Operational and Actuarial Aspects of TakafulValuation of Liabilities

Sub TopicsWhy Set Up a Provision for Claims Liability?Claims Liability Provisioning in General

TakafulEstimating General Takaful Claims ProvisionsLiability Provisioning (Reserving) for Family

Takaful ProductsRegulatory Aspects

Why Create Claim ReservesA takaful is a legal contract in which the risk of loss

occurring in a given period are covered and paid for by the takaful fund.

For any given point in time during the contract, coverage must remain in force until the expiry date of the takaful contract

For regulatory and prudential management purposes, it is essential that a quantification be done of the monetary amount a takaful contract is still ‘on risk’ at a given point in time

‘Amount on Risk’ at a given point in time is known as the provision for claims or claims liability.

Why Create Claim ReservesHence Operator have to determine the following:

What is the takaful claims reserves/liability at a given date?

What is the excess of takaful fund assets over liabilities (i.e. surplus) of the takaful fund? [this will be of interest to participants (and operator) who may have a share in the underwriting surplus]

What is the profit generated for the year up to the given date? (If operator revenue is also derived from a share of underwriting surplus then obviously claims reserving will have an important impact on operator revenue and profit)

Takaful Fund at Nov 1 2008

Claims Paid between Nov 1 & Dec 31 2008

Takaful Fund at Dec 31 2008

Operator Fund at Nov 1 2008

Wakalah Fee Paid to Operator Nov 1 to Dec 31 2008

Wakalah Fee Income to Operator Nov 1 to Dec 31 2008

Operator Expenses from Nov 1 to Dec 31 2008

Operator Fund at Dec 31 2008

Illustrations of Fund Cash Flows

Takaful Fund Operator Fund

= =

Reserving in General TakafulAdditional questions:-

Is there a possibility that claims may have been reported to ABC but the payments have yet to be paid from the takaful fund. Such claims which have occurred but have not been paid yet should be provided for.

There is also the possibility that claims have occurred

but those claims have yet to be reported. These incurred but not reported claims represent a liability as well to the takaful fund.

As at valuation date, there is also the remaining unexpired contract period of coverage to expiry date in which claims can still arise.

Claims Provisioning DateStart Date of Contract Expiry Date of Contract

Outstanding Claims Provision

Unexpired Risk Provision

Components of a Claims Liability Provision

1/11/2009 31/10,201031/12/2009

Reserving in General TakafulClaim Reserves comprise:a provision for claims which may occur in the

remaining period to expiry of the takaful contract – this is also known as the claims provision or reserve for unexpired risk; plus

a provision for claims already occurred – this is also known as the claims provision or reserve for outstanding claims made up of:A provision for claims occurred and reported but not yet

paidA provision for claims occurred but not yet reported also

known as provisions for claims Incurred But Not Reported (IBNR)

Reserving in General TakafulUnexpired Contribution Reserve (at reserve

valuation date) =

Contribution x (1-E) x Unexpired Contract Period Original Contract Duration

Where E = margin for operator expenses

Additional Unexpired Risk Reserve (AURR) which is the reserve held in excess of the unearned contribution reserve for unexpired risks.

Claims Estimation in General Takaful

The outstanding claims reserve would largely consist of the sum total of individual claims estimates in respect of all outstanding claims as at a given accounting or reserve valuation date.

Individual claims estimation which is typically carried out by the claims department of a takaful operator would require assumptions as to : the severity of the claim the time taken to final claims settlement the rate of inflation on claims costs between the accounting

date and settlement trends in the court system with respect to court awards in

relation to settlement of liability claims, etc

Claim Estimation Methods in General TakafulClaim run-off analysis is the

technique of triangulating claimsThe technique requires basic claims

settlement data to be tracked or sorted by year of claim since the original year of claims occurrence or issue of coverage.

The analysis may be in terms of claim numbers or claim amounts.

Claims Tringulation

Year of Issue

0 1 2 3 4

20032003 80,00080,000 50,00050,000 30,00030,000 20,00020,000 10,00010,000

20042004 120,000120,000 75,00075,000 45,00045,000 30,00030,000 --

20052005 160,000160,000 100,000100,000 60,00060,000 -- --

20062006 200,000200,000 125,000125,000 -- -- --

20072007 24,00024,000 -- -- -- --

Paid Claims

Claims Triangulation – Cumulative Basis

Year of Issue

0 1 2 3 4

20032003 80,00080,000 130,000130,000 160,000160,000 180,000180,000 190,000190,000

20042004 120,000120,000 195,000195,000 240,000240,000 270,000270,000 --

20052005 160,000160,000 200,000200,000 320,000320,000 -- --

20062006 200,000200,000 325,000325,000 -- -- --

20072007 240,000240,000 -- -- -- --

Paid Claims

Claim Estimation Method in General TakafulThe Chain Ladder Method (also known as the

linked ratio method) is based on extrapolating claims using the above claims triangulation table.

