Value at Risk and Bank Capital Management

7.5 Managing Risk and Pricing Limits for Credit Risk

Risk management tools linked to VaR measurement can be used to support risk policies

and procedures for credit risk control processes too. While for market risks VaR can be

used, especially to set maximum limits for the trading desks, in the case of credit risk,

potential applications include:

•

The defi nition of the autonomy limits for lending decisions (at the individual loan

level)

•

The defi nition of pricing limits (i.e., minimum required profi tability for loans) as

a necessary condition to have a loan approved

We briefl y explain how these limits can work and — since their implementation can be

extremely different depending on the type of bank and of counterparty — we then analyze

their potential application in two extreme cases: the case of a loan to a large corporation

by a large wholesale-oriented investment bank and the case of a small loan to an SME

by a smaller, retail-oriented commercial bank.

7.5.1 Setting Loan Autonomy Limits: From Notional Size

to Expected Loss

Any bank has credit approval policies defi ning who is entitled to approve a loan. When

defi ning these policies, the usual problem is how to divide those loans that could be

authorized at lower hierarchical levels from those requiring approval by senior managers,

by credit committees, or even by the board. Traditionally, the notional size of the loan has

been the main driver for defi ning the approval process for a loan. For instance, internal

lending procedures may have stated that any loan with size up to x could be approved by a

senior credit offi cer, while loans with size between x and y should require approval by the

central credit committee, and those over y should be approved by the board. Of course, any

bank could defi ne a number of different intermediate steps in any way it considers conve-

nient to promote effi ciency as well as credit control. However, the development of internal

rating systems and credit portfolio models suggests that autonomy limits could be defi ned

in terms of either expected loss or value at risk rather than in terms of notional size.

Defi ning autonomy limits in terms of expected loss is easier, and it is possible when-

ever there is an internal rating-based system associating expected loss rates to rating

classes (i.e., even if the bank had not yet developed a credit portfolio risk model reliable

enough to set autonomy limits based on VaR). Since expected loss (EL) can be obtained

as a product of the exposure at default (EAD) times probability of default (PD) times loss

given default (LGD), determining a maximum EL limit implies that the maximum size

of the loan that can be approved by a given decision maker is no longer a constant, but

depends (inversely) on the loan’s PD and LGD:

max EL max exposure PD LGD max exposure

max EL

PD LGD

=××⇒=

×

Hence, loans with a higher internal rating (i.e., lower PD) or more guarantees (and there-

fore lower LGD) can be approved at lower hierarchical levels. At the same time, loans to

riskier customers and with lower guarantees might be checked at a higher hierarchical

MANAGING RISK AND PRICING LIMITS FOR CREDIT RISK 189