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JULY 2011 | accoUntancYmagazine.com70
n professionaL briefing | business risk analysis
a watertight risk model
uses the monte carlo
simulation as a predictive
tool. chris kelly and
david alexander explain
monte carlo
or bust
Japan has shown that the future is not only uncertain but that inter-
related risks can escalate into human as well as financial catastrophe.
Can board directors foresee in a systematic way the full range of
business risks and their interdependencies?
Directors will be familiar with the typical risk matrix which shows a
prioritised list of risks with estimates of likelihood and impact. If likelihood
and impact are multiplied together and aggregated, this will show the
organisation’s estimated mean exposure.
But such a number only describes, at best, the organisation’s average
risk exposure at a point in time. The probability of the best case scenario
(that none of the risks occur in a given year) may not be clear. Similarly
the theoretical worst case scenario (that all of the risks occur in a given
year) is usually not a realistic premise for decision-making. Most risks will
probably not occur in a given year, the financial impact of those that do
will differ from the estimates, and there may be hidden inter-relationships
between individual risks. These omissions limit the informational value
of the traditional risk matrix. Furthermore, as one unlucky CEO said of his
previous risk advisers: ‘The risk that brought down the company was not
even on the risk matrix’, it having been compiled in a vacuum with only
pitiful consultation.
While the future cannot be known with certainty, Monte Carlo
simulation can help in examining meaningfully a range of likely as well
as unlikely possibilities. Anecdotally it was developed by world war
two weapons scientists to predict what would occur in an atomic chain
reaction. Despite its macabre goal they gave it the euphemistic name
‘Monte Carlo’ due to its reliance on simulating thousands of random
events like a roulette wheel. Instead of producing just an average picture
of what might happen in the future, Monte Carlo goes one step further by
producing a probability distribution. This can show a range of outcomes
as well as the likelihood of a range of best or worst case scenarios;
information simply not given by the average.
Once the model is set up the inputs can be updated over time as new
information comes to light and the results can be modified with ‘what if’
testing. When presented to management the underlying assumptions,
scenarios and any overlooked ‘known unknowns’ can be updated in real-
time. This can help with improving the robustness of the model’s input
assumptions and in testing the financial implications of cost-benefit decisions.
How it works
Monte Carlo simulation involves taking the organisation’s best estimates
of what the future might bring and then computing thousands of random
events reflecting those assumptions. Effectively it allows us to create
thousands of potential versions of what the future might bring. These
70
accoUntancYmagazine.com | JULY 2011 71
business risk analysis | professionaL briefing n
Chris Kelly is an Australian
chartered accountant and
consultant at advisory firm
Kelly Partners LLP,
ckelly@kellypartners.co.uk.
Dr David Alexander is
a statistician at the
Commonwealth Scientific and
Industrial Research Organisation,
david.alexander@csiro.au
futures can then be aggregated into a probability
distribution for further analysis.
In setting up the simulation it is important to input
our best assumptions within consistent timeframe and
quantification boundaries. Illustrating with the risk
matrix example, the following questions can help frame
the analysis: What future time period is assumed by the
probability estimations? What interdependencies are
likely to exist between risks? Are impact cost ranges
before or after insurance recoveries? Before or after tax?
The simulation model, straightforward enough that it
can be done in a spreadsheet, is powerful enough that it
can take these factors in its stride.
To maintain the quality and usefulness of the output,
the preferred approach is to keep it understandable and
simultaneously harness as much of the organisation’s
internal brainpower as practicable. Facilitated sessions,
group brainstorming and experimentation all help in
harnessing those with insights, competitor intelligence
or relevant experiential knowledge from shop floor to
board directors.
Once entered into the model, the simulated events can
be generated. Typically 10,000 iterations are examined,
which supplies a reasonable degree of confidence that
most realistic future scenarios have been captured.
A simple check on the sufficiency of iterations is to
recalculate a few times; if the summary results do not
change much then the current number of iterations is
sufficient to iron out the random variations. If the results
change too much each time then the number of iterations
can be increased until the distribution stabilises.
The thousands of individual events computed by the
simulation are summarised in a probability distribution
as shown in business risk probability distribution. The
shape of the distribution will vary depending on what
is being analysed. The purpose of the distribution is
to illustrate the likelihood of realistic best and worst
case scenarios as well as the average and everything in
between in a single diagram. It is not a crystal ball but
might be the next best thing.
In risk analysis, the distribution is skewed, never
following a normal Gaussian curve. Monte Carlo, when
properly used in finance, often results in non-normal
curves which is reassuring: from experience, financial
world phenomena frequently do not have statistically
‘normal’ characteristics. Instead of using standard
deviations as the summarisation basis, the output is
aggregated into meaningful cost bands so a board can
see its range of likely exposures, noting the worst case
scenarios require special attention as their occurrence,
albeit low in probability, are precisely the catastrophes
to avoid. With this information, the organisation can
make rational cost-benefit decisions on risk mitigation
measures and the required level of insurance cover.
best case scenarios
Monte Carlo simulation is a great tool for engaging
with the best brains in the business and for providing
insights well beyond mere averages. In this synopsis
future business risks have been used to illustrate how
Monte Carlo can appreciably improve risk management.
Monte Carlo has other uses for finance professionals
beyond risk prediction. Inverting the above approach
a company can seek out best case scenarios. With this
mindset Monte Carlo can be used to seek out either the
best possible outcome or to improve the chances of the
best likely outcome based on an input set of variables.
For a business this might involve analysing future
customer demand based on different pricing options
using the sales team’s experiential customer and
competitor intelligence, and then feeding those results
into production capacity, procurement or forward
purchasing needs. Or among a range of existing and
potential projects or assets with uncertain returns, which
combination of start-ups and closures will optimise
the overall returns over the next five years. Or which
combination of local, overseas, fixed and variable rate
borrowing options is most likely to reduce the overall cost
of finance within a range of foreign exchange and interest
rate upper and lower limits.
In all these cases, Monte Carlo provides not just
an average nor even a high/medium/low estimation,
but a fuller snapshot of all possible outcomes which
the future might bring, but also points to the actions
needed today to either minimise future risks or to
maximise future opportunities.
0
1000
2000
3000
4000
5000
0 2 4 6 8 10 12 14 16 18 20 22
20.00%
60.00%
80.00%
100.00%
120.00%
40.00%
0.00%
Number of occurrences
Cost £ millions
Cumulative probability
Frequency of events Cumulative probability
business risk probability distribution Monte Carlo
simulation is
a great tool
for engaging
with the best
brains in the
business and
for providing
insights well
beyond mere
averages