Practical ERM Applications: Capital Allocation
November 2002
In this article on enterprise risk management,
Jerry Miccolis outlines a process for assessing capital adequacy using the insurance
industry as an example.
by Jerry
Miccolis
Tillinghast-Towers
Perrin
In the preceding article in this series ("Practical
ERM Applications: Assessing Capital Adequacy", September 2002), the determination
of an appropriate amount of economic capital for an enterprise was discussed.
This article will address the next logical step in the process. Consistent with
previous articles, and to keep the discussion grounded in practical reality,
a process for assessing capital adequacy is outlined based on an example that
is specific to a certain industry, namely, the insurance industry.
Background
"Enterprise risk management" (ERM) for an insurance company has been defined
as the optimization of the dynamic relationship between risk and value throughout
the enterprise. The ERM process consists of the development, implementation,
and monitoring of financial and operational strategies for assessing, mitigating,
financing, and exploiting risks of all types for the purpose of increasing enterprise
value. Enterprise value is increased by first establishing the minimum amount
of capital to provide security to the policyholders, and then selecting business
strategies that optimize—on a risk/reward basis—growth, return, and consistency
for the benefit of the shareholders.
Enterprise-level capital determination and capital
allocation to individual business segments are particularly critical
elements of the ERM process.
Overall Process
Once the required enterprise-level capital has been determined, most well-managed
companies allocate that capital to each of the business segments that constitute
the enterprise. This is not a physical allocation of capital, but an "attribution"
of capital for purposes of evaluating the financial performance of each business
segment in a risk-adjusted manner. That is, the attributed capital amounts represent
the base, or denominator, against which business segment profits are measured.
A business segment that contributes a disproportionate share to the solvency
risk of an enterprise should draw a disproportionate amount of attributed capital,
and thus should be required to provide a disproportionate share of profits,
all else equal. Thus, business segment performance is evaluated on a rigorous
risk/reward basis.1 (We will not go into the details
of performance measurement here, except to point out that this is the purpose
for attributing capital to business segment, i.e., to establish the proper risk/reward
framework for measuring business segment performance.)
Capital is attributed to business segment by adopting a common capital standard, and thus a common
risk threshold, across all business segments. Capital requirements by business
segment are then derived in the same manner as for the enterprise overall. Note
that the enterprise enjoys the benefits of risk diversification since it encompasses
various business segments that are not perfectly correlated with one another.
This diversification benefit needs to be
equitably allocated to each business segment.
Common Capital Standard
There are a number of ways to attribute capital to business segments. A simple
way is to simply attribute it proportionately based on the present value of
liabilities generated by each business segment. However, this approach does
not reflect the relative "riskiness" that each business segment contributes
to the overall risk profile of the enterprise.
A better way is to establish a common quantitative risk threshold across
all business segments, and to use that threshold to determine segment capital
requirements, in much the same way as was done for the overall enterprise capital
requirement. For example, if a threshold based on a probability of ruin or an
economic cost of ruin (ECOR)—both of which were defined in the preceding article—was
used to establish enterprise-level economic capital, then that same threshold
can be used to determine segment-level economic capital.
Actually, for purposes of attributing capital below the enterprise level,
ECOR measures have more desirable statistical properties than probability of
ruin measures.2 Thus, even if enterprise-level capital
is established using a probability of ruin measure, it is advisable to convert
that threshold to its equivalent enterprise-level ECOR threshold (as can be
seen from the previous article, there is a one-to-one correspondence between
a probability of ruin threshold and an ECOR threshold), and to use that ECOR
threshold to determine capital attribution to each business segment.
Diversification Benefit
In any event, if the capital requirement for each business segment is determined
on a stand-alone or "first-in" basis, then it will virtually always be the case
that the sum of the segment-level capital requirements will be greater than
the enterprise-level capital requirement, even though the same quantitative
threshold was used at each level. This is because at the enterprise level, there
is an implicit "diversification benefit." That is, since in practice all business
segments are typically not perfectly positively correlated, the enterprise benefits
from diversification of risk, otherwise known as the portfolio effect. Therefore,
the capital requirement of the aggregate portfolio is necessarily less than
the sum of the individual first-in capital requirements of each segment in the
portfolio.
To properly attribute capital then, this diversification benefit must be
equitably allocated to each business segment. There is a straightforward way
to do this.
The segment-level capital requirement derived on a first-in basis, as described
above, can be viewed as a ceiling for the equitable attribution of capital to
each segment. Segment-level capital requirements can also be determined on a
marginal or "last-in" basis. Thus, the capital requirement for Business Segment
A is the difference between the requirement derived for the enterprise overall
and the requirement derived for the enterprise with Segment A removed. This
difference represents the marginal amount of capital needed by adding Segment
A to the portfolio on a last-in basis.
Segment-level capital determined on this basis represents the floor for an
equitable attribution, since if Segment A is brought into the portfolio in any
other order but last, it will typically generate a higher capital requirement.
The equitable attribution for any segment is therefore between its ceiling and
its floor, as illustrated below.
Figure
1
When the ceilings and floors are reasonably close, it is a simple matter
of judgment to select a capital attribution amount between them. When they are
far apart, an additional step may be needed (this is the so-called "Shapley
method," described by means of example below).
If there are five business segments to which enterprise capital must be attributed,
then there are five different orders in which Segment A can be brought into
the portfolio, i.e., first through fifth. If Segment A is first in, its derived
capital requirement will be at its ceiling; if it is second in, the requirement
will be lower; if third in, lower still; until, at fifth or last in, it will
be at its floor.
An equitable attribution for Segment A then is simply the average derived
capital requirement over all five possibilities. A similar exercise is performed
for Segments B through E. Derived in this way, the sum of the resulting segment-level
capital requirements is guaranteed to equal the enterprise-level capital requirement.
When there are a large number of business segments, the necessary calculations
can be voluminous, but the logic, and thus the computer programming, is quite
straightforward.
Closing Considerations
It should be pointed out that there is an alternative, perfectly legitimate,
approach to risk-adjusted performance measurement by business segment that does
not involve capital attribution in the sense described above. This alternative
approach more explicitly recognizes the fact that each business unit can potentially
draw on the entire capital base of the enterprise, not just some attributed
portion of it. This recognition takes the form of deducting an appropriate "capital
charge" (reflecting each business segment’s relative potential of exercising
these "drawing rights") from the numerator of each business segment’s return-on-capital
ratio, rather than risk-adjusting the denominator.
Whatever approach is adopted, it is important to recognize that the risk
adjustments we have been discussing address risk from the perspective of the customer, i.e., the policyholder in the
case of our insurance company example. That is, these adjustments reflect solvency risk (through probability of ruin
or ECOR, for example), which occurs in the extreme tail of the probability distribution
of results.
This is only half the story. When comparing risk-adjusted returns on capital
among business segments, another dimension of risk must be reflected, namely
the earnings risk from the perspective of
the shareholder. This risk relates to the
"quality of earnings" (i.e., how likely it is that earnings will not deviate
too far from its expectation) and occurs in the heart of the probability distribution
of results. This distinction between customer-relevant and shareholder-relevant
measures of risk is more fully discussed 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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