# Loss given default

Loss given default
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Loss Given Default or LGD is a common parameter in Risk Models and also a parameter used in the calculation of Economic Capital or Regulatory Capital under Basel II for a banking institution. This is an attribute of any exposure on bank's client. Exposure is the amount that one may lose in an investment.

## Definition

LGD is the credit loss incurred if an obligor defaults.

Loss Given Default is facility-specific because such losses are generally understood to be influenced by key transaction characteristics such as the presence of collateral and the degree of subordination.

## How to calculate LGD

Theoretically, LGD is calculated in different ways, but the most popular is 'Gross' LGD, where total losses are divided by exposure at default (EAD). Another method is to divide Losses by the unsecured portion of a credit line (where security covers a portion of EAD). This is known as 'Blanco' LGD. If collateral value is zero in the last case then Blanco LGD is equivalent to Gross LGD. Different types of statistical methods can be used to do this.

Gross LGD is most popular amongst academics because of its simplicity and because academics only have access to bond market data, where collateral values often are unknown, uncalculated or irrelevant. Blanco LGD is popular amongst some practitioners (banks) because banks often have many secured facilities, and banks would like to decompose their losses between losses on unsecured portions and losses on secured portions due to depreciation of collateral quality. The latter calculation is also a subtle requirement of Basel II, but most banks are not sophisticated enough at this time to make those types of calculations.

### Calculating LGD under the foundation approach (for corporate, sovereign and bank exposure)

Under Basel II to calculate the risk-weighted asset, which goes into the determination of the required capital for a bank or financial institution, the institution has to use an estimate of the LGD for each corporate, sovereign and bank exposure. There are two approaches for deriving this estimate: a foundation approach and an advanced approach.

#### Exposure without Collateral

Under the foundation approach, BIS prescribes fixed LGD ratios for certain classes of unsecured exposures:

• Senior claims on corporates, sovereigns and banks not secured by recognized collateral attract a 45% LGD.
• All subordinated claims on corporates, sovereigns and banks attract a 75% LGD.

#### Exposure with Collateral

The effective loss given default (LGD*) applicable to a collateralized transaction can be expressed as

```LGD* = LGD x (E* / E)
```

Where:

• LGD is that of the senior unsecured exposure before recognition of collateral (45%);
• E is the current value of the exposure (i.e. cash lent or securities lent or posted);
• E* should be calculated based on the following formula:
```E* = max {0, [E x (1 + He) – C x (1 – Hc – Hfx)]}
```

Where:

• E* = the exposure value after risk mitigation
• E = current value of the exposure
• He = haircut appropriate to the exposure
• C = the current value of the collateral received
• Hc = haircut appropriate to the collateral
• Hfx = haircut appropriate for currency mismatch between the collateral and exposure (The standard supervisory haircut for currency risk where exposure and collateral are denominated in different currencies is 8%)

The *He and *Hc has to be derived from the following table of standard supervisory haircuts:

However, under certain special circumstances the supervisors, i.e. the local central banks may choose not to apply the haircuts specified under the comprehensive approach, but instead to apply a zero H.

### Calculating LGD under the advanced approach (and for the retail-portfolio under the foundation approach)

Under the A-IRB approach and for the retail-portfolio under the F-IRB approach, the bank itself determines the appropriate Loss given default to be applied to each exposure, on the basis of robust data and analysis. The analysis must be capable of being validated both internally and by supervisors. Thus, a bank using internal Loss Given Default estimates for capital purposes might be able to differentiate Loss Given Default values on the basis of a wider set of transaction characteristics (e.g. product type, wider range of collateral types) as well as borrower characteristics. These values would be expected to represent a conservative view of long-run averages. A bank wishing to use its own estimates of LGD will need to demonstrate to its supervisor that it can meet additional minimum requirements pertinent to the integrity and reliability of these estimates.

## Downturn LGD

Under Basel II, banks and other financial institutions are recommended to calculate 'Downturn LGD' (Downturn Loss Given Default), which reflects the losses occurring during a 'Downturn' in a business cycle for regulatory purposes. Downturn LGD is interpreted in many ways, and most financial institutions that are applying for IRB approval under BIS II often have differing definitions of what Downturn conditions are. One definition is at least two consecutive quarters of negative growth in real GDP. Often, negative growth is also accompanied by a negative output gap in an economy (where potential production exceeds actual demand).

The calculation of LGD (or Downturn LGD) poses significant challenges to modelers and practitioners. Final resolutions of defaults can take many years and final losses, and hence final LGD, cannot be calculated until all of this information is ripe. Furthermore, practitioners are of want of data since BIS II implementation is rather new and financial institutions may have only just started collecting the information necessary for calculating the individual elements that LGD is composed of: EAD, direct and indirect Losses, security values and potential, expected future recoveries. Another challenge, and maybe the most significant, is the fact that the default definitions between institutions vary. This often results in a so-called differing cure-rates or percentage of defaults without losses. Calculation of LGD (average) is often composed of defaults with losses and defaults without. Naturally, when more defaults without losses are added to a sample pool of observations LGD becomes lower. This is often the case when default definitions become more 'sensitive' to credit deterioration or 'early' signs of defaults. When institutions use different definitions, LGD parameters therefore become non-comparable.

Many institutions are scrambling to produce estimates of Downturn LGD, but often resort to 'mapping' since Downturn data is often lacking. Mapping is the process of guesstimating losses under a downturn by taking existing LGD and adding a supplement or buffer, which is supposed to represent a potential increase in LGD when Downturn occurs. LGD often decreases for some segments during Downturn since there is a relatively larger increase of defaults that result in higher cure-rates, often the result of temporary credit deterioration that disappears after the Downturn Period is over. Furthermore, LGD values decrease for defaulting financial institutions under economic Downturns because governments and central banks often rescue these institutions in order to maintain financial stability.

## Correcting for different default definitions

One problem facing practitioners is the comparison of LGD estimates (usually averages) arising from different time periods where differing default definitions have been in place. The following formula can be used to compare LGD estimates from one time period (say x) with another time period (say y):

LGDy=LGDx*(1-Cure Ratey)/(1-Cure Ratex)

## Country-specific LGD

In Australia, the prudential regulator APRA has set an interim minimum downturn LGD of 20 per cent on residential mortgages for all applicants for the advanced Basel II approaches. The 20 per cent floor is not risk sensitive and is designed to encourage the ADIs to undertake further work, which APRA believes would be closer to the 20 per cent on average than ADIs’ original estimates.

## Importance

LGD warrants more attention than what has been given to it in the past decade, where credit risk models often assumed that LGD was time-invariant. Movements in LGD result in often proportional movements in required economic capital. According to BIS (2006) institutions implementing Advanced-IRB instead of Foundation-IRB will experience larger decreases in Tier 1 capital, and the internal calculation of LGD is a factor separating the two Methods.

## References

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