arab reinsurance company, lebanon introduction to … technical provisions - v2_0.pdf · arab...

July 30th, 2011

Arab Reinsurance Company, Lebanon

Introduction to Non-Life Insurance reserving

Ronald P. Chidiac

The Various Reserves

The Technical Reserves are established to enable the company to meet its future obligations to

policyholders. The main reserves in respect of non-life insurance related liabilities are:

1. Unexpired risks reserves: Unearned Premium Reserve (UPR); Premium Deficiency Reserve

2. Deferred Acquisition Costs (DAC); Unearned Reinsurance Commission Income

3. Loss Reserves:

a. Outstanding Reported Claims

b. Loss Adjustment Reserve (LAR)

c. Incurred but Not Enough Reported Claims (IBNER) on existing notified claims

d. Incurred but Not Reported Claims (IBNR)

Reserves should be computed separately by class of business.

1- The Unexpired Risk Reserve (URR)

The insurer should provision for running risks, such reserve encompassing:

1. Unearned Premium Reserves (UPR)

2. Additional Unexpired Risk Reserves (AURR) or Premium Deficiency Reserves (PDR):

i. On a single risk / account

ii. On a product / class of business

1.1 - The Unearned Premium Reserve (UPR)

The following methods are commonly used to calculate the UPR in respect of one year

contracts:

1. The simple ratio method

2. The 1/8th method

3. The 24th method

4. The Prorata Temporis Method

Same ratio of UPR to written premiums is applied gross and net of reinsurance.

Earned in the Year: Unearned c/f

1/1/2008 31/12/2008

Policy 1

Unearned b/f

Policy 2

Policy 3


The Simple Ratio Method:UPR = 40% of GWP Non Marine + 25% of GWP Marine

The 1/8th Method:Assumes that the business has been written in the middle of each quarter of the year.

UPR = 1/8 of GWP written during Q1

+ 3/8 of GWP written during Q2




The 24th Method :Assumes that the business has been written in the middle of each month. The UPR is

then calculated for each month of the year as follows:

UPR = 1/24 of GWP written during month 1

+ 3/24 of GWP written during month 2

+ …

+ 23/24 of GWP written during month 12

UPR = (2m-1)/24

Where m (=1,…,12) is the number of the month in which the business has been written.

E.g. $100,000 have been written in May (m=4)

UPR = $100,000*(2*4-1)/12 = $58,333


Earned in the Year: Unearned c/f

1/1/2008 31/12/2008

Policy 1

Unearned b/f

Policy 2

Policy 3

The Prorata Temporis Method :UPR is calculated for each policy. For 1 year duration policy:

UPR = (365 – n)/365

Where n is the number of days earned during the calendar year

E.g. $1,000 have been written on 12th February 2008

UPR = (365-323)/365* $1,000 =$115

1.1 - The Unearned Premium Reserve (UPR) – Multi-year contracts e.g. Engineering ProjectsA scale of earned factors by year is estimated according to the duration of the contract,

for example:

E.g. $50,000 have been written on 30/6/2006 for a 4-years project: UPR at 31/12/2008 = (1-80%)*$50,000=$10,000

Duration of Project (in

years)1st Year 2nd Year 3rd Year 4th Year 5th Year

1 50% 100%2 25% 75% 100%3 20% 60% 90% 100%4 15% 50% 80% 95% 100%

Earned Factors (Assuming Premium is Written at Mid-Calendar Year)

1.2 - Premium Deficiency Reserve (PDR)

The UPR may be insufficient to cover administrative expenses, acquisition costs and future claims.

In that case we have a deficit in the UPR ⇒ Premium Deficiency Reserve (PDR).

PDR is calculated by multiplying the UPR (of a specific business e.g. Class Of Business, category of risk, or product) by the percentage in excess of 100% of the Expected Loss Ratio (ELR).

The ELR can be computed as the average loss ratio for the two preceding years, subject to a minimum of zero:

PDR = UPR *Max (Average Loss Ratio over the last 2 years -100%,0%)


In calculating the average loss ratio over the last two years the following should be observed:

Incurred Claims may be gross of reinsurance.

Incurred Claims should be tabulated by underwriting year:

Exceptional large claims may be excluded.

