Loss Given Default (II) - observed LGD

In this article we will be dealing with the calculation of the observed LGD given by:

Where CFt and rt is the discount rate, both referred in more detail in the following sections.

Cash Flows

?Cash flows (CFt) include both recoveries and costs.

Recoveries

We can distinguish recoveries by:

• Cash: refer to actual cash flows collected from defaulters during the workout period. Cash recoveries are easy to track since the details are typically recorded in databases by the bank.
• Non-cash: refers to repossession of collateral or restructuring loans to support borrowers with their payments. These are obviously harder to record and require more work from the bank side.

Recoveries can also be classified according to their source:

• Product: Related to trade credit[1] when outstanding balances are reduced if the underlying goods can be easily and quickly sold to buyers.
• Collateral: Collateral recoveries include appraisal collateral values, carrying cost, and liquidation. In practice, one collateral can be pledged for multiple loans as we saw previously when we discussed collateral allocation. In these cases, collateral recovery should be reallocated specifically to each loan based on either pledge value or EAD of each loan.
• Guarantee: Guarantee recoveries are related unfunded protection in which a third party assumes the willingness to pay fully of partially the outstanding balance owed in case of default. The se guarantees can be accounted on either PD (when the guarantor and borrower are related entities, i.e. parent companies) or LGD (in case the entities don’t have these close ties).
• Residual (unsecured): Unsecured recoveries include remaining parts of the assets that banks can claim after product, collateral, and guarantee recoveries.

Costs

We already mentioned that LGD represents an economic loss and therefore indirect costs should also be taken into account. The problem here is that indirect costs are not tracked on a defaulter-by-defaulter basis so usually banks conduct a small accounting exercise to calculate the indirect cost rate.

See the example below:

We can now calculate cost rates rates based on two different denominator and methods.

Denominator:

• Total EAD: The assumption here is that higher workout costs are incurred for higher exposures at default.
• Amount recovered: The assumption here is that higher workout costs are incurred for higher recoveries.

Mehods

• Time-weighted
• Pooled

Based on these dimensions and on the example above, here are the cost rates calculated:

Discount Factor

At this moment you heard already that ‘LGD represents economic loss’ around 300 times, so it comes that it should also reflect the the time value of money. Your Finance 101 professor was probably repeating ad infinitum: One dollar today is worth more than one dollar tomorrow. So, you know that like getting a present value of cash flows for a company, also here you will need to apply a discount rate.

The Basel regulation states that the discount rate includes the time value of money and a risk premium for undiversifiable risk. Time value of money is usually reflected in the risk-free discount rate. The premium for undiversifiable risk should reflect economic downturn conditions for positions when there is uncertainty in the cash recoveries. When there is no uncertainty (cash flows from cash collaterals), a risk-free discount rate only is in principle sufficient.

A number of discount rate approaches have been proposed in the literature:

• Contract rate
• Weighted average cost of capital (WACC)
• Return on equity (ROE)
• Market return on defaulted bonds
• Equilibrium returns based on the capital asset pricing model (CAPM)

Discount rates have recently been identified as a source of risk weight inconsistencies between financial institutions, so regulators are now imposing minimum floors.

EBA prescribes 5% addon for the premium and the use of 3-month EURIBOR as risk-free rate.

Workout Period

The length of the workout period can vary depending upon the type of credit, the workout policy of the financial institution, and the local regulation. Some regulators such as the Bank of International Settlements (BIS) provided further input on this. On average, many financial institutions have workout periods of two to three years.

Incomplete Workouts treatment is prescribed in the section 6.3.2.3 Treatment of incomplete recovery processes of the document ‘Guidelines on PD estimation, LGD estimation and the treatment of defaulted exposures’ that can be found here:

https://www.eba.europa.eu/sites/default/documents/files/documents/10180/2033363/6b062012-45d6-4655-af04-801d26493ed0/Guidelines%20on%20PD%20and%20LGD%20estimation%20%28EBA-GL-2017-16%29.pdf?retry=1

Sources:

Credit Risk Analytics: Measurement Techniques, Applications, and Examples in SAS, 2016

‘Guidelines on PD estimation, LGD estimation and the treatment of defaulted exposures’

[1] Trade credit is a business-to-business (B2B) agreement in which a customer can purchase goods without paying cash up front, and paying the supplier at a later scheduled date. Usually, businesses that operate with trade credits will give buyers 30, 60, or 90 days to pay, with the transaction recorded through an invoice.