Value-at-Risk

Before going into more detail about credit risk management models, it would be
instructive to say a few words about Value-at-Risk. The credit risk management
modeling framework shares many features with this other modeling framework called
Value-at-Risk. This has resulted in some confusions and mistakes in the industry,
so it is worth-while explaining the relationship between the two frameworks.
Notice we were careful to write framework because Value-at-Risk (VaR) is a
framework. There are many different implementations of VaR and each of these
implementations may be used differently.
Since about 1994 bankers and regulators have been using VaR as part of their
risk management practices. Specifically, it has been applied to market risk management.
The motivation was to compute a regulatory capital number for market risk.
Given a portfolio of assets, Value-at-Risk is defined to be a single monetary capital
number which, for a high degree of confidence, is an upper bound on the amount of
gains or losses to the portfolio due to market risk. Of course, the degree of confidence
must be specified and the higher that degree of confidence, the higher the capital
number. Notice that if one calculates the capital number for every degree of confidence
then one has actually calculated the entire probability distribution of gains or losses
(see Best, 1998).
Specific implementation of VaR can vary. This includes the assumptions, the
model, the input parameters, and the calculation methodology. For example, one
implementation may calibrate to historical data and another to econometric data.
Both implementations are still VaR models, but one may be more accurate and
useful than the other may. For a good debate on the utility of VaR models see
Kolman, 1997.
In practice, VaR is associated with certain assumptions. For example, most VaR
implementations assume that market prices are normally distributed or losses are
independent. This assumption is based more on convenience than on empirical
evidence. Normal distributions are easy to work with.
Value-at-Risk has a corresponding definition for credit risk. Given a portfolio of
assets, Credit Value-at-Risk is defined to be a single monetary capital number which,
for a high degree of confidence, is an upper bound on the amount of gains or losses
to the portfolio due to credit risk.
One should immediately notice that both the credit VaR model and the credit risk
management model compute a probability distribution of gains or losses. For this
reason many risk managers and regulators do not distinguish between the two.
However, there is a difference between the two models. Though the difference may
be more of one of the mind-frame of the users, it is important.
The difference is that VaR models put too much emphasis on distilling one number
from the aggregate risks of a portfolio. First, according to our definition, a credit risk
management model also computes the marginal affect of a single asset and it
computes optimal portfolios which assist in making business decisions. Second, a
credit risk management model is a tool designed to assist credit risk managers in a
broad range of dynamic credit risk management decisions.
This difference between the models is significant. Indeed, some VaR proponents
have been so driven to produce that single, correct capital number that it has been
at the expense of ignoring more important risk management issues. This is why we
have stated that the model, its implementation, and their applications are important.
Both bankers and regulators are currently investigating the possibility of using the
VaR framework for credit risk management. Lopez and Saidenberg (1998) propose a
methodology for generating credit events for the purpose of testing and comparing
VaR models for calculating regulatory credit capital.