Fishing for complements
Christopher C. Finger
Stress testing works as a complement,
rather than as a supplement, to major
risk management tools such as Value-
Though long a staple risk management practice,
stress testing has received little formal discussion.
An important step was the survey of stress testing
practices by the Bank for International Settlements
(BIS) in 2005; the quotation above is the ﬁrst sen-
tence of the survey’s conclusion.
This is a particularly subtle use of language for a reg-
ulatory document, and I imagined the writer chuck-
ling as I headed to the dictionary to ascertain the
precise distinction between supplement and comple-
ment. There are two: ﬁrst, supplement simply means
to add to, while complement brings to notion of com-
pleting; second, when supplement is used, it carries
the connotation that the thing being supplemented is
somehow deﬁcient, while something that we com-
plement is usually ﬁne as it stands.
So are stress tests truly complements—that is a com-
pletion of tools that are already quite good—as the
BIS survey suggests, or are they merely supplements,
attempting to bolster something that is not all that
great to begin with?
In part, we should ask whether the “major risk man-
agement tools” are of value on their own. Let us as-
sume that these tools incorporate statistical risk mod-
els broadly. Generally, statistical risk models incor-
porate two elements: a forecast for the joint distri-
bution of the future state of a (typically large) set of
market factors, and a link from these market factors
to a speciﬁc set of holdings. At a basic level, we
use statistical risk models because there are a lot of
different things that can happen to the market, and
we cannot hope to assess each of the different pos-
sibilities individually. We use statistical models to
merge an objective view of plausible market events
with our own portfolio sensitivities, and to summa-
rize how bad things might get.
Are today’s statistical risk models useful on their
own (and in need of a complement) or deﬁcient (and
in need of a supplement)? It is easiest to ﬁnd pro-
ponents of the latter choice, though model defenders
exist. Rather than assess these models in detail, our
approach here will be to survey stress testing prac-
tices, and ask what these say implicitly about our
conﬁdence in the statistical models.
Last year’s model
Moving to actual stress test practices, let us begin
with stress tests used in implementations of risk-
based capital. In these cases, a supervisory body
speciﬁes a (possibly large) set of prescriptive tests,
and the party being tested is said to “pass” if its worst
loss across all the tests is less than a predetermined
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