ABSTRACT - Institut des actuaires - Accueil€¦ · Dissertation ISFA – Nguyen Quang Huy Page 4...
Transcript of ABSTRACT - Institut des actuaires - Accueil€¦ · Dissertation ISFA – Nguyen Quang Huy Page 4...
Dissertation ISFA – Nguyen Quang Huy Page 2
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.
Dissertation ISFA – Nguyen Quang Huy Page 3
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.
Dissertation ISFA – Nguyen Quang Huy Page 4
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.
Dissertation ISFA – Nguyen Quang Huy Page 5
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
Dissertation ISFA – Nguyen Quang Huy Page 6
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
Dissertation ISFA – Nguyen Quang Huy Page 7
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
Dissertation ISFA – Nguyen Quang Huy Page 8
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.
Dissertation ISFA – Nguyen Quang Huy Page 9
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
Dissertation ISFA – Nguyen Quang Huy Page 10
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
Dissertation ISFA – Nguyen Quang Huy Page 11
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
Dissertation ISFA – Nguyen Quang Huy Page 12
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.
Dissertation ISFA – Nguyen Quang Huy Page 13
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.
Dissertation ISFA – Nguyen Quang Huy Page 14
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.
Dissertation ISFA – Nguyen Quang Huy Page 15
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.
Dissertation ISFA – Nguyen Quang Huy Page 16
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).
Dissertation ISFA – Nguyen Quang Huy Page 17
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.
Dissertation ISFA – Nguyen Quang Huy Page 18
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.
Dissertation ISFA – Nguyen Quang Huy Page 19
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.
Dissertation ISFA – Nguyen Quang Huy Page 20
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.
Dissertation ISFA – Nguyen Quang Huy Page 21
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,…
Dissertation ISFA – Nguyen Quang Huy Page 22
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
Dissertation ISFA – Nguyen Quang Huy Page 23
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
Dissertation ISFA – Nguyen Quang Huy Page 24
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.
Dissertation ISFA – Nguyen Quang Huy Page 25
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
Dissertation ISFA – Nguyen Quang Huy Page 26
: 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
Dissertation ISFA – Nguyen Quang Huy Page 27
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
Dissertation ISFA – Nguyen Quang Huy Page 28
∑
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
| ( ) ∑
∑
|
Dissertation ISFA – Nguyen Quang Huy Page 29
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
Dissertation ISFA – Nguyen Quang Huy Page 30
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
Dissertation ISFA – Nguyen Quang Huy Page 31
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.”
(Term 3.2 Article 18, circular 50/TT 2017)
Dissertation ISFA – Nguyen Quang Huy Page 32
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”
(Term 3.3 Article 18, circular 50/TT 2017)
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;
Dissertation ISFA – Nguyen Quang Huy Page 33
- 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.”
(Term 3.4 Article 18, circular 50/TT 2017)
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.”
(Term 3.5 Article 18, circular 50/TT 2017)
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”.
(Term 3.6 Article 18, circular 50/TT 2017)
Dissertation ISFA – Nguyen Quang Huy Page 34
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:
∑
∑
∑
Dissertation ISFA – Nguyen Quang Huy Page 35
∑
∑
∑
∑
∑
∑
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.
Dissertation ISFA – Nguyen Quang Huy Page 36
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:
Dissertation ISFA – Nguyen Quang Huy Page 37
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.
Dissertation ISFA – Nguyen Quang Huy Page 38
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.
Dissertation ISFA – Nguyen Quang Huy Page 39
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
Dissertation ISFA – Nguyen Quang Huy Page 40
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:
Dissertation ISFA – Nguyen Quang Huy Page 41
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.
Dissertation ISFA – Nguyen Quang Huy Page 42
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.
Dissertation ISFA – Nguyen Quang Huy Page 43
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;
Dissertation ISFA – Nguyen Quang Huy Page 44
- 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.
Dissertation ISFA – Nguyen Quang Huy Page 45
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%.
Dissertation ISFA – Nguyen Quang Huy Page 46
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.
Dissertation ISFA – Nguyen Quang Huy Page 47
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
Dissertation ISFA – Nguyen Quang Huy Page 48
∑
(using pricing assumptions)
And
( )
( )
( )
( ∑
) ∑
And
Profitability Criteria.
