abstract - institut des actuaires - accueil€¦ · dissertation isfa – nguyen quang huy page 4...

Dissertation ISFA – Nguyen Quang Huy

ABSTRACT

Life insurance market in Vietnam is having a quite strong competition among life insurers. One of

the main tools of competition is product field. According to the data from Vietnam Insurance

Association, Endowment Product are still in high demand and account for a large share of Life

Insurance Premium in Vietnam.

Mirae Asset Prevoir Life insurance has just acquired an exclusive distribution channel and is

planning to widen its distribution channels. The demand for new products for new distribution

channel increases. To meet with current demand, the juvenile endowment is planned to be

developed, targeting on the savings for the education plan of the child while it also provides

protection cover for the parent. The benefits of the two lives are designed to be balanced in order to

reduce premium that the client could be affordable and to be competitive with other competitors in

the market while it must maintain the target profitability of the product under the pressure of

distribution channel for high compensation level and unfavorable financial market conditions.

To increase the competitiveness of the product, in designing process, we also attach with the product

some features and options that improve the persistency of the insurance policy.

Key words: Life insurance, pricing, reserve, profitability, profit test, endowment, participating

product, profit sharing, dividend, Non Participating product, sum insured, gross premium, net

premium, mortality table, lapse, surrender value, investment rate, deterministic model, stochastic

model, sensitivity test, scenario test, stress test, profit margin, ROI, breakeven year.


Résumé

Le marché de l’assurance-vie au Vietnam connaît une concurrence assez forte entre les assureurs-vie.

L'un des principaux outils de la concurrence est le domaine des produits. Selon les données de

l'Association Vietnamienne de l'Assurance, les produits d'asurance vie mixte (Endowment Product)

sont toujours très demandés et représentent une part importante des primes d'assurance-vie au

Vietnam.

Mirae Asset Prevoir Life vient d’acquérir un canal de distribution exclusif et envisage d’élargir ses

canaux de distribution. La demande de nouveaux produits pour de nouveaux canaux de distribution

augmente. Pour faire face à la demande actuelle, il est prévu de développer un produit assurance

mixte pour enfants (juvenile endowment), en ciblant les économies réalisées pour le plan d’éducation

de l’enfant tout en offrant une couverture de protection aux parents. Les avantages des deux côtés

sont conçus pour être équilibrés afin de réduire le prime qui serait abordable pour les clients et

compétitif par rapport aux autres concurrents du marché, tout en maintenant la rentabilité recherchée

du produit sous la pression du nouveau canal de distribution avec des rémunérations élevées et des

conditions défavorables des marchés financiers.

Pour renforcer la compétitivité du produit, dans le processus de conception, nous associons

également au produit certaines fonctionnalités et options qui améliorent la persistance de la police

d’assurance.

Mots-clés: Tarification, réserve, rentabilité, test de profit, dotation, produit participant, partage des

bénéfices, dividende, produit non participant, somme assurée, prime brute, prime nette, table de

mortalité, déchéance, valeur de rachat, taux d'investissement, modèle déterministe, modèle

stochastique , test de sensibilité, test de scénario, test de résistance, marge bénéficiaire, retour sur

investissement - ROI, seuil de rentabilité.


Acknowledgements

I would like to express my appreciation and gratitude to my supervisors, Professor Didier Rulliere

for his valuable time and helpful guidance and instructions during the long period of doing this

dissertation. I am really indebted to him for his instructions and comments on this dissertation, from

him that I gained great knowledge.

I would like to thank Professor Stéphane LOISEL, Mr Brias Samy and Professors in ISFA for giving

me the chance to complete the final dissertation.

I would like to thank Mr Khamsaya Soukhavong for his encouragement and supports during the

period I make the dissertation in the Mirae Asset Prevoir Life Insurance Company.

Finally, I would like to express my thanks to my family, my French teacher and my colleagues for

their encouragement and support to complete the dissertation.


Contents

1. Brief on Vietnam Life Insurance Market. ................................................................................................... 7

2. Product Development Process ................................................................................................................... 11

3. Product Design .......................................................................................................................................... 13

3.1 Product Objective and Product Positioning ............................................................................................. 13

3.2 Product features ................................................................................................................................. 14

4. Competitor’s Product Comparison ............................................................................................................ 19

5. Pricing Assumptions .................................................................................................................................. 20

5.1 Mortality Table ........................................................................................................................................ 20

5.2 Pricing Interest rate .................................................................................................................................. 20

5.3 Commissions. .......................................................................................................................................... 20

5.4 Expenses Assumptions. ........................................................................................................................... 21

5.5 Back Test Assumptions. .......................................................................................................................... 23

6. Pricing ....................................................................................................................................................... 25

6.1 Notation ................................................................................................................................................... 25

6.2 Formula ................................................................................................................................................... 27

6.3 Premium Allocation Analysis. ................................................................................................................. 29

7. Reserves and Solvency .............................................................................................................................. 31

7.1 Regulatory Stipulations on Reserve ........................................................................................................ 31

7.2 Mathematical Reserve. ...................................................................................................................... 34

7.3 Dividend reserve ................................................................................................................................ 35

7.4 Claim Reserve ......................................................................................................................................... 35

7.5 Contingency Reserve ............................................................................................................................... 35

7.6 Regulatory Stipulations on Solvency Requirement ................................................................................. 35

8. Profit Sharing............................................................................................................................................. 37

8.1 Regulatory Stipulations on Dividend ...................................................................................................... 37

8.2 Profit Sharing Feature .............................................................................................................................. 37

8.3 Determination of Surplus and dividable profit ........................................................................................ 39

8.4 Dividend Calculation ............................................................................................................................... 40

9. Endorsement. ............................................................................................................................................. 42

9.1 Surrender and Surrender Value. .............................................................................................................. 42

9.2 Paid up Sum Insured when the policyholder cease paying premium. ..................................................... 43

9.3 Change of Sum Insured. .......................................................................................................................... 43

9.4 Loan on Surrender Value and Automatic Premium Loan. ...................................................................... 44


10. Profitability and Testing. ....................................................................................................................... 46

10.1 Profitability requirement ....................................................................................................................... 46

10.2 Profitability base ................................................................................................................................ 47

10.3 Model and Risk Measure ....................................................................................................................... 49

10.3.1 Deterministic Model ....................................................................................................................... 49

10.3.2 Stochastic Model ............................................................................................................................ 49

10.3.3 Risk Measure .................................................................................................................................. 49

10.4 Profit Tests. ........................................................................................................................................... 50

10.4.1 Best Estimate Scenario ................................................................................................................... 50

10.4.2 Sensitivity Test ................................................................................................................................ 58

10.4.3 Scenario Test. ................................................................................................................................. 64

10.4.4 Stress Test. ...................................................................................................................................... 78

CONCLUSION ................................................................................................................................................. 87

ABBREVIATION. ............................................................................................................................................ 88

ACADEMIC BIBLIOGRAPHY ....................................................................................................................... 89

11. Appendix ............................................................................................................................................... 90

Appendix 1: Individual Mortality Table CSO1980 for Male ....................................................................... 90

Appendix 2: Summary of Assumptions ..................................................................................................... 91

Appendix 3: Tariff table ............................................................................................................................. 92

Appendix 4: Best Estimate Profit Test Result ............................................................................................ 94

Appendix 5: Scenarios and Stress Test ...................................................................................................... 96

Appendix 6: Comparison with competitor products ............................................................................... 118

Appendix 7: Sensitivity Results ................................................................................................................ 120


1. Brief on Vietnam Life Insurance Market.

Vietnam is a developing country with GDP growth of around 6.0%. The rising income level of

household mean the people are affordable to more insurance products. Besides, the people’s

awareness of insurance increase by time.

Vietnam sizable population of 90 million and low market penetration of around 1% of GDP is a huge

chance for life insurer to exploit this potential market. Actually, life insurance segments have been

growing at double digits for the long time and is expected to continue the high growth in the future.

However, the high growth is coming off from a small base. In 1997, 10 years after the life insurer

sell the first life insurance policy in Vietnam, the life insurance premium volume is only at VND

9,437 billion (about USD 402 million at Exchange rate USD/VND 23,500).

Life insurance premium volume and growth as per below.

Figure 1.1 - Life insurance premium volume and growth from 2007 to2018

While in 2007 life insurance premium is 9,437 billion VND (USD 402 million), it strongly increases

to VND 66,226 billion (USD 2,818 million) in 2017, and is estimated at VND 80,882 billion (USD

3,442 million) in 2018. On average the annual growth of the life insurance premium during period

2007-2018 is 21.6%.

9,437 10,307 11,839 13,772

15,998 18,397

23,330

28,355

38,271

49,677

66,226

80,882

0%

5%

10%

15%

20%

25%

30%

35%

40%

0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

80,000

90,000

2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018E

Life Insurance Premium

Life Insurance Premium Growth


One of the main drivers of this growth will be the increasing affordability of life insurance as

household income levels gradually increase throughout the country. In particular, the number of

middle-income family increase significantly, earning about USD10,000 a year.

The increased earning power of Vietnamese households will result in higher levels of disposable

income and hence demand for savings and investment products

The other driver is the strong operation of the agency distribution in Vietnam. Massive agency

network will continue to increase premium volume.

Significant regulatory improvements have further facilitated growth in Vietnam's life insurance

sector. In the past, foreign companies had noted difficulties with regard to operating in Vietnam,

highlighting excessive and unnecessary regulation in the market which made the market entry

process much slower and less profitable. The Vietnamese government has recognized this and has

introduced a new set of regulations in the insurance sector, the Decree 73/2016/ND-CP and the

circular 50/2017/TT-BTC. In particular, the government is trying to streamline the regulatory

framework in line with international best practices and standards and to comply with Vietnam's

WTO Commitments. The Decree 73/2016 stipulate clearly necessary conditions and the required

minimum charter capital to set up insurance company in Vietnam. It reduces the procedures to set up

insurance company and clearly stipulate the time the Ministry of Finance must reply the submission

from foreign investor. It also updates the necessary criteria of the CEO and the Appointed Actuary of

the insurance company. It clearly stipulates the procedure to have the product submission approval

process so as to facilitate to the launching of the product. It also stipulates the Ministry of Finance

(Ministry of Finance) is the only office to receive the product submission instead of sending product

submission to both of the Ministry of Finance and Ministry of Industry and Commerce as life

insurers might have to do before. It reduces the response time of the Ministry of Finance for the

product submission so as to facilitate the insurance business of insurers. Besides, it also updates on

the reserve stipulations to meet with international practices.

Life insurance products.

Targeting the emerging middle classes, the leading companies offer a broad range of savings and

protection products. In term of collected premium, the endowment and Universal Life product are

two main drivers that account for about 90% of the total Premium volume of the market according to

report of Vietnam Insurance Association (VIA).

In terms of number of policy, in addition of endowment and universal life, term life product sold

through bancassurance channel are three main drivers.


Figure 1.2: Structure of types of life insurance product as per Number of policy in the Market.

With:

Endowment: a type of insurance policy to pay a lump sum after a specific term (on the maturity

date) or on Death or Total & Permanent Disability (TPD)

Universal Life: a type of cash value life insurance. Under the terms of the policy, the excess of

premium payments above the current cost of insurance is credited to the cash value of the policy,

which is credited each month with interest. The policy is debited each month by a cost of insurance

(COI) charge as well as any other policy charges and fees drawn from the cash value, even if no

premium payment is made that month. Interest credited to the account is determined by the insurer

but has a contractual minimum rate.

Term Life: is a type of life insurance product that provides coverage at a fixed rate of payments for

a limited period of time, the relevant term. If the life insured dies during the term, the death benefit

will be paid to the beneficiary.

Pension: is a type of life insurance product that specifies pension plan contributions to an

insurance undertaking in exchange for which the pension plan benefits will be paid when the

members reach a specified retirement age or on earlier exit of members from the plan

Others: Other types of products (whole life, annuities, health ..).

The life insurers use a variety of distribution channels-bancassurance, tied agents, independent

brokers and direct sale. Some companies are also targeting corporate customers with group products.

Education saving plans continued to be developed by life insurers in Vietnam. The speedy growth of

the middle-class coupled with a culture that places a high value on children's education should mean

the Vietnamese is willing to pay more on premium on this type of product.

58.30%

32.90%

7.20%

0.40% 1.20%

Endownment

Universal Life

Term Life

Pension

Others

https://en.wikipedia.org/wiki/Interest

https://en.wikipedia.org/wiki/Life_insurance

https://en.wikipedia.org/wiki/Beneficiary

https://en.wikipedia.org/wiki/Pension


Market share of life insurers

There were 17 life insurance companies with about 1,000 representative offices and general

insurance agents. Total revenue of life operators in 2017 was estimated at VND 66.226 billion, up

31.1% over the last year which stood at VND 50,497 billion, the Ministry of Finance (MoF) reported

at the end of 2017, with 7.38 million contracts in force.

Figure 1.3 – Market share of life insurance premium in 2017 of life insurers in Vietnam

A few companies divide the lion's share of the life segment between them, with Prudential (market

share 24.48% and the former state monopoly BaoViet Life (market share 26.38%) taking more than a

half of total life insurance premiums in the market. We remain of the view that, over time, these two

companies' combined shares will be eroded due to the stronger competition from current smaller

companies and potential new entrants come to the Vietnamese life insurance market.

Prudential, 24.48%

Bao Viet Life, 26.38%

Manu Life, 12.27%

AIA, 9.51%

Daiichi Life, 12.16%

Chubb Life, 3.92%

Generalli, 2.95%

Hanhwa, 2.32%

Others, 6.02%

Market share

Prudential Bao Viet Life Manu Life AIA Daiichi Life Chubb Life Generalli Hanhwa Others


2. Product Development Process

A carefully managed product development process can ensure a higher percentage of success of

product. It also hastens the time to the market and reduce the overall cost of product development.

The product development process helps to use the resources more effectively. It ensures the

consistency quality in design and development.

The product development process follows the below principle.

Figure 2.1 – Product Development Process

The new product will be made under the following Product Development Process.

A. Conception.

Idea Generation and Product Concept: Ideas for new products are suggested from Sale

Department or Product Marketing and will be reviewed by the Product Committee. Business

cases or feasibility studies are prepared. Initial ideas of the product are formed.

B. Design

Product Planning and Design: Products features are designed by Actuary, Sales and

Operation. Sale volumes are planned. Product development Process timeline is set up.

C. Construction

a. Product Pricing: Actuarial pricing that includes setting the tariff rates, reserves,

compensation and any other data. These data are stress tested against product profit

objectives and expected or actual data. Model double check is required.

b. Establish Underwriting Guidelines: Underwriting rules and processes are established, with

an appropriate classification of risks.

Conception

Design

Construction

Launch

Evaluation


c. Legal prepare Policy Wording. Reinsurance treaty negotiation is executed.

d. Update IT Systems: Systems requirements are developed and implemented to cover

anything a customer can do. This includes illustration systems. Systems requirements are

developed and implemented for any further functionalities and organizational requirements.

e. Update Business Procedures: Operations and business procedures are developed.

f. Marketing Plans: Marketing materials are developed.

D Launch

a. Approval Process: Actuary, Operation and Legal prepare necessary document to submit to

Ministry of Finance for Product Approval. All new products must be approved by the

Ministry of Finance.

Ministry of Finance will check: Formulae of the premium rates calculation, Pricing

assumptions, Liability Reserves and surrender values, all policy conditions.

Liability reserve assumptions for Mortality and Interest rate are stipulated by Ministry of

Finance as standard valuation assumptions.

b. Product Launch: Marketing campaign is prepared, other necessary jobs for products to be

launched.

E. Evaluation

Tracking of results vs. Plan/Business case: comparing actual business results to pricing/plan

to gauge assumptions versus experience.

This dissertation will mainly focus on step C of the product development process.


3. Product Design

3.1 Product Objective and Product Positioning

In the market, companies often seem to have little choice but to engage in an almost continuous

progress for product development as the company strive to respond to both competitors’ initiatives

and changes in the market. The general objective of producing a new product is to fulfill a need of a

target market at the same time meet the financial objectives of the company.

Juvenile endowment is a key product of the life insurance market in Vietnam. All life insurance

companies in Vietnam have at least one of this kind of product as the demand for this product in the

market is often in high demand. It remains clear that people want to “secure” and “save” their money

to ensure a good future for their children. These products meet the need for choice.

A juvenile endowment is produced so as to meet the demand of the market and to enhance the

company s’ sale volumes.

Both Non Participating and participating version of the product have been developed. As a key

competitive product it has been deliberately designed to be competitive against other life insurers in

Vietnam.

The main objective of the product design is to increase sale volume and profitability, while

remaining competitive. It is quite rare to be possible to achieve both sales and profit objectives.

Normally the process become one of compromise, but for the initial phase, sale volume may be put

higher priority by some life insurers.

The position of this product is very important. As the company is developing a new distribution

channel. This is one of the first products for this distribution channel. Management have sought to

ensure this is a successful product in terms of sales.

The target client of this product is the families with young children. The parent will have a financial

plan for the education expenses of their child whether they are alive or pass away, the education plan

of their child is not impacted.


3.2 Product features

Product type: we develop two versions, a Non Participating product and a participating product.

The insured: individual, child or under guardianship of the Policyholder, from 180 days’ old (age 0)

to age 10 at underwriting.

Policyholder: individual having full capacity of civil acting or an entity duly established in Vietnam,

from age 18 to age 62 at underwriting .

We aim at protecting the financial source of the family and guarantee the financial support for the

child’s education. As a result, the Policyholder is the parent or the legal guardian of The insured.

Both the insured and the policyholder are covered in this policy.

Condition on age of the main insured and policyholder: age of policyholder minus age of the

main insured < = 52 so that the Max insured age of the policyholder is 70.

Beneficiary: the policyholder, or an individual appointed by the policyholder.

Age Definition: Age of last birthday.

Risks covered: Death, Total Permanent Disability (TPD) for the policyholder and the insured. The

definition of TPD in the below.

Total and Permanent Disability definition: TPD means any event where the Insured suffers injury

leading to one of the states as described below:

(a) The Insured is completely lost, paralyzed and unrecoverable functions of:

(i) Two arms, or;

(ii) Two legs, or;

(iii) One arm and one leg, or;

(iv) Two eyes, or;

(v) One arm and one eye, or;

(vi) One leg and one eye.

In the fore-going cases, completely lost and unrecoverable functions of:

(i) arm, means from wrist up;

(ii) leg, means from ankle up;

(iii) eye, means lost eye or blindness.

Or

(b) The Insured suffers from at least 81% loss of health and more as prescribed by a medical

agency/ Medical Assessment Council at provincial level or higher. The rate of the disability of the

Insured shall has the same meaning with the rate of the loss of working capacity, the loss of health,

the injury rate, the illness rate, the morbidity rate.


The Sum Insured (SI): the policyholder chooses the Sum Insured when signing the policy. The

minimum Sum Insured is stipulated by the company at each time. The current minimum SI is set at

VND 50 million. The maximum Sum Insured is up to underwriter’s decision.

Insurance Benefits: as per below.

Installment period: is the period during which the main insured receives the annual installments.

The installment period is from the anniversary date of the policy when the main insured’s age gets 18

and terminates at the last anniversary date of the policy when the main insured is 21. Four annual

installments will be made at anniversary dates when the insured get age 18, 19, 20, 21.

Premium period: The premium payment period terminates at the anniversary date when the main

insured is 18 years’ old, i.e. when the main insured begins receiving the education installments.

Insurance Period: is the difference between 21 and entry age of the main insured. Insurance period

therefore range from 11 years to 21 years.

Waiting Period: Not applied.

Premiums:

Premium depend on the insured's entry age, the policyholder’s entry age and the Sum Insured.

Premiums are flat and not changed in the premium payment period.

Annual premium could be converted into semi-annual premium, quarterly premium, and not less

than the minimum premium/payment.

Premium frequency:

Monthly Premium

Quarterly Premium

Semi-annual Premium

Annual Premium.

Insurance Benefits

In case of Death or TPD of the Policyholder before the anniversary date when the main

insured’s age attains 18

If the policyholder is dead or TPD during premium payment period, the insurance policy will be

exempted from the future premiums (premiums after insured event).

The policy is still in force and the insurance benefits for the main insured are still maintained the

same as registered in the insurance policy (Waiver of Premium).

If the policyholder is dead or TPD, the insurer will pay 100% of the Sum Insured.


Besides, if the policyholder is dead or TPD due to accident, the insurer will pay additional 100% of

the Sum Insured.

In case of Death or TPD of the main insured before the anniversary date when the main

insured’s age attains 18.

The insurer will pay 150% of the Sum Insured to the Beneficiary.

The policy is terminated.

In case of Death or TPD of the main insured during installment period

Company will pay the amount equal to the Sum of unpaid installment(s).

The policy is terminated.

Annual Cash Benefit

The company will calculate the Cash Benefit which equal to 2% of the Cash value of the latest

previous anniversary date (the policy not under premium waiver condition) at the end of each year

from the third policy year until the policy year before the insured reach age 18.

The Cash Benefit Payment will be made from the anniversary date of policy year 4 till the

anniversary date when the insured attain age 18.

Policyholder can choose to receive the Cash benefits immediately or leave them unwithdrawn to

receive the interest with the interest rate announced and determined by the company in each period.

Installments Benefit

The Education benefit corresponds to the payment of the annual installment at the policy anniversary

dates when the main insured’s age attains 18, 19, 20 and 21 (three last anniversary dates and the

maturity date). The payment of the installment is paid under the condition of the main insured is still

alive and not under TPD at its payment date.

The installments are percentages of the Sum Insured. The annuity coefficient is based on the main

insured’s age y(t) from 18 to 21, as n = 21- y(0), we have :

Installment Coefficient ( )

% of the Sum Insured 30% 35% 40% 45%

Table 3.1- Installment coefficient for Annuities Benefit.

Policyholder can choose to receive the installment benefit immediately or leave them unwithdrawn

to receive the interest with the interest rate announced and determined by the company in each

period.

Surrender

The policyholder can require full surrender from the third policy year and receive the surrender value

(if any).


Paid up policy due to unpaid premium

Allowed. If the policyholder required, the policyholder can cease premium payment and the new

Sum Insured is determined.

Changing Sum Insured

If the policyholder can request to reduce the sum insured. The new premium will be determined

according to the new Sum Insured.

Automatic Premium Loan

After the policy has been effective for 24 months, in case the policyholder

cease to pay premium and

the grace period of 60 days is over and

the policyholder do not require to surrender the insurance policy and

the unwithdrawn accumulated Cash benefits is not sufficient to pay the due premium.

Then the insurer will provide the policyholder with automatic premium loan. Automatic Premium

Loan terms and condition is as per policy wording.

In case the policyholder has the unwithdrawn Accumulated Cash Benefit, this amount will be used to

offset with the automatic premium loan unless the policyholder request otherwise.

The insurer will continuously supervise the policies with loans to examine the validity of those

insurance policies.

The policy is still effective as long as:

Where:

: Surrender Value at time t

: Outstanding balance of Automatic Premium Loan with accumulated interest at time t (if any)

If the total amount of the loans (automatic premium loans, if any) plus its accumulated interest is

equal to or exceeds 90% of the Surrender value, the policy will be terminated at this incurred date.

At this terminated date, the company will pay the difference between the Surrender Value and the

debt (accumulated loans and interest till the terminated date) to the policyholder.

Reinstatement of policy:

The policy may be reinstated at any time within 2 years from policy termination date (included).

Grace period: 60 days from premium due date

Attached riders: This product can be sold with current riders, upon permission of the insurer.


Underwriting: follow the underwriting process of the company.

Marketing and distribution.

How the product is marketed and distributed is an important step. The cost of marketing and

distribution will affect pricing. The cost of marketing and distribution is mention in the expense

assumption in the section 5.4 below. The target market will affect the underwriting standard and the

aggressiveness of the marketing campaign will affect the volume of sales.

The sale person of this product may be the tied agent or employees of the exclusive bank channel.

We need to plan the training of people who will be involve in the sale of the product. The sale person

may have to explain to the customer when the product has complex features. So they must

understand well the product before it is launched to the market. Not only that they must also be train

on the selling and soft skills to communicates with customers.


4. Competitor’s Product Comparison

We have collected information of some competitors’ products in the market to make sure that the

new product is comparative competitive with them in the market. We will take some snaps short on

for comparison purpose.

* Benefit comparison

Product of Prudential:

Prudential provide the death cover for the policyholder (the parent) but it does not cover for the Total

& Permanent Disability (TPD) risk. It also provides the waiver of premium benefit in case the

policyholder is dead. It however does not cover the death benefit and TPD benefit due to accident.

Prudential’s product does not cover for the death and TPD of the insured (the child). This product

cover death and TPD Benefit for only one person.

The Education Benefits is paid in 5 times at the anniversary dates when the children get age 18 to 22.

The total Education Benefits accumulates up to 150% of the Sum Insured.

This product of Prudential is a participating product. The dividend is announced annually but

unguaranteed.

Product of AIA:

The product of AIA cover for the death and TPD exposure for the policyholder.

In case the policyholder is dead or under TPD due to accident, the company will pay 200% of the

Sum Insured. This product also does provide the waiver of premium benefit if the policyholder is

dead or under TPD.

The child is not covered under this product.

The policyholder may choose one of the two option for the Education benefit. At maturity date when

the insured attain age 22, the insured may receive the maturity benefit which is 150% of the sum

insured or the insured may receive education benefit at 5 times, 30% of the sum insured is paid out

each time.

In addition, the policyholder may have the cancer benefit which is 25% of the sum insured if he is

diagnosed cancer at early stage. This is a supplementary benefit of this product.

* Tariff comparison

Despite the differences in benefit structures, we make a relative comparison in premiums of our

products and those of competitor's products, we try to keep our tariff competitive and close to those

of competitors’.

Details of comparison with competitor products is found in the appendix 6.


5. Pricing Assumptions

For pricing this product, we apply the marginal cost and contribution pricing strategy. Once the

marginal costs are covered, charges have to be set at a level that meets the company’s profit targets.

The excess over marginal costs represents the contribution which must, in total, cover overheads and

generate profits. The relationship between the charges and the contribution for this product is quite

close.

The pricing assumptions used in pricing will take into consideration the following factors:

The company’s profit expectation;

Actual experience;

Acceptable level of risk.

Desired competitive position.

5.1 Mortality Table

Only some large life insurers in Vietnam such as Prudential and Bao Viet Life, who has large client

data base study their own experience mortality table. Other small life insurers in Vietnam use the

Mortality Table CSO 1980 for their pricing purpose as their experience data base is not sufficient to

create his own mortality table.

As the CSO 1980 Mortality table is used as the standard mortality table for valuation calculation. It is

accepted by the Ministry of Finance and widely used for pricing purpose by life insurers in Vietnam.

For this product we also use the Mortality Table CSO 1980 for Pricing (Attached in the appendix).

5.2 Pricing Interest rate

To price this product will apply the pricing interest rate of 4.0%/year for Non Par product and 3.0%

for participating product.

5.3 Commissions.

One of condition that make the product failure is the insufficient commission to distributors and

agents. Distributors always ask for high commission level. In order to have a competitive premium

rate we however have to balance the benefits of distributors which is the commission, the benefit of

the life insurers which is the profitability, and the insurance benefits of the customers.

We have set the below commission for the distributors base on the current commission rates of

competitors in the market.

The commissions is considered as an element of the total expenses and is shown in the below table.


5.4 Expenses Assumptions.

To come up with the expense assumptions for pricing purpose, the company have carried out the unit

expense analysis.

It is however sometime difficult to recover expenses through premium because of the company’s

desire to achieve the sale target and increased market share.

The inadequate expense loading, especially for smaller policies, was a major contributory factor to

the “poor profitability” of the product.

Pricing process is the link between current expense levels and the recovery of future expenses

through pricing premium. Due to the differences between the current applying expense assumptions

in pricing and the actual future expenses, this may lead to underpricing problems and as the result

lowering the profitability of the product, especially for small sized policy with low premium levels.

The actual maintenance costs and acquisition costs are much higher than those apply in pricing due

to the market competition and reasonableness and affordability of the premium, especially small

sized policies

Pricing however is the dynamic and iterative process with both internal and external feedback loops.

Pricing should reflect these changes if possible. The expense analysis shall be reviewed frequently to

ensure the reasonableness of expenses assumptions and to review whether the current applying

expense assumptions in pricing deviate much from actual expenses.

The expense assumptions may base on the passive extrapolation of historical levels.

Below is the process of unit expense analysis for expense assumptions in pricing.

a. Establish the methodology for expense analysis: the method to reflects and allocate expenses.

The methodology includes some following factor:

Selection of exposure units to be used in the development of unit expense

assumptions

Selection units used as expense categories

Degree of refinement and aggregation of expense categories

b. Gather historical experience data

Relevant historical and current expense data are available from cost accounting Department.

The company also carried out time survey analysis for expense analysis purposes.

Data are adjusted to more suitably match with expense analysis for pricing purpose.

Expenses are classified as acquisition, maintenance; first year or renewal expenses; individual

or group expenses, line of business,…


c. Determine drivers and expense allocation.

Expense drivers are determined. Expense allocation is made on expense drivers on unit basis.

Determine the unit expense factors that are used in pricing by dividing the allocated expenses

by the unit measure.

d. Review for reasonableness and validity

The result of expense analysis has to be reviewed for overall reasonableness. The review may

include comparison of expense assumption with those in prior period, comparison of expense

assumptions among similar products, external studies and the market competition.

e. Test overall expense adequacy

Test will be carried out to ensure the expense adequacy and the profitability goal of product

(mentioned in part session 10). Adjustments may be necessary to ensure that acceptable

amount of expense recovery. Sets of alternative assumptions can be used to determine the

sensitivity of the expense in achieving the desired expense recovery and profitability

f. Monitoring for experience, profitability and competition

To ensure the suitable expense assumptions are applied, expense analysis is conducted

frequently to compare actual experience and applying assumptions. This is considered the

experience analysis. Objectives may be the important expense assumptions and competitive

position.

We have carried out the company expense analysis and determine the following expense

assumptions.

Acquisition cost : that relates to initial

expenses per Sum Insured (SI) to issue the

insurance policy.

Premium collection cost per Premium =2.50%

Maintenance cost per SI that relates to

Administrative expenses during premium

period

/year

Maintenance cost per SI that relates to

s


Administrative expenses

Acquisition Cost and Commission per

Premium at policy year t+1

The details of the is broken down as follow:

Table 5.1: Details of the acquisition expense

5.5 Back Test Assumptions.

Back Testing is the process of reviewing the pricing process in general and the pricing assumptions

in particular after the actual experiences happens, and comparing the pricing assumption with the

actual experiences over the period of time.

