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Opalesque Islamic Finance Intelligence

Featured Structure: How Conventional Insurance and Takaful Differ Numerically By Mohammed Amin

Friday, July 30, 2010


Mohammed Amin

Mohammed Amin is an Islamic finance specialist, with a particular interest in how Islamic finance is treated in Western tax and regulatory systems. He is a member of the HM Treasury Islamic Finance Experts Group, established by the Economic Secretary to the Treasury to advise the Government on Islamic Finance strategy, and is the only practicing accountant on that group. Until he retired at the end of 2009 Amin led PricewaterhouseCoopers' Islamic Finance practice in the UK as well as being a member of PwC's four-person Global Islamic Finance Leadership Team. He shares his thoughts on Muslim community issues and Islamic finance topics on his website (see reference link).

Insurance is a key financial service in all advanced economies. There are very few people who choose to live without any form of insurance cover. For certain activities, such as driving a car, insurance is compulsory in the UK. However, outside the insurance industry there is a surprising lack of knowledge of how insurance actually works. Meanwhile takaful (usually described as the Islamic equivalent of insurance) is relatively new and even less widely understood.

One of the difficulties in understanding insurance is the complexity of the industry, the arcane terminology used and the extensive regulations governing insurance business. Theoretical physicists, when faced with similar complexity often commence by analysing a much simplified hypothetical case, and then consider what can be generalised to the real world. Isaac Newton could never have found real point masses moving without frictional constraints, but his theoretical analysis of them led to his laws of motion and to Newtonian mechanics. In a similar (but humbler) vein, I would like to consider insurance and takaful from first principles. In the case of insurance, all one needs to think about is one person who is exposed to risk. In the case of takaful, which involves mutual sharing of risk, one needs to think about a minimum of two people who share risk with each other.

In this minimalist vein, assume there are two individuals concerned about the risk of house fires, Abdul with a house worth $1m and Bilal with a house worth $100,000. Both also have significant amounts of cash savings, $1m in Abdul's case and $100,000 in Bilal's case. They also have a very wealthy friend, Chowdhury, who is willing to take on risks for a fee, and has the money to honour his commitments. Chowdhury charges 0.1% of the value of the house per year, and it is assumed that this represents the statistical likelihood of loss. In other words, if we had a large enough sample of houses, 0.1% of the total value of the houses would disappear in fire losses each year.

Let us consider a period of one year, when a house fire either happens, with total destruction of the house concerned, or does not happen.

(A) Example 1 - Abdul with no risk transfer

Assume that Abdul buys no insurance. A fire may or may not happen.

Scenario 1 - No Fire


Before

After

House

$1,000,000

$1,000,000

Cash

1,000,000

1,000,000

Total

$2,000,000

$2,000,000


If there is no fire, Abdul suffers no loss. Both before and after, his net worth is $2,000,000.

Scenario 2 - Fire destroys house


Before

After

House

$1,000,000

-

Cash

1,000,000

$1,000,000

Total

$2,000,000

$1,000,000


Abdul's house has been destroyed by fire, and he has suffered a loss of $1m. Even if he uses his $1m cash to reinstate his house, his loss is still $1m.

(B) Example 2 - Abdul insures his house with Chowdhury. The premium charged is $1,000 per year.

Instead of being exposed to the risk of loss if his house burns down, Abdul transfers that risk to Chowdhury by paying him $1,000.

Scenario 1 - No Fire


Before

After

House

$1,000,000

$1,000,000

Cash

1,000,000

999,000

Total

$2,000,000

$1,999,000

If there is no fire, Abdul has suffered a loss of $1,000 being the insurance premium he paid to Chowdhury. Conversely Chowdhury has earned $1,000 by being exposed to the risk of loss on Abdul's house for a year.

Scenario 2 - Fire destroys house


Before

After

House

$1,000,000

-

Cash

1,000,000

$999,000

Cash from insurance claim

-

1,000,000

Total

$2,000,000

$1,999,000

Abdul has suffered an overall loss of $1,000, which is equal to the amount of his insurance premium. His house, worth $1,000,000 has burned down, but this has been replaced by $1,000,000 from the fire insurance claim since Chowdhury has to pay him the full value of the house since it has been destroyed. The cash from the insurance claim may be used to reinstate his house, but either way his loss remains $1,000. Abdul has achieved a complete risk transfer to Chowdhury under the insurance contract. For simplicity, Abdul's other losses from a house fire such as the loss of irreplaceable personal possessions are ignored. Instead, the analysis just looks at his financial position.

