Expert Commentary

# Practical ERM Applications: Assessing Capital Adequacy

The first step in effective capital management is the assessment of the capital necessary to run the enterprise. Jerry Miccolis outlines a process for assessing capital adequacy.

In prior articles in this series (e.g., "Enterprise Risk Management in the Financial Services Industry: from Concept to Management Process," November 2000; and "ERM and September 11," November 2001), capital management was cited as a critical component of enterprise risk management (ERM). The first step in effective capital management is the assessment of the necessary level of overall capital with which to run the enterprise. The role of capital—and thus the determination of adequate capital levels—is, in a significant sense, industry-specific.

To keep the discussion grounded in practical reality, we outline a process for assessing capital adequacy based on an example that is specific to a certain industry. In keeping with the convention adopted in earlier articles, the example industry is the insurance industry.

## Background and Overview

In this series, 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 the desired degree of 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.

In the discussion that follows, it is assumed that the assessment, calibration,
and interrelationships of risks of various types—e.g., hazard, financial, operational,
strategic—have already been modeled (as described in earlier articles in this
series, such as "Modeling the Reality of Risk: The Cornerstone of Enterprise Risk Management," July
2001; and "The Language of Enterprise Risk Management: A Practical Glossary and Discussion of Relevant Terms, Concepts, Models, and Measures," May 2002). This modeling is accomplished
by first expressing these risks in terms of their potential impact on the key
performance indicators (e.g., earnings, growth in surplus) used to manage the
organization. The organization's pro forma financial model is used to link the
risks to these "downstream" performance outcomes within a causal framework.
Interrelationships among risks are captured by recognizing the linkage of the
risks to common higher-level "upstream" causes. By incorporating the probability
distributions around the risks that are produced by a risk assessment exercise,
the financial pro forma model is converted into a very powerful *structural simulation model* of the enterprise.

Capital adequacy for the enterprise is determined by first articulating a *qualitative capital standard*, which is typically
expressed in terms of insurance or bond rating agency criteria. This qualitative
standard is converted into a *quantitative risk
threshold* by examining the actual performance of similarly rated companies
over time. Measures for the quantitative risk threshold that are commonly used
within the insurance sector are *probability of
ruin* and *economic cost of ruin*. The
quantitative threshold is then used to determine a *capital requirement* by means of the structural
simulation model described above. This model is also used to evaluate the sensitivity
of required capital levels to changes in quantitative risk thresholds, and to
test the effect of changes in the organization's risk profile and/or its strategies
on its required capital. Each of these steps is described in turn below.

(Capital management also typically includes the attribution of the required enterprise-level capital to each business segment within the enterprise. This attribution of capital provides an appropriate basis to compare the relative performance of each business segment, within a risk-adjusted measurement framework. Capital attribution below the enterprise level will be addressed in a subsequent article in this series.)

## Qualitative Capital Standard

The primary purpose of capital in an insurance company is to provide a desired degree of protection to the company's policyholders. The first step in capital management, then, is for the organization to express, in qualitative terms, the degree of policyholder security it desires—this represents the organization's "capital standard." There are a number of ways an organization can qualitatively express its desired level of policyholder security or capital standard. Some of the more common expressions are:

- Meeting (or, more typically, exceeding by a specified degree) the minimum regulatory capital requirements (such as Risk Based Capital) in relevant jurisdictions
- Achieving or maintaining a specified rating (e.g., A or A+) from an insurance rating agency such as A.M. Best
- Achieving a security level for policyholders equivalent to that for bondholders represented by a specified bond rating (e.g., Aaa or Aa) from a rating agency such as Moody's or Standard & Poor's

Whichever qualitative capital standard an organization adopts, a "best practice" is to document that standard by means of a Capital Policy Statement.

## Quantitative Risk Threshold

The second step is to convert the stated qualitative capital standard into an implied quantitative risk threshold. Typically, these quantitative thresholds are expressed in terms of an expected probability of ruin or related measure. In some cases, the organization's senior management and/or board of directors can express their capital standard directly in terms of such quantitative measures (effectively eliminating the need for the first step, above), but this is a rare situation; most executives and board members do not think about their risk tolerances and desired security levels in such technical terms.

