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Loss-given-default is a measure of the loss severity in the case of the default of an exposure, expressed as a percentage of the EAD.26_{LGD estimates represent the ex-ante expectation}

of the loss conditional on the default of an exposure that is yet non-defaulted, whereas the realized LGD or ”loss rate”-given-default is an ex post measure of the loss severity of a defaulted exposure. The LGD of a particular exposure is assumed to depend on a limited set of characteristics such as the type of credit product, estimated PD or risk grade, seniority, collateral and country of origination. Complementary, LGD = 1 - RR can be expressed in terms of a recovery rate RR, which is defined as the expected or actual discounted value of uncertain or actual recoveries net of workout costs at the time of default divided by the EAD amount.

In credit risk modelling, the LGD is assumed to be either deterministic or random. In the latter case, the LGD of exposures with equal properties are typically assumed to be i.i.d. In the specification of LGD distributions, pooled information from a bank’s or public loan loss experience from rating agencies or supervisory authorities are often used, as well as rating agencies’ corporate bond LGD data. Obviously, for reasons of estimation conformity, the type of instrument, default definition, reference value, risk grade, regional and seasonal origin of pooled LGD data must coincide.

For the estimation of LGD, there are subjective methods, such as expert judgement, and objective, mostly quantitative methods. Objective methods are subdivided into implicit and explicit methods. Implicit methods do not take into account single-exposure loss rates, but use model-derived expected credit loss of single exposures or the historical aggregate

25_{Cf. Gordy and Heitfield (2000) and D¨ullmann and Scheule (2002).} 26_{Cf. BCBS (2005b), paragraph 468–473.}

loss of credit portfolios for LGD estimates. Implicit market LGD methods derive LGD estimates from market prices of non-defaulted credit exposures, such as corporate bonds or credit default swaps (CDS), using an asset pricing model. Though market-implied LGD estimates typically suffer from a lack of identification in the decomposition of credit spreads into PD and LGD components, they are considered to be the only manageable way to estimate appropriate LGD for large, ”too-big-to-fail” corporate exposures. For retail portfolios implicit historical LGD estimates are derived from PD estimates and the aggregate loss experience of a portfolio.

Explicit methods derive LGD estimates for non-defaulted exposures from loss rates of defaulted claims. The actual credit loss of single exposures can be computed either from market prices of defaulted bonds or loans (explicit market LGD) or by discounting the expected cash flows, including workout cost from the date of default to the end of the recovery process (workout LGD). Factors that affect the workout LGD are (1) the amount and date of cash and non-cash recoveries, (2) direct and indirect workout cost, (3) the definition of workout completion, (4) the treatment of recovery profits and (5) the discount factor, as well as (6) the reference value of the exposure.

Cash recoveries are easy to handle in LGD calculations. If all cash flows from the date of default to the end of the recovery process are known with certainty, to obtain actual LGD one subtracts the value of discounted net recoveries from a reference value conventionally set to the face value of the debt. Direct workout costs, such as legal costs or the costs of the appraisal of collateral are associated with a particular exposure. Indirect costs, such as the office and staff costs of the workout department emerge from the recovery process itself, and the allocation of indirect costs to defaulted exposures affects the estimation of workout LGD.

The recovery process is definitely complete when all non-cash recoveries, such as collat- eral, repossessions or restructured claims, have been sold to a third party. However, it seems more appropriate to consider the recovery process complete when the non-cash recoveries are transferred, because the change in the management of seized assets may impact valuations, and because costs attributable to the workout process can no longer be unambiguously identified. In principle, the exposure to credit risk is terminated at the time of recovery transfer, and other sort of risks, such as market risk become relevant afterwards. Furthermore, the time lag between the time of transfer and the disposal to a third party can be considerable, which prevents recently defaulted exposures with un- completed workout and distorts effective LGD estimates from being taken into account. Hence, non-cash recoveries are often transformed into artificial cash recoveries including a haircut to the book value of repossessed goods which is carried out to be prudent. Ob- viously, workout and collection expertise significantly impacts recovery rates and LGD estimates.

