# Expected Adverse Development as a Measure of Risk Distribution

April 25, 2018

Last week, we talked about the need for a captive insurer's board of directors to be actively involved in risk oversight and strategy. (See "Strategy and Risk: 5 Key Questions for Captive Insurers.") One of the early major tasks many captive boards need to determine is whether the premiums paid for the insurance policy are deductible for tax purposes. Bruce Wright, Kristan Rizzolo, and Saren Goldner cover this question in detail in "When Are Premiums Paid to a Captive Insurance Company Deductible for Federal Income Tax Purposes?" They said, "The basic requirements for insurance treatment are insurance risk, risk transfer, risk distribution, and a policy that embraces common notions of insurance." But the question of risk distribution is not well defined. Pinnacle Actuarial Resources has proposed a new method for answering this question using expected adverse development.

Robert Walling, FCAS, MAAA, CERA, and Derek Freihaut, FCAS, MAAA, from Pinnacle recently conducted an APEX webinar to introduce a new methodology for determining whether risk distribution exists using expected adverse development. This article will cover some of the highlights from the presentation. For those captives interested in pursuing this new method in greater detail, we encourage you to reach out to either Rob Walling or Derek Freihaut for additional information.

The presentation began with a discussion on the notion of risk distribution. As we have already noted, risk distribution is a prerequisite for an insurance transaction to have been deemed to occur. Particularly in the eyes of the Internal Revenue Service (IRS), the real question is how much risk distribution is enough to qualify as insurance? Mr. Walling and Mr. Freihaut take the position that the best way to determine the answer to this question is through a statistical quantitative analysis performed by an actuary.

While the IRS does not provide a single definition of what constitutes "risk distribution," there is a growing body of case law to inform this question. As Bruce Wright, et al., noted in the article mentioned above, "Until [recently], based on existing case law and IRS rulings, the focus in determining whether adequate risk distribution was present was the number of so-called brother/sister insureds and the amount of risk (generally determined by premium allocation) attributable to each. Thus, the IRS in Rev. Rul. 2002–90 published a 'safe harbor' indicating that if there were 12 such insureds each accounting for between 5 percent and 15 percent of the risk, there was adequate risk distribution. Various rulings have refined this test. In one ruling, the IRS noted that if there were to be a single insured that accounts for 90 percent of the risk, there is inadequate risk distribution. The IRS also has ruled that if certain types of entities are insured the risk may be treated as risk of their owner (e.g., single member LLCs). Unrelated risk insured directly or through a reinsurance pool could add to the number of insureds and the spread of the risk providing a strong risk distribution position under the IRS rulings."

Mr. Walling and Mr. Freihaut discussed four common methods used to determine risk distribution and evaluated these risk distribution methods against three main criteria.

- Transparency: the result should be easy to explain to all interested parties, including accountants, captive owners, lawyers, and regulators.
- Acceptability: these same constituents need to approve of the method being employed to determine risk distribution.
- Reduced manipulation: the method used should not be subject to a great degree of manipulation.

The four common methods that were evaluated along with their pros and cons included the following.

- Value at risk
- Tail value at risk
- Rigorous one-sided test
- Tests improvement in potential loss at a given percentile through risk distribution
- The underlying math is not easily explained
- The reliance on loss distribution could lead to manipulation

- Coefficient of variation
- Easy to explain measure of volatility
- Becomes less as the amount of independent exposures increases
- Can be more easily manipulated than other tests
- Is not one-sided, reflects all risk

- Expected policyholder deficit
- One-sided and transparent
- Focuses on the net present value of the underwriting loss
- Reliance on premiums can lead to issues

The presenters said the pros and the cons of each of the four methods has led Pinnacle to suggest a new methodology for determining risk distribution.

Pinnacle Actuarial proposes captive insurers adopt the expected adverse deviation (EAD) method for measuring risk distribution. EAD represents the amount of loss the insurance company incurs in excess of the expected losses or the expected amount of adverse deviation to which the insurer is exposed. The formula looks like this.

EAD = E [max (X – E (X), 0)]

For purposes of measuring risk distribution, Pinnacle converts this into an EAD ratio expressed as EAD (X) / E (X). They explain the ratio in this manner: "To test for risk distribution we need to normalize the EAD value by dividing by the expected losses. The EAD ratio measures how much volatility or risk an insurance company is taking on relative to their expected losses. The higher the EAD ratio is, the riskier the insurance company is. As an insurance company diversifies its risk we should expect to see the EAD ratio decrease. The EAD ratio has a max value of 100% and a minimum value of 0% so it is easier to compare different types of insurance and exposures."

Looking to diversify their risk, many single-parent captives utilize a risk pool. According to Bruce Wright, risk pools in captives (1) allow organizations to spread risk and (2) provide for a tax benefit. Risk pools provide unrelated risk to a captive insurer so that the parent corporation can take a deduction for premium paid to the captive by reporting on the insurance method of accounting.

A pool is an arrangement where organizations share risk. A sound pool should have (1) similar risks, (2) a common underwriting methodology, (3) a pool manager, (4) the potential for loss or gain, and (5) setup on an annual basis. There are also different types of structures for pools, such as a (1) reinsurance treaty, (2) pooling entity, or (3) fronting company.

EAD provides a new method for captive owners to calculate whether there is sufficient risk distribution present to satisfy the IRS for premium deductibility. As an insurance company diversifies its risk, the EAD ratio should decrease.

April 25, 2018