A major assumption of the Chain Ladder method is that the pattern of claims delay over time is not affected by external factors such as inflation which will cause claims to increase over time or changes in the underlying risk or mix of takaful business.

Given such stability we can work out ratios of claims buildup from one development year (year claim is paid) to the next and use the ratios to project claims for all years of issue.

Chain Ladder Method- Objective

Year of Issue

0 1 2 3 4

20032003 80,00080,000 130,000130,000 160,000160,000 180,000180,000 190,000190,000

20042004 120,000120,000 195,000195,000 240,000240,000 270,000270,000 ??

20052005 160,000160,000 200,000200,000 320,000320,000 ?? ??

20062006 200,000200,000 325,000325,000 ?? ?? ??

20072007 240,000240,000 ?? ?? ?? ??

Paid Claims

Possible Claims Development Factors

Year of Issue

0-1 1-3 2-3 3-4

20032003 1.6251.625 1.2311.231 1.1251.125 1.0561.056

20042004 1.6251.625 1.2311.231 1.1251.125

20052005 1.2501.250 1.6001.600

20062006 1.6251.625

20072007 --

From Year to Year

Chain Ladder Method ExampleAs at 2007 end the estimated outstanding

reserves for 2003 is $5,000.Based on the previous paid claims triangulation

data and 2003 estimate, calculate the estimated outstanding claims as at 2007 for issue years 2004, 2005, 2006 and 2007.

Ultimate cumulative claims in respect of 2003 year of issues =2003 cumulative + 2003 estimated reserves =190,000 + 5,000 =195,000

The furthermost data we have on ultimate claims (projected cumulative) developing is for claims arising in year 4 which is in respect of the claims arising from 2003 year of issues. These are the cumulative claims paid up to 2007 plus any estimate of outstanding claims as at end of 2007 which originate from year of issue 2003.

Claims Development factor from development year 3 to year 4 for issue year 2003;

M3,4 = ultimate claims in respect of development year 4 Claims in development year 3

= 190,000 + 5,000 = 1.08333180,000

Calculation of Claims Development Factors

Claims development factor from year 2 to year 3 for issue years 2003 and 2004;

M2,3 = Total Cumulative Claims in development year 3 Total cumulative Claims in development year 2 = (180,000 + 270,000)= (450,000) = 1.125 160,000 + 240,000 400,000

• Claims development factor from year 1 to year 2 for issue years 2003, 2004 and 2005;M1,2 = Total Cumulative Claims in development year 2

Total Cumulative Claims in development year 1

= (160,000 + 240,000 + 320,000)= (720,000) = 1.231

130,000 + 195,000 + 260,000 585,000

Calculation of Claims Development Factors

20

Claims development factor from year 0 to year 1 for issue years 2003,2004,2005 and 2006;

M0,1 = Total Cumulative Claims in development year 1Total Cumulative Claims in development year 0

= (160,000 +195,000 + 260,000 + 325,000)= (910,000)

80,000 + 120,000 + 160,000 + 200,000 560,000

= 1.625

• Claims Development FactorsM3,4 = 1.083333M2,3 = 1.125M1,2 = 1.231M0,1 = 1.625

Calculation of Claims Development Factors

Calculations of Oustanding Claims Reserves (OCR)If PCC3,2004 refers to Projected Ultimate Cumulative

Claims for business issued in 2004 as at 2007 (3 years later);

Then PCC3,2004= 2004 Cumulative Claims to date x (M3,4)

= 270,000 x 1.083333 =292,500

Then OCR2004= (Projected Ultimate Cumulative Claims) – Cumulative claims paid to date)

= 292,500 – 270,000 = 22,500

Calculations of Oustanding Claims Reserves (OCR)If PCC2,2005 refers to Projected Ultimate

Cumulative Claims for business issued in 2005 as at 2007 (2 years later);

Then PCC2,2005= 2005Cumulative Claims to date x (M2,3)x(M3,4) = 320,000 x 1.125 x 1.083333 = 390,000Then OCR2005= (Projected Ultimate Cumulative

Claims) – Cumulative claims paid to date) = 390,000 – 320,000 = 70,000

Calculations of Oustanding Claims Reserves (OCR)If PCC1,2006 refers to Projected Ultimate Cumulative

Claims for business issued in 2006 as at 2007 (1 year later);

Then PCC1,2006= 2006Cumulative Claims to date x (M1,2) x (M2,3) x (M3,4) = 325,000 x 1.231 x 1.125 x

