Stressing VaR – covariance and Monte Carlo simulation methods

The adoption of VaR as a new standard for measuring risk has given rise to a new
class of scenario tests, which can be undertaken with any of the three main VaR
calculation methods: covariance, historical simulation and Monte Carlo simulation
(see Best, 1998). The use of historical simulation for scenario testing was discussed
in the preceding section. With the covariance and Monte Carlo simulation methods
the basic VaR inputs can be stressed to produce a new hypothetical VaR.

Scenario testing using either covariance or Monte Carlo simulation is essentially the
same, as volatilities and correlations are the key inputs for both the VaR methods.
Before describing the stress testing of VaR it is worth considering what the results
of such a stress test will mean. At the beginning of this chapter stress testing was
defined as the quantification of potential significant portfolio losses as a result of
changes in the prices of assets making up the portfolio. It was also suggested that
stress tests should be used to ascertain whether the bank’s portfolio represents a
level of risk that is within the bank’s appetite for risk. Scenario and stress testing
have been implicitly defined so far as investigating the portfolio impact of a large
change in market prices. Stress testing VaR is not an appropriate way to undertake
such an investigation, as it is simpler to apply price changes directly to a portfolio.
The stressing of volatility and correlation is asking how the bank’s operating, or dayto-
day, level of risk would change if volatilities or correlations changed. This is a
fundamentally different question than is answered by stress testing proper.
Nonetheless it is a valid to ask whether the bank would be happy with the level of
risk implied by different volatilities and correlations. Given that changes in volatilities
and correlations are not instantaneous they do not pose the same threat to a trading
institution as a market shock or adjustment.