Operational and Actuarial
Aspects of Takaful
 Valuation of Liabilities
Sub Topics
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Why Set Up a Provision for Claims Liability?
Claims Liability Provisioning in General Takaful
Estimating General Takaful Claims Provisions
Liability Provisioning (Reserving) for Family Takaful
Products
 Regulatory Aspects
Why Create Claim Reserves
 A 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 Reserves
 Hence 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)
Reserving in General Takaful
Illustrations of Fund Cash Flows
Takaful Fund
Operator Fund
Takaful Fund at Nov 1
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
Claims Paid between
Nov 1 & Dec 31 2008
Operator Expenses from
Nov 1 to Dec 31 2008
=
Takaful Fund at Dec
31 2008
=
Operator Fund at Dec 31
2008
Reserving in General Takaful
 Additional 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.
Reserving in General Takaful
Components of a Claims Liability Provision
Start Date of Contract
Claims Provisioning Date
1/11/2009
Outstanding
Claims
Provision
Expiry Date of Contract
31/10,2010
31/12/2009
Unexpired
Risk
Provision
Reserving in General Takaful
 Claim 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 paid
 A provision for claims occurred but not yet reported also known as
provisions for claims Incurred But Not Reported (IBNR)
Reserving in General Takaful
 Unexpired 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
Takaful
 Claim run-off analysis is the technique of
triangulating claims
 The 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
Paid Claims
Year of
Issue
0
1
2
3
4
2003
80,000
50,000
30,000
20,000
10,000
2004
120,000
75,000
45,000
30,000
-
2005
160,000
100,000
60,000
-
-
2006
200,000
125,000
-
-
-
2007
24,000
-
-
-
-
Claims Triangulation – Cumulative
Basis
Paid Claims
Year of
Issue
0
1
2
3
4
2003
80,000
130,000
160,000
180,000
190,000
2004
120,000
195,000
240,000
270,000
-
2005
160,000
200,000
320,000
-
-
2006
200,000
325,000
-
-
-
2007
240,000
-
-
-
-
Claim Estimation Method in General Takaful
 The 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
Paid Claims
Year of
Issue
0
1
2
3
4
2003
80,000
130,000
160,000
180,000
190,000
2004
120,000
195,000
240,000
270,000
?
2005
160,000
200,000
320,000
?
?
2006
200,000
325,000
?
?
?
2007
240,000
?
?
?
?
Possible Claims
Development Factors
From Year to Year
Year of
Issue
0-1
1-3
2-3
3-4
2003
1.625
1.231
1.125
1.056
2004
1.625
1.231
1.125
2005
1.250
1.600
2006
1.625
2007
-
Chain Ladder Method Example
 As 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
Calculation of Claims Development Factors
 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 = 1.08333
180,000
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
 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 1
Total 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 Factors
 M3,4 = 1.083333
 M2,3 = 1.125
 M1,2 = 1.231
 M0,1 = 1.625
20
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
= 390,000
 Then 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
= 487,591
 Then 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
= 585,110
 Then OCR2007= (Projected Ultimate Cumulative Claims)
– (Cumulative claims paid to date)
= 585,110 – 240,000
= 345,110
Chain Ladder Method- Results
Projected Cumulative Claims
D.Factors
Year of
Issue
1. 625
1. 231
1.125
1.0833
0
1
2
3
4
2003
80,000
130,000
160,000
180,000
195,000
2004
120,000
195,000
240,000
270,000
292,500
2005
160,000
200,000
320,000
?
390,000
2006
200,000
325,000
?
?
487,591
2007
240,000
?
?
?
585,110
Claims Outstanding as at 2007
Year of
Issue
2003
2004
2005
Claims Outstanding Estimate (Reserves)
2006
2007
Total
$162,591
$345,110
$605,201
$5,000
$22,500
$70,000
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
Takaful
 Relatively 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 Takaful
 As 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 Takaful
 For 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 Takaful
 The 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 Takaful
 The 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.

t
Vx = Ax+t – Cont.x ax+t
Regulations on Reserving
 The 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)
ISSUES (…contd)
Profit Distribution
(Risk Contribution)
At End of
Contract Period
Accumulation of
Surplus
Actuarial Valuation
Annually
End