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

Capital Structure in Banks 213
lated, is all of the economic capital allocated by that approach. 373 “Grossing
up” 374 the single allocated amounts by the percentage of unallocated economic
capital also does not really address the problem, because it provides
the wrong incentives. For instance, it would indicate higher benefits from
reducing economic capital by shedding business units or transactions than
would actually appear to be the case.
The suggested approach for the three types of risk and the consideration
of correlations between these types of risk calculates the marginal economic
capital, which is sensible for determining whether a transaction creates value
or not. However, because we basically use proxies for the “with or without”
approach to do so, the aggregation and allocation problem, as indicated, is
unresolved.
This problem is fundamental to using VaR-type-based approaches to
determine the required capital amount and is also identified by Artzner et
al., 375 for example, who relate the problem that top-down and bottom-up
results may not be the same 376 to the problem that VaR is not coherent. 377
They formulate four conditions required for a risk measure to be coherent.
378 VaR violates the so-called subadditivity condition (while meeting the
other three), that is:
VaR (X + Y) ≠ VaR (X) + VaR (Y) (5.38)
the condition that the sum of the standalone VaR of two positions X and Y
be equal to the VaR of the portfolio consisting of the two positions is violated,
making VaR a risk measure that is not coherent.
Practitioners as well as theorists mention another problem of calculating
VaR on a standalone basis. 379 VaR can be subject to manipulation, because
there are situations in which all traders are within their VaR limit but the
overall bank might experience losses larger than VaR in any of the possible
economic situations.
373 For a mathematical proof of this proposition, see for example, Merton and Perold
(1993), p. 32.
374 See Merton and Perold (1993), p. 29, footnote 29. For a discussion of the various
methods to reallocate the difference (e.g., proportional scaling after diversification,
using internal betas), see Kimball (1998), pp. 44–52.
375 See Artzner et al. (1997) and (1999).
376 They approach the problem, however, from the perspective of an exchange calculating
margin requirement of single transactions. Here it is impossible and also not
desired to view a single position in a portfolio context.
377 A term first introduced by Artzner et al. (1997), p. 68.
378 These are subadditivity, homogeneity, monotonicity, and a risk-free condition. For
a detailed definition of these conditions see Artzner et al. (1997), pp. 68+.
379 See, for example, Johanning (1998), p. 95, and Artzner et al. (1997), p. 68.