The above pricing assumptions therefore will be back tested annually or more frequently in case the

business environment volatiles.

With the back testing, we can see whether and to what degree pricing assumptions fits with the actual

experiences The back testing is to ensure that the current experiences follows or slightly fluctuate

around the above pricing assumptions, which means that the product is properly priced, premium

cover reasonably the various kind of expenses, claims, savings, etc...

The objective of the back testing is to give the guidance as to if and how the management and the

Appointed Actuary may want to adjust the product pricing with the new trend of the pricing

assumption or make decision on sales.

Decisions may be temporary cease selling the product for a given period of time, premium may be

adjusted with the new pricing assumptions and new tariff table may be submitted to the MoF to

Premium

Term

Commiss

ion

Sale

Incentive

Sale

Support Sale Contest Marketing

Operation

Expense

Total

α_(p,0) Commission

Total

α_(p,1) Commission

Total

α_(p,2)

8 22.00% 8.25% 2.75% 15.00% 5.00% 14.80% 67.80% 5.50% 5.50% 5.50% 5.50%

9 24.00% 9.00% 3.00% 15.00% 5.00% 14.80% 70.80% 6.00% 6.00% 6.00% 6.00%

10 26.00% 9.75% 3.25% 15.00% 5.00% 14.80% 73.80% 6.50% 6.50% 6.50% 6.50%

11 28.00% 10.50% 3.50% 15.00% 5.00% 14.80% 76.80% 7.00% 7.00% 7.00% 7.00%

12 30.00% 11.25% 3.75% 15.00% 5.00% 14.80% 79.80% 7.50% 7.50% 7.50% 7.50%

13 32.00% 12.00% 4.00% 15.00% 5.00% 14.80% 82.80% 8.00% 8.00% 8.00% 8.00%

14 34.00% 12.75% 4.25% 15.00% 5.00% 14.80% 85.80% 8.50% 8.50% 8.50% 8.50%

15 36.00% 13.50% 4.50% 15.00% 5.00% 14.80% 88.80% 9.00% 9.00% 9.00% 9.00%

16 38.00% 14.25% 4.75% 15.00% 5.00% 14.80% 91.80% 9.50% 9.50% 9.50% 9.50%

17 40.00% 15.00% 5.00% 15.00% 5.00% 14.80% 94.80% 10.00% 10.00% 10.00% 10.00%

18 40.00% 15.00% 5.00% 15.00% 5.00% 14.80% 94.80% 10.00% 10.00% 10.00% 10.00%

Policy Year 1 Policy year 2 Policy year 3


replace the existing one or even in worse case, the product is stopped selling and the current product

portfolio will be run off.

Back testing is an important step in Pricing process which will be implemented frequently to ensure

optimal internal control.


6. Pricing

6.1 Notation

n : Insurance Period n = 21-y(0)

m : Premium Payment Period m = 18- y(0) or 8

t : policy year (t+1)th ‘t = 0, 1, 2, 3,…,n-1

‘x+t : Age of the policyholder at policy year (t+1)th

‘y+t : Age of the insured at policy year (t+1)th

i : Annual interest rate

v : Discount factor

: The Sum Insured

: Death and TPD Benefit Coefficient for the insured

: Installment Coeficient for Education Benefit at time t

(the insurer will pay 4 Installments at anniversary date

when the insured attain age 18, 19, 20, 21 with the

correspoding proportion of the Sum Insured of 30%,

35%, 40%, 45%).

= 30%

= 35%

= 40%

= 45%

= 0% with t <n-3

: Assumed Death or TPD rate of the policyholder at

age x+t

: Number of people who are alive at age x

: Number of people who are still in the group of the

policyholder at age x+t

: Number of people in the portfolio of the policyholder

who die or under TPD in age x+t

:

:

: Assumed Annual lapse rate of the insured at age y+t `

: Assumed Death or TPD rate of the insured at age y+t

: Number of people of the insured who are alive at age y


: Number of people of the insured who are still in the

group of the insured at age y+t

: Number of people in the portfolio of the insured who

die or under TPD in age y+t

(

)

: Number of people in the portfolio of the insured who

lapse in age y+t

(

)

:

:

:

: Death or TPD claim probability of the policyholder

of entry age x in policy year (t+1)th

: Death or TPD claim probability of the insured of

entry age y in policy year (t+1)th

: Lapse probability of the insured of entry age y in

policy year (t+1)th

: Probability of the policyholder with entry age x that

is still in force at beginning of policy year (t+1)th

Where

: Probability of the insured with entry age y that is still

in force at beginning of policy year (t+1)th

Where

: Probability of death or TPD due to accident

: Acquisition cost per SI (

,p t : Acquisition cost and Commission in policy year

(t+1)th per premium

: Premium collection expense per premium

: Maintenance expense during premium payment

period per SI (

: Maintenance expense after premium payment period

per SI (

NP : Net Premium

: Gross Premium

s

s

s


6.2 Formula

Death and TPD Benefit of the policyholder

∑

Death and TPD Benefit due to Accident of the policyholder

∑

Death and TPD Benefit of the insured before age 18

∑

∑

Death and TPD Benefit of the insured after age 18

∑

∑

Cash Benefit.

∑

With is determined in the below.

∑

∑

∑

∑

∑

∑

∑

∑

And


∑

With

∑

∑

∑

∑

∑

∑

∑

Installment Benefits

∑

Total Expected Benefit (1)

+

Total Expected Collected Premium (2)

∑

Total Assumed Expenses (3)

o Acquisition Cost : ∑

o Premium Collection: ∑

o Maintenance Cost: ∑ ∑

|

|

We have (1) = (2)-(3) then

| ( ) ∑

∑

|


6.3 Premium Allocation Analysis.

To investigate how the gross premium is made up, we break down the contribution of each element

(such as insurance benefits, commission and Marketing expenses, maintenance expenses, premium

collection expenses and acquisition expenses) to make up the Gross Premium.

The policy with the age of father of 30 and age of the child of 4 is the investigated model point.

Non Par Product Par Product

Figure 6.1 – Gross premium allocation analysis

We find that majority of the Gross Premium is constructed from the Insurance Benefits.

The structure of gross premium will be determined as about 80% of the Gross Premium is used to

pay the Insurance Benefits to Clients, about 9% of Gross Premium is paid to Commission and

Marketing Expense, about 7% of Gross Premium is the Maintenance Premium and the rest of

premium will be used to pay for collection expense and Acquisition Expenses.

79.52%

7.59%

9.41%

2.50% 0.98%

Total Benefit

Mainternance Exp

Commission & Marketing Exp

Premium collection Exp

Acquisition Exp

81.13%

6.90% 8.66%

2.50% 0.80%

Total Benefit

Mainternance Exp

Commission & Marketing Exp

Premium collection Exp

Acquisition Exp


We look at more detailed analysis to see the contribution of each type of insurance benefit that make

up the Total Insurance Benefit.

Non Par Product Par Product

Figure 6.2 – Total Insurance Benefits analysis

Of the total Benefits, Annuities Benefit account for the major contribution with 84%, Loyalty Cash

account for 10.8% of total Insurance Benefit, rank second, the Death Benefit of the policyholder all

causes more than 2% of the total Benefit and, Other type of insurance benefits such as Death benefit

due to accident of policyholder, Death Benefits of the insured take only a small contribution in the

total Benefit Structure.

We realize that savings for education benefit is the main purpose of this product, Loyalty Cash is

also important insurance benefit as required by product marketing as client may need some cash

during the policy term. Other kind of insurance benefits are the supplements and contribute slightly

to insurance benefits.

2.48% 1.00%

1.51% 0.24%

83.89%

10.88%

DB Policyholder(all causes)

DB Policyholder(Accident)

DB Child before18 DB Child After18

Annuities Loyalty Cash

2.22% 0.88%

1.35%

0.24%

84.53%

10.78%

DB Policyholder(all causes)

DB Policyholder(Accident)

DB Child before18 DB Child After18

Annuities Loyalty Cash


7. Reserves and Solvency

7.1 Regulatory Stipulations on Reserve

In the middle of the year 2017, the Ministry of Finance launched the circular 50/TT 2017 to govern

the operations of insurers in Vietnam. Life insurers must set reserve in accordance with stipulations

under this circular.

a. Mathematical reserve.

Mathematical reserve is utilized to pay for insurance benefits that are guaranteed when the insured

event occurs.

The circular 50/TT 2017 stipulates the following requirements on the Mathematical Reserve of an

endowment product with insurance term more than 5 years as follow:

“In any case the mathematical reserve to be set up must not be lower than that of the method and

basis as follow:

Method: The Net Premium Reserve with zillmerisation adjustment of 3% of sum insured. The

adjusted net premium for valuation calculation may not exceed 90% of Gross Premium.”

Basis: The mortality table CSO 1980 and other technical basis in conformity with insurance benefits

that the insurer has committed to provide for clients with insurance products endorsed by the

Ministry of Finance. In any case, mortality rate and risks rates to be used in setting reserve may not

be less than those used in Pricing.

+ Maximum technical interest rate may not exceed 70% of average interest rate of Government

bonds with a term of more than 10 years which have been issued in the latest 6 months before the

reserve has been set. The technical interest rate to be used for setting reserve may not exceed the

average investment return rate of the past 4 consecutive quarters of the insurer and the pricing

interest rate of each insurance product.

The mathematical reserve shall be deemed as zero if it is a negative value.”

(Term 3.1 Article 18, circular 50/TT 2017)

b. Unearned Premium Reserve

Unearned premium reserve is utilized to pay for insurance benefits that may occur in the insurance

term in the next year.

This circular stipulates the following requirement on the Unearned Premium Reserve

“Unearned premiums reserve: is calculated according to gross premium valuation using methods

1/8 or 1/24 regarding insurance policies with a term of less than or equal to 1 year.”



c. Claim Reserve

Claim reserve is utilized to pay for the client when the insured event occurred, not yet claim or

claimed but not resolved at the end of financial year.

The circular 50 stipulates the following requirement on the Claim Reserve

“Claims reserve for claims that have not been resolved at the end of the fiscal year: to be set for

each individual claim with the reserve calculated according to statistics on the total payable for

claims that have been reported but have not been settled at the end of fiscal year.

Claims reserve for IBNR (incurred but not reported): only applicable to insurance policies with a

term of less than or equal to 1 year”


d. Profit Sharing Reserve (Dividend Reserve)

Profit sharing reserve is utilized to pay dividend that the life insurer agreed with the client according

to the insurance policy.

Profit sharing reserve are stipulated as follow:

“Profit sharing reserve include two types of reserves:

Reserve for published profit

- With regard to cash profit sharing:

Profit sharing

reserve =

Total published

profit to be shared to

policyholder in the

fiscal year

+

Total accumulated published profit to be

shared to policyholder in the previous

fiscal year but have not been paid

- With regard to profit sharing contracts in form of accumulated dividends:

Profit sharing

reserve =

Total current published accumulated dividends to be shared

to policyholder until the current fiscal year

The basis for setting profit sharing reserve is similar to that for setting mathematical reserve.

Reserve for unpublished profit

Reserve for unpublished profit is the present value of the profit to be additionally distributed to the

policyholder in future, which is calculated as asset of the participating policyholder fund less fund’s

debt, owners’ capital and profits that have been allocated in the current year. The reserve must be

set in such a manner that:

- Annual reserve may not exceed 10% of total surplus of the participating policyholder fund

in that year;


- Total reserve for unpublished profit at any time may not exceed 0.5% multiplied by (x)

average remaining time of participating policies multiplied by (x) total liability of

participating policyholder fund at such time.”


e. Resilient reserve

Resilient reserve is utilized to ensure the guaranteed interest rate of life insurer with clients as per

insurance policy wording.

Resilient is stipulated as follow:

“In case of investment market fluctuations or investment earnings from insurance premiums lower

than the pricing interest rate, the insurer shall set resilience reserve. The reserve equals to the

difference between the investment earnings from insurance premium and pricing interest rate of the

insurer to clients as agreed in the insurance policy.”


f. Balance reserve

Balance reserve is utilized to pay for insurance benefits when the insured event occurred due to large

fluctuation of technical interest rate and claim ratio.

“The life insurer must set annually 1% of its pre-tax profit for reserve until this reserve reaches 5%

of insurance premium earned in the fiscal year”.



7.2 Mathematical Reserve.

On every valuation date the reserves held must be at least equal to the minimum legal reserve

requirement as required by the above stipulation.

For mathematical reserve we set up the reserve with the following:

Valuation Assumptions:

Mortality & TPD combined rate: we apply 100% of mortality table CSO 1980 for male

Probability of Death and TPD in combination due to accident: 0.09%/year

Valuation interest rate: 3.5%/year

Lapse rate: 0%/year

Mathematical Reserve Methodology:

The Mathematical Reserve is calculated on a policy year basis and on a seriatim basis by using Net

level premium reserve without Zilmer Adjustment method, supplemented with management expense

after premium payment period, not greater than 90% of Gross Premium.

The supplement of management expense in the reserve after premium payment period ensure the

liabilities for the expense of the inforce policies after premium payment period.

When comparing the reserve under this method and that of Net level premium reserve with Zilmer

3% of Sum Insured method as per current stipulations, the reserves under this method are higher.

Mathematical Reserve on Policy Year Basis.

We apply the Mortality table CSO 1980 for Male, with the applied valuation interest rate of 3.5%. In

any cases, this valuation interest rate will meet the latest regulation on the valuation interest rate.

We denote as the mathematical reserve of a policy with entry age x at the policy’s anniversary

date t.

Mathematical Reserve will be determined as the following:

∑

∑

∑


∑

∑

∑

∑

∑

∑

With

Where: is net premium using valuation assumptions

is Annual Gross Premium using Pricing assumptions (Actual collected premium)

7.3 Dividend reserve

The company will reserve for the dividend announced to the policyholders by the end of each fiscal

year but not yet paid out.

Reserve for unannounced profit sharing is the present value of the dividend to be paid out in future.

This part of reserve will conform with stipulations in the Circular 50/2017/TT-BTC.

Annual additional reserving amount for the unannounced reserve will not exceed 10% of total

occurring surplus of policyholder fund in that year.

Total value of unannounced reserve at any time will not exceed 0.5% multiplied with average

remaining term of par policies multiplied with total liabilities of participating policyholder fund at

that time.

7.4 Claim Reserve

The reserve is calculated for each claim file with the amount established based on the statistics on the

insurance benefits payable for each claim reported but not yet settled at the end of fiscal year.

7.5 Contingency Reserve

This reserve is set at the end of financial year. 1% of annual earnings before tax of the company will

be put into this fund until this fund value accumulated to 5% of total premium of the company in the

financial year.

7.6 Regulatory Stipulations on Solvency Requirement

Life insurer must ensure to meet the solvency requirement during the business operation.

Life insurer is considered to have full solvency capacity if it has set fully technical reserves and has

the solvency not lower than the minimum solvency requirement.


According to the article 64 of the decree 73/2016/ND-CP issued by the Government, the minimum

solvency requirement for the life insurance products (excluding unit linked product, universal life

product, pension product) is as follow:

with insurance period not larger than 5 years:

with insurance period exceeding 5 years:


8. Profit Sharing

8.1 Regulatory Stipulations on Dividend

According to the article 76 of the decree 73/2016/ND-CP issued by the Government, the profit

sharing principles (dividend) will be executed as follows:

“The life insurers who sell the participating products must separate and keep track independently

the assets, sources of capital, revenues, costs relating to these participating insurance policies. This

is called the policy holder fund of participating products.

At the end of the financial year, the insurers can use a part of or the whole of the surplus of the

policyholder fund of participating products to pay dividend to policyholders. In any cases, the life

insurers must ensure all policyholders to receive not lower of 70% of Max of (total surplus,

differences of actual experience and pricing assumptions of mortality, investment return and

expenses)”

8.2 Profit Sharing Feature

At the end of each financial year, the actual investment return of policyholder fund and actual

investment income will be provided by Investment Department, the dividend rate for policyholders

will be then determined.

The company will determine the dividend rate at the end of financial year (December 31 every year)

and announce dividend rate within the first quarter of the next year, after being audited

For the participating life insurance products, the company will execute profit sharing on Total

Surplus Method. The basis for the Total Surplus Method will be presented in the below section.

Dividend payment

The Profit sharing dividend to policyholder may be used either to

Be accumulated until Maturity or

Be paid out in cash to policyholder every three years or

In case the policy terminates, the profit sharing account value at that time will be paid

to policyholder or the beneficiary.

Proportion of sharing:

The company guarantee that at least 70% of total dividable profit will be allocated to all

policyholders or group of policyholders. The company however will not guarantee to pay at least

70% of dividable profit on each policy basis.


Using owners’ capital to cover for the deficit of the participating policyholder fund to advance

dividend.

In case the participating policyholder fund is under deficit, the company will utilize owner’s capital

to cover for this deficit. The company is however entitled to be reimbursed this advance (without

interest) provided that after reimbursement the participating policyholder fund is not under deficit

again.

In case the company utilize its owner’s capital to advance dividend so that is participating products

remain competitive against other competitors’. The company is entitled to be reimbursed this

advance (without interest) provided that after reimbursement the participating policyholder fund is

not under deficit again.

Profit sharing before closing the participating policyholder fund.

Before closing the participating policyholder fund, the company will have a period of time (from the

point to stop selling participating product to the point of time to close the policyholder fund) to

allocate dividable profit in a reasonable and fair basis to policyholders.


8.3 Determination of Surplus and dividable profit

The profit sharing for the year n is calculated on the basis of the technical and financial result, i.e. the

following:

(+) Premiums

(-) Commissions and sales expenses actually paid

(-) The company administration costs (on fund split result after being audited)

(-) Insurance Benefits paid during the year

(-) Early surrenders reimbursements

(-) Maturity dividend paid in the year

(+) Mathematical Reserves at the 31/12//n-1

(-) Mathematical Reserves at the 31/12//n

(+) Claims Reserves at the 31/12//n-1

(-) Claims Reserves at the 31/12//n

(+) Net result from Reinsurance operations

(+) Financial Incomes from assets of fund

(+) Other Incomes

(-) Other Expenses

= Technical and Financial Result


The result will in priority compensate the eventual Loss Carry Forward (if any) till the end of

the year n-1 ( )

A part of the surplus is set in the unannounced Profit Sharing Reserve

The profit sharing is calculated minimum at 70% of the part of Technical and financial Result

exceeding the Loss Carry Forward and the difference of Unannounced Profit Sharing Reserve.

Then

Profit sharing for policyholders in the year n is determined as follow:

( )

Where: : the difference of Unannounced Profit Sharing Reserve between year

n and year n-1.

Distribution_rate: is the weight of profit sharing between policyholders and the company, upon each

participating product.

In any case, the company guarantee to distribute at least 70% of accumulated dividable Profit

Sharing to policyholders

The announced rate of profit sharing will be determined annually and may vary according to actual

experiences.

8.4 Dividend Calculation

Dividend rate in the year n for policyholders is determined as follows:

∑

with: Math_res is determined at the end of financial year (closing figures)

For each policy in the year n, dividend is determined as follow:

For participating policies that terminate during the financial year as a result of surrender or claim,

accumulated dividend till the latest financial year will be paid. Dividend for the year of surrender or

claim will not be calculated.

Maturity Dividend for policy that terminate in the middle of the year is determined as follow:


Where:

, in case this rate is zero, upon actual

investment result in the year, a suitable expected dividend rate may be applied instead.

Last_Payment is the final payment to be paid at Maturity

‘m is the rounded number of month from January 1 of that year to the Maturity date.

Total Accumulated Dividend at Maturity for a participating policy (withdraw dividend once at

Maturity) is determined as below:

∑ ( )

Where:

N is the term of the insurance policy

If the policyholder fund has been in deficit (amount of assets is smaller than that of liabilities), the

life insurer must provide additional amount from the equity fund to the policyholder fund to make up

the deficit. When the policyholder fund has been in surplus (amount of assets is greater than that of

liabilities), the life insurer is refunded partly or wholly the above additional amount without interest,

provided that the refund does not constitute another deficit in such policyholder fund.

The life insurer may not transfer assets, sources of funds from the policyholder fund to equity fund,

except for refund of the amount of contribution to the fund’s establishment or the amount used for

make up the deficit.

If the life insurer maintains multiple policyholder funds, it may not transfer assets, sources of funds

between policyholder fund, except for allocation of premiums of investment-linked insurance or

retirement insurance products. The life insurer may not use surplus of a policyholder fund to make

up a deficit of another policyholder fund.

The life insurer must keep written records of every transaction relating to the amount of equity fund

which is used for making up deficit of the policyholder fund and refund from policyholder fund to

equity fund.


9. Endorsement.

During the inforce of the policy, the policyholder may require some changes such as surrender, cease

paying premium, change the sum insured or borrow money from surrender value.

9.1 Surrender and Surrender Value.

The policyholder can fully surrender the insurance policy from the third policy year and receive the

surrender values. The surrender value is based on the formula of Mathematical Reserve on a policy

year basis at the surrender date with surrender charge.

The Surrender value will be determined as follows:

With:

using pricing assumptions

: is determined as follow:

Premium Payment Period

Policy Year 10 + 9 8

1 100.00% 100.00% 100.00%

2 100.00% 100.00% 100.00%

3 50.00% 40.00% 30.00%

4 30.00% 20.00% 18.00%

5 20.00% 15.00% 12.00%

6 15.00% 10.00% 8.00%

7 10.00% 7.50% 5.00%

8 7.50% 5.00% 2.50%

9 5.00% 2.50% 0.00%

10 2.50% 0.00% 0.00%

11+ 0.00% 0.00% 0.00%

Table 9.1: Surrender charge rates

The above table is determined upon the analysis of the surrender charge with the following liner

formula.

{

( ∑

) }

After the policyholder requests surrender, he will receive the full surrender value after deducting

debts (if any) and the policy terminates.


9.2 Paid up Sum Insured when the policyholder cease paying premium.

To increase the sustainability of the policy, the company offer a choice to policyholder in financial

difficulty. Even when the policyholder cease premium payment at the anniversary dates from the

third policy year and require in writing to stop premium payment, the policy may still be inforce with

the new adjusted Sum Insured.

Paidup Policy

Paidup Sum Insured will be determined on the following principle:

The Mathematical reserve at time t will be equal to the expected future benenits of the paidup policy.

The paid up Sum Insured = 0S

Where

t

t

V

FB

and

∑

∑

∑

∑

∑

∑

∑

9.3 Change of Sum Insured.

The company also offer a choice to policyholder to change the sum insured when the policy has been

in force. When the policyholder requires to change to a lower new sum insured than the initial sum

insured, a new premium is calculated.

Due to the anti-selection risk, life insurers in Vietnam often do not allow the clients to increase the

sum insured of the endowment products during the insurance term.

If the sum insured is reduced before surrender value has been not realized The premium will be

reduced in accordance with the new sum insured (the reduced sum insured);

If the sum insured is reduced after surrender value has been realize:

- A part of surrender value relevant to the reduced part of sum insured will be paid to the

policy-holder;


- The premium will be reduced in accordance with the new sum insured.

Gross Premium in accordance with the reduced sum insured:

GP1= S1 x Premium rate (in accordance with the reduced sum insured S1)

9.4 Loan on Surrender Value and Automatic Premium Loan.

The insurer will continuously examine the financial status of those policies to determine the

effectiveness of the insurance policy.

The policy is still effective as long as:

Where:

: Surrender Value at time t

: Outstanding balance of Automatic Premium Loan with accumulated interest at time t (if any)

Outstanding Debt of the policy to date will be determined as below:

∑{ ∏

}

Where:

: Loan amount jth (automatic premium loan jth)

: Number of loan to date

: Number of time the company change the annual loan interest rate from the beginning of the jth

loan to date dir: daily loan interest rate (be converted from annual loan interest rate as below).

: Number of days from the beginning of the jth loan to the time the company first change the loan

interest rate, with k=0;

Number of days between the time the company change the loan interest rate, with k=1 to

;

Number of days from the time the company last change the loan interest rate to date k = .

The Accumulated Cash Benefit and Unwithdrawn Benefit Payment (if any), will can be used to

offset the outstanding loan unless the policyholder request otherwise.


In case the policyholder settle only a part of the outstanding debt with or

offsetting the loan with the Accumulated Cash Benefit or Unwithdrawn Benefit payments the

company will calculate the new debt of the policy. This new debt is then considered as the new first

loan of the policy with the loan value as below:

∑{ ∏

}

The stipulations on automatic premium loan are still applied with this policy with this new loan.

If the total loans (automatic premium loans, if any) and its accumulated interest is equal to or

exceeds 90% of the Surrender value, the policy will be terminated at this incurred date.

At this terminated date, the company will pay the difference between the Surrender Value and the

debt (accumulated loans and interest till the terminated date) to the policyholder.

Loan Interest

Loan interest is calculated on compound interest basis

Loan interest rate is applied on daily interest rate basis (converted from annual interest rate as per below)

Loan interest rate is determined by the insurer at each period of time.

-1

with

: daily loan interest rate

: annual loan interest rate (published by the company)

= A +/- adjustment

Where

· A=Max (Current overall portfolio’s rate of return on our company’s asset, Current 15Year

Government Bond rate)

· Adjustment is based on the current financial market and the policy loan rate of competitors, the

maximum adjustment is 1%.


10. Profitability and Testing.

This part provides an actuarial perspective on scenario analysis and profit test. This is the essential

tool for product profitability oversight and effective risk management. This enhance the

understanding of profitability of the product.

The profit margin that a company builds into its premium is going to depend on the company’s

approach to the assumptions that enter into the premium calculation. The company may calculate

premium on conservative estimates of future experience and not add specific profit margin.

The company determine the gross premium so that the premium will provide desired profit margin if

future experience equals the company’s best estimate of future experience. This is usually done by

choosing the gross premium so that the present value of the resulting profits equal present value of

desired profit margins. This method provides a straightforward means of determining the adequacy

of the gross premium.

There are many ways of incorporating profit margins into gross premium. Gross premium is

determined so that one of the following conditions is true:

The present value of profit equals a certain percentage of the present value of premiums.

The present value of the profit equal zero. (the Return on Investment ROI or Internal Rate of

Return IRR method). Under this method the discount interest rate is much higher than the

preceding method.

The policy break even by the end of a certain year (e.g 8th

year,..).

Sometimes the company will not allow for a specific profit margin in its premium rates. Instead, it

will use assumptions that are more conservative than its best estimates of future experience

(normally with participating product), the margin between the pricing assumptions and best estimates

assumptions permit the company to a relative expected profit. The margin in each assumption can

reflect the probability of adverse deviation for that assumption.

10.1 Profitability requirement

Product is expected to be profitable. The Product Committee of the company determine the profit

margin (PM) is expected to be around 5.0% and ROI exceed 12% for this product with 10.0% risk

discount rate.


10.2 Profitability base

The profit of a policy is determined under the following profitability base:

a. For Non Par product

Methodology

b. For Participating product

Methodology

Where:

is the profit before tax of the policy year t+1

is the profit after tax of the policy year t+1

is the Cash flow of policy year t+1

Probability of the policy is still in force with both the insured and policyholder alive and not

TPD

Probability of the policy is still in force with the insured alive and not under TPD

With

And


∑

(using pricing assumptions)

And

( )

( )

( )

( ∑

) ∑

And

Profitability Criteria.

∑

∑

(∑

)

∑


10.3 Model and Risk Measure

10.3.1 Deterministic Model

Model in which none of parameters is a random variable are said to be deterministic.

The deterministic model only produces a single result for a single set of assumptions. This single set

of assumptions may be a “Best Estimate”. This will helpful for a simple and single answer.

As the result it will be easier to compare the results of each run. It will be fast for implementation

and conclusion.

The deterministic model is useful for a fast decision making process so as to meet the urgent

deadline of launching date or in case the product is not complicated thanks to the model’s simplicity.

Deterministic model is convenient to answer regulatory questions such as predetermined scenarios

required by MoF.

10.3.2 Stochastic Model

The stochastic model considers the variability of the unknown future outcomes through application

of probability distribution and randomly generated inputs. It provides a distribution of outcomes

rather than a single outcome produced by deterministic model. The results are more complicated to

understand but on the other hand, it provides the better view of the situation.

As stochastic model is more complicated, it runs more slowly, so that, often aspects of the model

need to be simplified to reduce run time, this however may impair the validity of the results.

As there is no single result, so comparisons over time can be harder to interpret.

10.3.3 Risk Measure

The Value at Risk (VaR) is an accepted methodology for quantifying risk and a part of the evolution

of risk management.

VaR is a measure of the worst expected loss/profit that a firm may suffer over a period of time that

has been specified, under normal market conditions and a specified level of confidence.

We denote X is the profitability of the product/product portfolio.

is the cumulative distribution function of X.

We have ( )

We therefore have:

Besides,

( ) ( )

If the profitability of the product is , the probability of the profit exceed profitability is


Therefore if we know the law of distribution function of X, we can calculate with

parametric method by the formula:

Suppose that we wish to estimate VaR under the assumption that X is normally distributed. In this

case the VaR at confidence level is determined as follow:

Where:

: is the standard normal variate corresponding to .

: is the mean of X

: is the standard deviation of X.

Thus is the value of the standard normal variate such that of the probability density mass lies to

its left and of the probability density mass lies to its right

Another way to calculate VaR is the nonparametric method which is called Historical Simulation.

This approaches simplifies the procedure for computing the Value at Risk since it does not have to

determine the distribution function. The values of X are sorted in ascending order and the

of X that leave of the observations on its left side and )% on its right side.

This method of calculating VaR is simple and fast, it therefore is widely used in practice, however

the size of sample must be large enough.

In the following sections we will apply the Monte Carlo Simulation to calculate X and Historical

Simulation to calculate VaR.

The Var will be back tested to have a reality review on calculation and identify changes on risks.

10.4 Profit Tests.

In the product development, depending on the complexity of the product and the requirement to meet

the launching date, the company may implement the deterministic profit test model or stochastic

profit test model or combination of both kind of models for Sensitivity, Scenario & Stress Test.

10.4.1 Best Estimate Scenario

To have the initial view of the profitability of the product, we set up the Best Estimate Scenario with

the deterministic model.

Deterministic model is useful because it provides a simple and fast results. This will be done in the

first stage.

The result of Profit Test under Best Estimate Scenario will be shown in the documents which are

submitted to the Ministry of Finance for the its approval for product launching.


Below are the Best Estimate Scenario Assumptions

For Pricing For Valuation For Best Estimate

Mortality+TPD: 90% CSO Table 100% CSO 50% of CSO Table

Interest rate for Non Par 4.0%/year 3.0%/year 7.0%/year

Interest rate for Par 2.5%/year 2.5%/year 7.0%/year

Lapse rate: 0% 0% 5.0%/year

Loading Exp: As per below Same as pricing As per below

Discount rate (not used) (not used) 10.0%/year

Solvency Ratio (not used) (not used) 100.0%

Table 10.1 – Pricing, Valuation and Best Estimate Assumptions

Hereunder are loading expense assumptions for pricing purpose and best estimates.

