Stress test limits

A bank must limit the amount it is prepared to lose due to extreme market moves,
this is best achieved by stress test limits. As VaR only controls day-to-day risk, stress
test limits are required in addition to VaR limits. Stress test limits are entirely
separate from VaR limits and can be used in a variety of ways (see below). However
they are used, it is essential to ensure that stress test limits are consistent with the
bank’s VaR risk management limits, i.e. the stress test limits should not be out of
proportion with the VaR limits. Stress test limits should be set at a magnitude that
is consistent with the ‘occasional loss’ figure from Figure 8.10, above. However,
significantly larger price shocks should also be tested to ensure that the ‘extreme
tolerance number is not breached’.

Stress test limits are especially useful for certain classes of products, particularly
options. Traditional limits for options were based around the greeks; delta, gamma,
vega, rho and theta. A single matrix of stress tests can replace the first three greeks.
The advantage of stress tests over the greeks is that stress tests quantify the loss on
a portfolio in a given market scenario. The greeks, particularly, gamma, can provide
misleading figures. When options are at-the-money and close to expiry gamma can
become almost infinitely large. This has nothing to do with potential losses and
everything to do with the option pricing function (Black–Scholes). Figure 8.11 gives
an example of stress limits for an interest rate option portfolio. This example of stress
test limits could be used for the matrix of stress tests given above in Table 8.3.

Figure 8.11 shows three stress test limits, which increase in magnitude with the
size of the shift in interest rates and the change in volatility. Stress tests limits like
this make it easy for trading management to see that losses due to specified ranges
of market shifts are limited to a given figure. Using the greeks, the loss caused by
specific market shifts is not specified (except for the tiny shifts used by the greeks).
Stress test limits can be used as are standard VaR, or other, risk limits, i.e. when
a stress test identifies that a portfolio could give rise to a loss greater than specified
by the stress test limit, then exposure cannot be increased and must be decreased.
This approach establishes stress test limits as ‘hard’ limits and therefore, along with
standard risk limits, as absolute constraints on positions and exposures that can be
created.

Another approach is to set stress test limits but use them as ‘trigger points’ for
discussion. Such limits need to be well within the bank’s absolute tolerance of loss.
When a stress test indicates that the bank’s portfolio could give rise to a specified
loss, the circumstances that would cause such a loss are distributed to senior
management, along with details of the position or portfolio. An informed discussion
can then take place as to whether the bank is happy to run with such a risk.
Although EVT and statistics can help, the judgement will be largely subjective and
will be based on the experience of the management making the decision.