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

192 RISK MANAGEMENT AND VALUE CREATION IN FINANCIAL INSTITUTIONS
4, according to the quality of the model used, which is determined
during the backtesting.
Therefore, the daily VaR (= ([Φ -1 (1 – α 1
)⋅σ R
])⋅V) is transformed into the
regulatory VaR R
by the following formula:
Φ
VaRR
= VaR ⋅ 10 ⋅CF
⋅
Φ
−1
−1
( 1 − α )
R
( 1 − α )
1
(5.30)
which results in multiplying σ R
by a factor between 22.07 and 29.43, instead
of just 2.33. 267
Note that this approach—even though calculated for a longer period of
time—still ignores the fact that there is an expected return on the portfolio
that eventually flows to the real capital resources. This expected return would,
therefore, reduce the capital requirement. However, as discussed previously,
expected earnings are not relevant as a capital resource from a regulatory
point of view. It is, therefore, reasonable to assume that E(R) = 0 when
calculating VaR R
.
Economic Capital for Market Risk Economic capital for market risk is the amount
of (virtual) capital required to ensure a certain solvency standard of a bank
over a one-year horizon at a certain confidence level. This higher confidence
level usually differs from the one chosen by the bank for internal purposes
and is depicted in Figure 5.8 as α 2
.
Taking (daily) VaR as a starting point for the calculation of economic
capital for market risk, we will have to make three adjustments to translate
VaR into economic capital: 268
■ As already indicated, VaR is typically calculated at a 97.5% (or 99%)
confidence level, whereas economic capital is calculated at, for example,
a 99.97% level.
■ VaR is a daily measure of total risk, while economic capital is typically
measured on an annual basis. As already discussed, we can scale
daily VaR to an annual VaR by multiplying it by √t (i.e., applying the
“square-root-of-time rule”), with the caveat that this only holds under
267 This would be correct when we assume that changes in the portfolio value are
normally distributed.
268 These three adjustments ensure that VaR is transformed into economic capital in
a way that is consistent with the calculation of economic capital for the other types
of risk.