Which stress test combinations do I need?

The approach to determining which stress tests to perform is best described by
considering a simple portfolio. Consider a portfolio of two assets, a 5-year Eurobond
hedged with a 10-year government bond. The portfolio is hedged to be delta neutral,
or in bond terminology, has a modified duration of zero. In other words the value of
the portfolio will not change if the par yield curve moves up (or down) in parallel, by
small amounts. If the stress test matrix shown in Table 8.3 were performed on the
delta neutral bond portfolio the results would be close to zero (there would be some
small losses shown due to the different convexity8 of the bonds). The value of this
simple portfolio will behave in a linear manner and there is therefore no need to have
multiple parallel shifts. However, even with the large number of shifts applied in
Table 8.3, not all the risks present in the portfolio have been picked up.
Being delta neutral does not mean the portfolio is risk free. In particular this
portfolio is subject to spread risk; i.e. the risk that the prices of Euro and government
bonds do not move in line with each other. It is speculated that this is the risk that
sunk LTCM; it was purportedly betting on spreads narrowing and remaining highly
correlated. The knock-on effect of the Asian crisis was that spreads widened dramatically
in the US market. The other risk that the portfolio is subject to is curve risk;
i.e. the risk that yield curve moves are not parallel. Stress tests must be designed
that capture these risks. Curve risk can be investigated by applying curve tilts to the
yield curve, rather than the parallel moves used in Table 8.3. Spread risk can be
investigated by applying price shocks to one side of a pair of hedged asset classes.
In this example a price shock could be applied to the Eurobonds only.
This example serves to illustrate the approach for identifying the stress tests that
need to be performed. A bank’s portfolio must be examined to identify the different
types of risk that the portfolio is subject to. Stress tests should be designed that test
the portfolio against price shocks for all the significant risks identified.
There are typically fewer significant risks than there are assets in a portfolio and
stress tests can be tailored to the products present in the portfolio. A portfolio without
options does not need as many separate yield curve shocks as shown in Table 8.3,
as the price function of such a portfolio will behave approximately linearly. From this
example it can be seen that the actual number of stress tests that need to be
performed, whilst still significant, is much smaller than the theoretical number of
combinations.
The stress tests illustrated by Table 8.3 in the previous section did not specify whether it is for a single market or group of markets. It is well known that the world’s
interest rates are quite highly correlated and that a shock to one of the major
markets, such as America, is likely to cause shocks in many of the world’s other
markets. When designing a framework of systematic stress test such relationships
must be taken into account. A framework of systematic stress test should include:
Ω Stressing individual markets to which there is significant exposure
Ω Stressing regional groups, or economic blocks; such as the Far East (it may also
make sense to define a block whose economic fortunes are closely linked to Japan,
The Euro block (with and without non-Euro countries) and a block of countries
whose economies are linked to that of the USA9
Ω Stressing the whole portfolio together – i.e. the bank’s total exposure across all
markets and locations
stressing exposure in each trading location (regardless of the magnitude of the
trading activity – Singapore was a minor operation for Barings). Stress tests in
individual trading locations should mirror those done centrally but should be
extended to separately stress any risk factors that are specific to the location.