∑
∑
(∑
)
∑
Dissertation ISFA – Nguyen Quang Huy Page 49
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
Dissertation ISFA – Nguyen Quang Huy Page 50
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.
Dissertation ISFA – Nguyen Quang Huy Page 51
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
Dissertation ISFA – Nguyen Quang Huy Page 52
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
Dissertation ISFA – Nguyen Quang Huy Page 53
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
AGE CHILDProfit Margin
ROIAGE CHILD
BEYAGE CHILD
AG
E P
AR
ENT
AG
E P
AR
ENT
AG
E P
AR
ENT
Dissertation ISFA – Nguyen Quang Huy Page 54
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
Dissertation ISFA – Nguyen Quang Huy Page 55
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
Dissertation ISFA – Nguyen Quang Huy Page 56
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
Dissertation ISFA – Nguyen Quang Huy Page 57
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.
PV Prem PV Profit PM ROI No. Policy
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
Mode #N/A #N/A #N/A #N/A 577
Standard Deviation 41267031212 1133999353 0.000147 0.000816 200.1716552
Sample Variance 1.70297E+21 1.28595E+18 2.17E-08 6.66E-07 40068.69156
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
Dissertation ISFA – Nguyen Quang Huy Page 58
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%
Dissertation ISFA – Nguyen Quang Huy Page 59
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%
Dissertation ISFA – Nguyen Quang Huy Page 60
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:
Where Y: percentage change of Profit Margin
X: Percentage change of Lapse.
Details will be shown in the appendix.
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
Dissertation ISFA – Nguyen Quang Huy Page 61
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:
Where Y: percentage change of Profit Margin
X: Percentage change of Investment Return.
Details will be shown in the appendix.
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:
Where Y: percentage change of Profit Margin
X: Percentage change of Claim as percentage of CSO1980 Table.
Details will be shown in the appendix.
-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
Dissertation ISFA – Nguyen Quang Huy Page 62
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:
Where Y: percentage change of Profit Margin
X: Percentage change of Lapse.
Details will be shown in the appendix.
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%
Lapse vs Profit Margin
Dissertation ISFA – Nguyen Quang Huy Page 63
For the sensitivity test on Investment Return assumption, we arrive:
Where Y: percentage change of Profit Margin
X: Percentage change of Investment Return.
Details will be shown in the appendix.
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
Dissertation ISFA – Nguyen Quang Huy Page 64
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
Dissertation ISFA – Nguyen Quang Huy Page 65
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 2 Investment return is 6.0%/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 6 Lapse rate is 15%/year. Other assumptions keep unchanged as per best estimate
scenario.
Scenario 7 Commission and acquisition cost increase by 5.0%. Other assumptions keep
unchanged as per best estimate scenario.
Scenario 8 Commission and acquisition cost increase by 10%. Other assumptions keep
unchanged as per best estimate scenario.
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
best estimate scenario.
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 12 Investment return is 6.0%/year for the whole insurance period and Death Claim is
70% of the CSO1980. Other assumptions keep unchanged as per best estimate
scenario
Scenario 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.
Scenario 14 Investment return is 8.0%/year for the whole insurance period and lapse rates are
15%/year. Other assumptions keep unchanged as per best estimate scenario.
Scenario 15 Investment return is 8.0%/year for the whole insurance period and Death Claim is
Dissertation ISFA – Nguyen Quang Huy Page 66
70% of the CSO1980 and lapse rates are 15%/year. Other assumptions keep
unchanged as per best estimate scenario
Scenario 16 Investment return is 6.0%/year for the whole insurance period and Death Claim is
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
Dissertation ISFA – Nguyen Quang Huy Page 67
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
Dissertation ISFA – Nguyen Quang Huy Page 68
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%]
Dissertation ISFA – Nguyen Quang Huy Page 69
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%
Dissertation ISFA – Nguyen Quang Huy Page 70
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
Dissertation ISFA – Nguyen Quang Huy Page 71
Figure 10.12: Distribution of Profitability of the Portfolio of the Non Par product under 1,000
simulations for diversifiable risks.
