Loss Given Default (LGD)

The Loss Given Default (LGD) is one of the three main ingredients in the Basel model. It represents the percentage of the Exposure at Default (EaD) which you expect to lose if a counterparty goes into default. This chapter will explain the main issues when modeling the LGD.

What determines LGD

To model the LGD it is important to look at what happens after a counterparty goes into default. Dealing with companies who are in financial trouble is a specialty in itself. Most banks therefore have a separate department specialized in handling such companies. The best place to find information on that process after default is this department (often referred to as Special Asset Management).

There are several scenario’s of events which may occur after a company goes into default. The two most extreme are as follows:
- The counterparty recovers without any loss to the bank;
- Sale of assets and collateral is required.

There are also scenario’s in-between these two extremes with various possible associated losses. The finance could be restructured (a new term structure for instance) or the exposure could be sold to another bank.

Full Recovery
Because the definition of default is rather strict (90 days overdue) many defaults will fall in the first category. Most companies who are 90 days overdue simply recover. Often even without intervention by your bank.

Sale of assets and collateral
The sale of assets and collateral occurs less frequently but leads to higher losses. It can be assumes that this scenario only occurs when a company goes bankrupt. Note that bankruptcy is a lot worse than default (minimally 90 days overdue). Generally you can separate the returns in two types:
- Return on collateral
- Return on unpledged assets

Collateral are the assets which the customer has pledged to you. There is an agreement between you and the customer that the proceeds from the sales of the assets will be used to repay you.
Unpledged assets are the assets not pledged to anyone. The proceeds from the sales of these assets will be distributed first among the preferred creditors (usually the fiscus), second among thesenior creditors (this is determined in your loan specifications) and third among the subordinated creditors (again this is determined in the loan agreement).

Besides the actual amount retrieved it is also important to consider the time it takes and the costs you will have to make. Basically money now is better than money later and easy money is better than money which takes a lot of effort. Both these factors (time and effort) together with the actual retrieved amount determine the return.

The level of the returns during the sale of assets and collateral is dependant on the jurisdiction (country) you are in. In some countries (the Netherlands for instance) collateral may be sold separate from the bankruptcy proceedings. This gives the bank a high level of control and a good return on the collateral. It can be sold quickly at relatively low costs. In other countries the control is less and the costs of sales are higher. There is also a difference between the amount of preferred creditors. In France for instance employees are compensated (and considered a preferred creditor) during a bankruptcy.

Scenario’s in-between
Before a customer goes bankrupt your bank will probably have identified the counterparty as a default. Usually the default definition is triggered well before actual bankruptcy. Your bank may identify an increase in credit risk even before a counterparty goes into default. At this moment most banks open up a conversation with the customer to ensure a full recovery. If this is not possible several actions are possible. The bank may exempt a counterparty from interest payments (leading to an economic loss). The bank may restructure the loans with different term structures and interest rates, to re-match the payment requirements with the expected cash flow. The bank may sell the loans to a third party. Each of these scenarios have in common that the bank (or the third party) believes that the right strategic choices can reinstate the companies success. These scenarios can also be combined with the sale of assets. In such a situation part of the loan is repaid by the liquidation of assets (of a part of the company) and part is restructured to finance the remainder of the company.

Modeling LGD

As mentioned before the scenarios after default can be split into three groups:
- Full recovery;
- Sale of assets and collateral;
- In-between scenario’s

The first having zero (or almost zero) loss. The second having a loss depending on the amount of assets. In my experience this translates to a large amounts of defaults with zero loss, a smaller amount of defaults with a loss of 100% and the remaining defaults in-between. This is graphically represented below

An example of an LGD distribution

You should be able to reproduce a similar graph by comparing the documented exposures at default from known defaults at your bank with the eventual write offs on these exposures. If the definition of default is not available for historic data alternative (bank specific) credit risk grades can be used.

As the graph suggests the most important part will be to determine how to identify the counterparties which will recover. Spend time on modeling this, discus it with special asset management. The probability of recovery is perhaps the most important part of the model. After determining the probability of a full recovery the Loss in the remaining situations may be modeled.

This can be done using a simple model which relates a few factors directly to the expected loss if not recovered. For instance senior secured debt in a certain industry has a loss of X% if it does not recover fully. Important factors are: seniority, collateral (amount and quality) and jurisdiction. The effect can be directly modeled using regressions between the observed losses (of defaults which do not recover fully) and the value of the factors. This model can be combined with the model for recovery. In other words, the model for recovery gives a probability of zero loss. One minus this probability times the LGD model excluding recovery gives the total LGD model.

LGD = PR X zero loss + (1-PR) X average loss if not recovered

Where PR stands for the Probability of Recovery.

A more elaborate approach identifies the remaining scenarios (sale of assets and in-between scenarios) separately. First determine what the probability of the asset sales scenario is and how much will be recovered? Determine expected returns on asset types and an expected time it takes before you will receive your money. When calculating the return discount the expected proceeds using the expected time until receiving the money and a discount rate. You can use your funding rate, the risk free rate or the contract rate of the loan (this is hotly debated, but not further discussed here). Issues to take into account are the mentioned jurisdictions, collateral versus non collateral assets and covenants. The later is a difficult issue. A covenant allows the bank to request collateral if a counterparty’s credit worthiness diminishes. This means that the value of a covenant is dependant on your banks ability to identify counterparties in trouble and your banks ability to negotiate collateral once it becomes needed. The remainder is all the scenario’s in-between. This is more difficult. It is not possible to model all possible scenarios and all possible losses associated with them. It can be assumed that the expected loss lays somewhere in-between the two extreme scenarios. The probability of the three scenarios should add up to 100%.

Additionally workout costs will need to be embedded into the model.

Author: Muller, J.J.