**Probability of Ruin Measure.** The best way to
describe the translation from qualitative standard to quantitative threshold
is by means of an example. In this example, we will assume that an insurance
company, in its Capital Policy Statement, has adopted a capital standard of
meeting a policyholder security constraint equivalent to the bondholder security
level embodied by an Aa bond rating from Moody's Investor Services. (Note that
this capital standard does not equate to an Aa rating of the insurance company's
own bonds—it simply expresses the level of security the company desires for
its policyholders in terms of a more intuitive measure, namely the level of
security enjoyed by holders of Aa-rated bonds.) We will illustrate how this
qualitative constraint can be translated into a threshold probability of ruin
measure; other quantitative measures will be discussed thereafter.

There are a number of considerations that Moody's factors into its bond ratings. These include technical analysis, including estimates of default probabilities, salvage values, etc., and subjective analysis of such things as competitive advantage, product differentiation, customer behavior, and quality of management. Given the influence of these subjective factors on company ratings, the most objective and accurate way to convert a given rating level, e.g., Aa, into a probability of ruin is not to try to reproduce Moody's technical analysis of default probabilities (since this is only one input to the ultimate rating), but to analyze the actual historical performance of Moody's Aa-rated bonds.

Historical default probabilities are easily derived from published Moody's
data, and require no knowledge of Moody's internal technical analyses. The observed
default probabilities are calculated as a ratio, with the denominator being
the number of Aa-rated bonds at the beginning of a holding period, and the numerator
being the subset of those bonds that have since defaulted during that period.
It is important to group bonds based on their rating at the *beginning *of the period, since bonds that
eventually default often transition into lower ratings categories before default.
The results of these calculations on recent Moody's data for several ratings
categories are summarized in the table below.

Note that the default probabilities are quite dependent on the length of the bond holding period. Naturally, the longer the holding period, the greater the probability of default, all else equal. For example, Aa-rated bonds have had a 0.2 percent probability of default over a 5-year holding period, and a 2.2 percent probability of default over a 15-year holding period.

## Figure 1

Given this dependence on holding period, what is the proper holding period to use in our insurance company example? The "holding period" in this case is determined by the expected future payout of the insurance company's liabilities. If the average duration of these future payments is 10 years, then the appropriate default probability to use is that found in the 10-year holding period column of the table above. In this case then, an Aa-rating standard would equate to a 0.8% percent probability of ruin threshold. A more precise way to map the default probabilities in the table above to a single probability of ruin for an insurance company is to weight the probabilities in each column according to the distribution by year of the company's liability payouts.

**Economic Cost of Ruin and Other Measures.** Probability
of ruin is a useful measure because it is easily understood by insurance company
management and industry observers. However, one drawback is that it measures
only the likelihood of ruin and not the severity of ruin. The severity of ruin
is important to policyholders, since it determines the portion of their claims
on the insurance company that will be paid in the event of insolvency.

One measure that captures severity of ruin is Economic Cost of Ruin (ECOR). To describe ECOR, we make brief reference to the probability distribution of key performance indicators (KPIs) that was, as indicated earlier, a result of the precursor modeling exercise. In the event of insolvency, the amount of insurance company funds available to pay policyholders will fall short by some amount, i.e., the "shortfall."

To calculate ECOR, first calculate the shortfall that results from each possible outcome under the KPI probability distribution (note that under those outcomes that do not represent insolvency, the shortfall is zero). ECOR is the expected value of the shortfall over the entire range of possible outcomes. Sometimes ECOR is called the Expected Policyholder Deficit (EPD). An "ECOR ratio" is derived by dividing ECOR by the expected value of the insurance company's liabilities (all these calculations are done on a present value basis).

Moody's bond ratings can also be converted into equivalent ECOR ratios. This can be done by accessing Moody's historical data on "expected loss rates." Whereas Moody's default rates are equivalent to ruin probabilities, their expected loss rates are equivalent to ECOR ratios. A table of historical expected loss rates can be developed similar to the table of default rates above, and a similar mapping can be done of a desired rating level (e.g., Aa) into an equivalent ECOR ratio.

