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Hugh Rosenbaum, captive consultant and retired principal of Willis Towers Watson, addresses the entitlement to profits—the third and sometimes most difficult of obstacles to overcome in the design stages of a group captive.

From the previous two articles (Part 1) (Part 2) I showed the initial stages of a group captive, its obstacles and inner workings, and opened up the key element of *proportional parity* in allocating losses and premium increases.

The basics of the proposed captive are, from those previous articles, summarised in Table 1.

**Table 1: Detail of hypothetical group captive structure**

In this third and last article I will show how this proportional parity applies to the ongoing entitlement to the liquidation value of the group captive.

First, here is a simplified financial model of the outcomes of two cases for the hypothetical group captive. The first (Table 2) is the “expected” case and the second is the case with the heavy ($1,000,000) loss in the first year (Table 3). Note that for this heavy loss case we assumed the reinsurers would increase their premiums for a few years, and the administration costs would also increase.

We also assume (as discussed in the previous article) that the members decided to increase premiums by 1/3 of the previous year’s surprise retained loss, in this case the increase is $333,333, but only for two years, since no further surprise losses were experienced in those years. (Artificially, we included the hypothetical incurred loss of $500,000 every other year, even though no losses were incurred. As explained this was more for cosmetic purposes not to show zero losses to regulators, than a prediction.)

**Table 2: Expected case**

**Table 3: Heavy loss case (1,000,000 the first year)**

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**Modelling notes**

Simplified models are the key to this first step in the proportional parity projections. Things such as premium taxes, income taxes, letter of credit costs and domicile taxes are all put to one side (or, in the case of domicile charges, shown in the admin costs). The object of simplified models is to show the relative outcomes. For instance, in these two examples we see that after the heavy loss case there is not that much difference in the capital and retained earnings at the end of five years:

Expected case: 10,485,068

Heavy loss case: 10,299,484

An additional benefit of this kind of modelling is to show how well the undertaking can sustain an early loss and still come out well at the end of five years.

The simplified modelling I suggest for demonstrating the value of a proposed group captive also helps prepare the way for future decisions such as how to admit new members, and whether to increase retentions, reduce reinsurance and even annual premiums for all members.

**Entitlement**

Suppose the members decided at the end of year 5 to liquidate. A more realistic way of looking at it would be to show the estimated entitlement of each member at the end of year 5. This involves the same kind of allocation calculations I used in the second article, with half the entitlement percentage based on premiums, the other half based on losses presented to the group captive. In the absence of any losses, it would be entirely based on premiums. In our heavy loss case, though, one member did have a large loss.

The proportional parity calculation of entitlement to retained earnings is straightforward.

For all members: half the total amount allocated according to the percentage of premiums paid in by each, the total being 100 percent of that half, plus half the total amount allocated according to the percentage of total losses presented to the group captive.

In our heavy loss case this would have meant total losses presented (1,000,000), the resulting percentage (or proportion) being the *reduction* that member would experience. Our member with the one loss of 1,000,000 experiences a 100 percent reduction, while the others have none—so the other members divide up the other half of the retained earnings equally, ie, 1/9^{th} to each in our case of 10 members, large and small get larger or smaller entitlements, and the one that presented the losses gets the smallest of all 10.

The formula gets complicated as multiple loss years accumulate, and has to be adjusted to include the arrival of new members during the time frame of the calculation.

**Conclusion**

This example of one way of demonstrating entitlement to the retained earnings is meant to show a good way of convincing prospective members large and small to join the group captive. The point I have made in these three articles is this: by addressing some of the obstacles in advance, and modelling the inner workings of the proposed group captive, there should be a better chance of getting it off the ground.

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captive, entitlement, premiums, total, Willis, Towers, Watson