Group captives part 2: sharing losses


Group captives part 2: sharing losses

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To convince large members to join with smaller members, and vice versa, the prospective premium rating system needs to take account of loss experience. Hugh Rosenbaum, captive consultant and retired principal of Willis Towers Watson, explains the principle of proportional parity.

In my previous article I outlined some of the inner workings and obstacles to group captives for a hypothetical group captive. To recap, here is a summary of the way it might have looked at the beginning. This order of listing of the group captive’s real or proposed detail is the one I consider to be important or significant to any group captive venture (Table 1). 

Table 1: Detail of hypothetical group captive structure

Exposures underwritten Limited cyber - extra expense and legal expenses
Number of members 10
Retention per occurrence and annual $1 million per occurrence, $5 million over 3 years
Initial capital amount $5 million
Expected annual losses $500,000
Estimated annual premium $2.2 million
Underwriting and control By members' committee and appointed outside expert
Administrative details: domicile, managers, resinurance, board Guernsey, manager X, reinsurer Y (for next $5 million), board of members plus non-executive director expert Z

The next big obstacle: sharing losses
Before the captive gets off the ground, there has to be acceptance and understanding about sharing each other’s losses, and how that is going to work out for renewal premiums for the year or years following the loss. Here, we have had to make an assumption that there will be only one event in the year that will be covered by the group captive, and that the amount of that event has been evaluated, agreed, and actually paid in the year.

This is, of course, theoretical, since losses are usually more complicated to evaluate in this exposure area, but here we will assume the simplistic example to illustrate the next aspect of proportional parity. It will emerge when renewal premiums have to take into account loss experience. But first, a basic inner working point. 

The inner workings


One of the selling points to convince potential members to sign on is something I call membership modelling. In a joint venture such as this group captive, where everyone shares in the overall outcome proportional to something (of which more later), the selling point is that their individual share of the positive results of the group captive will increase over time, as shown in Figure 1.


What then needs to be explained is that this rosy picture of the future may be disrupted by the emergence of a loss. Another member’s large loss could change this, as depicted in Figure 2.


But what might happen could be your (my) loss, which is just as likely as the loss to the other member. This is the main argument to overcome the obstacle of sharing losses: that is, it could happen to any member, including you, as shown in Figure 3.


In Table 1 an amount of $500,000 is shown as expected losses. This is a place-holding number that is used for annual losses just to make the presentation and any eventual proforma financial model look realistic. It wouldn’t be realistic to show zero as expected losses, even though that may be actually what the members expect.


The reality should be the assumption that there will be one loss of over $1 million in the first year. The amount the captive will have to pay—$1 million—is more than any one of the members has paid in premium. The further reality is that by pooling their exposure and risk of loss, they have accepted the possibility of paying for the other’s loss, even though they themselves had none. That’s where the application of proportional parity works best, as I will try to simplify now.

Taking account of loss experience
In some group captives there is uniform loss-sharing, with no prospective adjustment for loss experience. The members decide on the overall increase needed and apply that percentage to all members, irrespective of whether they had presented losses to the group.

These are usually of the type we are looking at in my example—where the loss frequency scenario is zero or one. Members in these accept the idea that a loss could hit any one of them, in spite of their risk management efforts. However, I find that to convince large members to join with smaller members, and especially vice versa (small members to join with large ones), the prospective premium rating system needs to take account of loss experience.

In our cyber insurance example, we have assumed one large loss of $1 million from one member in the first year. We have not depleted capital because annual premiums were $2.2 million, enough to cover the group captive’s retention. But we have reduced the expected surplus by $1 million, which could cause consternation among those members who did not have the big loss.

The best way of alleviating this concern in advance is to take account of loss experience in the prospective rating formula. But how to do that? Increasing the member who had the loss by the full $1 million is not the answer. Spreading it over all the members is better, and spreading it in such a way that the member who had the loss suffers more of an increase is even better. Here’s a simplified explanation of how this aspect of proportional parity works for calculating next year’s premiums after a large loss.

Calculating next year’s premiums
The first step is to agree on the total premium to be collected next year. Assume they decide to add a surcharge over the next three years equal to one third of the amount of the retained loss in the first year, but with the member suffering the loss paying a higher surcharge, capped at $75,000 per year.

The next step is to agree on how they will assess the premium—in this case they have decided to assess it on the basis of 50 percent exposure, 50 percent losses. (Refer to the previous article to read how the higher and lower exposures are handled, using a 1 to 5 comparative rating system.)

In the absence of losses, it becomes 100 percent exposure-based. That means the total premium needed, for next year, $2,533,333 ($2.2 million plus the surcharge of $333,333), will be collected based on members’ exposures first, and loss experience second.

How it works
Take 50 percent of the premium needed, $1.1 million, and divide it up among the members according to the exposure rating described earlier. Take the other 50 percent, again $1.1 million, add the surcharge to all members proportionately, except for member I who pays more: the maximum of $75,000.

Table 2 shows how it works out. The largest member, E, pays an extra $56,000 next year, the smallest, member F an extra $14,000, while the unfortunate member I pays an extra $75,000. The total premium with no loss is $2.2 million; with a loss the total premium is $2,533,333. The important point to note about how this works is that in the year following the loss if an increase is decided, all pay something extra.

One member, the one who presented the loss to the group, pays significantly more—but not so much more that that member would be inclined to leave. In this case in the absence of losses in future years they could also decide to eliminate the surcharge in, say, the third year. That would also result in a proportional reduction, with member I receiving the largest reduction.

The proportional parity mechanism looks better where every member has presented losses to the group, and becomes complicated as the years progress and more than one member has losses. But it has proved robust for the group captives that have applied it or something similar. By using this kind of calculation the fears of the large members that they will be paying for the small, and vice versa, can be alleviated. It is a good way to convince them to join the proposed group captive.

Table 2: Second year premium calculation after member I’s loss of $1 million

Member Exposure Component ($) No loss  Total With loss Total
A 100,000 100,000 200,000 125,705 225,705


120,000 240,000 150,846 270,846
C 103,000 103,000 206,000 129,476 232,476
D 117,000 117,000 234,000 147,075 264,075


220,000 440,000 276,551 496,551
F 55,000 55,000 110,000 69,138 124,138
G 77,000 77,000 154,000 96,793 173,793
H 88,000 88,000 176,000 110,620 198,620
I 95,000 95,000 190,000 170,000 265,000
J 125,000 125,000 250,000 157,131 282,131
Totals 1,100,000 1,100,000 2,200,000 1,433,333 2,533,333


Next step: The final article in this series will address the entitlement to profits—a calculation similar to the premium one. It is the third and sometimes most difficult of obstacles to overcome in the design stages of a group captive.

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Hugh Rosenbaum, Captives, Group captives, North America

Captive International