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where UDR is a regulatory estimate of the unexpected default rate, PD is the
estimated average default rate, and LGD is the loss given default. The resulting
percentage of capital requirement (C) is multiplied by EAD, the exposure of
the receivable at default (in most cases equal to the actual outstanding amount),
to get the account level capital requirement in absolute terms. The calculation
is done at account level, but the result should reflect only the account's contribution
to unexpected risk within a well-diversified portfolio. The UDR is given by
a regulatory formula that depends only on PD (other key parameters of the formula,
i.e., correlation and probability level are set by the regulator as given constants,
with a possible adjustment depending on PD in the case of correlation). In other
words, the capital requirement C is a function of PD and LGD,
The logic of Formula 2 is to give an estimation of unexpected systematic loss
relative to the expected loss at 99.9% probability level. This goal is mainly
achieved through the first part of the formula, UDR(PD) - PD, that models the
difference between the unexpected default rate value and the expected mean default
rate. On the other hand, the LGD parameter is defined in principle as a conservative
estimate of the long-term average loss rates on defaulted loans. The regulator
in addition, requires the banks to rather vaguely reflect the economic downturn
conditions, dependence on PD or other factors to capture the relevant risks.
Nevertheless under normal circumstances, the long-term average is considered
as satisfactory. In that case, the possibility of an unexpectedly high loss
rate is not captured by the formula at all.
In practice, the parameters PD and LGD are obtained from historical data on
homogenous (in terms of product, segment and rating) sets of receivables. The
values strongly depend on the definition of default, which determines the number
of loans marked as defaulted. The definition of default must satisfy certain
regulatory conditions, but the banks have a significant discretion in its implementation.
Assume that a bank suffered a total loss L on its historical portfolio P and
recorded a number of defaults, ND. Some of the defaulted receivables
might have been recovered fully, while others contributed to the total loss
L. If = V/N (where V is the total portfolio P volume and N is the total number
of receivables) is the average exposure of the observed receivables and = L/ND is the average loss on defaulted receivables, then the loss given default parameter
can be actuarially estimated as LGD = /. Similarly, PD can be estimated as ND/N.
Consequently, we get that the product PD.LGD = L/V is the average percentage
of observed loss rate, LR = L/V, on the portfolio, which does not depend on
the definition of default. |