1.083333 = 487,591Then OCR2006= (Projected Ultimate Cumulative

Claims) – (Cumulative claims paid to date) = 487,591 – 325,000 = 162,591

Calculations of Oustanding Claims Reserves (OCR)If PCC2007 refers to Projected Ultimate Cumulative

Claims for business issued in 2007; Then PCC2007= 2007Cumulative Claims to date x (M0,1) x (M1,2) x (M2,3) x (M3,4) = 240,000 x 1.625 x 1.231 x 1.125 x

1.083333 = 585,110Then OCR2007= (Projected Ultimate Cumulative

Claims) – (Cumulative claims paid to date) = 585,110 – 240,000 = 345,110

Chain Ladder Method- Results

Year of Issue

0 1 2 3 4

20032003 80,00080,000 130,000130,000 160,000160,000 180,000180,000 195,000195,000

20042004 120,000120,000 195,000195,000 240,000240,000 270,000270,000 292,500292,500

20052005 160,000160,000 200,000200,000 320,000320,000 ?? 390,000390,000

20062006 200,000200,000 325,000325,000 ?? ?? 487,591487,591

20072007 240,000240,000 ?? ?? ?? 585,110585,110

Projected Cumulative Claims

D.Factors 1. 625 1. 231 1.125 1.0833

Claims Outstanding as at 2007Year of Issue

Claims Outstanding Estimate (Reserves)

2003 $5,000

2004 $22,500

2005 $70,000

2006 $162,591

2007 $345,110

Total $605,201

Note . If the claims statistics used includes claims which are reported late, then this method of estimating claims outstanding implicitly includes a provision for IBNR claims;

Other Claim Estimation Method in General TakafulRelatively easy to compute given but the main drawback

to the method lies in its assumption that the patterns of claims amount paid over time are relatively stable.

Another key ingredient of traditional chain ladder methods is that sufficient claims statistics exist in order to triangulate claims and thereby build claims development factors.

The Bornhuetter Ferguson Method may be used where claims data is not available. Ultimate losses projected based on an expected average claim size or an expected loss ratio. Usually an expected loss ratio based on industry statistics is used for projection of ultimate losses.

Providing for claims handling expense especially in respect of long tail claims where the expense of handling claims may stretch over many years also need to be made.

Reserving in Family TakafulAs the life (family) takaful fund is typically made

up of two funds, liability provisioning will need to be done for each of the funds.

Due to the long term nature of many life (family) takaful products, an expected annual rate of profit from money invested over time is typically incorporated into the liability provisioning (reserving) calculation

The liability provision for the savings fund just involve the adding up of the balances in each of the participants’ accounts ( same way a bank would account for the monies held in bank deposit accounts placed by individual depositors).

Reserving in Family TakafulFor life (family) takaful products in particular,

the liability provisioning or reserving process would need to take into account the duration of coverage provided under the product and the nature of contributions charged to finance the benefit

For example, a family (life) takaful plan which provides decreasing term takaful coverage (e.g. MRTT for house financing) over 10 years based on a single contribution would obviously have a pattern of liability that will be probably be highest at point of plan inception and then decline over time until contract expiry.

Reserving in Family TakafulThe pattern of liability will differ greatly

depending on the nature of renewability, the point being that a plan with guaranteed coverage or renewability over an extended period of time will carry a much higher liability risk profile compared to a plan with shorter term coverage or renewability.

For example, if the coverage of a plan is annually renewable then the takaful fund is technically only on risk for a year at a time. On each contract renewal date, the contract may be revised and repriced to reflect the risks covered and ascertained at that renewal date.

Reserving in Family TakafulThe liability calculation for longer term

takaful plans in the takaful risk fund would need to incorporate the opportunity cost of cash flows over future years and hence, discounting the expected benefit payment using an assumed investment profit rate forms part of the valuation process.

tVx = Ax+t – Cont.x ax+t

Regulations on ReservingThe regulator usually requires an assumption of

mortality that was heavier (i.e. higher probability) than that assumed in pricing the product.

For solvency/statutory purposes where the assumptions incorporate additional margins such that the reserves so calculated would usually be more than sufficient to meet claims to a high degree of certainty.

It is possible to find fund deficits occurring merely as a result of the difference between the pricing basis and the valuation basis.

ISSUES Valuation centers on the timing of income

recognition in the accounts and ensuring liabilities are set up accordingly. Conceptually reserving practices would be similar to conventional insurers, with a few special concerns:- To ensure that investment assumptions are

reasonable; considering Wakala and Mudharaba profit sharing

ISSUES (…contd) Need to build up contingency

/claims stabilization reserves Depending on the model some

surplus may be held back in a contingency reserves to act as a buffer for adverse experience (solvency margin)

Accumulation of Surplus

Profit Distribution (Risk Contribution)

AnnuallyAt End of

Contract Period

Actuarial Valuation