Actuarial Analysis: Tabarru – An actuary’s Dilemma

Mr Zainal Abidin Mohd Kassim of Actuarial Partners explores the conundrum faced by the actuary in trying to reconcile the concept of tabarru and equity in surplus distribution.

The concept of tabarru is one of the fundamental components of takaful. One reason conventional insurance is considered haram by Shariah is that there are elements of uncertainty (gharar) in the insurance exchange contract. Simply put, for a certain premium, the insured is covered for financial loss on the occurrence of a contingent. In this contract, both the amount of financial loss and whether the insured event will come to pass are uncertain.

The solution is to consider the premium as a donation (tabarru) as from the Shariah perspective, tabarru is not covered by the laws of Muamalat (the basic principles that govern commercial transactions in Islam). Being a donation, it is not considered a commercial contract of exchange. Instead it is considered as a unilateral gratuitous contribution. As such, the element of gharar in the uncertainty of loss is deemed acceptable as instead of a premium, a donation is being made into the takaful fund.

Tabarru – an actuary’s perspective

From an actuary’s perspective, the tabarru is the participant’s contribution to a risk pool that ultimately will be used to pay claims. The quantum of contribution has been determined using a cashflow model that has been constructed from observation of past experience. The take-away from this is that the tabarru has not been determined at “random”, nor has it been determined unilaterally by the contributor of that tabarru, but instead has been determined by the takaful operator’s actuary as being a best estimate of the risk of loss that the participant brings to the takaful risk pool.

No contribution, no cover

Another point to note is that the risk pool can only disburse out a claim to a participant who has duly paid his tabarru. This risk pool is not accessible to others. Takaful is not charity. So in effect we have a situation where a donation (the tabarru) is a condition of cover by the pool. A question that may arise is whether this compulsion to donate nullifies the nature of the contribution (ie, it is gratuitous).

Surplus distribution

Surplus distribution is a contentious issue in takaful. There are suggestions that any surplus should only be distributed to charities. For the purpose of this discussion, we will only consider the distribution of surplus among the participants.

The tabarru is an estimate of the amount each participant is required to make such that the pool has sufficient funds to meet claims – not necessarily just claims occurring in the year, as for those risks where the occurrence of a claimable event is rare, a part of the tabarru amount which if accumulated over time would be expected to be sufficient to pay those claims (the actuarial reserves).

Surplus is determined by the following formula:

Surplus = ∑ tabarru earned less ∑ incurred claims less actuarial reserves

The flow of this process within the risk pool is clear:

  • The tabarru is calculated mathematically as sufficient to cover the risk (defined by the probability of a claim) brought by each participant into the risk pool;
  • Contribution, as tabarru, is a pre-condition of coverage by the risk pool; and
  • Surplus is the amount left over after paying out incurred claims and setting aside actuarial reserves.

The question now is how should the surplus be distributed among the participants? From the concept of equity, the surplus should go back to those participants who contributed to the pool and did not claim from the pool. But the concept of tabarru implies that the contribution was a donation, and by definition a donation is not “recoverable”.

Should there then be a condition within the takaful contract that any surplus must go back to those participants who did not make a claim? If this condition is made, does it make the gratuitous nature of the arrangement null and void, changing the contract immediately from a gratuitous contract to an exchange contract?

Can the surplus be distributed to other participants than those who contributed towards the surplus in the first place? As an example, can the surplus be used to finance deficits incurred by participants covered by other risk pools or even the same risk pool but other products?

The dilemma

Therein lies the actuary’s dilemma. Should he literally take the Shariah view that the premium is a donation and by extension any surplus accruing to the risk pool is owned by no one? If this is so, then the surplus is available to be distributed to any participant in any way the takaful operator unilaterally decides. Or, as the tabarru has been determined actuarially, should he conclude that surplus should be paid back as excess contributions to those participants that contributed to the surplus and did not make a claim on the risk pool?

The surplus dilemma can be further compounded if in the process of calculating the tabarru amount for the individual participant the actuary has incorporated either a margin on top of best estimate, or a discount from best estimate. The discount may apply to certain ages or risks so as to make the policy competitive.

In such instances, when a margin or discount has been applied and a surplus from the takaful pool arises, how now should the surplus be distributed? Should those participants who had enjoyed a discount still be entitled to a share of the surplus?

It could be countered that the tabarru rate has been determined utilising an actuarial model and that model is not infallible. As such, any margin or discount is merely conjecture. The risks the lives assured bring to the risk pool need not necessarily be correctly modelled.

This argument, taken to the extreme, may suggest that given the uncertainty, why differentiate risks through risk factors such as age of insured? Why not charge a flat contribution altogether? The answer lies in the fact that the ultimate risk composition in the risk pool cannot be determined in advance when participation in the pool is voluntary. As such, the tabarru rate charged should reflect the probability of a claim that the participant brings to the pool. The higher the perceived risk of a potential claim, the higher the tabarru rate. Similarly, the higher the sum covered, the larger the contribution amount.

The actuary’s responsibility

How surplus is treated or utilised in takaful is problematic. In conventional life insurance, in any fund where policyholders are entitled to share in surplus arising (such a fund is termed a “participating fund”), the principles of equity and treating customers fairly dictate that the actuary does his best to be equitable when distributing surplus. This problem does not arise for non-participating contracts as any surplus or deficit in the risk pool is “owned” by the insurer. The insurer takes the risk that the total premiums collected may not be sufficient to pay claims but, if a surplus does arise, he is entitled to the entire surplus.

Notwithstanding the tabarru nature of the premium, and from an actuary’s perspective, the concept of equity is also applicable in takaful. The tabarru rate is set by the takaful operator and the participant has very little way of determining whether the tabarru contribution he made is fair or excessive. Thus, the same principles that apply in distributing surplus under a participating contract to policyholders in conventional insurance should apply to the participants in takaful.

How, then, should the actuary determine the distribution of the surplus in takaful? He does this by considering how the surplus arose in the first place; he will start from his pricing basis and assumptions and determine where experience eventually differed from the expected. The conclusion here is that the actuary should try to ensure that all participants contribute fairly to the risk pool. Only then can the surplus arising be easily distributed.

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