Current practice

We have already discussed the assumptions behind VaR. As with any model, we
must understand the sensitivity of our VaR model to the quality of its inputs. In a
perfect world we would also have implemented more than one model and have
reconciled the difference between the models’ results. In practice, this usually only
happens as we refine our current model and try to understand the impact of each
round of changes from old to new. Beder (1995) shows a range of VaR calculations
of 14 times for the same portfolio using a range of models – although the example is
a little artificial as it includes calculations based on two different time horizons. In a
more recent regulatory survey of Australian banks, Gizycki and Hereford (1998)
report an even larger range (more than 21 times) of VaR values, though they note
that ‘crude, but conservative’ assumptions cause outliers at the high end of the
range. Gizycki and Hereford also report the frequency with which the various
approaches are being used: 12 Delta-Normal Variance–Covariance, 5 Historical
Simulation, 3 Monte Carlo, 1 Delta-Normal Variance–Covariance and Historical
Simulation. The current best practice in the industry is historical simulation, using
factor sensitivities, while participants are moving towards historical simulation,
using full revaluation, or Monte Carlo.
Note that most implementations study the terminal probabilities of events, not
barrier probabilities. Consider the possibility of the loss event happening at any time
over the next 24 hours rather than the probability of the event happening when
observed at a single time, after 24 hours have passed. Naturally, the probability of
exceeding a certain loss level at any time over the next 24 hours is higher than the
probability of exceeding a certain loss level at the end of 24 hours. This problem in
handling time is similar to the problem of using a small number of terms in the
Taylor series expansion of a portfolio’s P/L function. Both have the effect of masking
large potential losses inside the measurement boundaries.
The BIS regulatory multiplier (Stahl, 1997; Hendricks and Hirtle, 1998) takes the
VaR number we first calculated and multiplies it by at least three – and more if the
regulator deems necessary – to arrive at the required regulatory capital. Even though
this goes a long way to addressing the modeling uncertainties in VaR, we would still
not recommend VaR as a measure of downside on its own. Best practice requires that we establish market risk reserves (Group of Thirty, 1993) and model risk reserves
(Beder, 1995). Model risk reserves should include coverage for potential losses that
relate to risk factors that are not captured by the modeling process and/or the VaR
process. Whether such reserves should be included in VaR is open to debate.