Chowdury has suffered a very big loss of $999,000 since he took in $1,000 from Abdul as an insurance premium, but had to pay out $1,000,000 when Abdul's house burned down. This shows that writing insurance contracts is an inherently risky business. The buyer of insurance reduces his risk; that risk has to go somewhere, and it goes to the insurer.

(C) Example 3 - Abdul and Bilal enter into a takaful arrangement with each other.

Many definitions of "takaful" are offered in Islamic finance sources, often using concepts such as" the charitable collective pooling of funds for mutual assistance."

However, as explained below, the process is not charitable, since charity means giving something with no prospect of direct benefit to oneself. Instead the arrangements involve an agreement to share risks on a mutual basis, with the initial payment of cash into a common pool which can be used to meet losses. As the contributor's own loss will be covered if it occurs, the process does not involve charity. Indeed, the contributor would not take part if his risks were not going to be covered, and he will assess the financial viability of participation by considering what his risks are, the likelihood of those risks materialising, and the costs of participation.

As illustrated above, the starting position is as follows.

Initial Position

Abdul

Bilal

House

$1,000,000

$100,000

Cash

1,000,000

100,000

Total

$2,000,000

$200,000


The takaful arrangement between Abdul and Bilal is intended to share between them the risk of their houses burning down. Abdul and Bilal agree to contribute to a common pool (the takaful pool) pro-rata to the value of their houses, and to share any pool surpluses pro-rata to their contributions. To ensure there is enough cash in the pool to cover all possible losses, they put in cash equal to the total value of both houses. This is unrealistically high and would not be met in real life. However, it makes the analysis much easier to follow, and does not change any of the principles involved.

As there are only two of them involved, Abdul and Bilal don't need a third party administrator. Between them they will ensure safe custody and investment of the cash in their common pool, and deal with the use of the money in the pool to pay their fire losses, and they will return any excess left over in the pool back to themselves when the takaful arrangement finishes. For simplicity I assume that the invested money does not earn anything, so the cash in the takaful pool is the same at the end of the year as at the beginning.

Scenario 1 - No Fire

Before

During Year

After

Abdul

Bilal

Abdul

Bilal

Abdul

Bilal

House

$1,000,000

$100,000

$1,000,000

$100,000

$1,000,000

$100,000

Personal cash

1,000,000

100,000

-

-

1,000,000

100,000

Total

$2,000,000

$200,000

$1,000,000

$100,000

$1,000,000

$100,000

Cash in takaful pool

$1,100,000

-


None of the cash in the takaful pool is needed for any purpose. At the end of the year, the cash in the takaful pool is returned to Abdul and Bilal in a 10:1 ratio, being the ratio in which they contributed it. Although they did share their risks during the year, it cannot be seen from the figures as no house burnt down.

Fire ¢â‚¬â€œ Variant 1: Assume that both houses burn down

Before

During Year

After

Abdul

Bilal

Abdul

Bilal

Abdul

Bilal

House

$1,000,000

$100,000

$1,000,000

$100,000

-

-

Personal cash

1,000,000

100,000

-

-

$1,000,000

$100,000

Total

$2,000,000

$200,000

$1,000,000

$100,000

$1,000,000

$100,000

Cash in takaful pool

$1,100,000

-


All $1,100,000 of cash in the takaful pool is used to pay fire losses suffered by Abdul and Bilal of $1,000,000 and $100,000 respectively. They can use this cash to reinstate their houses if they wish. There is no cash left in the takaful pool. Abdul and Bilal have suffered losses of $1,000,000 and $100,000 respectively from the destruction of their houses.

The losses have been borne in the ratios Abdul 10/11 and Bilal 1/11 being the 10:1 ratio of their house values and takaful contributions. However, any risk sharing is still invisible as both houses burnt down, and Abdul and Bilal are in the same positions they would have been in with no takaful but assuming both houses burnt down.

