schuermann 2004). Discounting the post-default cash flows usually captures the latter.

According to Miu and Ozdemir (2005), if the post-default cash flow volatility has already been captured elsewhere, then a risk-free discount rate should be used. Otherwise, there should be a risk premium.

EAD and LGD could theoretically be modelled using statistical methods, but the low numbers of defaults may make it infeasible. LGD is especially problematic due to problems obtaining data on the amount and timing of post-default cash flows, unless appropriate systems are in place. Irrespective, any bank hoping to use the advanced approach under Basel II needs to come up with these estimates, whether using own or pooled data.

And finally, in general, the possible post-default outcomes are cure (rehabilitation), restruc-ture (renegotiation), and liquidation, and if the latter, funds may be recovered by realising the collateral’s value, calling upon guarantees, any residual remaining after all senior debt has been settled, or other sources.⁵Studies have shown that the LGD tends to be a function of:

type of debt (bank loan, bond, store credit); contractual terms (seniority, collateral); market segment (higher in sectors with greater assets); and economic conditions (better when times are good). The LGD will also vary depending upon the lender’s bargaining power, experience in managing distressed borrowers, and ability to realise collateral’s value.

Finance calculations

Credit scoring was originally used for accept/reject decisions in fixed-offer scenarios, but is increasingly being used in more innovative ways. It has become the basis for the expected-loss calculation, which is used for risk-based decisioning and ‘value at risk’ (VaR) models. Risk-based decisioning includes: risk-Risk-based pricing, where prices and loan terms are adjusted according to the level of risk, which is especially common where the resulting portfolios will be securitised; and risk-based processing, where other actions are adjusted, such as the level of documentation, or number of security checks when processing applications.

In contrast, VaR models do not affect decisions on a deal-by-deal level, but instead focus on the portfolio. They are used to provide estimates of worst-case losses that can arise from mar-ket fluctuations, assuming a given time frame and confidence interval . . . the greater the EL and loss volatility, the greater the possible unexpected loss. At the extreme, the loss may be catastrophic, resulting from events that might occur once in a millennium. VaR models have become the basis for determining banks’ capital requirements, and have been adopted as part of the Basel II regulatory framework. The formula in Equation 3.4 is still quite simplistic, as it

5 The concepts relating to post-default outcomes and treatment presented in these two paragraphs were influenced by presentations by, and discussions with, Christian Endter and Evren Üçok of Mercer Oliver Wyman, during early 2006.

does not recognise the potential variation that can occur in the underlying values.⁶Regulators will thus increase capital requirements, to ensure that there is sufficient capital to handle unex-pected losses (see Chapter 36, Capital Adequacy).

Bad versus default definition

When dealing with corporate bonds, the definition of good and bad is clear-cut—either the obligor defaults, or does not. When dealing with loan accounts however, the situation is different—and there are usually differences between the default definition and the good/bad definition used for a scorecard development. The scorecard good/bad definition focuses upon providing the best possible risk ranking; whereas the default definition is used for finance calculations (but could be used as a good/bad definition).

Why is this? The primary goal of credit scoring models is to provide tools that aid case-by-case decision-making, and any extra benefits that come from aiding the finance function are secondary, unless the two are so intertwined they are indistinguishable. When deciding upon the scorecard definition, it must be ensured that: (i) the scores discriminate between cases the lender wants, and does not want, taking into consideration those that may not be clear cut; and (ii) there are sufficient bads to develop a model. Even so, the good/bad and not-default/default statuses should be very highly correlated, to the extent that if the good/bad scores cannot be used directly, it should still be possible to map them onto default probabilities.

While there may be some flexibility around the good/bad definition, the default definition will be set either by company policy or regulation, and may vary by type of organisation.

Perhaps the best illustration is the Basel II default definition, which classifies accounts as being in default, if at any time during the previous year:

(i) The customer was 90 days-past-due (for cheque accounts, 90 continuous days in excess of agreed limit) on any material obligation to the bank.

(ii) Other factors made it clear that there was a high probability of loss, such as when a specific loss provision was raised, financial difficulties caused the borrower to request a (distressed) loan restructuring, the account was passed on to a third-party recover-ies agency, the obligor was put under bankruptcy protection, or the lender filed for the obligor’s bankruptcy.

(iii) A loss was incurred, either because any or all of the debt was written- off, or sold for less than the outstanding balance.

Definitions versus estimates

Something that should be highlighted is the difference between a current-status and worst-ever definition, and a point-in-time versus through-the-cycle estimate. These concepts are sometimes confused. Definitions are the basis for the target variables used in scorecard

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6 Some people maintain that risks where accurate probabilities can be determined are no longer risks but a ‘cost of doing business,’ and that it is only the random exogenous or idiosyncratic risks that are threats.

developments and reporting. With a current-status definition, a case tests positive only if the condition holds true at the end of the period, whereas with a worst-ever definition, it tests posi-tive if the condition holds true at any point over the period. Basel II requires that banks use a worst-ever definition (covering a one-year period), while scorecards may be developed using either current- or worst-ever, and may have elements of both.

In contrast, estimates are probabilities derived using those definitions. A point-in-time (PIT) estimate refers to immediate probabilities, typically one-year, that will fluctuate up and down over the course of an economic cycle. In contrast, a through-the-cycle (TTC) estimate is one that approximates a stressed bottom-of-the-cycle scenario, with a horizon of five years or more. According to Aguais (2005), no risk estimate will ever be purely PIT or TTC, but will always be a combination of the two. For example, default estimates based upon account per-formance or the value of traded securities tend towards PIT, while rating agency grades tend towards TTC. All of them will vary over an economic cycle, some more than others.

Companies’ own internal grades are made up of a combination of ‘subjective assessments, statistical models, market information, and agency ratings’ that have a mixture of different time horizons. While it may be ideal to provide separate PIT and TTC estimates for each obligor, this is beyond the capabilities of today’s banks, and has not been required by Basel II.

Aguais et al. (2003) highlight that the two terms are relatively new additions to the credit lexicon, and were first used with respect to companies’ credit ratings. ‘Through-the-cycle’

was first used in Moody’s and Standard & Poor’s (S&P) literature—in 1995 and 1996 respectively—to highlight how they take economic fluctuations into account, and ‘point-in-time’ was coined in a 1998 article by two Federal Reserve researchers, William Treacy and Mark Carey, to illustrate the difference between the approaches used by the rating agencies and many banks.

Rather than focusing upon PIT or TTC, lenders should use whatever provides the best esti-mates over the longer term. These can then be transformed into PIT or TTC estiesti-mates at port-folio level, depending upon what they will be used for. If the goal is to determine capital reserving requirements, a TTC estimate will be used to provide estimates that ceteris paribus keep reserve requirements stable over the economic cycle. In contrast, if the goal is account management, a PIT estimate will be used to keep the decision-making consistent, as the level of risk changes over the cycle. Furthermore, if used for pricing, the term used for the estimate should approximate the deal term.