Base on the analysis of expense executed in the company, we apply the expense assumptions for

both Pricing and Best Estimates as follow.

Pricing Best Estimate (BE) Pricing-BE

1.1760% 0.9045% 0.2715%

2.50% 2.20% 0.3000%

0.7275% 0.538500% 0.1890%

0.6930% 0.51300% 0.1800%

Table 10.2 – Pricing, Best Estimate assumption on expenses

,p t Pricing BE Pricing -BE

Premium Term

(year) Year1 Year1 Year1

8 67.80% 62.80% 5.00%

9 70.80% 65.80% 5.00%

10 73.80% 68.80% 5.00%

11 76.80% 71.80% 5.00%

12 79.80% 74.80% 5.00%

13 82.80% 77.80% 5.00%

14 85.80% 80.80% 5.00%

15 88.80% 83.80% 5.00%

16 91.80% 86.80% 5.00%

17 94.80% 89.80% 5.00%

18 94.80% 89.80% 5.00%

Table 10.3 – Pricing, Best Estimate Assumption on the acquisition expense Alpha_p

s

s

s


In the Best Estimates Scenario, we assume the experience mortality & TPD Claim Ratio is equal to

50.0% that of the 1980 CSO Table.

The investment return is expected to be at 7.0%/year basing on the current and expected investment

return given the current financial market experience and macroeconomics forecasts.

Discount rate is estimated at 10.0%/year (10-year government bond yield which is risk free about

6.50%+ 3.50 % risk premium).

Profitability of the Best Estimate Scenario.

We have built the model for profit test purpose with the methodology as mentioned in the previous

section. Profitabilty of each individual policy for the Best Estimate (Base case) will be determined

under deterministic model as follow:

A. For Nonparticipating Product

Table 10.4 – Profitability of model point of Non Par Product under Best Estimate Scenario

0 1 2 3 4 5 6 7 8 9 10

20 10.37% 10.39% 10.63% 10.85% 11.03% 11.19% 11.32% 11.36% 11.37% 10.82% 10.42%

25 10.38% 10.39% 10.63% 10.85% 11.03% 11.18% 11.30% 11.34% 11.35% 10.79% 10.39%

30 10.60% 10.59% 10.81% 11.01% 11.17% 11.30% 11.42% 11.43% 11.43% 10.85% 10.44%

35 11.06% 11.03% 11.22% 11.38% 11.51% 11.62% 11.70% 11.69% 11.65% 11.05% 10.61%

40 11.82% 11.74% 11.89% 12.00% 12.08% 12.14% 12.18% 12.14% 12.05% 11.40% 10.91%

45 12.90% 12.77% 12.85% 12.90% 12.92% 12.91% 12.88% 12.79% 12.62% 11.91% 11.36%

50 14.40% 14.20% 14.21% 14.18% 14.12% 14.03% 13.91% 13.75% 13.49% 12.69% 12.04%

55 15.97% 15.83% 15.64% 15.39% 15.12% 14.77% 13.86% 13.08%

60 16.52% 15.48% 14.54%

0 1 2 3 4 5 6 7 8 9 10

20 17.67% 18.17% 19.00% 19.96% 21.04% 22.31% 23.78% 25.07% 26.56% 27.41% 28.79%

25 17.62% 18.12% 18.95% 19.90% 20.98% 22.24% 23.71% 24.99% 26.48% 27.32% 28.70%

30 17.72% 18.22% 19.04% 19.99% 21.07% 22.33% 23.83% 25.11% 26.58% 27.42% 28.79%

35 18.03% 18.53% 19.36% 20.31% 21.39% 22.66% 24.17% 25.52% 26.98% 27.81% 29.17%

40 18.57% 19.09% 19.93% 20.89% 21.99% 23.28% 24.83% 26.31% 27.75% 28.58% 29.93%

45 19.34% 19.89% 20.76% 21.73% 22.87% 24.20% 25.78% 27.48% 28.92% 29.75% 31.09%

50 20.45% 21.03% 21.93% 22.96% 24.15% 25.54% 27.20% 29.17% 30.69% 31.53% 32.87%

55 24.83% 26.12% 27.63% 29.39% 31.52% 33.58% 34.46% 35.84%

60 37.81% 38.83% 40.28%

0 1 2 3 4 5 6 7 8 9 10

20 10 10 9 9 8 8 7 7 6 6 6

25 10 10 9 9 8 8 7 7 6 6 6

30 10 10 9 9 8 8 7 7 6 6 6

35 10 9 9 8 8 7 7 7 6 6 6

40 9 9 9 8 8 7 7 6 6 6 5

45 9 9 8 8 7 7 7 6 6 6 5

50 8 8 8 7 7 7 6 6 6 5 5

55 7 6 6 6 5 5 5 5

60 5 5 4

AGE CHILDProfit Margin

ROIAGE CHILD

BEYAGE CHILD

AG

E P

AR

ENT

AG

E P

AR

ENT

AG

E P

AR

ENT


Profitability of each model point, each policy may be different, it depends on the entry age of the

insured and age of the policyholder.

The profitability of the Best Estimate scenario of the Non Par product is good with profit margin of

each individual policy may range from 10.37% to 16.52% and ROI ranges from 17.7% to 40.28%.

The target client group has the profit margin of about 10.8%-12.6% with the corresponding ROI

from 19% to 28.9% and breakeven year from 6- 9 year.

B. For Participating Product

Table 10.5 – Profitability of model point of Par Product under Best Estimate Scenario

The profitability of the best estimate scenario of the par product is acceptable with profit margin of

each individual policy may range from 2.1% to 4.8% and ROI ranges from 13.2% to 25.6%.

The target client group has the profit margin of about 2.3%-3.4% with the corresponding ROI from

13.7% to 19 % and breakeven year from 7- 11 year.

0 1 2 3 4 5 6 7 8 9 10

20 2.19% 2.12% 2.30% 2.46% 2.58% 2.70% 2.80% 2.90% 3.00% 2.87% 2.79%

25 2.18% 2.11% 2.28% 2.45% 2.57% 2.69% 2.79% 2.89% 2.98% 2.86% 2.78%

30 2.25% 2.17% 2.34% 2.50% 2.62% 2.72% 2.82% 2.92% 3.01% 2.88% 2.79%

35 2.43% 2.34% 2.50% 2.63% 2.74% 2.84% 2.93% 3.01% 3.09% 2.95% 2.85%

40 2.74% 2.64% 2.77% 2.87% 2.96% 3.04% 3.11% 3.18% 3.23% 3.07% 2.96%

45 3.17% 3.04% 3.13% 3.21% 3.28% 3.34% 3.39% 3.43% 3.44% 3.25% 3.12%

50 3.72% 3.58% 3.64% 3.70% 3.74% 3.77% 3.79% 3.77% 3.74% 3.53% 3.37%

55 4.38% 4.40% 4.37% 4.33% 4.26% 4.19% 3.95% 3.75%

60 4.81% 4.53% 4.29%

0 1 2 3 4 5 6 7 8 9 10

20 13.18% 13.15% 13.63% 14.16% 14.68% 15.25% 15.90% 16.65% 17.55% 17.94% 18.54%

25 13.15% 13.12% 13.59% 14.12% 14.64% 15.20% 15.85% 16.60% 17.49% 17.89% 18.49%

30 13.24% 13.21% 13.68% 14.21% 14.71% 15.27% 15.92% 16.66% 17.55% 17.94% 18.53%

35 13.53% 13.48% 13.96% 14.46% 14.96% 15.53% 16.17% 16.92% 17.81% 18.16% 18.75%

40 14.05% 13.98% 14.46% 14.93% 15.44% 16.01% 16.66% 17.42% 18.27% 18.61% 19.20%

45 14.80% 14.71% 15.14% 15.63% 16.15% 16.74% 17.42% 18.19% 18.95% 19.29% 19.90%

50 15.78% 15.67% 16.14% 16.66% 17.22% 17.85% 18.55% 19.23% 19.98% 20.34% 20.96%

55 18.28% 18.93% 19.55% 20.19% 20.90% 21.70% 22.11% 22.78%

60 24.26% 24.80% 25.59%

0 1 2 3 4 5 6 7 8 9 10

20 13 12 11 11 10 9 9 8 7 7 6

25 13 12 12 11 10 9 9 8 7 7 6

30 13 12 11 11 10 9 9 8 7 7 6

35 12 12 11 10 10 9 8 8 7 7 6

40 11 11 11 10 9 9 8 8 7 7 6

45 11 10 10 9 9 8 8 7 7 6 6

50 10 10 9 9 8 8 7 7 6 6 6

55 8 7 7 7 6 6 6 5

60 5 5 5


ROIAGE CHILD

BEYAGE CHILD

AG

E P

AR

ENT

AG

E P

AR

ENT

AG

E P

AR

ENT


We create a large simulation pool of insurance policies including 10,000 policies for this product

with different ages of the insured and ages of the policyholder and sum insured amounts to

investigate the profitability of the product under this Best Estimate Scenario, assuming technical

assumptions are true as per Best Estimate Assumptions. We consider two main profit criteria which

are the Profit Margin and ROI.

We have the statistics of Profit Margin and ROI of these 10,000 policies as per follow:

A. For NON PAR Product

Table 10.6: Statistics on profitability of the individual Non Par Policy under BE scenario

Profit margin of each individual policy in the portfolio range from 10.4% to 13.7% and the mean

profit margin of the individual Non Par policy is 11.4%

The ROI of each individual Non Par policy vary and range from 17.6% to 32.0% and the mean ROI

of the individual Non Par policy is 22.5%.

The confidence interval at confidence level of 95% of the Profit margin and ROI are [10.53%,

12.37%] and [17.8%, 29.1%] respectively.

VaR of Profit Margin at confidence level of 99.5% is 10.41%

VaR of ROI at confidence level of 99.5% are 17.6%

The mean present value of Profit of the individual Non Par policy is 42.5 million VND given the

Best Estimate assumptions are true.

The confidence interval at 95% of present value of profit range from [16.5 million VND, 76.5

million VND]

We find that under the Best Estimated Scenario, an individual Non Par policy may have a good

profitability.

Age Parent Age child SI PV Prem PV Profit PM ROI

Mean 34.54 4.53 498.03 372277629 42541246 0.114215 0.22508

Standard Error 0.04 0.03 1.751635 1436369.6 164987.41 4.65E-05 0.000327

Median 35.00 4.00 500 363313582 41537846 0.114519 0.222642

Mode 33.00 5.00 530 316250234 36991388 0.120189 0.202256

Standard Deviation 3.99 2.76 175.1635 143636959 16498741 0.004653 0.032726

Sample Variance 15.95 7.64 30682.25 2.063E+16 2.722E+14 2.17E-05 0.001071

Kurtosis (0.03) (0.79) -1.18931 -0.5629075 -0.7029511 0.346974 -0.80865

Skewness (0.02) 0.12 0.015339 0.3497834 0.3183432 0.179959 0.428564

Range 28.00 10.00 600 688730680 77090399 0.03373 0.144269

Minimum 21.00 - 200 115019934 11928673 0.10364 0.176199

Maximum 49.00 10.00 800 803750614 89019072 0.137371 0.320467

Sum 345,359.00 45,271.00 4980300 3.723E+12 4.254E+11 1142.146 2250.797

Count 10000 10000 10000 10000 10000 10000 10000


B. For PAR Product

Table 10.7: Statistics on profitability of the individual Par Policy under BE scenario

Profit margin of each individual policy in the portfolio range from 2.1% to 3.7% but the profit

margin of the of the individual par policy is 2.7%

The ROI of each individual policy vary and range from 13.1% to 20.4% but the mean ROI of the

individual par policy is 15.5%.

The confidence interval at confidence level of 95% of the Profit margin and ROI respectively are

[2.23%, 3.20%] and [13.24%, 18.75%] .

VaR of Profit Margin at confidence level of 99.5% is 2.15%

VaR of ROI at confidence level of 99.5% are 13.15%

The mean present value of Profit is 11.5 million VND given the Best estimate assumptions.

The confidence interval at confidence level of 95% of present value of profit is [4.18 million VND,

22.0 million VND]

We find that under the Best Estimated Scenario, par product may have an average and acceptable

profitability.

Age Parent Age child SI (million ) PV Prem PV Profit PM ROI

Mean 34.5359 4.5271 498.03 414306708.2 11542192.81 0.027601738 0.155176296

Standard Error 0.039931574 0.027641327 1.751634874 1571456.707 47972.41707 2.59101E-05 0.000159078

Median 35 4 500 404764958.6 11017362.21 0.02802878 0.153099934

Mode 33 5 530 350039734 10248709.03 0.026001796 0.145339804

Standard Deviation 3.993157362 2.764132709 175.1634874 157153527.8 4797481.563 0.002591144 0.015908589

Sample Variance 15.94530572 7.640429633 30682.24732 2.46972E+16 2.30158E+13 6.71403E-06 0.000253083

Kurtosis -0.031631696 -0.788682655 -1.189311449 -0.680909766 -0.441200298 -0.459695273 -0.705021891

Skewness -0.01668906 0.123055543 0.015338527 0.29126371 0.480938653 -0.32806834 0.500886839

Range 28 10 600 737771033.9 23583368.84 0.015844624 0.073452037

Minimum 21 0 200 131583859.6 2861820.866 0.021091339 0.13118576

Maximum 49 10 800 869354893.5 26445189.7 0.036935963 0.204637797

Sum 345359 45271 4980300 4.14348E+12 1.15433E+11 276.0449795 1551.918135

Count 10000 10000 10000 10000 10000 10000 10000


To investigate the profitability of the product portfolio instead of each individual policy, we create a

simulation of 1,000 portfolios with different number of insured with random entry ages and sum

insured amounts from a large simulated sample under the best estimate scenario (assuming that

technical assumptions are correct) to investigate the profitability of the portfolio and whether the risk

is diversified under the best estimate assumptions.

A. Non Par Product

Table 10.8: Statistics of the Profitability of the Portfolio of Non Par Product under 1,000

simulations.

This confirms that the risk is diversified under the portfolio with different number of the insured.

Under the 1,000 simulation of portfolio with random number of sum insured per each portfolio, the

random entry ages and random sum insured amounts, the profit margin of the portfolio stay quite

stable at 11.4% and only slightly volatile under the best estimate scenario (minimum Profit margin of

the portfolio under 1,000 simulations: 11.3%, maximum profit margin of the portfolio 11.6%).

ROI of the product portfolio volatile in a narrow range from 21.7% to 22.5%.

The mean present value of profit of the portfolio of around 647 policies is about 27.1 billion VND.

B. Par Product

We also simulate 1,000 portfolio with different number of insured with random entry ages of each

policy and random sum insured amounts from a large simulated sample under the best estimate

scenario (assuming that technical assumptions are correct) for Par Product.

PV Prem PV Profit PM ROI No. Policy

Mean 2.3705E+11 2.7165E+10 0.11459217 0.22128133 646.961

Standard Error 2395329478 274594558 8.6776E-06 4.1495E-05 6.52114122

Median 2.3473E+11 2.6915E+10 0.11458956 0.22131545 642.5

Mode #N/A #N/A #N/A #N/A 527

Standard Deviation 7.5747E+10 8683442357 0.00027441 0.00131218 206.216592

Sample Variance 5.7376E+21 7.5402E+19 7.5301E-08 1.7218E-06 42525.2828

Kurtosis -1.2334671 -1.2333534 1.04344821 -0.1204026 -1.2364136

Skewness 0.03360918 0.03540205 0.29009352 -0.0857264 0.02940958

Range 2.6563E+11 3.0433E+10 0.00225499 0.00817154 699

Minimum 1.0718E+11 1.2287E+10 0.11376717 0.21693744 301

Maximum 3.7282E+11 4.272E+10 0.11602216 0.22510898 1000

Sum 2.3705E+14 2.7165E+13 114.592174 221.281333 646961

Count 1000 1000 1000 1000 1000


Table 10.9: Statistics of the Profitability of the Portfolio of Par Product of 1,000 simulations under

Best Estimate Scenario.

The profit margin of the whole portfolio is 2.74% and fluctuate in a very narrow range from 2.70%

to 2.80%. Under the best estimate assumptions, the individual risks can be well diversified for

variable number of the insured with different entry ages and sum insured amounts.

The average ROI has mean of 15. 1% and fluctuate slightly from 14.8% to 15.4%.

The mean present value of profit of the portfolio of around 660 policies is about 5.95 billion VND.


Mean 2.1685E+11 5955702970 0.027464 0.151546 662.056

Standard Error 1304978109 35860208.22 4.66E-06 2.58E-05 6.329983535

Median 2.30648E+11 6337273879 0.027459 0.151572 671.5


Standard Deviation 41267031212 1133999353 0.000147 0.000816 200.1716552


Kurtosis -0.610204632 -0.609384 0.087449 0.188234 -1.126510454

Skewness -0.766550507 -0.76477337 0.043931 -0.02433 -0.098608176

Range 1.55367E+11 4310870396 0.000979 0.005866 698

Minimum 1.19336E+11 3304834579 0.027015 0.1483 302

Maximum 2.74703E+11 7615704975 0.027994 0.154166 1000

Sum 2.1685E+14 5.9557E+12 27.46449 151.5459 662056

Count 1000 1000 1000 1000 1000


10.4.2 Sensitivity Test

Sensitivity test involves running the model using different assumptions to check which assumptions

are important to the model. Each sensitive test can be considered a single “what if” scenario. The

sensitivity testing of a model often test changes in one assumption at a time and measure the

magnitude of that individual assumption or risk. Key uses of sensitivity testing include measuring

risk exposures, determining and evaluating key assumptions and better understanding the range of

profitability that can be expected for a new product. The use of sensitivity test often ends after

completing pricing process. The sensitivity test often bring initial idea on what assumptions are

having the largest impact on the profitability of the product.

For this product, the key factоrs that impact on profitability are identified as mortality rate,

investment earning, expenses and persistency.

As the deterministic can compare easily the results after each run, deterministic model is used for the

sensitivity test.

In order to gain an initial and fast understanding how the profit margin react when the above factors

change, the deterministic model have been executed for the entry age of policyholder at 30 and the

insured aged 4 in the analysis.

For NON PAR product.

Table 10.10 – Sensitivity Test under deterministic model of Non Par Product

Investment return : The investment return increase/decrease by 0.50 % will make the profit

margin decrease/increase by around 2.00%.

Lapses : The lapse rate increase/decrease by 1.0 % will make the profit margin

decrease/increase by about 0.2%.

Mortality& TPD : The death & TPD claim increase/decrease by 10% of the CSO 1980 rates

will make the profit margin decrease/increase by around 0.20%.

Expenses Expense increase/decrease by 10% of the BE assumption make the profit

margin decrease/increase by around 1.2%

Interest rate 4.50% 5.00% 5.50% 6.00% 6.50% 7.00% 7.50% 8.00% 8.50% 9.00% 9.50%

Profit Margin 1.23% 3.23% 5.22% 7.20% 9.19% 11.17% 13.14% 15.12% 17.10% 19.08% 21.05%

Lapse rate 0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 7.00% 8.00% 9.00% 10.00%

Profit Margin 12.73% 12.33% 11.99% 11.68% 11.41% 11.17% 10.96% 10.77% 10.62% 10.48% 10.36%

Mortality 0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00% 80.00% 90.00% 100.00%

Profit Margin 12.39% 12.15% 11.90% 11.66% 11.41% 11.17% 10.92% 10.68% 10.43% 10.19% 9.94%

Expense change as

per BE assumption -50.00% -40.00% -30.00% -20.00% -10.00% 0.00% 10.00% 20.00% 30.00% 40.00% 50.00%

Profit Margin 17.00% 15.84% 14.68% 13.52% 12.34% 11.17% 9.98% 8.79% 7.60% 6.40% 5.19%


For PAR product

Table 10.11– Sensitivity Test under deterministic model of Par Product

Investment return : The investment return increase/decrease by 0.50 % will make the profit

margin decrease/increase by around 0.70%.

Lapses : The lapse rate increase/decrease by 1.0 % will make the profit margin

decrease/increase by about 0.15%.

Mortality& TPD : The mortality increase/decrease by 10% of the CSO 1980 rates will make

the profit margin decrease/increase by around 0.10%.

Expenses Expense increase/decrease by 10% of the BE assumption make th profit

margin decrease/increase by around 0.8%

To investigate more details, we also simulate 500 policies to investigate how profit margin react to

each change of the underlying investigated assumption.

A. For NON PAR product.

For the sensitivity test on mortality and TPD claim assumption, we arrive:

Where Y: percentage change of Profit Margin

X: Percentage change of Claim as percentage of CSO1980 Table.

Details will be shown in the appendix.

Interest rate 4.50% 5.00% 5.50% 6.00% 6.50% 7.00% 7.50% 8.00% 8.50% 9.00% 9.50%

Profit Margin 0.25% 1.00% 1.74% 2.46% 3.18% 3.90% 4.62% 5.31% 6.01% 6.71% 7.41%

Lapse rate 0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 7.00% 8.00% 9.00% 10.00%

Profit Margin 3.90% 3.72% 3.54% 3.38% 3.23% 3.10% 2.98% 2.87% 2.78% 2.69% 2.62%

Mortality 0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00% 80.00% 90.00% 100.00%

Profit Margin 3.10% 3.00% 2.91% 2.81% 2.71% 2.62% 2.52% 2.42% 2.33% 2.22% 2.12%

Expense change as per BE

assumption -50.00% -40.00% -30.00% -20.00% -10.00% 0.00% 10.00% 20.00% 30.00% 40.00% 50.00%

Profit Margin 6.36% 5.67% 4.95% 4.22% 3.42% 2.62% 1.77% 0.90% 0.02% -0.93% -1.88%


Figure 10.1: Sensitivity of Non Par Product on Mortality Claim Ratio against the Profit Margin

We can see that mortality claim has a negative impact on the profitability of the product, under this

investigate, about the absolute increase of mortality claim of 10% CSO 1980 would decrease 0.324%

profit margin of the product. The linear regression with R square of: 86%.

For the sensitivity test on Lapse assumption, we arrive:


X: Percentage change of Lapse.


Figure 10.2: Sensitivity of Non Par Product on Lapse against the Profit Margin

-6.00%

-5.00%

-4.00%

-3.00%

-2.00%

-1.00%

0.00%

1.00%

2.00%

3.00%

-60.00% -40.00% -20.00% 0.00% 20.00% 40.00% 60.00% 80.00% 100.00% 120.00%

Mortality Claim Vs Profit Margin

-3.00%

-2.00%

-1.00%

0.00%

1.00%

2.00%

3.00%

4.00%

-6.0% -4.0% -2.0% 0.0% 2.0% 4.0% 6.0%

Lapse vs Profit Margin


This confirms lapse has a negative impact on the profitability of the product, under this investigate,

about the absolute increase of 1% of lapse rate would decrease 0.25% profit margin of the product.

The linear regression with R square of: 71%.

For the sensitivity test on Investment Return assumption, we arrive:


X: Percentage change of Investment Return.


Figure 10.3: Sensitivity of Non Par Product on Investment Return against the Profit Margin

We arrive that investment return has a very strong and close correlation with the profitability of the

product, under this investigate, about the absolute increase of 1% of investment return would

increase 3.85% profit margin of the product. The linear regression with R square of: 99%.

B. For Par product.

For the sensitivity test on mortality and TPD claim assumption, we arrive:


X: Percentage change of Claim as percentage of CSO1980 Table.


-10.00%

-5.00%

0.00%

5.00%

10.00%

15.00%

-3.00% -2.00% -1.00% 0.00% 1.00% 2.00% 3.00% 4.00%

Investment Return Vs Profit Margin


Figure 10.4: Sensitivity of Par Product on Mortality Claim Ratio against the Profit Margin

This confirms mortality claim has a negative impact on the profitability of the product, under this

investigate, about the absolute increase of mortality claim of 10% CSO 1980 would decrease 0.13%

profit margin of the product. The linear regression with R square of: 85%.

For the sensitivity test on Lapse assumption, we arrive:


X: Percentage change of Lapse.


Figure 10.5: Sensitivity of Par Product on Lapse against the Profit Margin

We arrive that lapse has a negative impact on the profitability of the product, under this investigate,

about the absolute increase of 1% of lapse rate would decrease 0.1% profit margin of the product.

The linear regression with R square of: 68%.

-2.50%

-2.00%

-1.50%

-1.00%

-0.50%

0.00%

0.50%

1.00%

1.50%

-60.00% -40.00% -20.00% 0.00% 20.00% 40.00% 60.00% 80.00% 100.00% 120.00%

Mortality vs Profit Margin

-1.00%

-0.50%

0.00%

0.50%

1.00%

1.50%

-6.0% -4.0% -2.0% 0.0% 2.0% 4.0% 6.0%



For the sensitivity test on Investment Return assumption, we arrive:


X: Percentage change of Investment Return.


Figure 10.6: Sensitivity of Par product on Investment Return against the Profit Margin

It is obvious that investment return has a very strong and close correlation with the profitability of

the product, under this investigate, about the absolute increase of 1.0% of investment return would

increase 1.17% profit margin of the product. The linear regression with R square of: 99%.

We can find that the Par product is less sensitive to changes of mortality, investment return and lapse

than the non par product due to impact of the profit sharing provision.

-3.00%

-2.00%

-1.00%

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

-3.00% -2.00% -1.00% 0.00% 1.00% 2.00% 3.00% 4.00%

Investment return vs Profit Margin


10.4.3 Scenario Test.

A scenario is a possible future environment either at a point of time or over period of time. A

projection of the effects of a scenario over the period of time is complicated. To determine the

relevant aspects, one or more changes in circumstances or assumptions may be forecasted. The effect

of these changes in a scenario can be generated from a shock resulting from a sudden change in a

single variable or risk factor.

Scenarios can be complicated with changes and interactions among many factors.

Figure 10.7: Scenario Test and Stress Test

While stress test is a future environment under a specific set of severely adverse conditions.

For the Scenario and Stress Test we will carry out the profit test with the main risks including the

investment return, mortality, lapse, acquisition & maintenance expenses.

As Best Estimate assumptions are the mean or averaging figures for pricing purposes, possibility for

actual experiences are the same as those of best estimate is very low, hence the analysis of

profitability of the product under different scenarios with different risk assumptions is required.

We created 16 scenarios for Scenario Test and 4 scenarios in the stress test in the deterministic

model.

The model point that is under investigation of the deterministic model is the policy with the insured

age of 4 and the policyholder age of 30.

The detailed results are shown in the Appendix 5.

Stress test

Scenarios

Severe Stress

Low Stress

Single risk Multiple risk Complexity


We carry out sixteen scenarios test as stated below:

Scenario 1 Investment return is 8.0%/year for the whole insurance period. Other assumptions

keep unchanged as per best estimate scenario



Scenario 3 Mortality claim increase to 70% that of the CSO1980 table. Other assumptions

keep unchanged as per best estimate scenario.

Scenario 4 Mortality claim fall to 30% that of the CSO1980 table. Other assumptions keep

unchanged as per best estimate scenario.

Scenario 5 Lapse rate is 10%/year. Other assumptions keep unchanged as per best estimate

scenario.


scenario.

Scenario 7 Commission and acquisition cost increase by 5.0%. Other assumptions keep


Scenario 8 Commission and acquisition cost increase by 10%. Other assumptions keep


Scenario 9 Maintenance cost increase by 5.0%. Other assumptions keep unchanged as per

best estimate scenario.

Scenario 10 Maintenance cost increase by 10%. Other assumptions keep unchanged as per


Scenario 11 Investment return is 8.0%/year for the whole insurance period and Death Claim is

70% of the CSO1980. Other assumptions keep unchanged as per best estimate

scenario



scenario

Scenario 13 Investment return is 8.0%/year for the whole insurance period and lapse rates are

10%/year. Other assumptions keep unchanged as per best estimate scenario.





70% of the CSO1980 and lapse rates are 15%/year. Other assumptions keep

unchanged as per best estimate scenario




Table 10.12: Description of scenario test cases under deterministic model

A. Non Par Product

Figure: 10.8 Profitability of Non Par product of deterministic model under Scenario Tests.

We see the profitability results of 16 scenarios tests.

Under different above scenarios the profit margin averaging at 10% range from [7%, 15%] and ROI

averaging at 20% and range from [17%, 25%].

It initially shows that under best estimate and under different scenarios profitability of the Non Par

product vary but still has good or acceptable profitability.

15%

7%

11% 12%

10% 10% 11%

10% 11% 11%

15%

7%

14% 13% 13%

7%

24%

18%

20% 22% 22%

22% 21%

19%

21% 21%

24%

17%

25% 25% 25%

19%

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

Scen1

Scen2

Scen3

Scen4

Scen5

Scen6

Scen7

Scen8

Scen9

Scen10

Scen11

Scen12

Scen13

Scen14

Scen15

Scen16

PM ROI


B. Par Product

Figure: 10.9 Profitability of par product of deterministic model under Scenario Tests

Under different above scenarios the profit margin averaging at about 2% range from [1%, 4%] and

ROI averaging at 14% and range from [12%,17%].

The profitability of the par version is less than those of the Non Par version. It is due to the

stipulation of MoF that at least 70% of the profit to be paid via dividend to the policyholder.

However due to the high demand of sales department. Many life insurers in Vietnam launched the

Par product to the market in the past thank to the high interest rate environment. Recently due to the

stable decrease of the interest rate, management of many companies do not encourage to the Par

Products due to lower profitability to those of Non Par Products.

In order to increase sale volume, however some companies still launch and sell par products in the

market and accept a modest profitability.

4%

1%

2% 3%

2% 2% 2%

2% 3% 2%

4%

1%

3% 3% 3%

1%

17%

13%

14%

15%

14% 14% 14% 13%

15% 14%

16%

12%

16% 16%

15%

12%

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

16.00%

18.00%

Scen1

Scen2

Scen3

Scen4

Scen5

Scen6

Scen7

Scen8

Scen9

Scen10

Scen11

Scen12

Scen13

Scen14

Scen15

Scen16

PM ROI


The above investigate profitability of an individual policy under different scenarios, a model point.

To investigate the distribution of profitability of individual policy, we also implement scenario test

for Non Par and Par products with 10,000 random Monte Carlo simulations.

We create a portfolio of 10,000 policies with random scenario of mortality claim, lapse rate,

investment return, acquisition and maintenance expenses fluctuate around the best estimate

assumptions.

Below are the distribution of Profit Margin and ROI of the Non Par and Par Product.

