each division reflects the effects of a 3.1% uptick in the housing market, scenario two reflects a .5% increase, and so on (as
shown in Figure 1, below).
Figure 1: The Generation of Coherent Scenarios
Div. 1 Investment Model
$2 M
0
$3 M
:
-$2 M
-$1 M
$2 M
Coherent Divisional
Output Scenarios
Div. 2 Loan Model
$1 M
-$1 M
$2 M
:
-$3 M
0
$2 M
Common
Input Scenarios
+ 3.1%
+.05%
+ 5.2%
:
- 2.6%
- 1.8%
2.2%
+ 3.1%
+.05%
+ 5.2%
:
- 2.6%
- 1.8%
2.2%
The key to this approach is that the coherent output scenarios of each division may be added together, element by
element, as shown in Figure 2 (below), to yield one thousand
scenarios of the financial condition of the bank as a whole —
or, in effect, a consolidated risk statement.
Figure 2: The Addition of Coherent Scenarios
Consolidated
Output Scenarios
$2 M
0
$3 M
:
-$2 M
-$1 M
$2 M
$1 M
-$1 M
$2 M
:
-$3 M
0
$2 M
$3 M
-$1 M
$5 M
:
-$5 M
-$1 M
$4 M
+=
The inputs may be individually designed stress scenarios,
historical prices (as in historical simulation value-at-risk) or
outputs from a simulation generator (the Libor Market Model
is a popular way to generate consistent scenarios for interest
and exchange rates calibrated by market data). This avoids
central risk management having to evaluate each business
unit’s complex positions.
The scenario approach to modeling probability distributions has been described in the literature2, 3, and has been applied in a number of industries; although the exact definition
of scenario may vary from case to case, the basic approaches
are the same. Steve Strommen, a senior actuary at Northwest-
ern Mutual, says that the Society of Actuaries, for example,
is developing a file format “for easily sharing stochastically
generated sets of economic scenarios, wherein each scenario
tracks multiple variables through time — e.g., inflation, interest rates and stock market returns.” Known as EconSML4, this
standard will provide a precise definition of “scenario” in this
context.
EconSML is also being designed to provide an open-source
software library that commercial developers can use to read
and write these files, as well as to access their data efficiently.
Royal Dutch Shell uses scenario libraries to analyze portfolios
of petroleum exploration sites.
5
Properly generated scenario libraries obey the conventional
rules of arithmetic. That is, the scenarios representing A+B
are found by adding the scenarios for A and the scenarios for
B, element by element. This is a big plus, but on the downside
they are extremely cumbersome, potentially containing hundreds of millions of numbers. This makes them impractical
for general use.
Technological Advances
Three technologies — distribution strings, interactive simulation and computer visualization — have taken the scenario
approach from a theoretical ideal to a practical reality. Distribution strings provide a standardized way to compress and
share scenarios; interactive simulation provides a new intuitive
paradigm for processing scenarios; and visualization provides
a method for validating and interpreting scenarios.
Distribution Strings
The distribution string (DIST) is a recently developed standard format for compressing thousands of scenarios (like those
previously described) into a single string of characters. Thus,
a cell in a spreadsheet or entry in a database may contain
thousands of numbers, which may be quickly expanded and
run through a risk model. First developed for use in strategic
planning at Shell in 2008, the DIST has recently been further
refined and standardized in collaboration with Merck & Co.,
Oracle Corp., SAS Institute and Frontline Systems.
6
Eric Wainwright is a member of the development team for
Oracle Corp’s Crystal Ball Monte Carlo simulation package.
He has long been a proponent of better standards for managing the distributions that feed simulations. “The challenge
for companies has been to model risk in a way that captures
the interrelationships between uncertainties across the enterprise,” says Wainwright. “The DIST standard, along with
