Operational and Actuarial Aspects of Takaful

1
Operational and Actuarial Aspects of Takaful

• Valuation of Liabilities

2
Sub Topics

• 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

3
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.

4
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)

5
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
Operator Expenses from Nov 1 to Dec 31 2008
Claims Paid between Nov 1 Dec 31 2008


Takaful Fund at Dec 31 2008
Operator Fund at Dec 31 2008
6
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.

7
Reserving in General Takaful
Components of a Claims Liability Provision
Claims Provisioning Date
Start Date of Contract
Expiry Date of Contract
31/10,2010
1/11/2009
31/12/2009
Outstanding Claims Provision
Unexpired Risk Provision
8
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)

9
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.

10
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

11
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.

12
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 - - - -
13
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 - - - -
14
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.

15
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 ? ? ? ?
16
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 -
17
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

18
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

19
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

20
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

21
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

22
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

23
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

24
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

25
Chain Ladder Method- Results
Projected Cumulative Claims
D.Factors 1. 625 1. 231 1.125
1.0833
Year of Issue 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
26
Claims Outstanding as at 2007
Year 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
27
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.

28
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).

29
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.

30
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.

31
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.
• tVx Axt Cont.x axt

32
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.

33
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

34
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)

35
ISSUES (contd)
Profit Distribution (Risk Contribution)
Annually
At End of Contract Period
Accumulation of Surplus
Actuarial Valuation
36
End