Supervisory agencies require LGD estimates to be non-negative. In this context, censoring recovery profits does not interfere with the definition of default in PD estimates, whereas the truncation of recovery profits biases LGD estimates.

Discount rates must reflect the uncertainty of the recoveries to be received over a workout period of unknown length. The recovery value can be computed by discounting expected net recoveries using a risk-adjusted discount rate or by discounting certainty-equivalent cash flows at a riskless rate. The impact of the discount rate on LGD estimates is partic- ularly important if the recovery period is long. Theoretically, appropriate risk-adjusted discount rates should be derived from liquid markets for recovery claims. However, as such markets typically do not exist, the historical or current rates of conventional credit markets are used. Historical discount rates are fixed at the date of default, and typically, either the contractual rate of the original exposure or a suitable rate for assets with a similar risk to that of the recovery claim is used. Current discount rates are fixed at each date on which recoveries are valued and effectively assess the marketability of the recovery claim, which facilitates the comparison of LGD estimates of different exposures.

The loss specified by the LGD represents the economic loss incurred by the lender from the default of an exposure, which may differ from the credit loss considered in financial accounting. For example, explicit market LGD typically compare the market price of a credit-risky asset shortly before the default event with the market price of the asset 30 days after the date of default. Compared to workout LGD, the use of explicit market LGD is straightforward because neither allocations of costs nor discount rates need to be taken into account. Though observable prices of defaulted assets are scarce, most rating agencies apply this approach.

In credit pricing applications, regression models are used for LGD forecasts that are conditional on current economic conditions. Though the predictive power of regression- based LGD estimates can be readily assessed by out-of-time and out-of-sample tests, the advanced IRB approach requires LGD estimates to represent long-run default-weighted average loss rates instead of point-in-time estimates.

The revised capital standards require LGD estimates under the advanced IRB approach to represent conditions during an economic downturn. Downturn conditions can be char- acterized by periods of expected negative GDP growth, increased unemployment rate or credit default rates, or by periods in which other risk factors, such as collateral values, are expected to jointly affect default and recovery rates. Loss rates are positively correlated to default rates, so that LGD estimates, which are assumed to be fixed or stochastically independent from default rates, will result in an underestimation of Credit-VaR. To qual- ify for the advanced IRB approach, LGD estimates must not be lower than the long-run average loss rate of defaulted exposures during periods of increased credit loss for the exposure type in question. The loss experience must span a complete credit cycle of at

least seven years and contain all defaults in a bank’s credit portfolios within this time frame. Obviously, the definition of default must be the same for PD and LGD estimates. No particular method is prescribed for the validation of LGD estimates by supervisory agencies,27 but an assessment of LGD estimates under conditions of an economic down- turn, along with a comparison to external LGD estimates and a backtesting of actual LGD against a bank’s LGD estimates is recommended.

Empirical LGD studies are available for corporate bond and syndicated loan markets and include a wide range of actual LGD.28 Different studies find average actual LGD for the overall US corporate bond market of between 58% and 78%, whereas for senior secured (senior subordinated, subordinated) corporate bonds average loss rates fall into the intervals from 42% −47% (58% − 66%, 61% −69%). For senior secured (senior unsecured, commercial) loans, average actual LGD in the interval from 13%−38% (21%−

48%, 31%−40%) have been observed. Obviously, loans suffer from lower actual LGD than corporate bonds, which can be attributed to stricter covenants and higher collateral pledged in loan contracts.

The distribution of single-exposure LGD is mostly found to be unimodal, highly dispersed and skewed to low LGD. Factors found to affect actual LGD are predominantly seniority and the type of collateralization of claims, macroeconomic conditions at default, industry affiliation of the obligor and the liquidity of collateral. In periods of high default frequency, loss rates are found to be higher than in periods of infrequent defaults. Liquid collateral such as cash and accounts receivable yield lower loss rates than illiquid collateral such as property, plant and equipment. Industries that provide less liquid collateral show higher actual LGD. The size of the borrower does not seem to affect LGD, whereas loss rates increase with the amount of other outstanding debt, especially for unsecured loans. The effect of loan size is therefore unclear.