A. For Non Par

Figure 10.10: Distribution of Profitability of an individual Non Par Product under Stochastic model

The distribution of profitability of the individual policy has the shape similar to normalized

distribution with the following details:

The mean of the distribution of Profit Margin is 11.5% and the standard deviation is 5.6%.

The profit margin range from [-10.2%, 34.6%]

The confidence interval of Profit Margin at confidence level of 95% from [0.91%, 22.69%]

The VaR of Profit Margin at confidence level of 99.5% is -2.35%

The mean of the distribution of ROI is 22.8% and the standard deviation is 7.3%.

The ROI range from [-3.8%, 58.2%]

The confidence interval of ROI at confidence level of 95% from [11.0%, 39.83%]


The VaR of ROI at confidence level of 99.5% is 7.40%

B. For PAR

Figure 10.11: Distribution of Profitability of an individual Par Product under Stochastic model

The distribution of profitability of the individual policy has the shape similar to normalized

distribution with the following details:

The mean of the distribution of Profit Margin is 2.7% and the standard deviation is 2.0%.

The profit margin range from [-6.1%, 10.0%]

The confidence interval of Profit Margin at confidence level of 95% from [1.14%, 6.56%]

VaR of Profit Margin at confidence level of 99.5% is -2.43%

The mean of the distribution of ROI is 15.9% and the standard deviation is 4.7%.

The ROI range from [1.4%, 37%]

The confidence interval of ROI at confidence level of 95% from [8.15%, 26.49%]

VaR of ROI at confidence level of 99.5% is 6.33%


Diversifiable risks and non-diversifiable risks

Diversifiable risk is the risk that can be mitigated through diversification. The mortality risk of an

individual insurance policy with an extremely high sum insured is not diversified and may cause

financial difficulty to the insurer. But if there is a pool of the insurance policies, with large number of

the insured of different ages, gender and different sum insured, each insurance policy will expose to

different mortality risks that are unlikely to occur at the same time. Therefore, it can be reduced

through diversification.

On the other hand, there are some non-diversifiable risks. Non-diversifiable risks are systemic in

nature that they are inherent. Systemic risks cannot be reduced by diversification. In insurance

sector the economic recession risk that affect all the insurance policy the same way, in particular,

investment return risk affects the whole portfolio in the same way. It is therefore the non-

diversifiable risk.

For the diversifiable risks we therefore simulate 1000 random product portfolio. In each

product portfolio we create random number of policies with random entry ages, random sum insured,

random claim ratio and lapse rate for each policy which fluctuate around the best estimate

assumptions.

We investigate the profitability of the product portfolio under the above simulated scenarios.

A. For the Non Par Product


Figure 10.12: Distribution of Profitability of the Portfolio of the Non Par product under 1,000

simulations for diversifiable risks.



Under different scenarios of diversifiable risks, both the profit margin and ROI of the investigated

portfolio Non par fluctuate in a very narrow range.

The mean profit margin of the portfolio under 1,000 simulations is 10.63%.

Profit margin of the portfolio only vary slightly and range from 10.38% to 10.87%.

Confidence interval at confidence level of 95% range from [10.51%, 10.74%]

VaR of Profit Margin of the portfolio at 99.5% is 10.46%

The mean ROI of the portfolio under 1,000 simulations is 21.9%.

ROI ranges within 21.4% to 22.4%.

Confidence interval at confidence level of 95% range from [21.65%, 22.25%]

VaR of ROI of the portfolio at 99.5% is 21.59%

We find that the profitability of the Portfolio for Non Par product stays stable under the fluctuation

of claim ratio and lapse rates.


Mean 2.08056E+11 22126602811 0.106348386 0.219486137 754.71

Standard Error 761535496.2 81151792.46 1.89217E-05 4.99245E-05 4.646870701

Median 2.15605E+11 22895852686 0.106366374 0.219415399 765


Standard Deviation 24081866869 2566245004 0.000598356 0.001578752 146.9469541


Kurtosis -0.889030617 -0.877908629 0.510452271 -0.209242396 -1.242858414

Skewness -0.60549593 -0.596953469 -0.219669089 0.095735239 -0.068019938

Range 95496819415 10234466738 0.004921591 0.009801322 500

Minimum 1.50008E+11 15902654207 0.103827695 0.214457214 500

Maximum 2.45505E+11 26137120945 0.108749286 0.224258536 1000

Sum 2.08056E+14 2.21266E+13 106.3483859 219.4861368 754710

Count 1000 1000 1000 1000 1000


B. For the Par Product

Figure 10.13: Distribution of Profitability of the Portfolio of the Par product under 1,000


Table 10.14: Statistics of the Profitability of the Portfolio of Par Product under 1,000 simulations for

diversifiable risks.

Under different scenarios of claim and lapse, the profitability of Par Product also still stays stable.

The mean profit margin of the portfolio is 2.4%, while the profit margin only fluctuates with the

narrow range [2.26%, 2.52%].


Mean 2.3322E+11 5616581100 0.024081475 0.147177776 750.338

Standard Error 820886479.7 20069706.15 1.26207E-05 3.84628E-05 4.46333094

Median 2.40275E+11 5788556905 0.02407392 0.147184296 747.5


Standard Deviation 25958709763 634659833.9 0.000399103 0.001216301 141.1429172


Kurtosis -0.74609058 -0.70007507 -0.02560259 -0.11475614 -1.16521135

Skewness -0.62304805 -0.58308929 0.036817608 0.057991659 -0.02356011

Range 1.05498E+11 2917004173 0.002577728 0.007377331 500

Minimum 1.70396E+11 3926828526 0.022647733 0.143778715 500

Maximum 2.75894E+11 6843832699 0.025225461 0.151156046 1000

Sum 2.3322E+14 5.61658E+12 24.08147543 147.1777763 750338

Count 1000 1000 1000 1000 1000


VaR of Profit Margin of the portfolio at 99.5% is 2.31%

VaR of ROI of the portfolio at 99.5% is 14.43%

Under the different scenario of claims and lapse rates, the profitability of the whole portfolio is still

stable thanks to the diversification nature of the relevant risks.

In addition, as also shown in the sensitivity test, mortality and lapse do not have significant impact

on the profitability of this product


For the non-diversifiable risk, to investigate the impact of the non-diversifiable risks on the

profitability of the product portfolio, we create a fixed portfolio including 1,000 policies

under 1,000 simulated scenarios of different investment return, acquisition and maintenance

expenses which fluctuate around the best estimate assumptions, other assumptions keep as

per the Best Estimate Scenario.

A. For the Non Par

Figure 10.14: Distribution of Profitability of the Portfolio of the Non Par product under 1,000

simulations for non-diversifiable risks.

PV Prem PV Profit PM ROI inv exp

Mean 372,286,217,008 38,952,812,789 0.104631 0.209055 0.069799 0.053281

Standard Error 0 475,549,410 0.001277 0.001369 0.000309 0.00342

Median 372,286,217,008 39,048,298,649 0.104888 0.207492 0.069895 0.054834

Mode 372,286,217,008 #N/A #N/A #N/A #N/A #N/A

Standard Deviation 0 15,038,192,748 0.040394 0.043297 0.009781 0.108145

Sample Variance 2.09757E-05 2.26147E+20 0.001632 0.001875 9.57E-05 0.011695

Kurtosis -2.004012036 0.067065835 0.067066 0.727567 0.081109 0.565249

Skewness -1.001502881 0.093417681 0.093418 0.39916 -0.01659 -0.2298

Range 0 95848591124 0.257459 0.30963 0.063941 0.767628

Minimum 372,286,217,008 (7,153,020,055) -0.01921 0.077096 0.040631 -0.36939

Maximum 372,286,217,008 88,695,571,068 0.238246 0.386726 0.104571 0.398242

Sum 372,286,217,008,311 38,952,812,788,559 104.6314 209.0549 69.79943 53.28105

Count 1,000 1,000 1000 1000 1000 1000




The figures show the distribution of profitability of the portfolio product. Unlike the profitability

under analyse of diversifiable risks, the profitability of the portfolio under the nondivisifiable risks

significantly fluctuate.

The profit margin of the portfolio has the shape of normal distribution with the mean of 10.46% and

standard deviation of 4.0%.

The profit margin of the poftfolio ranges within [-1.9%, 23.8%]

The confidence inteval of the profit margin of the portfolio at 95% is [2.86%, 19.19%]

VaR at 99.5% of the profit margin of the portfolio is 0.68%

The ROI of the portfolio has the shape of normal distribution with the mean of 20.9% and standard

deviation of 4.3%.

The ROI of the poftfolio ranges within [7.7%, 38.6%]

The confidence inteval of the ROI of the portfolio at 95% is [13.15, 30.55%]

VaR at 99.5% of the ROI of the portfolio is 10.79%

Under the simulation and assumptions, the mean present value of profit of each portfolio including

1,000 policies is 38.9 billion VND.

The confidence inteval of the Profit of the portfolio at 95% is [10.65 billion VND, 71.4 billion

VND]

The VaR of profit of each portflio at 99.5% confidence level is 2.5 billion VND.



Figure 10.15: Distribution of Profitability of the Portfolio of the Par product under 1,000








The VaR of profit margin of each portflio at 99.5% confidence level is -0.39%.

PV Prem PV Profit PM ROI Inv Rate Expense

Mean 3.12783E+11 8331105606 0.026785455 0.151385728 0.069449981 0.050597533

Standard Error 3228394643 148183582.9 0.000373447 0.000678107 0.000317289 0.003316413

Median 3.12783E+11 7605988820 0.026987155 0.152408518 0.069548766 0.048071324

Mode 2.10743E+11 #N/A #N/A #N/A #N/A #N/A

Standard Deviation 1.02091E+11 4685976338 0.011809425 0.021443638 0.010033561 0.104874186

Sample Variance 1.04225E+22 2.19584E+19 0.000139463 0.00045983 0.000100672 0.010998595

Kurtosis -2.004012036 0.087016679 -0.200154502 -0.093300522 -0.231015757 0.070834793

Skewness -7.65353E-14 0.602356697 -0.100497943 -0.252297941 -0.06507287 0.011128967

Range 2.04079E+11 28983564560 0.069869746 0.127434224 0.058998052 0.693465117

Minimum 2.10743E+11 -3481483579 -0.0083927 0.082512203 0.040288691 -0.300825533

Maximum 4.14823E+11 25502080982 0.061477045 0.209946427 0.099286743 0.392639584

Sum 3.12783E+14 8.33111E+12 26.78545509 151.385728 69.44998131 50.59753311

Count 1000 1000 1000 1000 1000 1000



deviation of 2.1%.

The ROI of the poftfolio ranges within [8.25%, 21%]


The VaR of ROI of each portflio at 99.5% confidence level is 9.20%.

Under the simulation and assumptions, the mean present value of profit of each portfolio including

1,000 policies is 8.3 billion VND.

The confidence inteval of the profit of the portfolio at 95% is [0.84 billion VND, 18.81 billion VND]

The VaR of profit of each portflio at 99.5% confidence level is -1.38 billion VND (loss).


10.4.4 Stress Test.

Stress test is a future environment under a specific set of severely adverse conditions.

The potential interaction of a number of assumptions should also test in stress tests. Stress test

provide an assessment of an extreme scenario, usually the severe impact on profitability of the

product. Stress test can be used to enhance the understanding of if and why profitability of product is

vulnerable to highly uncertain risks.

The results of stress testing, including description of particular scenarios and what might lead to

them shall be clearly understood by the Management.

For the deterministic model we create 4 stress test scenario for the model point.

Scenario 17 Investment return is 5%/year for the whole insurance period and Death Claim

is 100% of the CSO1980 and lapse rates are 30%/year. Other assumptions keep



is 120% of the CSO1980 and lapse rates are 30%/year. Other assumptions keep



is 120% of the CSO1980 and lapse rates are 30%/year and maintenance cost

increase by 10%. Other assumptions keep unchanged as per best estimate

scenario


is 120% of the CSO1980 and lapse rates are 30%/year and acquisition cost


scenario

Table 10.17: Description of stress test cases under deterministic model


A. For the Non Par product.

Figure: 10.16: Profitability of Non Par product under stress test and deterministic model

Under the extreme conditions, the profitability of this Non Par Product reduce significantly but

acceptable with ROI are about 15% and Profit margin approach 5%.


Figure: 10.17 Profitability of par product under stress test and deterministic model

Under the stress test scenario, the model point profitability of the Par Product reduces significantly

with the Profit margin approach zero or even negative with -1.18% in scenario 20. The ROI are

about 10% or even fall to 7.47% in the scenario 20.

0.00%

5.00%

10.00%

15.00%

20.00%

Scen 17Scen 18

Scen 19Scen 20

5.56% 5.19%

4.81%

2.55%

19.10% 18.39%

17.70%

13.65%

PM ROI

-2.00%

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

Scen 17Scen 18

Scen 19Scen 20

0.30% 0.15%

0.00% -1.18%

10.78% 10.38%

10.00%

7.47%

PM ROI


For the stochastic model, in this stress test we will carry out the stress test on the decrease of

investment return fall down to 5.0%/year, the high claim ratio up to 100% of CSO1980 and the high

lapse rate up to 20%/year and expense increase by 20%.

We will simulate 10,000 policies with different entry ages, sum insured, random investment return,

random claim ratio, lapse rate and expenses which fluctuate around the above stress test assumptions.

Below are distribution of Profit Margin and ROI of an individual Policy under stress test scenario.

A. For the NON PAR.

Figure 10.18: Distribution of Profitability of the Non Par policy under Stress Test Scenario

Table 10.18: Statistics of 10,000 simulation of the Non Par policy under Stress Test Scenario

The distribution of profit margin and ROI of a Non Par policy under the stress test scenarios is a

Normal distribution.

The mean of the profit margin of a Non Par policy is -0.1% and standard deviation is 4.76%.

PV Prem PV Profit PM ROI

Mean 219081973.4 929333.1436 -0.00113341 0.1082509

Standard Error 940962.7386 110481.5599 0.00047627 0.00061819

Median 208193891.7 148032.6628 0.00094488 0.10104051

Mode 100942351.5 -938302.6199 -0.00929543 0.08367431

Standard Deviation 94100978.56 11048708.39 0.04762921 0.06182238

Sample Variance 8.85499E+15 1.22074E+14 0.00226854 0.00382201

Kurtosis 0.323914739 1.249996015 -0.12149801 0.52043864

Skewness 0.705537699 0.410417132 -0.22069792 0.57078122

Range 551795367 100691563.5 0.3352386 0.54645911

Minimum 54482523.21 -44294085.61 -0.17739704 -0.13381177

Maximum 606277890.2 56397477.86 0.15784156 0.41264734

Sum 2.19104E+12 9294260769 -11.3352236 1082.61725

Count 10000 10000 10000 10000


The profit margin of a Non Par policy under the stress test scenarios range from [ -17.7%, 15.7%]

The confidence interval of profit margin at 95% of each individual policy under stress test scenarios

range from [-9.97%, 8.69%]

The VaR of profit margin at confidence level of 95% is -12.79%.

The mean of the ROI is 10.8% and standard deviation is 4.76%.

The ROI under the stress test scenarios range from [ -13.3%, 41.2%]

The confidence interval of ROI at 95% of each individual policy under stress test scenarios range

from [0.63%, 24.96%]

The VaR of ROI at confidence level of 99.5% is -2.24%.

We find the profit margin and ROI of the non par policy reduce significantly under the stress test

scenarios. This requires the reviewing assumptions and back testing frequently during the life of the

product to ensure the profitability of the product.

B. For the PAR Product

Figure 10.19: Distribution of Profitability of an individual PAR Product under Stress Test Scenario


Table 10.19: Statistics of 10,000 simulation of the par policy under Stress Test Scenario

The mean of the profit margin of a Non Par policy is -2.4 % and standard deviation is 2.4%.

The profit margin of a Non Par policy under the stress test scenarios range from [ -14.9%, 4.0%]

The confidence level of profit margin at confidence level of 95% range from [-7.66%, 1.59%]

The VaR of profit margin at 99.5% is -9.8%.

The mean of the ROI is 6.6% and standard deviation is 3.5%.

The ROI under the stress test scenarios range from [ -4.1%, 32.8%]

The confidence level of profit margin at confidence level of 95% range from [1.26%, 14.67%]

The VaR of ROI at 99.5% is 0.28%.

It arrives that profitability of an individual non par policy slump in the stress test scenario and even

may come with non profit or big loss.

PV Prem PV Profit PM ROI

Mean 248,860,707 (5,315,299) -0.0244646 0.06625139

Standard Error 1,124,799 59,418 0.0002442 0.00035212

Median 233,268,826 (4,590,265) -0.0221019 0.06119024

Mode 111,020,422 1,928,140 0.0173674 0.15190168

Standard Deviation 112,485,570 5,942,145 0.0244165 0.03521359

Sample Variance 1.2653E+16 3.53091E+13 0.0005962 0.00124

Kurtosis 0.646613415 1.965575525 0.3905214 1.96168553

Skewness 0.829253912 -0.757602149 -0.5473186 0.98059204

Range 724,250,685 67,328,696 0.1892723 0.36963899

Minimum 50,947,030 (51,181,258) -0.1489999 -0.0411213

Maximum 775,197,714 16,147,438 0.0402724 0.32851772

Sum 2.48886E+12 -53158304053 -244.67064 662.580157

Count 10,000 10,000 10,000 10,000


To investigate the profitability of the insurance portfolio, We create a Monte Carlo simulation for

1,000 product portfolios, each portfolio include 1,000 individual Policies.

We will carry out the stress test on the following assumptions, the decrease of investment return fall

down to 5.0%/year, the high claim ratio up to 100% of CSO1980 and the high lapse rate up to

20%/year and expense increase by 20% as per Best Estimate assumptions.

Below are the profitability analyze of the Non Par and the par product.

A. For the NON PAR.

Figure 10.20 Distribution of Profitability of a Portfolio including 1,000 random Non Par Policies

under Stress Test Scenarios.

Table 10.20: Statistics of of 1,000 simulations of the non par portfolio under Stress Test Scenario

PV Prem PV Profit PM ROI Inv rate Expense

Mean 220,124,125,066 649,146,486 0.003992182 0.108554775 0.049954527 0.1989781

Standard Error 1,253,521,175 256,904,198 0.001147992 0.001483867 0.00031683 0.003309961

Median 214,456,231,794 994,322,540 0.00492608 0.10724637 0.050194567 0.205629684

Mode #N/A #N/A #N/A #N/A #N/A #N/A

Standard Deviation 39639820089 8124024064 0.036302702 0.046924001 0.010019034 0.104670154


Kurtosis 1.288328101 0.645899057 0.046322061 1.000947958 -0.114558608 -0.001355779

Skewness 0.886841121 -0.343566892 -0.082125714 0.331236497 -0.07782858 -0.03537287

Range 2.77437E+11 60134211473 0.237501965 0.408374174 0.067895038 0.758522534

Minimum 138,709,413,842 (34,705,646,886) -0.111852804 -0.021119344 0.012278925 -0.189535419

Maximum 416,146,207,826 25,428,564,587 0.125649161 0.38725483 0.080173963 0.568987115

Sum 220,124,125,066,323 649,146,486,099 3.992182131 108.5547749 49.95452705 198.9781

Count 1,000 1,000 1000 1000 1000 1000


We simulate the different scenarios with assumptions fluctuate around the above stress test

assumptions.




The confidence interval of profit margin at confidence level of 95% range from [-6.60%, 7.49%]

The VaR of the profit margin of the portfolio at 99.5% is -9.16%

The ROI of the portfolio has the shape of normal distribution with the mean of 10.8% and


The ROI of the poftfolio ranges within [-2.1, 38.7%]

The confidence interval of ROI at confidence level of 95% range from [2.35%, 20.28%]

The VaR of the ROI of the portfolio at 99.5% is -0.30%

Under the simulation and stress test assumptions, the mean present value of profit of each

portfolio including 1000 policies is 649 million VND.

The confidence interval of profit of the portfolio at confidence level of 95% range from [-16.68

billion VND, 15.52 billion VND]


Under the extreme conditions, the profitability criteria for Non Par portfolio may become

vulnerable.


B. For the PAR.

Figure 10.21: Distribution of Profitability of a Portfolio including 1,000 Par Policies under Stress

Test Scenario

Table 10.21– Statistics of 1,000 Monte Carlo simulations of the insurance portfolio including 1,000

Par Policies under Stress Test Scenarios

The profit margin of the portfolio has the shape of normal distribution with the mean of -1.8% and



The confidence interval of profit margin at confidence level of 95% range from [-5.03%, 1.07%]

PV Prem PV Profit PM ROI inv exp

Mean 252,928,683,100 (4,722,855,372) -0.01866 0.069755 0.050544 0.199273

Standard Error 112,692,104 121,248,513 0.000479 0.000814 0.00032 0.003348

Median 252,953,595,098 (4,552,168,799) -0.01801 0.067775 0.050748 0.197111

Mode #N/A #N/A #N/A #N/A #N/A #N/A

Standard Deviation 3563637227 3834214650 0.015136 0.025741 0.010112 0.105863


Kurtosis -0.010359683 -0.057180229 -0.06629 0.700418 -0.23092 -0.17406

Skewness -0.004087772 -0.127436686 -0.12389 0.643604 -0.00408 -0.02142

Range 24,163,994,938 25,486,383,260 0.099008 0.172721 0.056738 0.63029

Minimum 240,806,223,494 (17,884,378,843) -0.06953 0.011814 0.022454 -0.09235

Maximum 264,970,218,432 7,602,004,418 0.029482 0.184536 0.079192 0.537943

Sum 252,928,683,100,069 (4,722,855,371,893) -18.6617 69.75454 50.54443 199.2734

Count 1,000 1,000 1000 1000 1000 1000


The VaR of the profit margin of the portfolio at 99.5% is -5.69%


deviation of 2.5%.

The ROI of the poftfolio ranges within [1.1, 18.4%]

The confidence interval of ROI at confidence level of 95% range from [2.61%, 12.93%]

The VaR of the ROI of the portfolio at 99.5% is 2.02%

Under the simulation and stress test assumptions, the mean present value of profit of each portfolio

including 1000 policies is -4.7 billion VND (loss 4.7 billion).

The confidence interval of profit of the portfolio at confidence level of 95% range from [-12.71

billion VND, 2.73 billion VND]


Under the extreme conditions of the stress test scenarios, the profitability criteria for par portfolio

may become very vulnerable.


CONCLUSION

Despite the increasing sale of Universal Life Products in recent year, the demand for juvenile

Products, especially products that serve the savings for education purpose for the children and the

relevant attached protection, is always in high demand in Vietnam as the tradition of Vietnamese

parent care much about the education of their children so they prepare a careful plan for savings for

their children education path and protection under unexpected exposures.

Profitability of the launched product is one of the major concerns of the management.

As shown in the above and in the appendix, we can find that Profitability of this product mainly

depends on the actual investment return, mortality claim ratio, the lapse rates, expenses and that the

company may experience or implement, of which investment return is the most sensitive factor that

impact on profitability on this product.

We also find that the profitability of the PAR version is much less than those of the NON PAR

version. It is due to the stipulation of Ministry of Finance that: For PAR Products, at least 70% of the

profit must be returned to policyholders via dividend. With the steady decline of interest rates in the

financial market in recent years, Profitability of the PAR Products are very slim.

Management of many companies do not encourage to sell the Par Products due to lower profitability

to those of Non Par Products. In order to increase sale volume and attain higher market share,

however some companies still launch and sell par products in the market and accept a modest

profitability.

Upon the profitability analysis result, the management of the company decide to sell the NON PAR

Product to exploit the sale potential of new distribution channel so as to recover faster the acquired

expenses for this distribution channel.

The dissertation also has some limitations in approaching.

The pricing process is based on the best estimates assumptions, which are the mean or average

figures. The profit of the product is created from the difference of pricing assumptions and best

estimate assumptions. Once the individual policy is launched, the premiums are guaranteed during

insurance period, the actual experiences may differ greatly with the best estimate assumptions that

may negatively affect the profitability of the launched policies. For optimal internal control,

assumptions back testing are carried out regularly for management decisions and to mitigate

unexpected consequences.

Besides, due to the experienced volatile interest rate in recent years, the financial market of Vietnam

which is the emerging market become unpredictable in long term, Economic Scenario Generator has

not been deeply studied and applied in this dissertation.


ABBREVIATION.

MoF: Ministry of Finance

TPD: Total & Permanent Disability

PM: Profit Margin

ROI: Return on Investment

IRR: Internal Rate of Return

SI: Sum Insured

CSO1980: Mortality Table CSO 1980

PAR: Participating Product

NON PAR: Non Participating Product.

BE : Best Estimates

VaR : Value at Risk


ACADEMIC BIBLIOGRAPHY

Clare Bellis, Richard Lyon, Stuart Klugman and John Shepherd. (2003) Understanding Actuarial

Management

Joseph B. MacClean (1937), Distribution of Surplus

Han U.Gerber (1997) Life Insurance Mathematics

Sam Gutterman (2007), Life Insurance Company Expense

BMI Research, BMI Report 2017 on Vietnam Insurance Market

Vietnam Insurance Association, Statistics from Vietnam Insurance Market from 2007-2018

Government, Decree 73/2016/ND-CP of the Government provide detailed guideline on insurance

law.

Ministry of Finance, Cicurlar 50/2017/TT-BTC guidelines on details implementation of the law

on insurance business.

Mirae Asset Prevoir Life Insurer, Product Development Procedure

Mirae Asset Prevoir Life Insurer, Expense Analysis Procedure

SOA, SOA Materials on Profit Testing and Profitability

Global Association of Risk Professionals, Financial Risk Manager materials

Simone Manganelli and Robert F.Engle (2001), Value at Risk Model in Finance


11. Appendix

Appendix 1: Individual Mortality Table CSO1980 for Male

(issued with circular 125/2012/TT-BTC dated on July 30, 2012 of Ministry of Finance)

AgeLx

CSO80 Mqx Age

Lx

CSO80 Mqx Age

Lx

CSO80 Mqx

0 1,000,000 0.2630% 34 952,105 0.2050% 68 663,545 3.4650%

1 997,370 0.1030% 35 950,154 0.2170% 69 640,554 3.7810%

2 996,343 0.0990% 36 948,092 0.2320% 70 616,334 4.1370%

3 995,356 0.0970% 37 945,892 0.2490% 71 590,836 4.5430%

4 994,391 0.0930% 38 943,537 0.2680% 72 563,995 5.0080%

5 993,466 0.0880% 39 941,008 0.2900% 73 535,750 5.5340%

6 992,592 0.0830% 40 938,279 0.3150% 74 506,102 6.1100%

7 991,768 0.0780% 41 935,324 0.3420% 75 475,179 6.7250%

8 990,994 0.0750% 42 932,125 0.3710% 76 443,223 7.3700%

9 990,251 0.0740% 43 928,667 0.4030% 77 410,557 8.0370%

10 989,518 0.0750% 44 924,924 0.4370% 78 377,561 8.7320%

11 988,776 0.0810% 45 920,882 0.4730% 79 344,592 9.4760%

12 987,975 0.0920% 46 916,527 0.5120% 80 311,939 10.2940%

13 987,066 0.1070% 47 911,834 0.5530% 81 279,828 11.2090%

14 986,010 0.1240% 48 906,792 0.5970% 82 248,462 12.2410%

15 984,788 0.1420% 49 901,378 0.6460% 83 218,048 13.3840%

16 983,389 0.1590% 50 895,555 0.7000% 84 188,864 14.6120%

17 981,826 0.1720% 51 889,286 0.7630% 85 161,267 15.8980%

18 980,137 0.1820% 52 882,501 0.8330% 86 135,629 17.2210%

19 978,353 0.1880% 53 875,150 0.9130% 87 112,272 18.5730%

20 976,514 0.1900% 54 867,160 1.0010% 88 91,420 19.9530%

21 974,658 0.1900% 55 858,479 1.0960% 89 73,179 21.3690%

22 972,806 0.1880% 56 849,070 1.1970% 90 57,541 22.8430%

23 970,978 0.1840% 57 838,907 1.3040% 91 44,397 24.4110%

24 969,191 0.1800% 58 827,968 1.4180% 92 33,559 26.1430%

25 967,446 0.1750% 59 816,227 1.5420% 93 24,786 28.2130%

26 965,7530.1720%

60 803,6411.6800%

94 17,79330.9970%

27 964,092 0.1710% 61 790,140 1.8360% 95 12,278 35.1860%

28 962,444 0.1700% 62 775,633 2.0120% 96 7,958 42.0990%

29 960,808 0.1720% 63 760,027 2.2090% 97 4,608 54.1000%

30 959,155 0.1750% 64 743,238 2.4270% 98 2,115 74.5150%

31 957,476 0.1800% 65 725,200 2.6620% 99 539 100.0000%

32 955,753 0.1870% 66 705,895 2.9130%

33 953,966 0.1950% 67 685,332 3.1790%


Appendix 2: Summary of Assumptions

Pricing

Assumptions

Valuation

Assumptions

Best Estimate

Assumptions

Death & TPD combined rate: 90% CSO1980 100% CSO1980 50% CSO1980

Death & TPD due to accident: 0.09%/ year 0.09%/ year 0.09%/ year

Interest rate 4.0%/year 3.0%/year 7.0%/year

Lapse rate: 0.0% 0.0% 5.0%/year

Expense Assumptions: As below As below As below

Expense Assumptions

Pricing

Assumptions

Valuation

Assumptions

Best Estimate

Assumptions

Acquisition Expense per SI αs 1.1760% Not applied 0.9050%

Collection Expense per Premium 2.50% Not applied 2.20%

Management Expense per SI during

Premium Period γs 0.7275% Not applied 0.5385%

Management Expense per SI after Premium

Period γ’s 0.6930% 0.6930% 0.5130%

Acquisition Expenses Assumptions

Pricing Assumptions Best Estimate Assumption

Premium

Term

Policy

Year 1

Policy

Year 2

Policy

Year 3

Policy

Year 1

Policy

Year 2

Policy

Year 3

8 67.80% 5.50% 5.50% 62.80% 5.50% 5.50%

9 70.80% 6.00% 6.00% 65.80% 6.00% 6.00%

10 73.80% 6.50% 6.50% 68.80% 6.50% 6.50%

11 76.80% 7.00% 7.00% 71.80% 7.00% 7.00%

12 79.80% 7.50% 7.50% 74.80% 7.50% 7.50%

13 82.80% 8.00% 8.00% 77.80% 8.00% 8.00%

14 85.80% 8.50% 8.50% 80.80% 8.50% 8.50%

15 88.80% 9.00% 9.00% 83.80% 9.00% 9.00%

16 91.80% 9.50% 9.50% 86.80% 9.50% 9.50%

17 94.80% 10.00% 10.00% 89.80% 10.00% 10.00%

18 94.80% 10.00% 10.00% 89.80% 10.00% 10.00%


Appendix 3: Tariff table

a. NON PAR Product

- 1 2 3 4 5 6 7 8 9 10

18 8.4793% 9.0025% 9.5797% 10.2371% 10.9920% 11.8678% 12.8957% 14.1186% 15.5974% 17.4788% 19.8420%

