Risk measured is too high

Possible causes
It is often difficult to aggregate risk across risk factors and broad risk categories in a
consistent way. Choosing too conservative a method for aggregation can give risk
figures that are much too high. An example would be using a simple sum across
delta, gamma, and vega risks, then also using a simple sum between interest rate,
FX, and equity risk. In practice, losses in these markets would probably not be
perfectly correlated, so the risk figure calculated in this way would be too high.
A similar cause is that figures received for global aggregation may consist of
sensitivities from some business units, but risk figures from others. Offsetting and
diversification benefits between business units that report only total risk figures
cannot be measured, so the final risk figure is too high.
Solutions
Aggregation across risk factors and broad risk categories can be done in a number
of ways. None of these is perfect, and this article will not discuss the merits of each
in detail. Possibilities include:
Ω Historical simulation
Ω Constructing a large correlation matrix including all risk factors
Ω Assuming zero correlation between broad risk categories (regulators would require
quantitative evidence justifying this assumption)
Ω Assuming some worst-case correlation (between 1 and 0) that could be applied to
the risks (rather than the sensitivities) no matter whether long or short positions
were held in each broad risk category.
To gain full offsetting and diversification benefits at a global level, sensitivities must
be collected from all business units. If total risks are reported instead, there is no
practical way of assessing the level of diversification or offsetting present.
P&L has a positive bias
There may be exceptions on the positive but not the negative side. Even without
exceptions, the P&L bars are much more often positive than negative (Figure 9.7). 282