Underwriting Year

31/12/2008 31/12/2009

2008 Paid +o/s Claims +IBNR + LAR

Paid +o/s Claims +IBNR + LAR

2009 Paid +o/s Claims +IBNR + LAR


The incurred claims and expenses in each year are then calculated as follows:

Incurred Claims (Paid + o/s claims + IBNR + LAR)

+ Commission Paid

+ Change in DAC

+ Operating expenses (i.e. Administrative Expenses + Claims Management Fees –Bank Charges if any) related to the specific business if available and if not then prorated by GWP

The average loss ratio over the last two years:

Loss Ratio = Total Incurred Claims and Expenses in 2008 & 2009

Total Earned Gross Premium in 2008 & 2009

1.2 - PDR Case Study

Premiums, Claims and Expenses in 2008

# 2008 MARINE MOTOR MEDICAL TOTAL(1) GWP 900,000 1,800,000 6,500,000 9,200,000(2) UPR B/F 180,000 650,000 2,250,000 3,080,000(3) UPR C/F (200,000) (700,000) (2,500,000) (3,400,000)(4) EARNED PREMIUM 880,000 1,750,000 6,250,000 8,880,000 =(1)+(2)+(3)(5) PAID CLAIMS (100,000) (1,100,000) (3,800,000) (5,000,000) Accident Year 2008

(6) OUTSTANDING CLAIMS+IBNR+LAR (100,000) (350,000) (1,700,000) (2,150,000) Accident Year 2008

(7) INCURRED CLAIMS (200,000) (1,450,000) (5,500,000) (7,150,000) =(5)+(6)(8) ADMINISTRATIVE EXPENSES (136,957) (273,913) (989,130) (1,400,000) Prorated to GWP(9) COMMISSION (180,000) (450,000) (950,000) (1,580,000)(10) CHANGE IN DAC 18,000 100,000 200,000 318,000(11) EXPENSES (298,957) (623,913) (1,739,130) (2,662,000) =(8)+(9)+(10)

(12) INCURRED CLAIMS & EXPENSES (498,957) (2,073,913) (7,239,130) (9,812,000)

=(7)+(11)(13) LOSS RATIO 2008 57% 119% 116% 110% =-(12)/(4)


Premiums, Claims and Expenses in 2009

# 2009 MARINE MOTOR MEDICAL TOTAL(1) GWP 1,000,000 2,000,000 7,000,000 10,000,000(2) UPR B/F 200,000 700,000 2,500,000 3,400,000(3) UPR C/F (250,000) (800,000) (2,800,000) (3,850,000)(4) EARNED PREMIUM 950,000 1,900,000 6,700,000 9,550,000 =(1)+(2)+(3)(5) PAID CLAIMS (150,000) (1,200,000) (3,500,000) (4,850,000) Accident Year 2009

(6) OUTSTANDING CLAIMS+IBNR+LAR (100,000) (300,000) (800,000) (1,200,000) Accident Year 2009

(7) INCURRED CLAIMS (250,000) (1,500,000) (4,300,000) (6,050,000) =(5)+(6)(8) ADMINISTRATIVE EXPENSES (150,000) (300,000) (1,050,000) (1,500,000) Prorated to GWP(9) COMMISSION PAID (200,000) (500,000) (1,000,000) (1,700,000)(10) CHANGE IN DAC 20,000 120,000 230,000 370,000(11) EXPENSES (330,000) (680,000) (1,820,000) (2,830,000) =(8)+(9)+(10)

(12) INCURRED CLAIMS & EXPENSES (580,000) (2,180,000) (6,120,000) (8,880,000)

=(7)+(11)(13) LOSS RATIO 2009 61% 115% 91% 93% =-(12)/(4)


PDR as at end 2009

# 2009 MARINE MOTOR MEDICAL TOTAL

(1)INCURRED CLAIMS & EXPENSES IN 2008 &2009

1,078,957 4,253,913 13,359,130 18,692,000

(2) EARNED PREMIUMS IN 2008 & 2009 1,830,000 3,650,000 12,950,000 18,430,000

(3) AVERAGE LOSS RATIO 59% 117% 103% 101% =(1)/(2)

(4)PDR (in % of UPR for 2009) 0% 17% 3% 6% =MAX(LR - 100%,0%)

(5) UPR c/f in 2009 250,000 800,000 2,800,000 3,850,000(6) PDR c/f in 2009 - 132,365 88,461 220,825 =(4)*(5)

1.2 - Premium Deficiency Reserve (PDR) – Medical (Guaranteed Renewability)

UPR related to medical insurance contracts with guaranteed renewability is unlikely to be sufficient for the following reasons:

Medical inflation could be more than expected;

Increasing premium rates would push off good risks while keeping high risks within the portfolio.