19 8.4817% 9.0043% 9.5808% 10.2377% 10.9921% 11.8675% 12.8950% 14.1177% 15.5964% 17.4780% 19.8415%

20 8.4843% 9.0060% 9.5818% 10.2379% 10.9916% 11.8664% 12.8933% 14.1155% 15.5938% 17.4751% 19.8385%

21 8.4878% 9.0085% 9.5833% 10.2385% 10.9914% 11.8654% 12.8916% 14.1131% 15.5907% 17.4714% 19.8344%

22 8.4925% 9.0122% 9.5859% 10.2401% 10.9920% 11.8650% 12.8904% 14.1110% 15.5878% 17.4677% 19.8300%

23 8.4992% 9.0176% 9.5902% 10.2433% 10.9941% 11.8660% 12.8903% 14.1100% 15.5858% 17.4647% 19.8260%

24 8.5081% 9.0254% 9.5967% 10.2486% 10.9982% 11.8690% 12.8922% 14.1108% 15.5855% 17.4634% 19.8237%

25 8.5197% 9.0357% 9.6058% 10.2564% 11.0048% 11.8743% 12.8963% 14.1137% 15.5873% 17.4641% 19.8233%

26 8.5343% 9.0491% 9.6179% 10.2672% 11.0142% 11.8825% 12.9033% 14.1195% 15.5919% 17.4676% 19.8256%

27 8.5520% 9.0655% 9.6330% 10.2810% 11.0267% 11.8937% 12.9131% 14.1281% 15.5992% 17.4737% 19.8306%

28 8.5727% 9.0850% 9.6511% 10.2977% 11.0422% 11.9078% 12.9259% 14.1394% 15.6093% 17.4826% 19.8382%

29 8.5967% 9.1078% 9.6727% 10.3179% 11.0610% 11.9252% 12.9419% 14.1541% 15.6227% 17.4947% 19.8491%

30 8.6241% 9.1340% 9.6974% 10.3413% 11.0830% 11.9459% 12.9612% 14.1720% 15.6391% 17.5098% 19.8629%

31 8.6549% 9.1635% 9.7256% 10.3682% 11.1085% 11.9700% 12.9839% 14.1933% 15.6590% 17.5282% 19.8799%

32 8.6893% 9.1966% 9.7573% 10.3985% 11.1374% 11.9975% 13.0100% 14.2180% 15.6823% 17.5501% 19.9004%

33 8.7274% 9.2333% 9.7926% 10.4324% 11.1699% 12.0286% 13.0397% 14.2462% 15.7091% 17.5755% 19.9243%

34 8.7699% 9.2741% 9.8317% 10.4700% 11.2062% 12.0635% 13.0732% 14.2783% 15.7397% 17.6047% 19.9521%

35 8.8169% 9.3192% 9.8750% 10.5117% 11.2463% 12.1022% 13.1106% 14.3143% 15.7743% 17.6379% 19.9838%

36 8.8690% 9.3692% 9.9228% 10.5576% 11.2906% 12.1449% 13.1519% 14.3543% 15.8129% 17.6752% 20.0197%

37 8.9264% 9.4242% 9.9754% 10.6080% 11.3390% 12.1917% 13.1971% 14.3981% 15.8554% 17.7163% 20.0596%

38 8.9896% 9.4848% 10.0333% 10.6633% 11.3921% 12.2428% 13.2465% 14.4459% 15.9018% 17.7615% 20.1035%

39 9.0588% 9.5514% 10.0970% 10.7242% 11.4504% 12.2987% 13.3003% 14.4981% 15.9524% 17.8109% 20.1516%

40 9.1344% 9.6243% 10.1669% 10.7911% 11.5143% 12.3599% 13.3591% 14.5547% 16.0073% 17.8642% 20.2037%

41 9.2167% 9.7037% 10.2431% 10.8642% 11.5842% 12.4267% 13.4231% 14.6161% 16.0665% 17.9218% 20.2597%

42 9.3062% 9.7902% 10.3263% 10.9440% 11.6608% 12.5000% 13.4931% 14.6831% 16.1309% 17.9838% 20.3201%

43 9.4038% 9.8844% 10.4169% 11.0312% 11.7445% 12.5803% 13.5699% 14.7565% 16.2011% 18.0514% 20.3852%

44 9.5103% 9.9870% 10.5156% 11.1262% 11.8359% 12.6680% 13.6540% 14.8370% 16.2779% 18.1249% 20.4559%

45 9.6270% 10.0992% 10.6232% 11.2297% 11.9355% 12.7640% 13.7462% 14.9253% 16.3624% 18.2057% 20.5331%

46 9.7552% 10.2223% 10.7412% 11.3429% 12.0444% 12.8689% 13.8472% 15.0224% 16.4555% 18.2948% 20.6182%

47 9.8962% 10.3577% 10.8707% 11.4670% 12.1636% 12.9836% 13.9578% 15.1290% 16.5580% 18.3932% 20.7124%

48 10.0512% 10.5069% 11.0135% 11.6037% 12.2947% 13.1095% 14.0791% 15.2461% 16.6710% 18.5022% 20.8171%

49 10.2216% 10.6712% 11.1710% 11.7545% 12.4392% 13.2482% 14.2126% 15.3749% 16.7955% 18.6228% 20.9336%

50 10.4083% 10.8519% 11.3446% 11.9210% 12.5987% 13.4012% 14.3596% 15.5165% 16.9324% 18.7555% 21.0624%

51 10.6127% 11.0499% 11.5354% 12.1045% 12.7749% 13.5701% 14.5217% 15.6724% 17.0829% 18.9015% 21.2043%

52 10.8358% 11.2661% 11.7441% 12.3056% 12.9683% 13.7559% 14.6999% 15.8436% 17.2476% 19.0609% 21.3591%

53 11.5021% 11.9718% 12.5255% 13.1803% 13.9598% 14.8958% 16.0316% 17.4283% 19.2352% 21.5279%

54 12.2198% 12.7648% 13.4114% 14.1826% 15.1102% 16.2375% 17.6259% 19.4252% 21.7111%

55 13.0255% 13.6628% 14.4254% 15.3443% 16.4627% 17.8420% 19.6328% 21.9106%

56 13.9370% 14.6899% 15.5996% 16.7088% 18.0788% 19.8602% 22.1288%

57 14.9788% 15.8784% 16.9780% 18.3383% 20.1102% 22.3687%

58 16.1839% 17.2729% 18.6233% 20.3855% 22.6338%

59 17.5971% 18.9365% 20.6889% 22.9272%

60 19.2813% 21.0231% 23.2513%

61 21.3906% 23.6080%

62 23.9990%

AGE CHILD

AG

E P

AR

EN

T


b. PAR Product

- 1 2 3 4 5 6 7 8 9 10

18 9,7003% 10,2463% 10,8459% 11,5282% 12,3109% 13,2182% 14,2822% 15,5470% 17,0753% 19,0217% 21,4643%

19 9,7031% 10,2483% 10,8472% 11,5288% 12,3110% 13,2178% 14,2814% 15,5460% 17,0742% 19,0207% 21,4637%

20 9,7061% 10,2504% 10,8484% 11,5292% 12,3106% 13,2167% 14,2796% 15,5437% 17,0715% 19,0177% 21,4606%

21 9,7101% 10,2533% 10,8502% 11,5300% 12,3105% 13,2157% 14,2779% 15,5411% 17,0682% 19,0138% 21,4563%

22 9,7157% 10,2576% 10,8533% 11,5320% 12,3114% 13,2156% 14,2767% 15,5390% 17,0652% 19,0100% 21,4517%

23 9,7232% 10,2639% 10,8583% 11,5356% 12,3138% 13,2168% 14,2768% 15,5381% 17,0632% 19,0069% 21,4477%

24 9,7334% 10,2726% 10,8656% 11,5416% 12,3184% 13,2201% 14,2789% 15,5390% 17,0631% 19,0057% 21,4452%

25 9,7463% 10,2841% 10,8757% 11,5502% 12,3257% 13,2260% 14,2835% 15,5422% 17,0651% 19,0065% 21,4449%

26 9,7625% 10,2989% 10,8889% 11,5620% 12,3360% 13,2349% 14,2910% 15,5485% 17,0700% 19,0102% 21,4474%

27 9,7821% 10,3170% 10,9055% 11,5770% 12,3495% 13,2469% 14,3016% 15,5576% 17,0778% 19,0167% 21,4527%

28 9,8048% 10,3383% 10,9252% 11,5952% 12,3662% 13,2621% 14,3152% 15,5698% 17,0885% 19,0260% 21,4607%

29 9,8313% 10,3632% 10,9486% 11,6171% 12,3864% 13,2808% 14,3323% 15,5854% 17,1026% 19,0388% 21,4720%

30 9,8612% 10,3917% 10,9755% 11,6423% 12,4101% 13,3029% 14,3529% 15,6043% 17,1200% 19,0546% 21,4865%

31 9,8948% 10,4238% 11,0060% 11,6713% 12,4375% 13,3286% 14,3770% 15,6268% 17,1409% 19,0740% 21,5043%

32 9,9323% 10,4597% 11,0403% 11,7039% 12,4685% 13,3580% 14,4048% 15,6530% 17,1654% 19,0969% 21,5256%

33 9,9738% 10,4995% 11,0783% 11,7403% 12,5032% 13,3911% 14,4363% 15,6828% 17,1936% 19,1235% 21,5505%

34 10,0200% 10,5436% 11,1205% 11,7807% 12,5420% 13,4283% 14,4718% 15,7167% 17,2258% 19,1541% 21,5795%

35 10,0712% 10,5925% 11,1671% 11,8254% 12,5849% 13,4695% 14,5113% 15,7547% 17,2622% 19,1889% 21,6127%

36 10,1278% 10,6465% 11,2186% 11,8746% 12,6321% 13,5149% 14,5551% 15,7968% 17,3027% 19,2279% 21,6501%

37 10,1903% 10,7061% 11,2752% 11,9286% 12,6838% 13,5646% 14,6030% 15,8430% 17,3473% 19,2710% 21,6917%

38 10,2590% 10,7716% 11,3376% 11,9879% 12,7404% 13,6188% 14,6552% 15,8935% 17,3961% 19,3182% 21,7374%

39 10,3343% 10,8437% 11,4062% 12,0532% 12,8026% 13,6783% 14,7122% 15,9484% 17,4493% 19,3698% 21,7875%

40 10,4165% 10,9226% 11,4815% 12,1249% 12,8708% 13,7433% 14,7743% 16,0080% 17,5068% 19,4256% 21,8418%

41 10,5060% 11,0086% 11,5637% 12,2033% 12,9455% 13,8143% 14,8421% 16,0728% 17,5690% 19,4858% 21,9001%

42 10,6035% 11,1023% 11,6533% 12,2890% 13,0273% 13,8922% 14,9162% 16,1434% 17,6365% 19,5507% 21,9630%

43 10,7097% 11,2043% 11,7510% 12,3826% 13,1168% 13,9776% 14,9975% 16,2208% 17,7103% 19,6213% 22,0308%

44 10,8258% 11,3155% 11,8574% 12,4846% 13,2145% 14,0711% 15,0867% 16,3057% 17,7910% 19,6982% 22,1045%

45 10,9530% 11,4371% 11,9736% 12,5957% 13,3210% 14,1732% 15,1844% 16,3990% 17,8798% 19,7827% 22,1849%

46 11,0927% 11,5707% 12,1009% 12,7173% 13,4375% 14,2849% 15,2915% 16,5015% 17,9777% 19,8761% 22,2737%

47 11,2464% 11,7175% 12,2407% 12,8507% 13,5649% 14,4070% 15,4088% 16,6140% 18,0854% 19,9792% 22,3719%

48 11,4155% 11,8793% 12,3948% 12,9975% 13,7051% 14,5411% 15,5374% 16,7377% 18,2043% 20,0933% 22,4812%

49 11,6014% 12,0577% 12,5649% 13,1596% 13,8596% 14,6888% 15,6789% 16,8736% 18,3351% 20,2195% 22,6026%

50 11,8052% 12,2537% 12,7523% 13,3385% 14,0302% 14,8516% 15,8346% 17,0230% 18,4790% 20,3585% 22,7369%

51 12,0281% 12,4686% 12,9584% 13,5357% 14,2186% 15,0314% 16,0064% 17,1875% 18,6371% 20,5112% 22,8848%

52 12,2716% 12,7033% 13,1838% 13,7519% 14,4256% 15,2292% 16,1953% 17,3681% 18,8102% 20,6780% 23,0462%

53 12,9595% 13,4298% 13,9882% 14,6524% 15,4464% 16,4030% 17,5666% 19,0000% 20,8604% 23,2221%

54 13,6979% 14,2457% 14,8997% 15,6838% 16,6304% 17,7839% 19,2077% 21,0593% 23,4131%

55 14,5261% 15,1691% 15,9426% 16,8787% 18,0218% 19,4350% 21,2766% 23,6211%

56 15,4627% 16,2246% 17,1497% 18,2819% 19,6841% 21,5149% 23,8486%

57 16,5328% 17,4458% 18,5664% 19,9572% 21,7768% 24,0990%

58 17,7702% 18,8782% 20,2572% 22,0653% 24,3757%

59 19,2209% 20,5869% 22,3833% 24,6819%

60 20,9498% 22,7335% 25,0201%

61 23,1187% 25,3923%

62 25,8003%

AGE CHILD

AG

E P

AR

EN

T


Appendix 4: Best Estimate Profit Test Result

Profitabilty for the Best Estimate (Base case) will be as follow:

A. For NON PAR Product

The profitability of the best estimate scenario of the Non Par product is good with profit margin

ranging from 10.4% to 16.5% and ROI ranges from 17.6% to 40.2%.

0 1 2 3 4 5 6 7 8 9 10

20 10.37% 10.39% 10.63% 10.85% 11.03% 11.19% 11.32% 11.36% 11.37% 10.82% 10.42%

25 10.38% 10.39% 10.63% 10.85% 11.03% 11.18% 11.30% 11.34% 11.35% 10.79% 10.39%

30 10.60% 10.59% 10.81% 11.01% 11.17% 11.30% 11.42% 11.43% 11.43% 10.85% 10.44%

35 11.06% 11.03% 11.22% 11.38% 11.51% 11.62% 11.70% 11.69% 11.65% 11.05% 10.61%

40 11.82% 11.74% 11.89% 12.00% 12.08% 12.14% 12.18% 12.14% 12.05% 11.40% 10.91%

45 12.90% 12.77% 12.85% 12.90% 12.92% 12.91% 12.88% 12.79% 12.62% 11.91% 11.36%

50 14.40% 14.20% 14.21% 14.18% 14.12% 14.03% 13.91% 13.75% 13.49% 12.69% 12.04%

55 15.97% 15.83% 15.64% 15.39% 15.12% 14.77% 13.86% 13.08%

60 16.52% 15.48% 14.54%

0 1 2 3 4 5 6 7 8 9 10

20 17.67% 18.17% 19.00% 19.96% 21.04% 22.31% 23.78% 25.07% 26.56% 27.41% 28.79%

25 17.62% 18.12% 18.95% 19.90% 20.98% 22.24% 23.71% 24.99% 26.48% 27.32% 28.70%

30 17.72% 18.22% 19.04% 19.99% 21.07% 22.33% 23.83% 25.11% 26.58% 27.42% 28.79%

35 18.03% 18.53% 19.36% 20.31% 21.39% 22.66% 24.17% 25.52% 26.98% 27.81% 29.17%

40 18.57% 19.09% 19.93% 20.89% 21.99% 23.28% 24.83% 26.31% 27.75% 28.58% 29.93%

45 19.34% 19.89% 20.76% 21.73% 22.87% 24.20% 25.78% 27.48% 28.92% 29.75% 31.09%

50 20.45% 21.03% 21.93% 22.96% 24.15% 25.54% 27.20% 29.17% 30.69% 31.53% 32.87%

55 24.83% 26.12% 27.63% 29.39% 31.52% 33.58% 34.46% 35.84%

60 37.81% 38.83% 40.28%

0 1 2 3 4 5 6 7 8 9 10

20 10 10 9 9 8 8 7 7 6 6 6

25 10 10 9 9 8 8 7 7 6 6 6

30 10 10 9 9 8 8 7 7 6 6 6

35 10 9 9 8 8 7 7 7 6 6 6

40 9 9 9 8 8 7 7 6 6 6 5

45 9 9 8 8 7 7 7 6 6 6 5

50 8 8 8 7 7 7 6 6 6 5 5

55 7 6 6 6 5 5 5 5

60 5 5 4


ROIAGE CHILD

BEYAGE CHILD

AG

E P

AR

ENT

AG

E P

AR

ENT

AG

E P

AR

ENT


B. For PAR Product

The profitability of the best estimate scenario of the par product is acceptable with profit margin

ranging from 2.2% to 4.5% and ROI ranges from 13.2% to 25.6%.

0 1 2 3 4 5 6 7 8 9 10

20 2.19% 2.12% 2.30% 2.46% 2.58% 2.70% 2.80% 2.90% 3.00% 2.87% 2.79%

25 2.18% 2.11% 2.28% 2.45% 2.57% 2.69% 2.79% 2.89% 2.98% 2.86% 2.78%

30 2.25% 2.17% 2.34% 2.50% 2.62% 2.72% 2.82% 2.92% 3.01% 2.88% 2.79%

35 2.43% 2.34% 2.50% 2.63% 2.74% 2.84% 2.93% 3.01% 3.09% 2.95% 2.85%

40 2.74% 2.64% 2.77% 2.87% 2.96% 3.04% 3.11% 3.18% 3.23% 3.07% 2.96%

45 3.17% 3.04% 3.13% 3.21% 3.28% 3.34% 3.39% 3.43% 3.44% 3.25% 3.12%

50 3.72% 3.58% 3.64% 3.70% 3.74% 3.77% 3.79% 3.77% 3.74% 3.53% 3.37%

55 4.38% 4.40% 4.37% 4.33% 4.26% 4.19% 3.95% 3.75%

60 4.81% 4.53% 4.29%

0 1 2 3 4 5 6 7 8 9 10

20 13.18% 13.15% 13.63% 14.16% 14.68% 15.25% 15.90% 16.65% 17.55% 17.94% 18.54%

25 13.15% 13.12% 13.59% 14.12% 14.64% 15.20% 15.85% 16.60% 17.49% 17.89% 18.49%

30 13.24% 13.21% 13.68% 14.21% 14.71% 15.27% 15.92% 16.66% 17.55% 17.94% 18.53%

35 13.53% 13.48% 13.96% 14.46% 14.96% 15.53% 16.17% 16.92% 17.81% 18.16% 18.75%

40 14.05% 13.98% 14.46% 14.93% 15.44% 16.01% 16.66% 17.42% 18.27% 18.61% 19.20%

45 14.80% 14.71% 15.14% 15.63% 16.15% 16.74% 17.42% 18.19% 18.95% 19.29% 19.90%

50 15.78% 15.67% 16.14% 16.66% 17.22% 17.85% 18.55% 19.23% 19.98% 20.34% 20.96%

55 18.28% 18.93% 19.55% 20.19% 20.90% 21.70% 22.11% 22.78%

60 24.26% 24.80% 25.59%

0 1 2 3 4 5 6 7 8 9 10

20 13 12 11 11 10 9 9 8 7 7 6

25 13 12 12 11 10 9 9 8 7 7 6

30 13 12 11 11 10 9 9 8 7 7 6

35 12 12 11 10 10 9 8 8 7 7 6

40 11 11 11 10 9 9 8 8 7 7 6

45 11 10 10 9 9 8 8 7 7 6 6

50 10 10 9 9 8 8 7 7 6 6 6

55 8 7 7 7 6 6 6 5

60 5 5 5


ROIAGE CHILD

BEYAGE CHILD

AG

E P

AR

ENT

AG

E P

AR

ENT

AG

E P

AR

ENT


Appendix 5: Scenarios and Stress Test

Scenarios Test

We carry out sixteen scenarios test as stated below:





Scenario 3 Mortality claim increase to 70% that of the CSO1980 table. Other assumptions

keep unchanged as per best estimate scenario.

Scenario 4 Mortality claim fall to 30% that of the CSO1980 table. Other assumptions keep



scenario.


scenario.

Scenario 7 Commission and acquisition cost increase by 5.0%. Other assumptions keep


Scenario 8 Commission and acquisition cost increase by 10%. Other assumptions keep


Scenario 9 Maintenance cost increase by 5.0%. Other assumptions keep unchanged as per


Scenario 10 Maintenance cost increase by 10%. Other assumptions keep unchanged as per




scenario



scenario












Stress Test

Scenario 17 Investment return is 5%/year for the whole insurance period and Death Claim is







120% of the CSO1980 and lapse rates are 30%/year and maintenance cost


scenario


120% of the CSO1980 and lapse rates are 30%/year and acquisition cost increase

by 10%. Other assumptions keep unchanged as per best estimate scenario


Below are profit test results under deterministic model:

