Market risk stress tests

As noted above, the dominant issue in stress testing for market risk is the number
of risk factors involved and the very large number of different ways in which they
can combine. Systematic stress testing for market risk should include the following
elements:
Ω Non-linear price functions (gamma risk)
Ω Asymmetries
Ω Correlation breakdowns
Ω Stressing different combinations of asset classes together and separately
Ω appropriate size shocks
This section looks at ways of constructing stress tests that satisfy the elements listed
above, subsequent sections look at how to determine the stress tests required and
the size of the shocks to be used. Table 8.3 shows a matrix of different stress tests
for an interest rate portfolio that includes options. The table is an example of a
matrix of systematic stress tests.

The columns represent different parallel shifts in the yield curve and the rows
represent different multiples of volatility. It should be noted that it is not normally
sufficient to stress only parallel shifts to the yield curve. Where interest rate trading forms a substantial part of an operation it would be normal to also devise stress test
matrices that shock the short and long end of the yield and volatility curves.
The stress test matrix in Table 8.3 is dealing with gamma risk (i.e. a non-linear
price function) by stressing the portfolio with a series of parallel shifts in the yield
curve. The non-linear nature of option pricing means that systematic stress testing
must include a number of different shifts at various intervals, rather than the single
shift that would suffice for a portfolio of linear instruments (for example, equities).
Also note that the matrix deals with the potential for an asymmetric loss profile by
using both upward and downward shifts of both interest rates and implied volatility.
The first thing to note is that the worst-case loss is not coincident with the largest
price move applied. In fact had only extreme moves been used then the worst-case
loss would have been missed altogether. In this example the worst-case loss occurs
with small moves in rates. This is easier to see graphically.

Stress test matrices are often presented graphically as well as numerically as the
graphical representation facilitates an instant comprehension of the ‘shape’ of the
portfolio – giving a much better feel for risks being run than can be obtained from a
table of numbers.
Table 8.3 shows a set of stress tests on a complete portfolio where price changes
are applied to all products in the portfolio at the same time. This is only one of a
number of sets of stress tests that should be used. In Table 8.3 there are a total of
69 individual scenarios. In theory, to get the total number of stress test combinations,
the number of different price shocks must be applied to each asset in turn and to all
combinations of assets. If the price shocks shown in Table 8.3 were applied to a
portfolio of 10 assets (or risk factors), there would be a possible 70 5876 stress tests.
With a typical bank’s portfolio the number of possible stress tests would render comprehensive stress testing impractical. In practice a little thought can reduce the
number of stress tests required.
Table 8.3 is an example of a stress test matrix within a single asset class: interest
rates. As a bank’s portfolio will normally contain significant exposures to several
asset classes (interest rates, equities, currencies and commodities), it makes sense
to devise stress tests that cover more than one asset class. Table 8.4 shows a stress
test matrix that investigates different combinations of shocks to a bank’s equity and
interest rate portfolios.

Table 8.4 Cross-asset class stress test for equities and interest rates – profit and loss impact on the
portfolio (£000s)
Index Parallel interest rate shift (basis points)
(%
change) ñ200 ñ100 ñ50 0 50 100 200
ñ50% 50 ñ250 ñ370 ñ500 ñ625 ñ700 ñ890
ñ30% 250 ñ50 ñ170 ñ300 ñ425 ñ500 ñ690
ñ10% 450 150 30 ñ100 ñ225 ñ300 ñ490
0 550 250 130 0 ñ125 ñ200 ñ390
10% 650 350 230 100 ñ25 ñ100 ñ290
30% 850 550 430 300 175 100 ñ90
50% 1050 750 630 500 375 300 110

As in the previous example, the columns represent different parallel shifts in the
yield curve; the rows represent different shocks to an equity index. It should be noted
that this stress test could be applied to a single market, i.e. one yield curve and the
corresponding index, to a group of markets, or to the whole portfolio, with all yield
curves and indices being shocked together.
Again, it can be helpful to view the results graphically. Figure 8.9 instantly proves
its worth, as it shows that the portfolio is behaving in a linear fashion, i.e. that there
is no significant optionality present in the portfolio.
In normal circumstances equity and interest rate markets are negatively correlated,
i.e. if interest rates rise then equity markets often fall. One of the important things a
stress test matrix allows a risk manager to do is to investigate the impact of changing
the correlation assumptions that prevail in normal markets. The ‘normal’ market
assumption of an inverse correlation between equities and interest rates is in effect
given in the bottom right-hand quarter of Table 8.4. In a severe market shock one
might expect equity and interest rate markets to crash together i.e. to be highly
correlated. This scenario can be investigated in the upper right-hand quarter of the
stress test matrix. 247