Variations on ECOR and EPD measures include Tail Value at Risk (Tail VaR) and Tail Conditional Expectation (TCE). Comparisons of all the risk measures described in this Quantitative Risk Threshold section can be found in the immediately prior article in this series, "The Language of Enterprise Risk Management: A Practical Glossary and Discussion of Relevant Terms, Concepts, Models, and Measures," May 2002. A more detailed discussion can be found in the Tillinghast-Towers Perrin monograph RiskValueInsights™—Creating Value Through Enterprise Risk Management. (These references also discuss the fundamental distinction between this class of solvency-related risk measures, which are important to policyholders, and the class of performance-related risk measures, which are important to shareholders, that are used elsewhere in the ERM process, outside the scope of capital management.)

## Economic Capital

Once the qualitative capital standard is converted into a quantitative risk threshold, it remains to translate the threshold into an economic capital requirement. This is done by means of the KPI probability distribution referenced earlier.

Once again, the concept is illustrated by means of an example. In this example, assume that the KPI distribution for the insurance company is one that describes the random variable "present value of surplus," i.e., the excess of the present value of assets over the present value of liabilities. A picture of the cumulative probability distribution of the present value of surplus is shown below. In the picture, the present value of surplus is shown on the x-axis, and the probability percentages are shown on the y-axis. The cumulative probability distribution of present value of surplus for this company is represented by the thick black curve.

## Figure 2

If the company were to conduct business without any capital, its probability of ruin (i.e., the probability that the present value of surplus is less than or equal to zero) would likely be unacceptably high. As capital is added, this effectively shifts the entire probability distribution curve to the right—or, equivalently, shifts the x-axis, and the vertical line that represents zero present value of surplus, to the left—by the amount of added capital. As this vertical line moves to the left, its point of intersection with the cumulative probability curve moves down. This point of intersection defines the probability of ruin.

Thus, it can be seen that the probability of ruin is reduced by a measurable amount as capital is added. By adding sufficient capital, the probability of ruin can be reduced to any desired level.

From the above picture it should now be clear how a probability of ruin threshold is uniquely translated into a required amount of economic capital. The required amount of economic capital is that amount of capital that reduces the probability of ruin to the specified threshold.

The picture above also illustrates how, by adding capital, ECOR (or the ECOR ratio) can be reduced to any desired level. Thus, a stated ECOR risk threshold can likewise be uniquely translated into a required economic capital amount. Similarly, any of the risk threshold measures cited in the preceding section can be used to determine a unique amount of required capital.

## Capital Standards in Other Sectors of the Financial Services Industry

The process described above is tailored to the insurance sector. Most importantly, it recognizes the peculiar nature of insurance company liabilities—in particular, the fact that the probability distributions of these liabilities are not symmetric, they are generally skewed and have "fat tails."

Capital standards and risk management approaches in other sectors of the financial services industry reflect the different business activities and risk characteristics of those sectors. For the most part, these standards and approaches concentrate on the portions of the balance sheet that represents the greatest relative risk within each sector. For example, compared to insurance companies, securities firms and banks place particular emphasis on credit risk.

Additional discussion of the differences in risk management and capital regulation in the different sectors can be found in the Basel Committee on Banking Supervision, Joint Forum, Risk Management Practices and Regulatory Capital: Cross-Sectoral Comparison, Bank for Institutional Settlements, November 2001.

As noted earlier, additional details on capital adequacy assessment and other
ERM applications can be found in the Tillinghast-Towers Perrin monograph *RiskValueInsights™: Creating Value Through Enterprise Risk Management-A Practical Approach for the Insurance Industry*.

Opinions expressed in Expert Commentary articles are those of the author and are not necessarily held by the author's employer or IRMI. Expert Commentary articles and other IRMI Online content do not purport to provide legal, accounting, or other professional advice or opinion. If such advice is needed, consult with your attorney, accountant, or other qualified adviser.

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