A. For the NON PAR PRODUCT

1. Scenario 1

2. Scenario 2

0 1 2 3 4 5 6 7 8 9 10

20 14.69% 14.62% 14.78% 14.90% 14.99% 15.04% 15.05% 14.97% 14.85% 14.15% 13.59%

25 14.71% 14.63% 14.79% 14.90% 14.99% 15.04% 15.04% 14.96% 14.83% 14.13% 13.57%

30 14.91% 14.82% 14.95% 15.06% 15.12% 15.15% 15.15% 15.05% 14.91% 14.19% 13.62%

35 15.35% 15.23% 15.33% 15.40% 15.44% 15.44% 15.41% 15.28% 15.12% 14.37% 13.77%

40 16.05% 15.88% 15.95% 15.98% 15.97% 15.93% 15.85% 15.69% 15.48% 14.69% 14.05%

45 17.04% 16.82% 16.83% 16.80% 16.74% 16.64% 16.49% 16.29% 16.01% 15.17% 14.47%

50 18.41% 18.13% 18.08% 17.99% 17.85% 17.67% 17.44% 17.17% 16.81% 15.89% 15.11%

55 19.63% 19.41% 19.14% 18.81% 18.43% 17.98% 16.96% 16.07%

60 19.60% 18.46% 17.42%

0 1 2 3 4 5 6 7 8 9 10

20 20.31% 20.91% 21.87% 22.97% 24.23% 25.71% 27.42% 28.89% 30.59% 31.75% 33.48%

25 20.25% 20.85% 21.81% 22.90% 24.16% 25.63% 27.35% 28.82% 30.51% 31.66% 33.39%

30 20.32% 20.93% 21.88% 22.97% 24.23% 25.70% 27.46% 28.92% 30.61% 31.75% 33.47%

35 20.60% 21.21% 22.16% 23.26% 24.52% 26.00% 27.77% 29.32% 31.00% 32.13% 33.85%

40 21.09% 21.71% 22.68% 23.80% 25.08% 26.59% 28.38% 30.08% 31.76% 32.89% 34.61%

45 21.80% 22.44% 23.44% 24.58% 25.90% 27.45% 29.27% 31.22% 32.91% 34.05% 35.77%

50 22.81% 23.49% 24.53% 25.73% 27.10% 28.71% 30.59% 32.86% 34.66% 35.81% 37.54%

55 27.50% 28.97% 30.66% 32.68% 35.13% 37.52% 38.74% 40.52%

60 41.74% 43.06% 44.86%

ROIAGE CHILD

AG

E P

AR

ENT

Profit MarginAGE CHILD

AG

E P

AR

ENT

0 1 2 3 4 5 6 7 8 9 10

20 6.05% 6.15% 6.47% 6.78% 7.07% 7.34% 7.58% 7.74% 7.89% 7.48% 7.25%

25 6.06% 6.15% 6.47% 6.77% 7.05% 7.32% 7.56% 7.71% 7.86% 7.45% 7.22%

30 6.28% 6.36% 6.65% 6.94% 7.20% 7.45% 7.68% 7.82% 7.94% 7.52% 7.27%

35 6.78% 6.83% 7.09% 7.34% 7.57% 7.79% 7.98% 8.09% 8.18% 7.73% 7.45%

40 7.60% 7.60% 7.81% 8.01% 8.20% 8.36% 8.50% 8.58% 8.61% 8.11% 7.77%

45 8.76% 8.70% 8.85% 8.99% 9.10% 9.18% 9.25% 9.28% 9.24% 8.66% 8.25%

50 10.37% 10.25% 10.33% 10.38% 10.40% 10.39% 10.37% 10.32% 10.17% 9.49% 8.98%

55 12.32% 12.24% 12.12% 11.98% 11.80% 11.55% 10.75% 10.09%

60 13.44% 12.49% 11.66%

0 1 2 3 4 5 6 7 8 9 10

20 14.77% 15.16% 15.84% 16.63% 17.53% 18.60% 19.82% 20.89% 22.15% 22.73% 23.77%

25 14.73% 15.12% 15.80% 16.58% 17.48% 18.54% 19.75% 20.82% 22.07% 22.64% 23.68%

30 14.86% 15.25% 15.92% 16.70% 17.59% 18.65% 19.89% 20.95% 22.19% 22.75% 23.78%

35 15.22% 15.61% 16.29% 17.06% 17.97% 19.02% 20.27% 21.38% 22.62% 23.16% 24.17%

40 15.83% 16.23% 16.92% 17.72% 18.64% 19.70% 20.97% 22.20% 23.43% 23.95% 24.94%

45 16.69% 17.12% 17.83% 18.65% 19.60% 20.69% 22.00% 23.42% 24.64% 25.14% 26.11%

50 17.90% 18.37% 19.14% 20.00% 20.99% 22.15% 23.53% 25.21% 26.46% 26.96% 27.91%

55 21.99% 23.08% 24.36% 25.88% 27.69% 29.40% 29.93% 30.90%

60 33.70% 34.34% 35.39%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT


3. Scenario 3

4. Scenario 4

0 1 2 3 4 5 6 7 8 9 10

20 9.70% 9.82% 10.10% 10.36% 10.59% 10.79% 10.95% 11.02% 11.07% 10.54% 10.17%

25 9.71% 9.83% 10.11% 10.36% 10.59% 10.78% 10.94% 11.01% 11.05% 10.52% 10.15%

30 9.85% 9.95% 10.22% 10.46% 10.68% 10.86% 11.01% 11.07% 11.10% 10.56% 10.19%

35 10.14% 10.23% 10.48% 10.70% 10.89% 11.05% 11.18% 11.23% 11.24% 10.69% 10.29%

40 10.62% 10.67% 10.89% 11.08% 11.24% 11.37% 11.48% 11.51% 11.49% 10.90% 10.48%

45 11.29% 11.31% 11.49% 11.64% 11.76% 11.84% 11.90% 11.91% 11.84% 11.22% 10.75%

50 12.24% 12.21% 12.34% 12.44% 12.50% 12.53% 12.53% 12.51% 12.37% 11.70% 11.17%

55 13.55% 13.55% 13.52% 13.45% 13.34% 13.15% 12.41% 11.81%

60 14.23% 13.41% 12.71%

0 1 2 3 4 5 6 7 8 9 10

20 17.03% 17.60% 18.42% 19.36% 20.44% 21.69% 23.13% 24.42% 25.91% 26.77% 28.15%

25 16.99% 17.56% 18.38% 19.32% 20.40% 21.65% 23.09% 24.38% 25.87% 26.72% 28.09%

30 17.04% 17.61% 18.43% 19.36% 20.44% 21.69% 23.17% 24.45% 25.93% 26.78% 28.14%

35 17.21% 17.78% 18.60% 19.54% 20.61% 21.86% 23.35% 24.69% 26.17% 27.01% 28.37%

40 17.50% 18.08% 18.90% 19.85% 20.93% 22.19% 23.69% 25.16% 26.62% 27.46% 28.82%

45 17.92% 18.51% 19.34% 20.30% 21.39% 22.66% 24.18% 25.84% 27.29% 28.14% 29.50%

50 18.53% 19.13% 19.98% 20.95% 22.06% 23.36% 24.91% 26.80% 28.30% 29.16% 30.52%

55 21.94% 23.09% 24.43% 26.04% 27.98% 29.89% 30.79% 32.17%

60 32.13% 33.12% 34.57%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT

0 1 2 3 4 5 6 7 8 9 10

20 11.04% 10.95% 11.15% 11.33% 11.48% 11.60% 11.69% 11.70% 11.68% 11.09% 10.67%

25 11.06% 10.96% 11.15% 11.32% 11.46% 11.58% 11.67% 11.67% 11.65% 11.06% 10.63%

30 11.34% 11.22% 11.40% 11.54% 11.66% 11.75% 11.82% 11.80% 11.76% 11.14% 10.70%

35 11.98% 11.83% 11.96% 12.06% 12.13% 12.18% 12.21% 12.16% 12.07% 11.41% 10.93%

40 13.03% 12.81% 12.88% 12.91% 12.92% 12.91% 12.88% 12.77% 12.61% 11.90% 11.35%

45 14.51% 14.22% 14.20% 14.15% 14.08% 13.98% 13.85% 13.66% 13.41% 12.61% 11.97%

50 16.55% 16.18% 16.07% 15.93% 15.75% 15.53% 15.27% 14.98% 14.60% 13.68% 12.91%

55 18.40% 18.09% 17.74% 17.33% 16.89% 16.38% 15.30% 14.35%

60 18.80% 17.53% 16.35%

0 1 2 3 4 5 6 7 8 9 10

20 18.34% 18.76% 19.61% 20.56% 21.66% 22.95% 24.44% 25.73% 27.21% 28.06% 29.45%

25 18.27% 18.69% 19.53% 20.48% 21.57% 22.85% 24.34% 25.62% 27.10% 27.94% 29.32%

30 18.41% 18.84% 19.67% 20.62% 21.71% 22.98% 24.51% 25.78% 27.24% 28.08% 29.44%

35 18.87% 19.31% 20.15% 21.10% 22.19% 23.48% 25.02% 26.38% 27.81% 28.63% 29.99%

40 19.68% 20.14% 20.99% 21.97% 23.10% 24.42% 26.01% 27.49% 28.93% 29.74% 31.08%

45 20.84% 21.33% 22.22% 23.25% 24.43% 25.81% 27.46% 29.19% 30.63% 31.43% 32.76%

50 22.49% 23.03% 24.01% 25.12% 26.40% 27.87% 29.61% 31.71% 33.25% 34.05% 35.38%

55 28.00% 29.42% 31.08% 33.04% 35.43% 37.67% 38.52% 39.84%

60 44.29% 45.25% 46.63%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT


5. Scenario 5

6. Scenario 6

0 1 2 3 4 5 6 7 8 9 10

20 8.56% 8.74% 9.27% 9.77% 10.24% 10.69% 11.10% 11.41% 11.71% 10.98% 10.58%

25 8.55% 8.73% 9.25% 9.75% 10.22% 10.67% 11.07% 11.39% 11.68% 10.95% 10.55%

30 8.76% 8.92% 9.42% 9.91% 10.36% 10.79% 11.19% 11.48% 11.76% 11.02% 10.60%

35 9.25% 9.38% 9.85% 10.30% 10.73% 11.13% 11.49% 11.76% 12.00% 11.23% 10.78%

40 10.05% 10.14% 10.57% 10.97% 11.35% 11.69% 12.00% 12.24% 12.43% 11.61% 11.12%

45 11.18% 11.22% 11.59% 11.93% 12.24% 12.52% 12.75% 12.94% 13.05% 12.18% 11.62%

50 12.75% 12.73% 13.04% 13.31% 13.53% 13.72% 13.86% 13.97% 13.98% 13.02% 12.36%

55 15.23% 15.35% 15.43% 15.47% 15.45% 15.36% 14.29% 13.49%

60 17.24% 16.05% 15.08%

0 1 2 3 4 5 6 7 8 9 10

20 17.10% 17.70% 18.79% 20.05% 21.53% 23.28% 25.30% 27.17% 29.38% 30.21% 31.98%

25 17.03% 17.64% 18.72% 19.98% 21.44% 23.19% 25.22% 27.08% 29.28% 30.10% 31.87%

30 17.14% 17.74% 18.82% 20.07% 21.53% 23.28% 25.35% 27.20% 29.39% 30.21% 31.96%

35 17.49% 18.09% 19.18% 20.43% 21.90% 23.64% 25.72% 27.66% 29.85% 30.66% 32.42%

40 18.10% 18.72% 19.82% 21.09% 22.58% 24.34% 26.44% 28.55% 30.74% 31.56% 33.32%

45 18.96% 19.60% 20.73% 22.03% 23.56% 25.35% 27.50% 29.89% 32.09% 32.94% 34.71%

50 20.19% 20.87% 22.04% 23.40% 24.98% 26.82% 29.05% 31.80% 34.12% 35.01% 36.77%

55 25.47% 27.13% 29.10% 31.48% 34.43% 37.44% 38.39% 40.18%

60 42.13% 43.27% 45.23%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT

0 1 2 3 4 5 6 7 8 9 10

20 7.29% 7.61% 8.39% 9.16% 9.89% 10.59% 11.26% 11.84% 12.40% 11.53% 11.13%

25 7.27% 7.58% 8.36% 9.13% 9.86% 10.56% 11.23% 11.81% 12.37% 11.50% 11.09%

30 7.45% 7.75% 8.52% 9.27% 9.99% 10.67% 11.34% 11.90% 12.44% 11.56% 11.14%

35 7.91% 8.19% 8.93% 9.65% 10.34% 11.00% 11.63% 12.18% 12.68% 11.77% 11.33%

40 8.70% 8.94% 9.63% 10.31% 10.95% 11.56% 12.15% 12.66% 13.11% 12.17% 11.67%

45 9.80% 9.99% 10.64% 11.25% 11.83% 12.38% 12.90% 13.36% 13.73% 12.74% 12.18%

50 11.33% 11.47% 12.06% 12.59% 13.10% 13.57% 14.00% 14.39% 14.66% 13.59% 12.95%

55 14.48% 14.90% 15.28% 15.60% 15.87% 16.04% 14.89% 14.12%

60 17.91% 16.67% 15.76%

0 1 2 3 4 5 6 7 8 9 10

20 16.68% 17.40% 18.80% 20.43% 22.33% 24.59% 27.28% 29.88% 32.98% 33.91% 36.19%

25 16.61% 17.32% 18.72% 20.34% 22.23% 24.48% 27.18% 29.77% 32.86% 33.78% 36.06%

30 16.71% 17.43% 18.81% 20.43% 22.32% 24.56% 27.31% 29.89% 32.97% 33.89% 36.16%

35 17.08% 17.80% 19.19% 20.81% 22.69% 24.94% 27.70% 30.39% 33.48% 34.38% 36.65%

40 17.74% 18.47% 19.87% 21.51% 23.40% 25.68% 28.47% 31.38% 34.45% 35.38% 37.67%

45 18.66% 19.42% 20.85% 22.50% 24.43% 26.76% 29.60% 32.86% 35.92% 36.89% 39.21%

50 19.98% 20.77% 22.24% 23.93% 25.92% 28.32% 31.26% 34.94% 38.11% 39.16% 41.53%

55 26.10% 28.22% 30.75% 33.87% 37.71% 41.70% 42.91% 45.43%

60 46.87% 48.39% 51.19%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT


7. Scenario 7

8. Scenario 8

0 1 2 3 4 5 6 7 8 9 10

20 10.37% 10.39% 10.63% 10.85% 11.03% 11.19% 11.32% 11.36% 11.37% 10.82% 10.42%

25 10.38% 10.39% 10.63% 10.85% 11.03% 11.18% 11.30% 11.34% 11.35% 10.79% 10.39%

30 10.60% 10.59% 10.81% 11.01% 11.17% 11.30% 11.42% 11.43% 11.43% 10.85% 10.44%

35 11.06% 11.03% 11.22% 11.38% 11.51% 11.62% 11.70% 11.69% 11.65% 11.05% 10.61%

40 11.82% 11.74% 11.89% 12.00% 12.08% 12.14% 12.18% 12.14% 12.05% 11.40% 10.91%

45 12.90% 12.77% 12.85% 12.90% 12.92% 12.91% 12.88% 12.79% 12.62% 11.91% 11.36%

50 14.40% 14.20% 14.21% 14.18% 14.12% 14.03% 13.91% 13.75% 13.49% 12.69% 12.04%

55 15.97% 15.83% 15.64% 15.39% 15.12% 14.77% 13.86% 13.08%

60 16.52% 15.48% 14.54%

0 1 2 3 4 5 6 7 8 9 10

20 17.67% 18.17% 19.00% 19.96% 21.04% 22.31% 23.78% 25.07% 26.56% 27.41% 28.79%

25 17.62% 18.12% 18.95% 19.90% 20.98% 22.24% 23.71% 24.99% 26.48% 27.32% 28.70%

30 17.72% 18.22% 19.04% 19.99% 21.07% 22.33% 23.83% 25.11% 26.58% 27.42% 28.79%

35 18.03% 18.53% 19.36% 20.31% 21.39% 22.66% 24.17% 25.52% 26.98% 27.81% 29.17%

40 18.57% 19.09% 19.93% 20.89% 21.99% 23.28% 24.83% 26.31% 27.75% 28.58% 29.93%

45 19.34% 19.89% 20.76% 21.73% 22.87% 24.20% 25.78% 27.48% 28.92% 29.75% 31.09%

50 20.45% 21.03% 21.93% 22.96% 24.15% 25.54% 27.20% 29.17% 30.69% 31.53% 32.87%

55 24.83% 26.12% 27.63% 29.39% 31.52% 33.58% 34.46% 35.84%

60 37.81% 38.83% 40.28%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT

0 1 2 3 4 5 6 7 8 9 10

20 9.10% 9.11% 9.39% 9.63% 9.85% 10.04% 10.18% 10.24% 10.26% 9.72% 9.32%

25 9.12% 9.12% 9.39% 9.63% 9.84% 10.02% 10.17% 10.22% 10.24% 9.69% 9.29%

30 9.33% 9.32% 9.56% 9.79% 9.98% 10.15% 10.28% 10.31% 10.32% 9.75% 9.34%

35 9.80% 9.75% 9.97% 10.16% 10.33% 10.46% 10.56% 10.57% 10.55% 9.95% 9.50%

40 10.56% 10.47% 10.64% 10.79% 10.91% 10.99% 11.04% 11.02% 10.94% 10.30% 9.81%

45 11.64% 11.49% 11.61% 11.69% 11.74% 11.75% 11.74% 11.67% 11.52% 10.82% 10.26%

50 13.13% 12.93% 12.97% 12.98% 12.94% 12.87% 12.77% 12.63% 12.38% 11.59% 10.93%

55 14.76% 14.64% 14.47% 14.26% 14.00% 13.66% 12.75% 11.97%

60 15.40% 14.37% 13.43%

0 1 2 3 4 5 6 7 8 9 10

20 16.31% 16.70% 17.42% 18.23% 19.17% 20.24% 21.45% 22.53% 23.76% 24.39% 25.41%

25 16.28% 16.67% 17.38% 18.19% 19.12% 20.19% 21.40% 22.46% 23.70% 24.32% 25.34%

30 16.38% 16.77% 17.48% 18.28% 19.21% 20.27% 21.51% 22.57% 23.80% 24.41% 25.42%

35 16.67% 17.07% 17.78% 18.59% 19.52% 20.58% 21.83% 22.94% 24.16% 24.76% 25.75%

40 17.18% 17.59% 18.31% 19.13% 20.08% 21.15% 22.42% 23.64% 24.85% 25.44% 26.41%

45 17.91% 18.33% 19.08% 19.93% 20.88% 21.98% 23.28% 24.68% 25.89% 26.45% 27.41%

50 18.95% 19.40% 20.19% 21.06% 22.06% 23.21% 24.57% 26.20% 27.43% 27.99% 28.94%

55 22.76% 23.84% 25.09% 26.57% 28.29% 29.92% 30.51% 31.47%

60 33.54% 34.22% 35.24%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT


9. Scenario 9

10. Scenario 10

0 1 2 3 4 5 6 7 8 9 10

20 10.11% 10.14% 10.39% 10.63% 10.83% 11.00% 11.14% 11.19% 11.22% 10.68% 10.29%

25 10.12% 10.15% 10.40% 10.62% 10.82% 10.99% 11.12% 11.17% 11.20% 10.65% 10.27%

30 10.34% 10.34% 10.57% 10.79% 10.96% 11.11% 11.24% 11.27% 11.28% 10.72% 10.32%

35 10.81% 10.78% 10.99% 11.17% 11.31% 11.43% 11.52% 11.53% 11.51% 10.91% 10.48%

40 11.58% 11.51% 11.66% 11.79% 11.89% 11.96% 12.00% 11.98% 11.90% 11.27% 10.79%

45 12.67% 12.54% 12.64% 12.70% 12.73% 12.73% 12.71% 12.63% 12.48% 11.78% 11.24%

50 14.18% 13.99% 14.01% 13.99% 13.94% 13.86% 13.75% 13.60% 13.35% 12.56% 11.93%

55 15.80% 15.66% 15.48% 15.24% 14.97% 14.63% 13.73% 12.97%

60 16.39% 15.36% 14.43%

0 1 2 3 4 5 6 7 8 9 10

20 17.45% 17.95% 18.78% 19.72% 20.80% 22.07% 23.52% 24.81% 26.30% 27.15% 28.53%

25 17.40% 17.90% 18.72% 19.67% 20.74% 22.00% 23.46% 24.74% 26.22% 27.07% 28.44%

30 17.50% 18.00% 18.82% 19.76% 20.83% 22.09% 23.58% 24.85% 26.33% 27.17% 28.53%

35 17.82% 18.32% 19.14% 20.09% 21.16% 22.42% 23.92% 25.27% 26.73% 27.56% 28.91%

40 18.36% 18.88% 19.72% 20.67% 21.77% 23.05% 24.58% 26.06% 27.50% 28.33% 29.67%

45 19.15% 19.69% 20.55% 21.52% 22.64% 23.96% 25.54% 27.23% 28.66% 29.49% 30.83%

50 20.27% 20.84% 21.74% 22.76% 23.94% 25.32% 26.96% 28.92% 30.43% 31.26% 32.61%

55 24.63% 25.91% 27.41% 29.15% 31.27% 33.31% 34.19% 35.57%

60 37.54% 38.55% 40.00%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT

0 1 2 3 4 5 6 7 8 9 10

20 9.84% 9.89% 10.16% 10.41% 10.62% 10.81% 10.96% 11.03% 11.07% 10.54% 10.17%

25 9.86% 9.90% 10.16% 10.40% 10.61% 10.79% 10.94% 11.01% 11.05% 10.52% 10.14%

30 10.08% 10.10% 10.34% 10.57% 10.76% 10.92% 11.06% 11.10% 11.13% 10.58% 10.19%

35 10.56% 10.54% 10.76% 10.95% 11.11% 11.24% 11.34% 11.37% 11.36% 10.78% 10.36%

40 11.33% 11.27% 11.44% 11.58% 11.69% 11.77% 11.83% 11.82% 11.75% 11.13% 10.67%

45 12.43% 12.32% 12.42% 12.49% 12.53% 12.55% 12.54% 12.48% 12.33% 11.65% 11.12%

50 13.96% 13.78% 13.81% 13.80% 13.76% 13.69% 13.58% 13.44% 13.21% 12.43% 11.81%

55 15.62% 15.49% 15.31% 15.09% 14.83% 14.50% 13.61% 12.85%

60 16.27% 15.24% 14.33%

0 1 2 3 4 5 6 7 8 9 10

20 17.23% 17.73% 18.55% 19.49% 20.57% 21.82% 23.27% 24.55% 26.05% 26.90% 28.28%

25 17.19% 17.68% 18.50% 19.44% 20.51% 21.76% 23.20% 24.48% 25.97% 26.82% 28.19%

30 17.29% 17.79% 18.60% 19.53% 20.60% 21.85% 23.33% 24.60% 26.08% 26.91% 28.28%

35 17.61% 18.11% 18.93% 19.86% 20.93% 22.18% 23.67% 25.01% 26.48% 27.31% 28.66%

40 18.16% 18.67% 19.51% 20.46% 21.54% 22.81% 24.33% 25.80% 27.25% 28.07% 29.42%

45 18.95% 19.49% 20.34% 21.31% 22.42% 23.73% 25.29% 26.98% 28.41% 29.23% 30.57%

50 20.08% 20.65% 21.54% 22.55% 23.72% 25.09% 26.72% 28.66% 30.18% 31.00% 32.34%

55 24.43% 25.70% 27.19% 28.92% 31.02% 33.05% 33.93% 35.30%

60 37.27% 38.28% 39.73%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT


11. Scenario 11

12. Scenario 12

0 1 2 3 4 5 6 7 8 9 10

20 14.03% 14.06% 14.27% 14.43% 14.56% 14.64% 14.69% 14.64% 14.55% 13.87% 13.34%

25 14.05% 14.08% 14.28% 14.44% 14.56% 14.64% 14.68% 14.63% 14.54% 13.86% 13.33%

30 14.18% 14.19% 14.38% 14.53% 14.64% 14.71% 14.75% 14.69% 14.59% 13.90% 13.36%

35 14.44% 14.44% 14.61% 14.74% 14.83% 14.89% 14.90% 14.83% 14.71% 14.01% 13.45%

40 14.87% 14.84% 14.98% 15.08% 15.15% 15.17% 15.17% 15.08% 14.93% 14.20% 13.62%

45 15.48% 15.41% 15.51% 15.58% 15.61% 15.59% 15.55% 15.43% 15.24% 14.48% 13.87%

50 16.32% 16.21% 16.27% 16.29% 16.27% 16.21% 16.11% 15.96% 15.71% 14.91% 14.25%

55 17.27% 17.20% 17.09% 16.92% 16.70% 16.41% 15.55% 14.82%

60 17.36% 16.45% 15.63%

0 1 2 3 4 5 6 7 8 9 10

20 19.65% 20.33% 21.29% 22.37% 23.61% 25.07% 26.76% 28.24% 29.93% 31.09% 32.81%

25 19.61% 20.29% 21.25% 22.32% 23.57% 25.02% 26.72% 28.20% 29.89% 31.03% 32.76%

30 19.64% 20.32% 21.27% 22.35% 23.59% 25.05% 26.78% 28.26% 29.94% 31.09% 32.80%

35 19.77% 20.46% 21.41% 22.49% 23.73% 25.19% 26.93% 28.49% 30.17% 31.31% 33.02%

40 20.02% 20.71% 21.67% 22.75% 24.01% 25.48% 27.24% 28.93% 30.61% 31.75% 33.46%

45 20.38% 21.08% 22.04% 23.14% 24.41% 25.90% 27.67% 29.57% 31.26% 32.41% 34.13%

50 20.92% 21.63% 22.60% 23.71% 25.00% 26.52% 28.32% 30.47% 32.23% 33.40% 35.13%

55 24.61% 25.93% 27.49% 29.34% 31.55% 33.77% 34.99% 36.76%

60 35.95% 37.27% 39.12%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT

0 1 2 3 4 5 6 7 8 9 10

20 5.36% 5.57% 5.94% 6.28% 6.61% 6.92% 7.20% 7.39% 7.57% 7.20% 6.99%

25 5.37% 5.57% 5.94% 6.28% 6.60% 6.91% 7.19% 7.38% 7.55% 7.18% 6.98%

30 5.51% 5.71% 6.06% 6.38% 6.70% 7.00% 7.27% 7.44% 7.61% 7.22% 7.01%

35 5.83% 6.01% 6.33% 6.64% 6.93% 7.21% 7.46% 7.62% 7.76% 7.36% 7.12%

40 6.36% 6.50% 6.79% 7.07% 7.33% 7.57% 7.79% 7.93% 8.03% 7.60% 7.33%

45 7.10% 7.20% 7.45% 7.69% 7.90% 8.09% 8.26% 8.38% 8.43% 7.95% 7.63%

50 8.15% 8.20% 8.40% 8.57% 8.73% 8.85% 8.96% 9.04% 9.03% 8.48% 8.10%

55 9.82% 9.90% 9.95% 9.97% 9.97% 9.90% 9.27% 8.80%

60 11.09% 10.38% 9.79%

0 1 2 3 4 5 6 7 8 9 10

20 14.14% 14.59% 15.27% 16.04% 16.94% 17.99% 19.19% 20.26% 21.51% 22.09% 23.14%

25 14.11% 14.57% 15.24% 16.01% 16.90% 17.95% 19.15% 20.22% 21.47% 22.04% 23.09%

30 14.19% 14.64% 15.31% 16.08% 16.96% 18.01% 19.24% 20.30% 21.54% 22.11% 23.15%

35 14.40% 14.86% 15.52% 16.29% 17.18% 18.22% 19.45% 20.57% 21.80% 22.36% 23.39%

40 14.76% 15.22% 15.89% 16.66% 17.55% 18.61% 19.85% 21.06% 22.28% 22.84% 23.86%

45 15.26% 15.73% 16.41% 17.19% 18.10% 19.16% 20.41% 21.78% 23.00% 23.56% 24.56%

50 15.97% 16.45% 17.15% 17.96% 18.89% 19.97% 21.25% 22.81% 24.08% 24.63% 25.61%

55 19.08% 20.05% 21.17% 22.51% 24.14% 25.75% 26.32% 27.31%

60 28.09% 28.73% 29.78%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT


13. Scenario 13

14. Scenario14

0 1 2 3 4 5 6 7 8 9 10

20 12.02% 12.16% 12.64% 13.10% 13.52% 13.90% 14.23% 14.48% 14.70% 13.87% 13.36%

25 12.02% 12.15% 12.64% 13.09% 13.51% 13.88% 14.21% 14.46% 14.67% 13.85% 13.33%

30 12.22% 12.34% 12.80% 13.24% 13.65% 14.00% 14.32% 14.55% 14.75% 13.91% 13.38%

35 12.69% 12.77% 13.21% 13.62% 13.99% 14.32% 14.61% 14.81% 14.98% 14.11% 13.55%

40 13.45% 13.49% 13.89% 14.25% 14.57% 14.85% 15.09% 15.26% 15.38% 14.47% 13.87%

45 14.52% 14.51% 14.85% 15.16% 15.41% 15.63% 15.80% 15.92% 15.96% 15.00% 14.33%

50 16.02% 15.95% 16.22% 16.45% 16.63% 16.76% 16.85% 16.89% 16.84% 15.80% 15.03%

55 18.25% 18.34% 18.38% 18.36% 18.29% 18.12% 16.99% 16.10%

60 19.88% 18.64% 17.61%

0 1 2 3 4 5 6 7 8 9 10

20 19.54% 20.24% 21.47% 22.89% 24.55% 26.48% 28.73% 30.82% 33.28% 34.46% 36.65%

25 19.47% 20.17% 21.40% 22.81% 24.46% 26.39% 28.64% 30.72% 33.18% 34.35% 36.53%

30 19.56% 20.26% 21.47% 22.88% 24.53% 26.46% 28.76% 30.84% 33.28% 34.45% 36.62%

35 19.87% 20.57% 21.79% 23.21% 24.86% 26.79% 29.11% 31.29% 33.73% 34.90% 37.05%

40 20.43% 21.15% 22.39% 23.82% 25.49% 27.44% 29.79% 32.16% 34.61% 35.79% 37.93%

45 21.24% 21.98% 23.24% 24.71% 26.40% 28.39% 30.79% 33.48% 35.95% 37.16% 39.27%

50 22.39% 23.17% 24.48% 25.99% 27.72% 29.78% 32.27% 35.35% 37.96% 39.17% 41.30%

55 27.94% 29.78% 31.97% 34.62% 37.90% 41.18% 42.48% 44.70%

60 45.84% 47.35% 49.76%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT

0 1 2 3 4 5 6 7 8 9 10

20 10.11% 10.41% 11.17% 11.91% 12.61% 13.28% 13.92% 14.46% 14.97% 14.04% 13.57%

25 10.09% 10.38% 11.15% 11.88% 12.58% 13.25% 13.89% 14.44% 14.94% 14.01% 13.53%

30 10.28% 10.55% 11.30% 12.02% 12.71% 13.37% 13.99% 14.52% 15.01% 14.07% 13.58%

35 10.73% 10.98% 11.70% 12.39% 13.05% 13.68% 14.27% 14.78% 15.24% 14.27% 13.76%

40 11.48% 11.69% 12.38% 13.02% 13.63% 14.22% 14.77% 15.24% 15.64% 14.65% 14.09%

45 12.55% 12.71% 13.33% 13.92% 14.47% 15.00% 15.48% 15.90% 16.23% 15.19% 14.57%

50 14.02% 14.13% 14.68% 15.20% 15.69% 16.13% 16.53% 16.87% 17.11% 16.00% 15.30%

55 17.00% 17.41% 17.76% 18.06% 18.28% 18.41% 17.23% 16.41%

60 20.19% 18.92% 17.97%

0 1 2 3 4 5 6 7 8 9 10

20 18.95% 19.77% 21.31% 23.07% 25.14% 27.61% 30.55% 33.38% 36.69% 37.98% 40.70%

25 18.88% 19.69% 21.22% 22.98% 25.04% 27.50% 30.44% 33.27% 36.57% 37.86% 40.57%

30 18.97% 19.78% 21.30% 23.06% 25.10% 27.56% 30.57% 33.38% 36.68% 37.96% 40.66%

35 19.30% 20.12% 21.65% 23.40% 25.45% 27.91% 30.93% 33.88% 37.16% 38.44% 41.15%

40 19.92% 20.75% 22.29% 24.05% 26.12% 28.62% 31.67% 34.85% 38.12% 39.43% 42.16%

45 20.80% 21.65% 23.20% 24.99% 27.10% 29.64% 32.76% 36.29% 39.57% 40.93% 43.70%

50 22.05% 22.93% 24.51% 26.35% 28.52% 31.14% 34.34% 38.29% 41.75% 43.18% 46.01%

55 28.45% 30.74% 33.50% 36.87% 40.99% 45.32% 46.93% 49.92%

60 50.51% 52.43% 55.73%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT


15. Scenario15

16. Scenario16

0 1 2 3 4 5 6 7 8 9 10

20 10.11% 10.41% 11.17% 11.91% 12.61% 13.28% 13.92% 14.46% 14.97% 14.04% 13.57%

