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

Capital Structure in Banks 167
The risk measure, which calculates that a certain dollar loss 157 will only
be exceeded with a given probability (α%) over some measurement period,
is commonly called (in the banking industry) value at risk (VaR). 158 Therefore,
we can generally define:
p(∆V ≤ – VaR) ≤ α% 159 (5.1)
where p = probability
∆V = change in value V; in this case a loss
The VaR at the probability level of α% is equivalent to the α-quantile
of the cumulative probability distribution F of the changes in the portfolio
value 160 (see Figure 5.5) between now and date H, 161 the end of the predetermined
measurement period. Therefore, without making any assumptions
about the shape of the distribution function, we can reformulate:
p
1
F( . )
α%
E( V)
V
Figure 5.5
Value at risk.
VaR
157 This loss is usually stated as a positive number.
158 See Stulz (2000), p. 4-9.
159 See for example, Schröck (1997), p. 43, and Hirschbeck (1998), p. 143, with a list
of references to the literature.
160 See Stulz (2000), p. 4-9.
161 See Artzner et al. (1997), p. 68. In a later version of their paper, Artzner et al.
emphasize that the definition relates to future values, that is, expectations; see Artzner
et al. (1999), p. 205.