Fire - Variant 2: Assume that only Abdul's house burns down

Before

During Year

After

Abdul

Bilal

Abdul

Bilal

Abdul

Bilal

House

$1,000,000

$100,000

$1,000,000

$100,000

-

$100,000

Personal cash

1,000,000

100,000

-

-

$1,091,000

9,000

Total

$2,000,000

$200,000

$1,000,000

$100,000

$1,091,000

$109,000

Cash in takaful pool

$1,100,000

-

Of the cash in the takaful pool, $1,000,000 is paid to Abdul to compensate him for the loss of his house. The surplus of $100,000 is shared between Abdul and Bilal in a 10:1 ratio, being the ratio of their contributions. Abdul receives $91,000 and Bilal receives $9,000. Abdul and Bilal started with a combined net worth of $2,200,000 which has fallen by $1,000,000 to $1,200,000. The loss of $1,000,000 has arisen from Abdul's house burning down. This loss has been shared Abdul $909,000, Bilal $91,000 i.e. Abdul 10/11 and Bilal 1/11 being the 10:1 ratio of their house values and takaful contributions.

Fire - Variant 3: Assume instead that only Bilal's house burns down

Before

During Year

After

Abdul

Bilal

Abdul

Bilal

Abdul

Bilal

House

$1,000,000

$100,000

$1,000,000

$100,000

$1,000,000

-

Personal cash

1,000,000

100,000

-

-

909,000

$191,000

Total

$2,000,000

$200,000

$1,000,000

$100,000

$1,909,000

$191,000

Cash in takaful pool

$1,100,000

-

Of the cash in the takaful pool, $100,000 is paid to Bilal to compensate him for the loss of his house. The surplus of $1,000,000 is shared between Abdul and Bilal in a 10:1 ratio. Abdul receives $909,000 and Bilal $91,000.

Abdul and Bilal started with a combined net worth of $2,200,000 which has fallen by $100,000 to $2,100,000. The loss of $100,000 has arisen from Bilal's house burning down. This loss has been shared Abdul $91,000, Bilal $9,000 i.e. Abdul 10/11 and Bilal 1/11 being the 10:1 ratio of their house values and takaful contributions.

(D) Conclusions and comments

This is a very simplified example. Nevertheless, some key points emerge.

Conventional insurance risk transfer

Under the conventional insurance contract, there is a complete transfer of fire risk from Abdul to the insurer Chowdhury.

In the long run, Chowdhury will make or lose money, depending on the level of premiums he charges and the actual experience of fire losses. Chowdhury's motivation is to charge the highest premium customers will bear, but this is constrained by competition from other insurers. Chowdhury needs expertise in assessing the probability of house fires. Competitive pressures from other insurers may drive down premium rates and if premiums fall so low that Chowdhury expects to lose money taking into account the probability of houses fires then Chowdhury would be better off ceasing to write any insurance contracts. Having achieved complete fire risk transfer to Chowdhury, Abdul is theoretically indifferent whether his house burns down. He may therefore take less care to prevent house fires, e.g. by switching off electrical items at night. This is one example of the concept of "moral hazard" in economics, whereby a party to a contract starts to behave in an improper way because the terms of the contract mean that the cost of the inappropriate behaviour falls on the other party. In practice of course even with the insurance contract Abdul retains a significant element of fire risk, both to his personal safety and because a fire will destroy treasured personal memorabilia which are irreplaceable.

Risk sharing in takaful

Whereas conventional insurance transfers risk from the customer to the insurer, (for a price equal to the premium), the takaful arrangement socialises risk by sharing it between the participants. In our example, Abdul moves from carrying a 100% risk of his own house burning down to carrying 91% (10/11) of the risk of either house burning down. On both houses, Abdul and Bilal would of course prefer to have no losses, but a fire at Abdul's will cost both of them more money as it is the more valuable house. However note that Bilal's loss of $91,000 if Abdul's house burns down equals Bilal's saving (compared with no takaful) if his own house burns down. If the probabilities of the two houses catching fire are equal, this is a fair relationship for Bilal, and therefore also for Abdul. Expanding the number of pool participants will socialise the risk further.

