The March Toward
a Consolidated Risk
Statement
The scenario approach to modeling probability distributions is now
practical, and consolidated risk models are now possible, thanks largely
to technological advances such as distribution strings, interactive
simulation and computer visualization.
BY SAM SAVAGE AND AARON BROWN
hat did Fibonacci bring to Western Culture in the 13th Century? Absolutely
nothing. Nada. Zilch. ZERO!
1 And
along with it, he brought the rest of the
Arabic digits for good measure. This
more transparent numerical representation quickly displaced Roman numerals
in commerce, due to its greatly superior arithmetic. Today, a
confluence of technologies has the potential to bring a similar
transparency to the arithmetic of uncertain quantities — i.e.,
probability distributions — with beneficial consequences for
numerous industries.
“In order to model increasingly complex business problems,
we need to be able to decompose them into simpler models,
with clearly assigned accountabilities, and then consolidate the
results back up to the top,” says Stefan Scholtes, professor of
management science at Cambridge University’s Judge Business
School. Scholtes notes that while this is the way that financial
statements are currently constructed, “risk models typically do
not have this additive property.” That is, even if divisions A
and B can calculate their risk exposures accurately (as RA and
RB), the total risk of the two divisions is not RA plus RB.
Daniel Zweidler, senior vice president at Merck & Co.’s Research Laboratories, summarizes this dilemma as follows: “In
the presence of global uncertainties, the lack of coherence in
W
simulation results has been a major obstacle in both scientific
and business related stochastic models. Commodity futures,
energy price predictions and GDP growth rate forecasts, for
example, should all be incorporated in a consistent manner
across all enterprise assets.”
Without the benefit of additivity, the required consistency
cannot be accomplished by rolling up simpler models into more
complex ones. Instead, firms tend to create large, all-encom-passing systems that may collapse under their own complexity.
Scenario Libraries
One solution to this problem, familiar to many risk managers,
is to represent probability distributions of such uncertainties
as prices, interest rates, and other global economic factors, as
sets of common scenarios. To aggregate exposures across an
organization, the scenarios may be sent to each business unit,
whereupon they are run through local models to provide the
P&L impact of each scenario on that unit.
Consider, for example, a bank with two divisions, one for
investments and one for loans. Suppose further that the primary uncertainty for each division is the state of the housing
market. The same set of one thousand market scenarios would
be sent to each division, which would then be sequentially run
through that division’s financial model. The output scenarios
of each division are said to be coherent — i.e., scenario one for
