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172 RISK MANAGEMENT AND VALUE CREATION IN FINANCIAL INSTITUTIONS
economic cycle, but rather the long-run average loss level across a range of
typical economic conditions. 178
There are three components that determine EL:
■
■
■
The probability of default (PD), 179 which is the probability that a
borrower will default before the end of a predetermined period of
time (the estimation horizon typically chosen is one year) or at any
time before the maturity of the loan
The exposure amount (EA) of the loan at the time of default
The loss rate (LR), that is, the fraction of the exposure amount that
is lost in the event of default, 180 meaning the amount that is not
recovered after the sale of the collateral
Since the default event D is a Bernoulli variable, 181 that is, D equals 1
in the event of default and 0 otherwise, we can define the expected amount
lost (EL) in the event of a default as follows (see Figure 5.6):
(1 – PD H
)
EA H
EA 0
PD H
EA H
(1 – LR H
)
Figure 5.6 Deriving expected losses.
Source: Adapted from Ong (1999), p. 101.
178 Note that Expected Losses are the unconditional estimate of losses for a given
(customer) credit rating. However, for a portfolio, the grade distribution is conditional
on the recent economic cycle. Thus, losses from a portfolio as predicted by a
rating model will have some cyclical elements.
179 Often also labeled expected default frequency (EDF); see, for example, Kealhofer
(1995), p. 53, Ong (1999), pp. 101–102.
180 Therefore also called severity, loss given default (LGD), or loss in the event of
default (LIED); see, for example, Asarnow and Edwards (1995), p. 12. The loss rate
equals (1 – recovery rate), see, for example, Mark (1995), pp. 113+.
181 See Bamberg and Baur (1991), pp. 100–101, that is, a binomial B(1; p) random
variable, where p = PD.