25 10.09% 10.38% 11.15% 11.88% 12.58% 13.25% 13.89% 14.44% 14.94% 14.01% 13.53%

30 10.28% 10.55% 11.30% 12.02% 12.71% 13.37% 13.99% 14.52% 15.01% 14.07% 13.58%

35 10.73% 10.98% 11.70% 12.39% 13.05% 13.68% 14.27% 14.78% 15.24% 14.27% 13.76%

40 11.48% 11.69% 12.38% 13.02% 13.63% 14.22% 14.77% 15.24% 15.64% 14.65% 14.09%

45 12.55% 12.71% 13.33% 13.92% 14.47% 15.00% 15.48% 15.90% 16.23% 15.19% 14.57%

50 14.02% 14.13% 14.68% 15.20% 15.69% 16.13% 16.53% 16.87% 17.11% 16.00% 15.30%

55 17.00% 17.41% 17.76% 18.06% 18.28% 18.41% 17.23% 16.41%

60 20.19% 18.92% 17.97%

0 1 2 3 4 5 6 7 8 9 10

20 18.95% 19.77% 21.31% 23.07% 25.14% 27.61% 30.55% 33.38% 36.69% 37.98% 40.70%

25 18.88% 19.69% 21.22% 22.98% 25.04% 27.50% 30.44% 33.27% 36.57% 37.86% 40.57%

30 18.97% 19.78% 21.30% 23.06% 25.10% 27.56% 30.57% 33.38% 36.68% 37.96% 40.66%

35 19.30% 20.12% 21.65% 23.40% 25.45% 27.91% 30.93% 33.88% 37.16% 38.44% 41.15%

40 19.92% 20.75% 22.29% 24.05% 26.12% 28.62% 31.67% 34.85% 38.12% 39.43% 42.16%

45 20.80% 21.65% 23.20% 24.99% 27.10% 29.64% 32.76% 36.29% 39.57% 40.93% 43.70%

50 22.05% 22.93% 24.51% 26.35% 28.52% 31.14% 34.34% 38.29% 41.75% 43.18% 46.01%

55 28.45% 30.74% 33.50% 36.87% 40.99% 45.32% 46.93% 49.92%

60 50.51% 52.43% 55.73%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT

0 1 2 3 4 5 6 7 8 9 10

20 4.47% 4.82% 5.61% 6.39% 7.16% 7.90% 8.61% 9.22% 9.82% 9.01% 8.68%

25 4.44% 4.78% 5.57% 6.36% 7.12% 7.86% 8.57% 9.18% 9.78% 8.97% 8.65%

30 4.62% 4.95% 5.73% 6.50% 7.25% 7.98% 8.68% 9.28% 9.86% 9.04% 8.70%

35 5.10% 5.40% 6.16% 6.90% 7.62% 8.32% 8.99% 9.57% 10.11% 9.27% 8.90%

40 5.91% 6.18% 6.89% 7.59% 8.27% 8.91% 9.53% 10.07% 10.57% 9.68% 9.26%

45 7.05% 7.27% 7.93% 8.57% 9.18% 9.76% 10.31% 10.81% 11.23% 10.28% 9.79%

50 8.64% 8.81% 9.41% 9.98% 10.51% 11.00% 11.46% 11.90% 12.20% 11.18% 10.59%

55 11.96% 12.40% 12.79% 13.15% 13.45% 13.66% 12.54% 11.82%

60 15.63% 14.42% 13.54%

0 1 2 3 4 5 6 7 8 9 10

20 14.26% 14.88% 16.13% 17.60% 19.33% 21.39% 23.83% 26.19% 29.02% 29.57% 31.45%

25 14.20% 14.81% 16.06% 17.51% 19.24% 21.29% 23.72% 26.08% 28.90% 29.44% 31.32%

30 14.32% 14.94% 16.18% 17.63% 19.35% 21.39% 23.87% 26.21% 29.02% 29.56% 31.42%

35 14.73% 15.34% 16.59% 18.04% 19.76% 21.80% 24.29% 26.74% 29.54% 30.08% 31.93%

40 15.44% 16.07% 17.32% 18.80% 20.54% 22.59% 25.11% 27.75% 30.56% 31.12% 32.96%

45 16.43% 17.08% 18.37% 19.87% 21.64% 23.73% 26.31% 29.25% 32.09% 32.67% 34.53%

50 17.82% 18.51% 19.85% 21.41% 23.22% 25.38% 28.04% 31.39% 34.34% 34.97% 36.88%

55 23.68% 25.60% 27.91% 30.75% 34.32% 37.95% 38.75% 40.79%

60 43.15% 44.25% 46.55%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT


17. Scenario17

18. Scenario18

0 1 2 3 4 5 6 7 8 9 10

20 0.01% 1.07% 2.56% 4.03% 5.51% 6.98% 8.41% 9.73% 11.04% 10.16% 10.06%

25 0.01% 1.08% 2.56% 4.03% 5.50% 6.97% 8.40% 9.72% 11.03% 10.15% 10.04%

30 0.10% 1.15% 2.63% 4.09% 5.56% 7.02% 8.45% 9.77% 11.06% 10.18% 10.07%

35 0.27% 1.31% 2.77% 4.22% 5.68% 7.13% 8.56% 9.87% 11.16% 10.28% 10.16%

40 0.54% 1.55% 3.00% 4.43% 5.88% 7.32% 8.73% 10.05% 11.32% 10.45% 10.32%

45 0.93% 1.89% 3.32% 4.73% 6.16% 7.58% 8.97% 10.30% 11.54% 10.69% 10.56%

50 1.51% 2.41% 3.81% 5.19% 6.58% 7.97% 9.33% 10.67% 11.88% 11.06% 10.91%

55 5.82% 7.17% 8.53% 9.86% 11.16% 12.37% 11.59% 11.45%

60 13.04% 12.33% 12.18%

0 1 2 3 4 5 6 7 8 9 10

20 10.01% 11.35% 13.50% 16.02% 19.08% 22.85% 27.42% 32.21% 38.07% 39.75% 44.33%

25 10.01% 11.35% 13.50% 16.01% 19.06% 22.83% 27.41% 32.20% 38.05% 39.72% 44.29%

30 10.11% 11.44% 13.56% 16.06% 19.10% 22.85% 27.49% 32.27% 38.11% 39.78% 44.34%

35 10.31% 11.61% 13.71% 16.19% 19.20% 22.92% 27.53% 32.43% 38.26% 39.95% 44.52%

40 10.61% 11.88% 13.95% 16.39% 19.36% 23.04% 27.60% 32.70% 38.50% 40.25% 44.85%

45 11.02% 12.25% 14.28% 16.67% 19.58% 23.20% 27.69% 33.08% 38.84% 40.69% 45.32%

50 11.62% 12.79% 14.77% 17.11% 19.95% 23.48% 27.87% 33.53% 39.37% 41.34% 46.04%

55 17.74% 20.50% 23.93% 28.20% 33.69% 40.12% 42.30% 47.12%

60 41.17% 43.63% 48.61%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT

0 1 2 3 4 5 6 7 8 9 10

20 -0.66% 0.59% 2.12% 3.63% 5.14% 6.65% 8.11% 9.47% 10.80% 9.96% 9.88%

25 -0.63% 0.61% 2.14% 3.64% 5.15% 6.66% 8.12% 9.48% 10.81% 9.96% 9.87%

30 -0.55% 0.67% 2.19% 3.69% 5.19% 6.69% 8.16% 9.51% 10.84% 9.98% 9.89%

35 -0.46% 0.75% 2.27% 3.76% 5.25% 6.75% 8.22% 9.57% 10.89% 10.04% 9.95%

40 -0.34% 0.85% 2.35% 3.84% 5.33% 6.82% 8.28% 9.65% 10.96% 10.13% 10.05%

45 -0.16% 0.98% 2.47% 3.95% 5.43% 6.91% 8.37% 9.76% 11.05% 10.26% 10.18%

50 0.13% 1.21% 2.68% 4.14% 5.60% 7.06% 8.52% 9.93% 11.21% 10.46% 10.39%

55 4.38% 5.82% 7.26% 8.70% 10.10% 11.41% 10.74% 10.69%

60 11.68% 11.11% 11.10%

0 1 2 3 4 5 6 7 8 9 10

20 9.25% 10.73% 12.86% 15.34% 18.35% 22.06% 26.58% 31.32% 37.12% 38.78% 43.29%

25 9.28% 10.76% 12.88% 15.36% 18.37% 22.08% 26.62% 31.36% 37.16% 38.80% 43.31%

30 9.37% 10.83% 12.94% 15.40% 18.39% 22.09% 26.68% 31.41% 37.20% 38.84% 43.34%

35 9.49% 10.91% 12.99% 15.42% 18.37% 22.03% 26.58% 31.42% 37.18% 38.84% 43.33%

40 9.63% 11.00% 13.03% 15.42% 18.31% 21.89% 26.36% 31.36% 37.06% 38.77% 43.27%

45 9.82% 11.13% 13.09% 15.40% 18.21% 21.68% 26.05% 31.25% 36.87% 38.65% 43.15%

50 10.14% 11.35% 13.23% 15.46% 18.15% 21.48% 25.70% 31.05% 36.66% 38.52% 43.03%

55 15.54% 18.08% 21.23% 25.22% 30.29% 36.26% 38.26% 42.77%

60 35.83% 37.99% 42.49%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT


19. Scenario19

20. Scenario 20

0 1 2 3 4 5 6 7 8 9 10

20 -1.17% 0.11% 1.67% 3.21% 4.75% 6.29% 7.79% 9.17% 10.53% 9.71% 9.66%

25 -1.14% 0.13% 1.69% 3.23% 4.76% 6.30% 7.80% 9.18% 10.53% 9.71% 9.65%

30 -1.06% 0.20% 1.75% 3.28% 4.81% 6.34% 7.84% 9.21% 10.56% 9.74% 9.68%

35 -0.95% 0.28% 1.83% 3.35% 4.87% 6.39% 7.89% 9.27% 10.62% 9.80% 9.74%

40 -0.81% 0.39% 1.92% 3.44% 4.95% 6.47% 7.96% 9.36% 10.69% 9.89% 9.83%

45 -0.62% 0.54% 2.06% 3.56% 5.06% 6.57% 8.06% 9.47% 10.79% 10.02% 9.97%

50 -0.29% 0.81% 2.29% 3.77% 5.25% 6.74% 8.22% 9.65% 10.96% 10.23% 10.19%

55 4.05% 5.50% 6.96% 8.41% 9.83% 11.17% 10.51% 10.49%

60 11.46% 10.90% 10.91%

0 1 2 3 4 5 6 7 8 9 10

20 8.67% 10.13% 12.23% 14.69% 17.66% 21.32% 25.79% 30.50% 36.25% 37.88% 42.34%

25 8.71% 10.16% 12.26% 14.71% 17.68% 21.34% 25.83% 30.53% 36.28% 37.90% 42.36%

30 8.81% 10.24% 12.32% 14.76% 17.70% 21.35% 25.89% 30.59% 36.33% 37.94% 42.39%

35 8.95% 10.34% 12.39% 14.80% 17.71% 21.30% 25.81% 30.60% 36.31% 37.94% 42.39%

40 9.12% 10.46% 12.46% 14.82% 17.67% 21.19% 25.62% 30.57% 36.22% 37.90% 42.35%

45 9.35% 10.62% 12.56% 14.84% 17.61% 21.03% 25.35% 30.49% 36.05% 37.80% 42.25%

50 9.70% 10.89% 12.75% 14.95% 17.60% 20.88% 25.05% 30.33% 35.88% 37.71% 42.16%

55 15.09% 17.59% 20.69% 24.62% 29.64% 35.53% 37.50% 41.96%

60 35.17% 37.30% 41.74%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT

0 1 2 3 4 5 6 7 8 9 10

20 -3.71% -2.43% -0.78% 0.86% 2.50% 4.11% 5.70% 7.18% 8.61% 7.86% 7.86%

25 -3.68% -2.40% -0.76% 0.88% 2.51% 4.12% 5.71% 7.18% 8.61% 7.86% 7.86%

30 -3.60% -2.34% -0.70% 0.93% 2.55% 4.16% 5.75% 7.22% 8.64% 7.88% 7.88%

35 -3.50% -2.26% -0.63% 0.99% 2.61% 4.21% 5.80% 7.28% 8.69% 7.94% 7.94%

40 -3.38% -2.16% -0.54% 1.07% 2.69% 4.28% 5.86% 7.36% 8.76% 8.03% 8.03%

45 -3.20% -2.03% -0.42% 1.18% 2.78% 4.37% 5.94% 7.46% 8.85% 8.15% 8.16%

50 -2.90% -1.79% -0.21% 1.37% 2.96% 4.52% 6.08% 7.62% 9.01% 8.35% 8.37%

55 1.61% 3.17% 4.71% 6.25% 7.77% 9.20% 8.62% 8.66%

60 9.46% 8.98% 9.06%

0 1 2 3 4 5 6 7 8 9 10

20 6.17% 7.30% 9.06% 11.13% 13.59% 16.56% 20.18% 24.11% 28.75% 29.53% 32.58%

25 6.21% 7.34% 9.09% 11.15% 13.61% 16.57% 20.21% 24.14% 28.77% 29.55% 32.59%

30 6.31% 7.42% 9.16% 11.21% 13.65% 16.60% 20.26% 24.19% 28.81% 29.59% 32.63%

35 6.46% 7.54% 9.26% 11.27% 13.70% 16.61% 20.23% 24.22% 28.82% 29.61% 32.65%

40 6.66% 7.70% 9.37% 11.35% 13.72% 16.58% 20.14% 24.22% 28.77% 29.62% 32.67%

45 6.91% 7.90% 9.52% 11.44% 13.75% 16.53% 19.99% 24.19% 28.68% 29.60% 32.67%

50 7.29% 8.21% 9.77% 11.61% 13.84% 16.52% 19.85% 24.12% 28.60% 29.62% 32.70%

55 11.82% 13.94% 16.49% 19.65% 23.69% 28.41% 29.57% 32.69%

60 28.21% 29.55% 32.70%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT


B. For the PAR PRODUCT.

1. Scenario 1

2. Scenario 2

0 1 2 3 4 5 6 7 8 9 10

20 3.50% 3.42% 3.55% 3.67% 3.78% 3.87% 3.95% 4.03% 4.05% 3.87% 3.75%

25 3.49% 3.41% 3.54% 3.66% 3.77% 3.86% 3.94% 4.01% 4.04% 3.86% 3.74%

30 3.55% 3.47% 3.60% 3.71% 3.81% 3.90% 3.97% 4.04% 4.06% 3.88% 3.75%

35 3.72% 3.62% 3.73% 3.84% 3.93% 4.00% 4.07% 4.12% 4.13% 3.94% 3.81%

40 3.99% 3.87% 3.97% 4.06% 4.13% 4.20% 4.25% 4.27% 4.26% 4.06% 3.92%

45 4.37% 4.24% 4.32% 4.38% 4.44% 4.48% 4.50% 4.48% 4.45% 4.24% 4.07%

50 4.89% 4.74% 4.79% 4.84% 4.87% 4.87% 4.84% 4.79% 4.73% 4.50% 4.31%

55 5.48% 5.45% 5.40% 5.34% 5.26% 5.16% 4.90% 4.67%

60 5.75% 5.45% 5.16%

0 1 2 3 4 5 6 7 8 9 10

20 14.94% 14.94% 15.45% 16.01% 16.62% 17.32% 18.11% 19.03% 19.91% 20.44% 21.26%

25 14.90% 14.91% 15.41% 15.97% 16.58% 17.27% 18.05% 18.97% 19.86% 20.38% 21.20%

30 14.99% 14.99% 15.49% 16.04% 16.65% 17.33% 18.12% 19.03% 19.91% 20.43% 21.24%

35 15.26% 15.23% 15.73% 16.29% 16.90% 17.59% 18.37% 19.27% 20.13% 20.65% 21.46%

40 15.72% 15.68% 16.19% 16.75% 17.37% 18.07% 18.87% 19.71% 20.58% 21.10% 21.93%

45 16.40% 16.34% 16.87% 17.45% 18.09% 18.82% 19.61% 20.38% 21.27% 21.81% 22.65%

50 17.38% 17.30% 17.86% 18.48% 19.17% 19.89% 20.60% 21.39% 22.31% 22.87% 23.74%

55 20.10% 20.74% 21.44% 22.21% 23.07% 24.06% 24.69% 25.64%

60 26.68% 27.46% 28.36%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT

0 1 2 3 4 5 6 7 8 9 10

20 0.88% 0.83% 1.01% 1.19% 1.37% 1.53% 1.66% 1.78% 1.91% 1.84% 1.83%

25 0.87% 0.82% 1.00% 1.18% 1.35% 1.52% 1.65% 1.77% 1.89% 1.82% 1.82%

30 0.94% 0.88% 1.06% 1.23% 1.40% 1.56% 1.68% 1.80% 1.92% 1.84% 1.83%

35 1.13% 1.06% 1.23% 1.39% 1.54% 1.68% 1.79% 1.90% 2.00% 1.92% 1.89%

40 1.46% 1.37% 1.52% 1.66% 1.79% 1.89% 1.99% 2.08% 2.17% 2.07% 2.01%

45 1.92% 1.81% 1.94% 2.05% 2.13% 2.21% 2.28% 2.34% 2.41% 2.28% 2.18%

50 2.55% 2.42% 2.50% 2.56% 2.61% 2.66% 2.70% 2.73% 2.74% 2.56% 2.44%

55 3.29% 3.31% 3.32% 3.32% 3.27% 3.22% 3.01% 2.84%

60 3.88% 3.62% 3.40%

0 1 2 3 4 5 6 7 8 9 10

20 11.33% 11.27% 11.66% 12.08% 12.55% 13.09% 13.60% 14.20% 14.90% 15.18% 15.75%

25 11.31% 11.25% 11.62% 12.04% 12.51% 13.04% 13.56% 14.15% 14.85% 15.12% 15.69%

30 11.41% 11.34% 11.72% 12.13% 12.60% 13.12% 13.63% 14.22% 14.91% 15.18% 15.74%

35 11.70% 11.63% 12.00% 12.42% 12.88% 13.38% 13.89% 14.47% 15.17% 15.44% 15.96%

40 12.23% 12.13% 12.52% 12.94% 13.41% 13.86% 14.37% 14.97% 15.67% 15.94% 16.40%

45 12.99% 12.88% 13.28% 13.72% 14.13% 14.60% 15.12% 15.72% 16.44% 16.69% 17.07%

50 14.10% 13.97% 14.35% 14.76% 15.21% 15.70% 16.25% 16.88% 17.56% 17.73% 18.11%

55 16.39% 16.90% 17.47% 18.09% 18.64% 19.26% 19.46% 19.88%

60 21.79% 22.09% 22.59%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT


3. Scenario 3

4. Scenario 4

0 1 2 3 4 5 6 7 8 9 10

20 1.89% 1.87% 2.06% 2.24% 2.40% 2.53% 2.65% 2.76% 2.87% 2.76% 2.69%

25 1.88% 1.87% 2.06% 2.24% 2.40% 2.52% 2.64% 2.75% 2.86% 2.76% 2.68%

30 1.93% 1.91% 2.09% 2.27% 2.42% 2.55% 2.66% 2.77% 2.87% 2.77% 2.69%

35 2.04% 2.01% 2.19% 2.36% 2.50% 2.62% 2.72% 2.83% 2.92% 2.81% 2.73%

40 2.24% 2.20% 2.36% 2.52% 2.63% 2.74% 2.84% 2.93% 3.01% 2.88% 2.79%

45 2.51% 2.46% 2.61% 2.73% 2.83% 2.92% 3.00% 3.08% 3.15% 2.99% 2.89%

50 2.89% 2.82% 2.93% 3.03% 3.11% 3.18% 3.24% 3.30% 3.33% 3.16% 3.04%

55 3.45% 3.51% 3.56% 3.60% 3.62% 3.60% 3.41% 3.27%

60 3.96% 3.76% 3.59%

0 1 2 3 4 5 6 7 8 9 10

20 12.67% 12.72% 13.19% 13.72% 14.27% 14.84% 15.48% 16.22% 17.10% 17.55% 18.14%

25 12.66% 12.70% 13.17% 13.69% 14.25% 14.81% 15.45% 16.19% 17.06% 17.52% 18.11%

30 12.71% 12.76% 13.23% 13.74% 14.29% 14.85% 15.49% 16.22% 17.10% 17.55% 18.14%

35 12.88% 12.92% 13.39% 13.91% 14.44% 15.00% 15.63% 16.37% 17.24% 17.68% 18.26%

40 13.18% 13.21% 13.68% 14.21% 14.71% 15.27% 15.91% 16.65% 17.53% 17.93% 18.52%

45 13.62% 13.63% 14.12% 14.61% 15.11% 15.68% 16.33% 17.08% 17.96% 18.31% 18.91%

50 14.23% 14.23% 14.70% 15.17% 15.70% 16.28% 16.95% 17.71% 18.52% 18.88% 19.49%

55 16.03% 16.59% 17.21% 17.92% 18.68% 19.42% 19.82% 20.45%

60 20.70% 21.16% 21.86%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT

0 1 2 3 4 5 6 7 8 9 10

20 2.48% 2.37% 2.53% 2.66% 2.77% 2.87% 2.96% 3.05% 3.13% 2.98% 2.89%

25 2.47% 2.35% 2.51% 2.64% 2.75% 2.85% 2.94% 3.03% 3.11% 2.96% 2.87%

30 2.56% 2.44% 2.59% 2.71% 2.81% 2.90% 2.99% 3.07% 3.14% 2.99% 2.89%

35 2.81% 2.67% 2.80% 2.89% 2.98% 3.06% 3.13% 3.20% 3.25% 3.08% 2.97%

40 3.22% 3.06% 3.14% 3.22% 3.29% 3.34% 3.39% 3.44% 3.44% 3.26% 3.13%

45 3.77% 3.59% 3.65% 3.69% 3.73% 3.76% 3.77% 3.76% 3.72% 3.51% 3.36%

50 4.53% 4.32% 4.35% 4.36% 4.36% 4.33% 4.28% 4.22% 4.15% 3.90% 3.70%

55 5.27% 5.20% 5.12% 5.02% 4.91% 4.79% 4.49% 4.23%

60 5.65% 5.27% 4.92%

0 1 2 3 4 5 6 7 8 9 10

20 13.72% 13.60% 14.09% 14.58% 15.10% 15.68% 16.33% 17.10% 18.00% 18.35% 18.95%

25 13.67% 13.55% 14.03% 14.53% 15.04% 15.61% 16.26% 17.02% 17.93% 18.27% 18.87%

30 13.80% 13.68% 14.16% 14.64% 15.14% 15.71% 16.36% 17.11% 18.00% 18.34% 18.94%

35 14.21% 14.07% 14.53% 15.00% 15.51% 16.08% 16.73% 17.48% 18.33% 18.66% 19.25%

40 14.94% 14.77% 15.20% 15.68% 16.20% 16.79% 17.45% 18.23% 18.98% 19.31% 19.91%

45 15.96% 15.76% 16.22% 16.72% 17.27% 17.89% 18.58% 19.25% 19.99% 20.33% 20.94%

50 17.46% 17.23% 17.74% 18.30% 18.91% 19.51% 20.11% 20.78% 21.55% 21.92% 22.55%

55 20.70% 21.30% 21.95% 22.64% 23.41% 24.27% 24.71% 25.42%

60 28.50% 28.88% 29.41%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT


5. Scenario 5

6. Scenario 6

0 1 2 3 4 5 6 7 8 9 10

20 1.29% 1.30% 1.59% 1.87% 2.14% 2.40% 2.64% 2.84% 3.03% 2.88% 2.84%

25 1.28% 1.29% 1.57% 1.85% 2.12% 2.39% 2.63% 2.82% 3.01% 2.87% 2.83%

30 1.35% 1.35% 1.63% 1.91% 2.17% 2.43% 2.66% 2.85% 3.04% 2.89% 2.84%

35 1.53% 1.52% 1.79% 2.05% 2.31% 2.55% 2.77% 2.95% 3.12% 2.96% 2.91%

40 1.85% 1.82% 2.08% 2.32% 2.55% 2.78% 2.95% 3.12% 3.27% 3.10% 3.03%

45 2.30% 2.25% 2.48% 2.70% 2.91% 3.08% 3.23% 3.37% 3.50% 3.30% 3.21%

50 2.92% 2.85% 3.05% 3.24% 3.39% 3.51% 3.63% 3.73% 3.83% 3.61% 3.48%

55 3.94% 4.05% 4.14% 4.22% 4.28% 4.33% 4.07% 3.88%

60 4.98% 4.66% 4.41%

0 1 2 3 4 5 6 7 8 9 10

20 12.04% 12.09% 12.72% 13.42% 14.22% 15.13% 16.13% 17.18% 18.41% 18.86% 19.81%

25 12.01% 12.06% 12.68% 13.38% 14.17% 15.08% 16.08% 17.12% 18.35% 18.79% 19.74%

30 12.11% 12.16% 12.77% 13.47% 14.25% 15.16% 16.15% 17.19% 18.41% 18.85% 19.79%

35 12.41% 12.44% 13.06% 13.76% 14.55% 15.45% 16.42% 17.45% 18.68% 19.11% 20.06%

40 12.95% 12.96% 13.59% 14.30% 15.10% 16.03% 16.93% 17.97% 19.21% 19.65% 20.62%

45 13.74% 13.73% 14.38% 15.11% 15.94% 16.79% 17.70% 18.76% 20.02% 20.49% 21.48%

50 14.87% 14.84% 15.53% 16.31% 17.08% 17.91% 18.85% 19.95% 21.25% 21.76% 22.80%

55 17.98% 18.79% 19.70% 20.73% 21.91% 23.31% 23.92% 24.82%

60 26.16% 26.70% 27.60%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT

0 1 2 3 4 5 6 7 8 9 10

20 0.63% 0.70% 1.12% 1.53% 1.90% 2.24% 2.58% 2.90% 3.22% 3.06% 3.03%

25 0.61% 0.68% 1.10% 1.51% 1.88% 2.23% 2.56% 2.89% 3.21% 3.05% 3.02%

30 0.68% 0.74% 1.15% 1.56% 1.93% 2.26% 2.59% 2.91% 3.23% 3.07% 3.04%

35 0.87% 0.92% 1.32% 1.71% 2.05% 2.38% 2.70% 3.01% 3.31% 3.14% 3.10%

40 1.20% 1.23% 1.61% 1.97% 2.29% 2.59% 2.89% 3.19% 3.47% 3.29% 3.21%

45 1.66% 1.68% 2.03% 2.33% 2.62% 2.90% 3.18% 3.44% 3.70% 3.48% 3.38%

50 2.30% 2.28% 2.56% 2.83% 3.10% 3.35% 3.59% 3.82% 4.01% 3.76% 3.64%

55 3.56% 3.79% 4.00% 4.20% 4.36% 4.47% 4.20% 4.03%

60 5.11% 4.80% 4.58%

0 1 2 3 4 5 6 7 8 9 10

20 11.07% 11.21% 12.06% 13.04% 14.06% 15.17% 16.47% 18.01% 19.89% 20.54% 21.78%

25 11.04% 11.17% 12.02% 12.98% 14.01% 15.12% 16.41% 17.94% 19.81% 20.45% 21.71%

30 11.14% 11.27% 12.11% 13.08% 14.09% 15.20% 16.48% 18.01% 19.88% 20.52% 21.76%

35 11.47% 11.58% 12.43% 13.40% 14.38% 15.49% 16.78% 18.31% 20.18% 20.83% 22.03%

40 12.06% 12.15% 13.01% 13.95% 14.93% 16.04% 17.35% 18.90% 20.80% 21.45% 22.58%

45 12.92% 12.99% 13.87% 14.75% 15.74% 16.88% 18.22% 19.81% 21.76% 22.28% 23.43%

50 14.15% 14.17% 14.99% 15.90% 16.94% 18.13% 19.52% 21.17% 22.96% 23.52% 24.70%

55 17.70% 18.84% 20.14% 21.65% 23.24% 24.93% 25.58% 26.86%

60 27.79% 28.64% 30.11%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT


7. Scenario 7

8. Scenario 8

0 1 2 3 4 5 6 7 8 9 10

20 1.81% 1.74% 1.92% 2.10% 2.26% 2.38% 2.49% 2.59% 2.69% 2.58% 2.51%

25 1.80% 1.73% 1.91% 2.08% 2.25% 2.36% 2.47% 2.58% 2.67% 2.57% 2.50%

30 1.87% 1.79% 1.97% 2.13% 2.29% 2.40% 2.51% 2.60% 2.70% 2.59% 2.51%

35 2.05% 1.96% 2.13% 2.28% 2.41% 2.52% 2.61% 2.70% 2.78% 2.66% 2.57%

40 2.36% 2.25% 2.40% 2.54% 2.63% 2.72% 2.80% 2.87% 2.93% 2.79% 2.68%

45 2.79% 2.67% 2.79% 2.88% 2.95% 3.02% 3.07% 3.12% 3.16% 2.98% 2.84%

50 3.37% 3.23% 3.30% 3.36% 3.41% 3.44% 3.47% 3.49% 3.46% 3.25% 3.09%

55 4.05% 4.06% 4.07% 4.04% 3.98% 3.91% 3.67% 3.47%

60 4.53% 4.25% 4.00%

0 1 2 3 4 5 6 7 8 9 10

20 12.50% 12.46% 12.89% 13.37% 13.89% 14.40% 14.97% 15.62% 16.39% 16.77% 17.27%

25 12.48% 12.43% 12.86% 13.33% 13.86% 14.36% 14.93% 15.58% 16.34% 16.71% 17.22%

30 12.57% 12.52% 12.94% 13.41% 13.93% 14.43% 14.99% 15.63% 16.40% 16.76% 17.26%

35 12.83% 12.77% 13.20% 13.67% 14.17% 14.66% 15.23% 15.87% 16.63% 17.00% 17.46%

40 13.31% 13.24% 13.68% 14.15% 14.60% 15.11% 15.68% 16.33% 17.10% 17.42% 17.87%

45 14.02% 13.93% 14.37% 14.80% 15.27% 15.78% 16.37% 17.04% 17.81% 18.05% 18.50%

50 14.99% 14.87% 15.29% 15.75% 16.25% 16.79% 17.41% 18.11% 18.75% 19.00% 19.46%

55 17.24% 17.80% 18.42% 19.03% 19.64% 20.31% 20.60% 21.09%

60 22.62% 23.01% 23.59%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT

0 1 2 3 4 5 6 7 8 9 10

20 1.43% 1.36% 1.55% 1.73% 1.90% 2.05% 2.17% 2.28% 2.38% 2.27% 2.23%

25 1.42% 1.35% 1.54% 1.72% 1.89% 2.04% 2.16% 2.26% 2.36% 2.26% 2.22%

30 1.49% 1.41% 1.59% 1.77% 1.93% 2.08% 2.19% 2.29% 2.39% 2.28% 2.23%

35 1.67% 1.58% 1.75% 1.92% 2.07% 2.19% 2.29% 2.38% 2.47% 2.35% 2.29%

40 1.98% 1.87% 2.03% 2.17% 2.30% 2.40% 2.48% 2.55% 2.62% 2.49% 2.40%

45 2.41% 2.29% 2.42% 2.54% 2.62% 2.69% 2.75% 2.80% 2.85% 2.70% 2.56%

50 3.01% 2.87% 2.96% 3.02% 3.08% 3.12% 3.15% 3.17% 3.18% 2.97% 2.81%

55 3.71% 3.73% 3.74% 3.74% 3.70% 3.63% 3.39% 3.19%

60 4.25% 3.97% 3.72%

0 1 2 3 4 5 6 7 8 9 10

20 11.89% 11.83% 12.22% 12.65% 13.12% 13.63% 14.13% 14.70% 15.36% 15.63% 16.13%

25 11.87% 11.81% 12.19% 12.62% 13.09% 13.60% 14.09% 14.66% 15.31% 15.58% 16.09%

30 11.95% 11.89% 12.27% 12.69% 13.16% 13.66% 14.15% 14.71% 15.37% 15.63% 16.13%

35 12.20% 12.13% 12.52% 12.94% 13.41% 13.88% 14.37% 14.93% 15.59% 15.85% 16.31%

40 12.65% 12.57% 12.96% 13.39% 13.85% 14.29% 14.79% 15.36% 16.01% 16.28% 16.69%

45 13.31% 13.20% 13.61% 14.05% 14.46% 14.92% 15.43% 16.00% 16.67% 16.93% 17.26%

50 14.25% 14.13% 14.53% 14.93% 15.37% 15.85% 16.38% 16.98% 17.65% 17.81% 18.13%

55 16.30% 16.80% 17.34% 17.94% 18.51% 19.08% 19.26% 19.61%

60 21.18% 21.44% 21.86%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT


9. Scenario 9

10. Scenario 10

0 1 2 3 4 5 6 7 8 9 10

20 2.09% 2.03% 2.21% 2.38% 2.51% 2.63% 2.74% 2.84% 2.94% 2.83% 2.75%

25 2.08% 2.02% 2.19% 2.36% 2.50% 2.62% 2.73% 2.83% 2.93% 2.81% 2.73%

30 2.15% 2.08% 2.25% 2.42% 2.54% 2.66% 2.76% 2.86% 2.95% 2.83% 2.75%

35 2.33% 2.25% 2.41% 2.56% 2.67% 2.77% 2.86% 2.95% 3.04% 2.90% 2.81%

40 2.64% 2.55% 2.69% 2.80% 2.89% 2.97% 3.05% 3.12% 3.18% 3.02% 2.92%

45 3.09% 2.97% 3.06% 3.14% 3.21% 3.27% 3.33% 3.38% 3.39% 3.21% 3.08%

50 3.65% 3.50% 3.57% 3.63% 3.67% 3.70% 3.73% 3.72% 3.69% 3.48% 3.33%

55 4.32% 4.33% 4.32% 4.27% 4.22% 4.15% 3.91% 3.71%

60 4.77% 4.49% 4.25%

0 1 2 3 4 5 6 7 8 9 10

20 13.02% 13.00% 13.47% 14.00% 14.53% 15.10% 15.74% 16.49% 17.38% 17.79% 18.39%

25 12.99% 12.97% 13.44% 13.96% 14.49% 15.05% 15.69% 16.43% 17.32% 17.74% 18.33%

30 13.09% 13.06% 13.52% 14.05% 14.56% 15.12% 15.76% 16.50% 17.38% 17.79% 18.38%

35 13.37% 13.33% 13.80% 14.31% 14.82% 15.38% 16.01% 16.75% 17.64% 18.01% 18.60%

40 13.89% 13.83% 14.31% 14.78% 15.29% 15.86% 16.50% 17.25% 18.12% 18.46% 19.04%

45 14.65% 14.57% 15.00% 15.48% 16.00% 16.59% 17.25% 18.03% 18.80% 19.14% 19.74%

50 15.64% 15.54% 16.00% 16.51% 17.07% 17.69% 18.39% 19.08% 19.82% 20.18% 20.79%