A contingent reserve needs to be set for these contracts. The estimation of such a reserve should for instance take into account :

The morbidity rates of the insured population (i.e. how likely they are to fall sick in future periods), and the mortality rates of the insured population (i.e. death probability);

Medical inflation;

Lapse rates correlated to tariff increase.

Risk Covered: Own Damage

Claims Inflation: Average 7% per year

Depreciation rate on New Spare Parts: 15% (Yr 2), 10% (Yr 3), 10% (Yr 4)

Discount Rate: 6% per year

:

1.3 - The Unexpired Risk Reserve (URR) – Multi-year contracts e.g. Motor with Single Premium

1st Year 2nd Year 3rd Year 4th YearType of CostLabor 50$ 54$ 57$ 61$ Paint Material 20$ 21$ 23$ 25$ Spare Parts 75$ 67$ 65$ 56$

Used 21$ 36$ 40$ New 75$ 45$ 29$ 16$

Average Claims Cost 145$ 142$ 145$ 142$ Average Frequency 45% 57% 69% 81%Burning Cost 65$ 81$ 100$ 115$ Discounted Burning Cost 63$ 74$ 87$ 94$ URR at End of Year 254$ 180$ 94$ -$ Risk Premium 318$ 318$ 318$ 318$ URR in % of Premium 80% 57% 29% 0%

Computation of the URR

2 - Deferred Acquisition Costs (DAC) and Unearned Reinsurance Commission

Unearned acquisition costs are accounted for in the same way as the UPR. For example, if 40% of the GWP is unearned, then the DAC carried forward to next year will be 40% of total acquisition costs for the year.

The same accounting principle also applies for unearned reinsurance commission income.

3 - Loss Reserves

Loss Reserves encompass the following:

1. Reserves with respect to claims that have been reported but are still outstanding (Outstanding claims);

2. Potential payments related to closed claims after they are re-opened;

3. Loss Adjustment Reserves (LAR).

4. Claims that have incurred but have not been reported yet by the insured (IBNR);

5. An adjustment for over or under-estimation of previous year case reserves (IBNER);

3 - Loss Reserves

Outstanding Claims reserves can be estimated using either case reserves (where an claims assessor uses judgment to estimate the ultimate amount for each claim) -based on sampling techniques - or statistical methods.

IBNR and IBNER are estimated using only statistical methods, for which we commonly use:

1. The Ultimate Loss Ratio Method

2. Average Cost method

3. The Basic Chain Ladder Method

4. The Bornhuetter-Ferguson Method

3.1 - The Ultimate Loss Ratio Method

This method calculates directly the ultimate loss as being the earned premium multiplied by the ultimate loss ratio.

The difference between the ultimate loss and the incurred claims (i.e. paid amount + outstanding claims amount) would represent the IBNRs/IBNERs.

The ultimate loss ratio would be estimated by the underwriting department / chief underwriter based on past experience and/or benchmarks.

3.1 - The Ultimate Loss Ratio Method – Case Study

Earned Premiums

$100,000

Ultimate Loss Ratio

60%

Ultimate Incurred Claims

$60,000 =$100,000*60%

Incurred Claims to Date

$40,000

IBNR/IBNER $20,000 =$60,000-$40,000

3.2 - The Average Cost Method

This method is based on the expected number of claims andtheir respective average cost

A development table is introduced = average cost table Future claims are obtained Nb claims * Avg Cost. This

method could hence be introduced per Underwriting Year orper Calendar Year:

• Adjustment of past claims to adjust for inflation• Cumulative cost, number of claims, and average cost triangles• Development factors for the number of claims ⇒ projecting future # claims• Computation of the average cost per year of development• Nb claims * average cost provides the reserve at constant currency• Adjustment of future amounts as per expected inflation

3.3 - The Basic Chain Ladder Method

This is the most widely used reserving method and is based on the following assumptions:

• The starting accident year is supposed to be fully run-off;

• The claims development pattern is stable over time;

• Future inflation is ignored (but could be taken into account in a refined version of the Chain Ladder).

