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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¹ A full discussion of how returns on risk-adjusted capital are used to evaluate business segment performance can be found in the section on "strategy evaluation from the owners’ perspective" in the Tillinghast-Towers Perrin monograph RiskValueInsights™: Creating Value Through Enterprise Risk Management-A Practical Approach for the Insurance Industry.

² A simple example of how these properties manifest themselves can be found in Appendix G: Use of Appropriate Risk Measures in Determining Capital, in the Tillinghast monograph cited above.

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