# Practical ERM Applications: Risk Integration

September 2003

This enterprise risk management column explains
how to model the integration of risks from various sources, describing the process
using the insurance industry as an example. The most critical step in integrating
risks of disparate types, and from various sources, is to express each risk
in terms of its potential impact on the key performance indicators (KPIs) used
to manage the organization. Once built, the structural financial model can be
used to create a probability distribution of KPI outcomes by means of simulation.

by Jerry Miccolis

Brinton
Eaton Associates, Inc.

Earlier articles in this series have treated certain "Practical ERM Applications,"
specifically, Assessing
Capital Adequacy (September 2002) and Capital Allocation (November 2002). This article describes an application that logically precedes
those two in the overall enterprise risk management (ERM) process, i.e., how
to model the integration of risks from various sources.

Consistent with previous articles, and to keep the discussion grounded in
practical reality, we will describe the process in terms of an example that
is specific to a certain industry, namely, the insurance industry.

## Preliminaries

Our discussion of the risk integration stage of the ERM process assumes that
individual risk factors already will have been identified and prioritized through
an enterprise risk assessment exercise.
It also assumes that probability distributions for certain risk factors will
have been determined. It is not assumed that probability distributions will
have been determined around all risk factors, only those that have been determined
to be (1) high priority and (2) of specific relevance to the question under
study, e.g., capital management.

For capital management purposes, one would expect to have probability distributions
around such risk factors as claim cost trends, natural catastrophe frequency
and severity, asset values, and investment returns, for example.

A discussion of both the risk assessment exercise and the determination of
probability distributions can be found in the Tillinghast-Towers Perrin monograph, RiskValueInsights:
Creating Value Through Enterprise Risk Management.

## Key Performance Indicators and Structural Financial Models

Perhaps the most critical step in integrating risks of disparate types, and
from various sources, is to express each risk in terms of its potential impact
(favorable or unfavorable) on the key performance indicators (KPIs) used to
manage the organization. For any given organization, these KPIs may be one or
more of such measures as revenue growth, earnings growth, earnings per share,
growth in surplus, growth in embedded value, customer satisfaction, and brand
image, for example.

For publicly traded companies, the KPIs are often explicitly or implicitly
defined by the market (i.e., they are the measures focused upon by the
organization's
stock analysts). Ideally, the prioritization of risks that emerge from the
organization's
enterprise risk assessment exercise will have been done in terms of each
risk's
impact on these KPIs.

Most organizations will have at least a simple financial model of their operations
that describe how various inputs (i.e., risk factors, conditions, strategies,
and tactics) will impact their KPIs. These models are often used in developing
strategic and operational plans. For example, insurance companies typically
make assumptions regarding future trends in claim costs by business segment
(e.g., by line of business, by region), which are used to determine needed rate
levels by segment. These rate level projections are then combined with assumptions
on volume growth and other relevant inputs to derive a pro forma estimate of
overall corporate earnings (or some other KPI).

Often, business decisions (e.g., rate level, volume growth) are fine-tuned
to produce the desired expected KPI result. Because these models explicitly
capture the structure of the cause-and-effect relationships linking inputs to
outcomes, they are termed structural (or causal)
financial models.

While some organizations develop more sophisticated structural financial
models than others, these models represent an excellent tool for integrating
individual risk factors. We will return to this idea momentarily.

## Stochastic Models

The structural financial models described above are generally deterministic models, i.e., they describe
expected outcomes from a given set of inputs without regard to the probabilities
of outcomes above or below the expected values. These models can be transformed
into stochastic (or probabilistic) models by treating certain
inputs as variable. For example, an expected future claim cost trend might be
an input to a deterministic model of corporate earnings; recognizing that there
is uncertainty in this trend, a probability distribution around the expected
trend would be an input to a stochastic model. The model output (corporate earnings,
in this case) would then also be a probability distribution.

## Risk Correlations

Some of the variable inputs may be correlated with one another. For example,
economic inflation (a driver of claim cost trends across multiple lines of business)
is highly correlated with interest rates (a driver of asset values and investment
returns). It is important to capture these correlationsâ€"indeed, this is the
essence of ERM. A structural financial model of the enterprise is a practical
way to do this.

In essence, a structural financial model allows one to capture the correlations
among variable inputs in a simple, accurate, and logically consistent way by
virtue of the model's cause-and-effect linkages of these inputs to common
higher-level inputs. How this works can be seen in the sidebar examples given
in Chapter V of RiskValueInsights:
Creating Value Through Enterprise Risk Management. To the extent that certain
inputs are not related to a common higher-level input, yet one believes that
correlation exists between them, these correlations can be stated explicitly
in terms of a covariance matrix, whose values can be determined through data
analysis and/or expert opinion.

## Structural Simulation Models

Once built, the structural financial model can be used to create a probability
distribution of KPI outcomes by means of simulation. Such a model is termed
a structural simulation model. A class of
structural simulation models specific to the property/casualty insurance sector
are termed Dynamic Financial Analysis (DFA)
models. The KPI distributions that result from a structural simulation model
can then be used for a number of purposes, including strategy optimization and
capital management; the latter was described in the earlier two "Practical
ERM Applications" articles cited above.

The marginal contribution of each individual risk factor to the overall risk
profile of the organization can be determined by "turning off" that risk
factor (i.e., by changing that particular input from stochastic to deterministic)
and examining the impact on the KPI probability distribution. This technique
provides a straightforward way of isolating the impact of a particular risk
factor (such as natural catastrophes) on overall capital adequacy, for example.
In this way, the prioritization of risk factors, which is typically done by
informed judgment in the risk assessment step, can be more rigorously validated.

## The Statistical Analytic Approach

It should be noted that an alternative to the structural simulation approach
is the statistical analytic approach. Statistical analytic approaches make a
number of simplifying, often restrictive, assumptions that allow the user to
generate results quickly by solving equations "in closed form", i.e., without
the need for simulations. These models therefore generally sacrifice structure
and realism for speed and simplicity. They also are designed around a getting
an answer to a specific narrowly defined question and thus lack the flexibility
and robustness of structural simulation models.

Moreover, statistical analytic models also require that the correlations
between all risk factors be explicitly stated in a covariance matrix,
without regard to cause-and-effect relationships; spurious results are
therefore more likely. Statistical analytic models are more prevalent and
relevant in the banking sector than in the insurance sector; in the banking
sector, risks are more "symmetric"
and well-behaved, and speed of calculation is more critical. Within the insurance
sector, statistical analytic models are more appropriate for industry oversight
bodies than for individual companies; they can generally be run using publicly
available data.

A fuller comparison of these two approaches is contained in an earlier article
in this series, The
Language of Enterprise Risk Management: A Practical Glossary and Discussion
of Relevant Terms, Concepts, Models, and Measures (May 2002).

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