This method is appropriate for mature classes of business that have a relatively stable development pattern.

Reserves using this method are calculated as follows:

• Cumulated paid or incurred claims are tabulated by underwriting year and calendar year;

• Development factors are calculated based on the claims triangulation;

• The ultimate claims amounts are projected for each underwriting year using the development factors; deduction of the paid claims leading to OS + IBNR/IBNER.

3.3 - The Basic Chain Ladder Method – Case Study

Underwriting Year Year 1 Year 2 Year 3 Year 4 Year 5

2005 7,835 4,453 3,888 3,335 2,0882006 9,763 6,517 3,563 3,9842007 10,745 6,184 4,5492008 14,137 8,1162009 15,162

Underwriting Year Year 1 Year 2 Year 3 Year 4 Year 5

2005 7,835 12,288 16,176 19,511 21,5992006 9,763 16,280 19,843 23,8272007 10,745 16,929 21,4782008 14,137 22,2532009 15,162

...

Development Year

Paid Claims by Underwriting and Development Year

Cumulated Paid Claims by Underwriting and Development Year

Development Year

59.1137,14745,10763,9835,7

253,22929,16280,16288,121 =

++++++

=f

11.1511,19599,21

4 ==f

3.3 - The Basic Chain Ladder Method – Case Study

1.59 1.111.26 1.20

Underwriting Year

Year 1 Year 2 Year 3 Year 4 Year 5 O/S +IBNR/IBNER

2005 7,835 12,288 16,176 19,511 21,599 -2006 9,763 16,280 19,843 23,827 26,377 2,5502007 10,745 16,929 21,478 25,842 28,608 7,1302008 14,137 22,253 28,122 33,837 37,458 15,2052009 15,162 24,181 30,559 36,769 40,704 25,542

50,426

Development YearCumulated Paid Claims by Underwriting and Development Year

1f 2f 3f 4f

3.4 - The Bornhuetter-Ferguson Method

The Bornhuetter-Ferguson (BF) method combines:

• The Expected Ultimate Loss Ratio Method; AND

• The Chain-Ladder Method

⇒ Estimated Loss Reserve = Total Expected Ultimate Losses * % of Losses to be paid in the future

The starting point is the Ultimate Loss Ratio estimate:

Total Expected Ultimate Losses=Earned Premium in the given year * Expected Ultimate Loss Ratio

Then the use of the development factors (= those used under the Chain Ladder).

% of Losses to be paid in the future=1-1/FA, FA being the « paid loss development factor » (i.e. the product of the factors related to future years)

3.4 - The Bornhuetter-Ferguson Method - Case Study

Earned Premiums

Underwriting Year

Year 1 Year 2 Year 3 Year 4 Year 5Ultimate Claims

Amount*

O/S + IBNR/IBNER

39,226 2005 7,835 12,288 16,176 19,511 21,599 21,599 -21,599

47,251 2006 9,763 16,280 19,843 23,827 25,988 2,51223,476

49,918 2007 10,745 16,929 21,478 27,455 6,84220,612

64,090 2008 14,137 22,253 35,249 14,30820,941

70,536 2009 15,162 38,795 24,34414,451

48,007

* Loss Ratio = 55% for all Underwriting Years

Cumulated Paid Claims by Underwriting and Development YearDevelopment Year

1f 2f 3f 4f

F4=1.11

F4*F3= 1.11*1.2 = 1.332

F4*F3*F2= 1.332 * 1.26 = 1.678

F4*F3*F2*F1= 1.678 * 1.59 = 2.669

The Basic Steps of a Reserving Exercise

Obtain background information and data sets;

Analyze and check the data to identify any unusual features and reconcile the data with the accounts;

Clarify issues with the claims manager, underwriter, loss adjustor, IT staff and possibly the management of the company;

Set reserving assumptions using historical data, benchmarks and actuarial judgment;

Perform projections using several reserving techniques;

Analyze and interpret the results and obtain feedback from the company’s management;

Finalize the projections and document the assumptions and calculations rationale.

arab reinsurance company, lebanon introduction to … technical provisions - v2_0.pdf · arab...

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