House fires are infrequent events, but "lumpy" in that a fire represents a big cost to the person who suffers it. Adding more pool participants with uncorrelated fire risks (i.e. the participants should not have houses next to each other) will eventually result in a situation where Abdul has a low percentage of the risk of any house in the pool burning down. Instead of a lumpy exposure (either no loss or large loss) he will most probably suffer a small share of fire losses every year. With a large enough number of uncorrelated risks in the takaful pool, Abduls expected annual loss will be roughly equivalent to the conventional insurance premium currently being charged by Chowdhury, since we have assumed that the premium is based upon an actuarially fair assessment of the risk.

Setting the level of takaful contributions

In our two person situation, each of Abdul and Bilal need to be confident that there is enough money in the takaful pool to cover the cost of reinstating their house in the event of it burning down. As house fires are rare, in most years neither Abdul nor Bilal would experience a fire so the entire pool would be returned to them. Of course this level of takaful contribution is unrealistic in practice. Few people could afford to make a takaful contribution in cash equal to the value of their house, albeit in the expectation of most probably receiving all or most of it back at the end of the year. With a large number of pool members, the annual contribution that each of them makes becomes a much smaller fraction of the value of their house. The level should be set high enough to cover expected fire losses plus a safety margin; the precise amount of the safety margin is relatively unimportant since at the end of the year the surplus cash in the takaful pool is returned to the participants. Of course, once pool participants are contributing to the pool less than the full value of every house, there will be insufficient money in the pool to cover the simultaneous destruction of all the houses. However, this is no different from conventional insurance, where no normal insurance company could remain solvent if all of the risks that it had insured materialised simultaneously.

Allocating the takaful surplus

One arithmetical question regarding the allocation of the surplus is whether a participant should share in the surplus if during the year in question he has already claimed on the pool for an actual fire loss suffered. From the examples, if Abdul could not share in the surplus in the version where his house burnt down, his loss would become $1,000,000 while Bilal's loss would become zero i.e. Abdul would have a 100% exposure to the loss of his house while Bilal would have no exposure to a loss on Abdul's house. Accordingly, in this example it is essential that a pool participant is not debarred from sharing in the surplus merely because he has suffered a fire loss, in order to achieve proper risk sharing. With a large number of participants whose contributions are a much lower proportion of their house values, the surplus sharing question becomes less acute. If the contributions are set carefully enough each year the cash in the pool should just cover the total fire losses experienced, with no surplus or deficit. While this ideal scenario is somewhat unlikely, in practice the pool surplus or deficit should be quite small compared with the aggregate value of the houses at risk so the risks are socialised irrespective of the precise method used for allocating the pool surplus amongst participants.

Are the contributions fair to the participants?

Abdul and Bilal have houses with dramatically different values. However in the example they are able to pool their risks in a manner which leaves both Abdul and Bilal sharing proportionately in the fire risk of both houses. This seems fair. However, it would not be fair if one house was more likely to catch fire than the other. For example, if Abdul's house is made of stone, with an expectation of getting burnt down once every hundred years, while Bilal's house is made of wood with the expectation of burning down once every decade, then Bilal's house is ten times as risky as Abdul's. This needs to be factored into the risk sharing arrangements. The conventional insurer Chowdhury will simply allow for the relative probabilities when quoting insurance premiums to Abdul and Bilal. He would quote a premium of $1,000 to Abdul (being 0.1% * $1,000,000) while also quoting a premium of $1,000 to Bilal (calculated as 10 * 0.1% * $100,000 since Bilal's house is ten times as risky.) Accordingly, when operating the takaful pool, Abdul and Bilal need to allow for these risk probabilities (assuming they can estimate them) when devising the arrangements. For example, Bilal and Abdul might agree that Bilal's share of the pool surplus will be 9/10 of what it would otherwise be, to reflect the riskiness of his house. Accordingly, in years when no fire losses were experienced, the arithmetic would be as follows:

Abdul

Bilal

Total

Pool contribution

$1,000,000

$100,000

$1,100,000

Fire losses

-

-

-

Pool surplus to allocate

1,100,000

Initial allocation based on contribution

1,000,000

100,000

1,100,000

Reduce Bilal's surplus to 9/10

10,000

(10,000)

