Risk Management and Value Creation in ... - Arabictrader.com

Capital Structure in Banks 183
EL P
Probability
Confidence Level
UL P = σLoss
Losses
Economic Capital
= UL P x CM
Figure 5.7 Economic capital for credit risk.
Source: Adapted from Ong (1999), p. 169.
0
Since the sum of ULC i
s equals UL P
, we can attribute the necessary economic
capital at the single transaction level as follows:
Therefore:
Economic Capital P
= UL P
⋅ CM (5.21)
Economic Capital i
= ULC i
⋅ CM (5.22)
that is, the required economic capital at the single credit transaction level is
directly proportional to its contribution to the overall portfolio credit risk.
The crucial task in estimating economic capital is, therefore, the choice
of the probability distribution, because we are only interested in the tail of
this distribution. Credit risks are not normally distributed but highly skewed
because, as mentioned previously, the upward potential is limited to receiving
at maximum the promised payments and only in very rare events to
losing a lot of money.
One distribution often recommended 222 and suitable for this practical
222 See Ong (1999), p. 164. Other recommended distributions for finding an analytic
solution to economic capital are the inverse normal distribution (see Ong (1999), p.
184) or distributions that are also used in extreme value theory (EVT) such as Cauchy,
Gumbel, or Pareto distributions. For a detailed discussion of EVT, see Reiss and
Thomas (1997), Embrechts et al. (1997 and 1998), McNeil and Saladin (1997), and
McNeil (1998).