# The Loan Equivalency Factor for Revolving Lines of Credit in Commercial Lending

By Pan, Kelin | The RMA Journal, June 2009 | Go to article overview

# The Loan Equivalency Factor for Revolving Lines of Credit in Commercial Lending

Pan, Kelin, The RMA Journal

BASEL II ALLOWS banks to use their own measures of credit risk to calculate appropriate levels of economic capital. Prior to implementing this Advanced IRB (internal ratings based) approach, however, the bank must model three major credit risk parameters:

1. Probability of default (PD), which is the probability that a borrower will default in the next year.

2. Exposure at default (EAD), which is the bank's exposure to borrowers upon their default.

3. Loss given default (LGD), which is the percentage of EAD that the bank ends up losing.

As outlined by the Basel Committee on Banking Supervision in June 2006, Basel II requires banks to consider on- or off-balance-sheet exposures in their own EAD estimates. For on-balance-sheet exposures, the following formula can be adopted to estimate EAD:

1 EAD = Ave(CCF) x NB,

where NB is the current net book balance for each obligation, and CCF is the credit conversion factor specified for on-balance-sheet exposures. The following empirical formula can be used to estimate CCF:

2 CCF = (NB + Accrued Interest + Accrued Fee)/NB.

Usually, accrued interest and accrued fee are equal to or greater than zero. Therefore, CCF is always equal to or slightly greater than 1. The empirical CCF expressed in equation 2 is an obligation level and can be considered a random variable with some statistical characteristics. A statistic of CCF at the portfolio level, as expressed in equation 1, can be used to capture such characteristics.

The Advanced IRB approach emphasizes that banks should use estimates of off-balance-sheet items and reflect the probability of additional drawings by borrowers up to and after a default event is triggered. In this case, EAD is defined as

3 EAD = NB + Ave(LEQ) x (NE - NB),

where average LEQ is the mean of the loan equivalency factor in a special bucket based on rating grade and/or other factors that will be determined by statistical characteristics or business practice. In equation 3, net exposure (NE) minus net book balance (NB) is equal to the amount off balance sheet.

For commercial loans, when granting a revolving line of credit, a bank usually provides a credit limit. A borrower obtains an immediate loan amount and the future availability of the total loan amount. Accordingly, the corresponding exposure for the bank has two parts: the outstanding balance (NB) and the current commitment (NE). The outstanding balance refers to the amount drawn by the obligor, while the current commitment includes drawn and undrawn portions that the bank has promised to lend to the borrower at his or her request. The probability of drawing the undrawn portion in the next 12 months is defined as the loan equivalency factor (LEQ) off balance sheet. Since a probability always has values from 0 to 1, LEQ is constrained into a range of 0 to 1.

A few published papers have discussed LEQ in commercial lending. A sarnow and Marker (1995) showed that LEQ decreases with increasing facility rating. The authors studied 50 facilities for Citibank covering the 1988-93 period. They looked at LEQ for facilities with rating grades of BB/B or worse, then extrapolated the results to facilities with better ratings. They found an inverse relationship between LEQ and facility ratings--a conclusion based on inference from a limited sample rather than actual observations for better rated facilities.

Araten and Jacobs (2001) estimated LEQ for revolving credits and advised lines from JPMorgan Chase. The authors used 408 facilities covering the period 1995 to 2000. The data showed an increasing trend of average LEQ for the best rated grades (for example, AAA/AA- to A+/A-) and a decreasing trend for the worst ones. However, the model predicted a decreasing trend with increasing rating grades. The authors also found an increasing relationship between LEQ and time to default. Their results were similar to those of Asarnow and Marker on the relationship between LEQ and facility ratings. …

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