-

Final share of pool surplus

$1,010,000

$90,000

$1,100,000

Over a decade, this arrangement will cost Bilal $100,000 being the value of his house. This cost matches the expected total loss of once per decade that Bilal expects. In the year of loss, the outcome will be:

Abdul

Bilal

Total

Pool contribution

$1,000,000

$100,000

$1,100,000

Fire loss (Bilal's house)

-

(100,000)

(100,000)

Pool surplus to allocate

$1,000,000

Initial allocation based on contribution

$909,000

$91,000

$1,000,000

Reduce Bilal's surplus to 9/10

9,000

(9,000)

-

Final share of pool surplus

$918,000

$82,000

$1,000,000

The overall outcome appears slightly unfair to Bilal, since as well as suffering the cost of $10,000 per year in the years when there is no fire, he also suffers a similar cost in the year of loss. It shows how hard it is to be fair in all circumstances. Accordingly it would seem more appropriate to not scale down Bilal's share of any pool surplus to 9/10 in the year when he actually suffers the house fire.

Takaful in practice

The extremely simplified examples above enable one to think about some of the issues that arise when devising real takaful arrangements.

In practice however takaful arrangements for retail risks are not devised by the parties seeking to socialise their risks, they are devised by takaful operators seeking to sell their expertise to potential pool participants.

Some of the factors the takaful operator needs to take into account are:

    • Pool participants will want to share the risks of their houses starting from random dates in the year (e.g. the date they purchase the house) so that the simple example of assessing the pool on an annual basis with all outcomes known is not possible. Instead, the pool operator will need to allocate the participant contributions between accounting years to calculate the surplus for each year.
    • Pool participants will primarily see their contribution to the takaful pool as a cost, reduced perhaps by any small share in pool surplus. Furthermore, they will compare this cost with the price of conventional insurance. In economic terms it makes little difference to a pool participant whether he is socialising risk with a large number of pool participants or paying a conventional insurer to take on the risk. (Of course the two may be seen as completely different from a religious perspective).
    • A conventional insurer bears all of the losses experienced, in exchange for the premiums it receives. Accordingly, it is incentivised to quote premiums that at least cover the expected losses in respect of each customer. The more scientifically the insurer can assess the riskiness of each customer, the more profitable it will be, as it can decline more risky business or quote higher premiums.
    • A takaful operator is reimbursed by a fee, and does not share in actuarial gains or losses. Typically the operator will make an interest free loan to cover pool deficits, repayable out of pool surpluses. Otherwise, pool surpluses are all returned to pool participants. Accordingly, the takaful operator has an incentive to avoid pool losses, but limited incentive to screen out bad risks, since the losses arising from these bad risks are borne by the other pool participants, not by the operator.
    • There is however some incentive to screen out bad risks or to charge them a higher contribution, since customers will decide to join a particular operator's pool based upon the experience of contribution rates and pool surpluses. As bad risks cause increased contributions/reduced surpluses, the operator's business is likely to expand if he can exclude them. However this incentive is less strong than with conventional insurance where the insurer bears all losses directly.

Conventional insurance and takaful compared

Most Muslim scholars consider that conventional insurance is prohibited in Islam, except where required by local law (such as compulsory driving insurance in the UK) while there is no Shariah compliant alternative. The scholars point towards two factors:

      1. The conventional insurance contract with its risk transfer from the customer to the insurer is inherently prohibited. The most important reason given is that the contract is speculative, like gambling, as either the insurer will have a small gain from keeping the premium or a large loss from paying out on the claim.
      2. Conventional insurers invest their premium income (pending payment of claims) in prohibited ways, by purchasing interest bearing investments (regarded as prohibited) and equity investments in prohibited businesses such as alcohol production.

The above two reasons are logically distinct. While a conventional insurer could remedy reason (ii) by changing its investment policy, it could not remedy reason (i) while continuing to write risk transfer contracts.

In comparison, takaful is generally approved from a Shariah perspective on the grounds that the parties at risk are effectively indemnifying each other through the takaful risk sharing mechanism. The takaful provider is merely providing a service for a fee charged to participants (normally via charging the pool) but is not taking on the customers risks which they share with each other.

Your feedback and comments are very important to us, please feel free to contact the author via email.



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