55 18.13% 18.77% 19.41% 20.04% 20.74% 21.54% 21.95% 22.61%

60 24.09% 24.62% 25.41%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT

0 1 2 3 4 5 6 7 8 9 10

20 1.99% 1.93% 2.12% 2.29% 2.44% 2.56% 2.67% 2.78% 2.89% 2.78% 2.70%

25 1.98% 1.92% 2.10% 2.28% 2.43% 2.55% 2.66% 2.77% 2.87% 2.77% 2.69%

30 2.05% 1.99% 2.16% 2.33% 2.47% 2.59% 2.70% 2.80% 2.90% 2.78% 2.71%

35 2.23% 2.16% 2.33% 2.48% 2.60% 2.70% 2.80% 2.89% 2.98% 2.85% 2.76%

40 2.55% 2.46% 2.61% 2.72% 2.82% 2.91% 2.99% 3.06% 3.13% 2.98% 2.88%

45 3.00% 2.89% 2.98% 3.07% 3.14% 3.21% 3.27% 3.32% 3.34% 3.16% 3.04%

50 3.57% 3.43% 3.50% 3.56% 3.61% 3.64% 3.67% 3.67% 3.64% 3.44% 3.29%

55 4.26% 4.27% 4.27% 4.22% 4.17% 4.10% 3.86% 3.67%

60 4.73% 4.45% 4.21%

0 1 2 3 4 5 6 7 8 9 10

20 12.86% 12.84% 13.32% 13.84% 14.38% 14.94% 15.58% 16.33% 17.21% 17.64% 18.24%

25 12.84% 12.81% 13.28% 13.80% 14.34% 14.90% 15.54% 16.27% 17.15% 17.59% 18.18%

30 12.93% 12.91% 13.37% 13.89% 14.42% 14.97% 15.60% 16.34% 17.21% 17.64% 18.23%

35 13.22% 13.18% 13.65% 14.17% 14.67% 15.22% 15.86% 16.59% 17.47% 17.86% 18.44%

40 13.73% 13.68% 14.16% 14.64% 15.14% 15.70% 16.35% 17.09% 17.97% 18.30% 18.89%

45 14.50% 14.42% 14.86% 15.33% 15.85% 16.43% 17.09% 17.86% 18.65% 18.99% 19.58%

50 15.50% 15.40% 15.86% 16.36% 16.92% 17.53% 18.22% 18.94% 19.67% 20.03% 20.63%

55 17.98% 18.61% 19.27% 19.90% 20.59% 21.38% 21.78% 22.44%

60 23.93% 24.45% 25.23%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT


11. Scenario 11

12. Scenario 12

0 1 2 3 4 5 6 7 8 9 10

20 3.20% 3.18% 3.34% 3.48% 3.60% 3.70% 3.80% 3.88% 3.93% 3.77% 3.66%

25 3.20% 3.17% 3.34% 3.47% 3.59% 3.70% 3.79% 3.88% 3.92% 3.76% 3.65%

30 3.24% 3.21% 3.38% 3.50% 3.62% 3.72% 3.81% 3.89% 3.94% 3.77% 3.66%

35 3.35% 3.31% 3.46% 3.58% 3.69% 3.79% 3.87% 3.95% 3.98% 3.81% 3.69%

40 3.53% 3.48% 3.60% 3.71% 3.81% 3.90% 3.97% 4.04% 4.05% 3.88% 3.75%

45 3.78% 3.70% 3.81% 3.91% 3.99% 4.07% 4.13% 4.17% 4.17% 3.98% 3.84%

50 4.10% 4.01% 4.10% 4.18% 4.25% 4.31% 4.35% 4.35% 4.33% 4.13% 3.98%

55 4.57% 4.62% 4.66% 4.65% 4.62% 4.58% 4.36% 4.19%

60 4.92% 4.69% 4.49%

0 1 2 3 4 5 6 7 8 9 10

20 14.40% 14.49% 15.04% 15.59% 16.20% 16.88% 17.66% 18.57% 19.50% 20.02% 20.83%

25 14.38% 14.47% 15.02% 15.57% 16.17% 16.85% 17.63% 18.53% 19.47% 19.99% 20.80%

30 14.43% 14.52% 15.07% 15.61% 16.21% 16.89% 17.67% 18.57% 19.50% 20.02% 20.82%

35 14.60% 14.68% 15.21% 15.75% 16.36% 17.03% 17.81% 18.71% 19.62% 20.14% 20.95%

40 14.89% 14.96% 15.46% 16.01% 16.62% 17.31% 18.09% 19.00% 19.87% 20.39% 21.20%

45 15.31% 15.34% 15.84% 16.40% 17.02% 17.71% 18.50% 19.38% 20.25% 20.78% 21.60%

50 15.84% 15.86% 16.38% 16.95% 17.59% 18.30% 19.12% 19.92% 20.80% 21.35% 22.19%

55 17.80% 18.48% 19.24% 19.99% 20.79% 21.70% 22.29% 23.18%

60 22.97% 23.65% 24.62%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT

0 1 2 3 4 5 6 7 8 9 10

20 0.58% 0.58% 0.78% 0.97% 1.16% 1.34% 1.50% 1.64% 1.77% 1.71% 1.72%

25 0.57% 0.57% 0.77% 0.96% 1.15% 1.33% 1.49% 1.63% 1.76% 1.70% 1.72%

30 0.62% 0.61% 0.81% 1.00% 1.18% 1.36% 1.52% 1.65% 1.78% 1.72% 1.73%

35 0.75% 0.73% 0.91% 1.10% 1.27% 1.44% 1.58% 1.71% 1.83% 1.76% 1.77%

40 0.95% 0.92% 1.10% 1.27% 1.43% 1.59% 1.70% 1.82% 1.93% 1.85% 1.84%

45 1.25% 1.20% 1.36% 1.51% 1.66% 1.78% 1.88% 1.98% 2.08% 1.99% 1.94%

50 1.65% 1.58% 1.73% 1.86% 1.97% 2.06% 2.14% 2.22% 2.29% 2.18% 2.10%

55 2.33% 2.40% 2.47% 2.52% 2.57% 2.62% 2.46% 2.35%

60 3.01% 2.83% 2.69%

0 1 2 3 4 5 6 7 8 9 10

20 10.85% 10.87% 11.24% 11.66% 12.12% 12.65% 13.20% 13.79% 14.49% 14.76% 15.35%

25 10.84% 10.85% 11.23% 11.64% 12.10% 12.62% 13.18% 13.76% 14.45% 14.73% 15.31%

30 10.91% 10.92% 11.29% 11.69% 12.15% 12.67% 13.22% 13.80% 14.49% 14.76% 15.34%

35 11.09% 11.09% 11.46% 11.86% 12.32% 12.84% 13.37% 13.95% 14.64% 14.91% 15.49%

40 11.40% 11.39% 11.76% 12.17% 12.63% 13.16% 13.66% 14.24% 14.93% 15.20% 15.75%

45 11.85% 11.82% 12.20% 12.62% 13.09% 13.57% 14.08% 14.67% 15.36% 15.64% 16.14%

50 12.47% 12.44% 12.84% 13.28% 13.73% 14.19% 14.71% 15.30% 16.01% 16.31% 16.72%

55 14.20% 14.64% 15.13% 15.68% 16.32% 17.06% 17.27% 17.67%

60 18.36% 18.61% 19.06%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT


13. Scenario 13

14. Scenario14

0 1 2 3 4 5 6 7 8 9 10

20 2.33% 2.33% 2.62% 2.90% 3.16% 3.39% 3.59% 3.77% 3.94% 3.77% 3.70%

25 2.32% 2.32% 2.61% 2.88% 3.15% 3.38% 3.57% 3.76% 3.93% 3.75% 3.69%

30 2.38% 2.38% 2.66% 2.93% 3.19% 3.42% 3.61% 3.78% 3.95% 3.77% 3.70%

35 2.56% 2.55% 2.82% 3.08% 3.32% 3.53% 3.71% 3.87% 4.03% 3.84% 3.77%

40 2.87% 2.84% 3.09% 3.33% 3.55% 3.72% 3.89% 4.03% 4.17% 3.98% 3.88%

45 3.30% 3.25% 3.48% 3.70% 3.86% 4.01% 4.15% 4.27% 4.39% 4.17% 4.06%

50 3.90% 3.82% 4.02% 4.17% 4.30% 4.42% 4.53% 4.62% 4.71% 4.47% 4.30%

55 4.84% 4.94% 5.03% 5.10% 5.15% 5.19% 4.89% 4.66%

60 5.77% 5.44% 5.16%

0 1 2 3 4 5 6 7 8 9 10

20 13.58% 13.66% 14.37% 15.18% 16.10% 17.07% 18.09% 19.28% 20.70% 21.36% 22.60%

25 13.54% 13.62% 14.33% 15.13% 16.04% 17.02% 18.04% 19.22% 20.63% 21.29% 22.52%

30 13.64% 13.71% 14.42% 15.22% 16.12% 17.09% 18.10% 19.28% 20.69% 21.34% 22.57%

35 13.93% 13.99% 14.70% 15.50% 16.42% 17.35% 18.36% 19.55% 20.96% 21.62% 22.85%

40 14.47% 14.51% 15.23% 16.05% 16.95% 17.85% 18.87% 20.07% 21.49% 22.17% 23.42%

45 15.25% 15.27% 16.02% 16.87% 17.68% 18.60% 19.65% 20.87% 22.32% 23.03% 24.32%

50 16.38% 16.38% 17.16% 17.92% 18.77% 19.72% 20.80% 22.06% 23.57% 24.33% 25.46%

55 19.55% 20.48% 21.51% 22.69% 24.06% 25.68% 26.30% 27.34%

60 28.24% 28.99% 30.15%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT

0 1 2 3 4 5 6 7 8 9 10

20 1.50% 1.58% 2.00% 2.37% 2.72% 3.07% 3.40% 3.71% 4.02% 3.83% 3.76%

25 1.49% 1.56% 1.98% 2.36% 2.71% 3.05% 3.38% 3.70% 4.01% 3.81% 3.75%

30 1.55% 1.62% 2.03% 2.41% 2.75% 3.09% 3.41% 3.73% 4.03% 3.83% 3.76%

35 1.74% 1.79% 2.19% 2.54% 2.88% 3.20% 3.51% 3.82% 4.11% 3.90% 3.82%

40 2.06% 2.10% 2.46% 2.78% 3.10% 3.41% 3.70% 3.99% 4.25% 4.02% 3.93%

45 2.51% 2.51% 2.83% 3.13% 3.42% 3.71% 3.98% 4.24% 4.45% 4.21% 4.10%

50 3.08% 3.06% 3.34% 3.62% 3.88% 4.14% 4.38% 4.59% 4.74% 4.48% 4.34%

55 4.32% 4.55% 4.77% 4.95% 5.08% 5.19% 4.90% 4.72%

60 5.80% 5.48% 5.26%

0 1 2 3 4 5 6 7 8 9 10

20 12.50% 12.67% 13.62% 14.61% 15.68% 16.92% 18.36% 20.07% 22.17% 22.88% 24.25%

25 12.46% 12.63% 13.58% 14.56% 15.63% 16.86% 18.29% 20.00% 22.09% 22.82% 24.18%

30 12.57% 12.73% 13.67% 14.65% 15.71% 16.93% 18.36% 20.07% 22.16% 22.87% 24.22%

35 12.89% 13.03% 13.98% 14.93% 16.00% 17.22% 18.66% 20.37% 22.45% 23.13% 24.49%

40 13.48% 13.60% 14.51% 15.46% 16.54% 17.78% 19.23% 20.97% 22.97% 23.67% 25.04%

45 14.34% 14.41% 15.28% 16.25% 17.35% 18.62% 20.11% 21.89% 23.77% 24.50% 25.90%

50 15.44% 15.49% 16.39% 17.40% 18.55% 19.88% 21.43% 23.19% 24.97% 25.74% 27.19%

55 19.21% 20.47% 21.91% 23.50% 25.09% 26.94% 27.83% 29.39%

60 29.83% 30.92% 32.70%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT


15. Scenario15

16. Scenario16

0 1 2 3 4 5 6 7 8 9 10

20 1.22% 1.36% 1.79% 2.21% 2.57% 2.93% 3.27% 3.60% 3.92% 3.74% 4.77%

25 1.21% 1.35% 1.78% 2.20% 2.56% 2.92% 3.26% 3.60% 3.91% 3.74% 3.69%

30 1.27% 1.40% 1.83% 2.24% 2.60% 2.95% 3.28% 3.59% 3.91% 3.75% 3.68%

35 1.41% 1.53% 1.95% 2.34% 2.69% 3.03% 3.36% 3.61% 3.93% 3.80% 3.73%

40 1.65% 1.75% 2.16% 2.52% 2.85% 3.18% 3.36% 3.68% 4.09% 3.89% 3.81%

45 1.99% 2.07% 2.45% 2.77% 3.09% 3.40% 3.50% 3.80% 4.24% 3.89% 3.93%

50 2.46% 2.51% 2.83% 3.14% 3.43% 3.71% 3.98% 4.24% 4.46% 4.02% 4.11%

55 3.65% 3.43% 3.71% 4.41% 4.63% 4.78% 4.22% 4.39%

60 5.21% 4.94% 4.77%

0 1 2 3 4 5 6 7 8 9 10

20 11.98% 12.25% 13.18% 14.21% 15.27% 16.49% 17.91% 19.60% 21.66% 22.46% 23.81%

25 11.96% 12.23% 13.16% 14.19% 15.24% 16.46% 17.87% 19.56% 21.61% 22.42% 23.76%

30 12.04% 12.31% 13.23% 14.25% 15.31% 16.51% 17.92% 19.61% 21.66% 22.45% 23.80%

35 12.28% 12.53% 13.45% 14.45% 15.50% 16.71% 18.12% 19.80% 21.86% 22.63% 23.97%

40 12.68% 12.92% 13.85% 14.81% 15.87% 17.08% 18.50% 20.19% 22.26% 22.98% 24.33%

45 13.27% 13.48% 14.41% 15.34% 16.40% 17.62% 19.05% 20.76% 22.79% 23.51% 24.88%

50 14.10% 14.29% 15.15% 16.10% 17.18% 18.42% 19.88% 21.62% 23.54% 24.28% 25.68%

55 17.22% 18.35% 19.65% 21.16% 22.98% 24.72% 25.55% 27.01%

60 26.38% 27.33% 28.92%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT

0 1 2 3 4 5 6 7 8 9 10

20 -0.52% -0.39% 0.04% 0.46% 0.88% 1.28% 1.63% 1.98% 2.31% 2.18% 2.21%

25 -0.53% -0.40% 0.03% 0.45% 0.87% 1.27% 1.62% 1.97% 2.30% 2.17% 2.20%

30 -0.47% -0.35% 0.07% 0.49% 0.90% 1.30% 1.65% 1.99% 2.32% 2.19% 2.21%

35 -0.32% -0.21% 0.20% 0.61% 1.01% 1.39% 1.73% 2.06% 2.39% 2.24% 2.26%

40 -0.07% 0.02% 0.42% 0.82% 1.20% 1.55% 1.88% 2.19% 2.50% 2.35% 2.36%

45 0.29% 0.36% 0.74% 1.11% 1.48% 1.79% 2.09% 2.39% 2.67% 2.51% 2.50%

50 0.78% 0.83% 1.19% 1.54% 1.85% 2.13% 2.40% 2.67% 2.93% 2.75% 2.70%

55 2.10% 2.37% 2.62% 2.86% 3.09% 3.31% 3.11% 3.00%

60 3.81% 3.56% 3.41%

0 1 2 3 4 5 6 7 8 9 10

20 9.13% 9.33% 10.07% 10.91% 11.88% 12.98% 14.13% 15.48% 17.12% 17.50% 18.63%

25 9.12% 9.31% 10.05% 10.89% 11.85% 12.95% 14.09% 15.44% 17.07% 17.45% 18.58%

30 9.21% 9.40% 10.13% 10.96% 11.92% 13.02% 14.15% 15.49% 17.12% 17.49% 18.62%

35 9.46% 9.64% 10.36% 11.20% 12.16% 13.23% 14.36% 15.70% 17.33% 17.70% 18.83%

40 9.88% 10.04% 10.78% 11.61% 12.58% 13.61% 14.75% 16.09% 17.72% 18.12% 19.26%

45 10.49% 10.63% 11.37% 12.22% 13.20% 14.18% 15.32% 16.67% 18.32% 18.74% 19.92%

50 11.33% 11.45% 12.22% 13.10% 14.01% 15.01% 16.16% 17.54% 19.21% 19.68% 20.77%

55 14.31% 15.22% 16.26% 17.46% 18.89% 20.63% 21.17% 22.11%

60 22.48% 22.99% 24.03%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT


17. Scenario17

18. Scenario18

0 1 2 3 4 5 6 7 8 9 10

20 -2.14% -1.74% -1.06% -0.39% 0.28% 0.95% 1.55% 2.13% 2.70% 2.59% 2.72%

25 -2.13% -1.74% -1.06% -0.39% 0.28% 0.95% 1.55% 2.13% 2.70% 2.59% 2.72%

30 -2.08% -1.70% -1.03% -0.37% 0.30% 0.97% 1.57% 2.14% 2.71% 2.60% 2.72%

35 -2.00% -1.63% -0.96% -0.31% 0.35% 1.02% 1.61% 2.17% 2.74% 2.63% 2.75%

40 -1.86% -1.51% -0.86% -0.22% 0.44% 1.09% 1.67% 2.23% 2.79% 2.68% 2.80%

45 -1.66% -1.35% -0.72% -0.09% 0.55% 1.19% 1.76% 2.31% 2.85% 2.75% 2.86%

50 -1.38% -1.12% -0.51% 0.11% 0.73% 1.35% 1.89% 2.43% 2.96% 2.86% 2.97%

55 0.37% 0.97% 1.57% 2.08% 2.60% 3.11% 3.02% 3.12%

60 3.32% 3.24% 3.34%

0 1 2 3 4 5 6 7 8 9 10

20 5.91% 6.52% 7.71% 9.08% 10.72% 12.72% 14.89% 17.43% 20.59% 21.70% 24.37%

25 5.92% 6.52% 7.71% 9.08% 10.72% 12.72% 14.89% 17.42% 20.58% 21.69% 24.34%

30 6.00% 6.60% 7.78% 9.14% 10.78% 12.77% 14.93% 17.46% 20.61% 21.72% 24.38%

35 6.17% 6.75% 7.92% 9.28% 10.91% 12.90% 15.04% 17.56% 20.70% 21.82% 24.48%

40 6.43% 7.00% 8.14% 9.49% 11.12% 13.10% 15.22% 17.72% 20.85% 22.00% 24.67%

45 6.80% 7.32% 8.46% 9.80% 11.41% 13.38% 15.47% 17.95% 21.05% 22.25% 24.94%

50 7.33% 7.78% 8.91% 10.25% 11.85% 13.81% 15.84% 18.30% 21.37% 22.63% 25.35%

55 10.85% 12.45% 14.38% 16.37% 18.79% 21.83% 23.19% 25.98%

60 22.46% 23.97% 26.85%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT

0 1 2 3 4 5 6 7 8 9 10

20 -2.45% -1.97% -1.25% -0.56% 0.12% 0.81% 1.44% 2.03% 2.61% 2.51% 2.65%

25 -2.43% -1.96% -1.24% -0.56% 0.13% 0.82% 1.45% 2.03% 2.61% 2.51% 2.65%

30 -2.39% -1.92% -1.21% -0.53% 0.15% 0.83% 1.46% 2.04% 2.62% 2.52% 2.65%

35 -2.33% -1.88% -1.17% -0.50% 0.17% 0.85% 1.48% 2.06% 2.64% 2.54% 2.67%

40 -2.27% -1.83% -1.13% -0.47% 0.20% 0.88% 1.50% 2.08% 2.65% 2.56% 2.69%

45 -2.18% -1.77% -1.08% -0.42% 0.24% 0.90% 1.53% 2.10% 2.67% 2.58% 2.72%

50 -2.04% -1.66% -0.98% -0.34% 0.30% 0.96% 1.58% 2.14% 2.70% 2.63% 2.76%

55 -0.25% 0.38% 1.02% 1.64% 2.19% 2.74% 2.68% 2.83%

60 2.80% 2.77% 2.92%

0 1 2 3 4 5 6 7 8 9 10

20 5.46% 6.16% 7.36% 8.70% 10.31% 12.27% 14.48% 16.98% 20.09% 21.18% 23.79%

25 5.48% 6.18% 7.38% 8.72% 10.33% 12.29% 14.50% 17.00% 20.11% 21.19% 23.80%

30 5.56% 6.24% 7.44% 8.77% 10.38% 12.33% 14.53% 17.03% 20.13% 21.22% 23.82%

35 5.67% 6.34% 7.52% 8.85% 10.44% 12.38% 14.57% 17.04% 20.13% 21.22% 23.82%

40 5.82% 6.47% 7.63% 8.94% 10.50% 12.42% 14.60% 17.04% 20.09% 21.20% 23.79%

45 6.03% 6.63% 7.78% 9.05% 10.59% 12.46% 14.62% 17.02% 20.02% 21.15% 23.73%

50 6.33% 6.89% 8.00% 9.24% 10.73% 12.55% 14.69% 17.03% 19.95% 21.11% 23.67%

55 9.46% 10.89% 12.64% 14.74% 16.99% 19.79% 21.01% 23.54%

60 19.63% 20.91% 23.41%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT


19. Scenario19

20. Scenario 20

0 1 2 3 4 5 6 7 8 9 10

20 -2.66% -2.17% -1.42% -0.72% -0.03% 0.67% 1.33% 1.93% 2.52% 2.43% 2.57%

25 -2.64% -2.16% -1.40% -0.71% -0.02% 0.68% 1.34% 1.93% 2.52% 2.43% 2.57%

30 -2.60% -2.12% -1.38% -0.69% 0.00% 0.69% 1.35% 1.94% 2.53% 2.44% 2.58%

35 -2.54% -2.08% -1.34% -0.66% 0.03% 0.72% 1.37% 1.96% 2.54% 2.45% 2.59%

40 -2.47% -2.02% -1.29% -0.62% 0.06% 0.74% 1.39% 1.98% 2.56% 2.47% 2.61%

45 -2.37% -1.95% -1.23% -0.57% 0.10% 0.78% 1.43% 2.00% 2.58% 2.50% 2.64%

50 -2.22% -1.83% -1.13% -0.48% 0.17% 0.83% 1.48% 2.05% 2.61% 2.55% 2.69%

55 -0.38% 0.26% 0.90% 1.55% 2.10% 2.65% 2.61% 2.76%

60 2.72% 2.70% 2.85%

0 1 2 3 4 5 6 7 8 9 10

20 5.14% 5.83% 7.04% 8.35% 9.93% 11.86% 14.10% 16.57% 19.64% 20.71% 23.27%

25 5.16% 5.85% 7.06% 8.37% 9.95% 11.88% 14.12% 16.59% 19.66% 20.72% 23.28%

30 5.24% 5.92% 7.12% 8.43% 10.00% 11.92% 14.15% 16.62% 19.68% 20.74% 23.30%

35 5.36% 6.02% 7.21% 8.51% 10.07% 11.97% 14.19% 16.64% 19.69% 20.75% 23.31%

40 5.52% 6.16% 7.33% 8.61% 10.15% 12.02% 14.23% 16.65% 19.66% 20.74% 23.29%

45 5.74% 6.34% 7.49% 8.74% 10.25% 12.08% 14.27% 16.64% 19.60% 20.70% 23.24%

50 6.06% 6.61% 7.73% 8.95% 10.41% 12.20% 14.36% 16.66% 19.55% 20.68% 23.20%

55 9.19% 10.60% 12.31% 14.43% 16.65% 19.42% 20.61% 23.10%

60 19.30% 20.54% 23.00%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT

0 1 2 3 4 5 6 7 8 9 10

20 -4.16% -3.64% -2.82% -1.99% -1.21% -0.47% 0.27% 1.01% 1.63% 1.57% 1.75%

25 -4.13% -3.63% -2.80% -1.98% -1.20% -0.47% 0.27% 1.01% 1.63% 1.58% 1.75%

30 -4.09% -3.59% -2.77% -1.95% -1.18% -0.45% 0.29% 1.02% 1.64% 1.58% 1.75%

35 -4.03% -3.55% -2.74% -1.92% -1.16% -0.43% 0.30% 1.03% 1.65% 1.60% 1.77%

40 -3.96% -3.50% -2.70% -1.89% -1.13% -0.41% 0.32% 1.05% 1.67% 1.61% 1.79%

45 -3.86% -3.43% -2.64% -1.84% -1.09% -0.38% 0.34% 1.06% 1.68% 1.64% 1.81%

50 -3.71% -3.32% -2.55% -1.77% -1.03% -0.33% 0.38% 1.09% 1.71% 1.68% 1.86%

55 -1.69% -0.96% -0.27% 0.42% 1.12% 1.75% 1.73% 1.92%

60 1.80% 1.81% 2.00%

0 1 2 3 4 5 6 7 8 9 10

20 3.51% 4.05% 5.00% 6.13% 7.42% 8.90% 10.70% 12.94% 15.31% 15.82% 17.44%

25 3.53% 4.06% 5.01% 6.15% 7.43% 8.91% 10.71% 12.96% 15.32% 15.83% 17.44%

30 3.60% 4.12% 5.07% 6.19% 7.47% 8.95% 10.74% 12.99% 15.35% 15.85% 17.46%

35 3.70% 4.21% 5.15% 6.27% 7.54% 9.00% 10.78% 13.01% 15.36% 15.87% 17.48%

40 3.85% 4.33% 5.26% 6.37% 7.62% 9.06% 10.82% 13.02% 15.36% 15.89% 17.50%

45 4.05% 4.50% 5.41% 6.49% 7.73% 9.14% 10.86% 13.02% 15.34% 15.90% 17.51%

50 4.34% 4.75% 5.63% 6.69% 7.89% 9.27% 10.95% 13.05% 15.35% 15.94% 17.55%

55 6.92% 8.09% 9.41% 11.02% 13.04% 15.31% 15.96% 17.57%

60 15.28% 16.01% 17.61%


AG

E P

AR

ENT

ROIAGE CHILD

AG

E P

AR

ENT


Appendix 6: Comparison with competitor products

Comparison with Prudential Product.

ITEMS PRUDENTIAL (PĐKTT) PREVOIR

Age of the parent 32 32

Age of the child Don’t insured 0

SI 100M 100M

Premium 8.4M 8.3M

Premium Period 18 18

Contract Period 22 21

Death/ TPD benefit of the

parent

150M, before age of 46 (Up to age of 18) 100M

100M, after age of 46 in case of Accidental Death/TPD

+ waiver of premium


child (before age of 18) N/A 150M


child (after age of 18) N/A

The rest of education benefit

Total Education Benefit 150M 150M

Total Premium 150.9M 150.3M

Dividend Yes No

Loyalty Benefit 20.4M

Total Benefits 150MM 170.4M

Total Benefits/Total Premium 99.50% 113.40%


Comparison with AIA Product

ITEMS AIA MAP Life

Age of the parent 32 32

Age of the child N/A 8

SI 70M 67M

Premium 10,3M 10.3M

Premium Period 10 10

Contract Period 14 13


parent

70M

(Up to age of 18) 67M in case of

Accidental Death/TPD

+ 70M in case of Accidental

Death/TPD + waiver of premium

+ 17.5M in case of Cancer


child (before age of 18) N/A 100.5M


child (after age of 18) N/A The rest of education benefit

Total Education Benefit 105M 100.5M

Total Premium 103M 102M

Dividend (not guaranteed) Yes No

Loyalty Benefit 6.9M

Total Benefits 105M 107.4 M

Total Benefits/Total Premium 102.00% 103.90%


Appendix 7: Sensitivity Results

A. For Non Par Product.

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.9968 R Square 0.9937 Adjusted R

Square 0.9936 Standard Error 0.0046 Observations 499

ANOVA

df SS MS F Significance F

Regression 1 1.6584

1.6584

77,807.60 -

Residual 497 0.0106

0.0000

Total 498 1.6690

Coefficients Standard Error t Stat P-value Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept (0.0002) 0.0002

(1.0183)

0.3090 (0.0007)

0.0002

(0.0007)

0.0002

0.005 3.8544 0.0138 278.9401

- 3.8272

3.8815

3.8272

3.8815

-10.00%

-5.00%

0.00%

5.00%

10.00%

15.00%

-3.00% -2.00% -1.00% 0.00% 1.00% 2.00% 3.00% 4.00%

Investment Return Vs Profit Margin


SUMMARY OUTPUT


Multiple R

0.8419

R Square

0.7088

Adjusted R Square

0.7082

Standard Error

0.0049

Observations 499

ANOVA


Regression 1 0.02856128 0.02856128 1209.66441 3.046E-135 Residual 497 0.01173462 2.3611E-05

Total 498 0.04029591


Upper 95%

Lower 95.0%

Upper 95.0%

Intercept 0.0013

0.0002

5.7996

0.0000

0.0008

0.0017

0.0008

0.0017

-0.0125 (0.2502)

0.0072

(34.7802)

0.0000

(0.2643)

(0.2360)

(0.2643)

(0.2360)

-3.00%

-2.00%

-1.00%

0.00%

1.00%

2.00%

3.00%

4.00%

-6.0% -4.0% -2.0% 0.0% 2.0% 4.0% 6.0%



SUMMARY OUTPUT


Multiple R 0.9272 R Square 0.8598 Adjusted R

Square 0.8595 Standard Error 0.0057 Observations 499 ANOVA


Regression 1 0.0985

0.0985

3,047.74 0.0000

Residual 497 0.0161

0.0000

Total 498 0.1146


Upper 95%

Lower 95.0%

Upper 95.0%

Intercept (0.0001) 0.0003

(0.1952)

0.8453 (0.0006)

0.0005

(0.0006)

0.0005

0.6 (0.0324) 0.0006

(55.2063)

0.0000 (0.0336)

(0.0312)

(0.0336)

(0.0312)

-6.00%

-5.00%

-4.00%

-3.00%

-2.00%

-1.00%

0.00%

1.00%

2.00%

3.00%

-60.00% -40.00% -20.00% 0.00% 20.00% 40.00% 60.00% 80.00% 100.00% 120.00%

Mortality Claim Vs Profit Margin


B. For Par Product

SUMMARY OUTPUT


Multiple R

0.9972

R Square

0.9945

Adjusted R Square

0.9945

Standard Error

0.0013

Observations 499

ANOVA

df SS

MS F Significance F

Regression 1

0.1532

0.1532 ########## 0

Residual 497

0.0008

0.0000

Total 498

0.1540

Coefficients Standard Error

t Stat P-value Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept (0.0002)

0.0001

(2.8078) 0.0052

(0.0003)

(0.0001)

(0.0003)

(0.0001)

0.005 1.1714

0.0039

299.7907 -

1.1638

1.1791

1.1638

1.1791

-3.00%

-2.00%

-1.00%

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

-3.00% -2.00% -1.00% 0.00% 1.00% 2.00% 3.00% 4.00%

Investment return vs Profit Margin


SUMMARY OUTPUT


Multiple R 0.8258

R Square

0.6820

Adjusted R Square

0.6814

Standard Error

0.0021

Observations 499

ANOVA


Regression 1

0.0046

0.0046

1,065.9021 9.744E-126

Residual 497

0.0022

0.0000

Total 498

0.0068


Upper 95%

Lower 95.0%

Upper 95.0%

Intercept 0.0005

0.0001

4.9740

0.0000

0.0003

0.0006

0.0003

0.0006

-0.0125 (0.1008)

0.0031

(32.6482)

0.0000

(0.1069)

(0.0947)

(0.1069)

(0.0947)

-1.00%

-0.50%

0.00%

0.50%

1.00%

1.50%

-6.0% -4.0% -2.0% 0.0% 2.0% 4.0% 6.0%



SUMMARY OUTPUT


Multiple R 0.9216

R Square

0.8493

Adjusted R Square

0.8490

Standard Error

0.0024

Observations 499

ANOVA


Regression 1

0.0159

0.0159

2,801.1170 2.21E-206

Residual 497

0.0028

0.0000

Total 498

0.0187


Upper 95%

Lower 95.0%

Upper 95.0%

Intercept (0.0001)

0.0001

(0.6801)

0.4967

(0.0003)

0.0002

(0.0003)

0.0002

0.6 (0.0130)

0.0002

(52.9256)

0.0000

(0.0135)

(0.0125)

(0.0135)

(0.0125)

-2.50%

-2.00%

-1.50%

-1.00%

-0.50%

0.00%

0.50%

1.00%

1.50%

-60.00% -40.00% -20.00% 0.00% 20.00% 40.00% 60.00% 80.00% 100.00% 120.00%

Mortality vs Profit Margin

abstract - institut des actuaires - accueil€¦ · dissertation isfa – nguyen quang huy page 4...

Documents