Table 10.13: Statistics of the Profitability of the Portfolio of 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.
PV Prem PV Profit PM ROI No. Policy
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
Mode #N/A #N/A #N/A #N/A 945
Standard Deviation 24081866869 2566245004 0.000598356 0.001578752 146.9469541
Sample Variance 5.79936E+20 6.58561E+18 3.5803E-07 2.49246E-06 21593.40731
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
Dissertation ISFA – Nguyen Quang Huy Page 72
B. For the Par Product
Figure 10.13: Distribution of Profitability of the Portfolio of the Par product under 1,000
simulations for diversifiable risks.
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%].
PV Prem PV Profit PM ROI No. Policy
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
Mode #N/A #N/A #N/A #N/A 570
Standard Deviation 25958709763 634659833.9 0.000399103 0.001216301 141.1429172
Sample Variance 6.73855E+20 4.02793E+17 1.59283E-07 1.47939E-06 19921.32308
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
Dissertation ISFA – Nguyen Quang Huy Page 73
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
Dissertation ISFA – Nguyen Quang Huy Page 74
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
Dissertation ISFA – Nguyen Quang Huy Page 75
Table 10.15: Statistics of the Profitability of the Portfolio of Non Par Product under 1,000
simulations for non-diversifiable risks.
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.
B. For the Par Product
Dissertation ISFA – Nguyen Quang Huy Page 76
Figure 10.15: Distribution of Profitability of the Portfolio of the Par product under 1,000
simulations for non-diversifiable risks.
Table 10.16: Statistics of the Profitability of the Portfolio of Non Par Product under 1,000
simulations for non-diversifiable risks.
The profit margin of the portfolio has the shape of normal distribution with the mean of 2.67% and
standard deviation of 1.18%.
The profit margin of the poftfolio ranges within [-0.8%, 6.14%]
The confidence inteval of the profit margin of the portfolio at 95% is [0.35%, 4.88%]
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
Dissertation ISFA – Nguyen Quang Huy Page 77
The ROI of the portfolio has the shape of normal distribution with the mean of 15.1% and standard
deviation of 2.1%.
The ROI of the poftfolio ranges within [8.25%, 21%]
The confidence inteval of the profit margin of the portfolio at 95% is [10.76%, 18.94%]
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).
Dissertation ISFA – Nguyen Quang Huy Page 78
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
unchanged as per best estimate scenario
Scenario 18 Investment return is 5%/year for the whole insurance period and Death Claim
is 120% of the CSO1980 and lapse rates are 30%/year. Other assumptions keep
unchanged as per best estimate scenario
Scenario 19 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
increase by 10%. Other assumptions keep unchanged as per best estimate
scenario
Scenario 20 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 acquisition cost
increase by 10%. Other assumptions keep unchanged as per best estimate
scenario
Table 10.17: Description of stress test cases under deterministic model
Dissertation ISFA – Nguyen Quang Huy Page 79
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%.
B. For the Par Product
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
Dissertation ISFA – Nguyen Quang Huy Page 80
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
Dissertation ISFA – Nguyen Quang Huy Page 81
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
Dissertation ISFA – Nguyen Quang Huy Page 82
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
Dissertation ISFA – Nguyen Quang Huy Page 83
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
Sample Variance 1.57132E+21 6.59998E+19 0.001317886 0.002201862 0.000100381 0.010955841
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
Dissertation ISFA – Nguyen Quang Huy Page 84
We simulate the different scenarios with assumptions fluctuate around the above stress test
assumptions.
The profit margin of the portfolio has the shape of normal distribution with the mean of 0.3% and
standard deviation of 3.6%.
The profit margin of the poftfolio ranges within [-11.1%, 12.5%]
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
standard deviation of 4.6%.
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]
The VaR of profit of each portflio at 99.5% confidence level is -23.3 billion VND (loss).
Under the extreme conditions, the profitability criteria for Non Par portfolio may become
vulnerable.
Dissertation ISFA – Nguyen Quang Huy Page 85
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
standard deviation of 1.5%.
The profit margin of the poftfolio ranges within [-6.9%, 2.9%]
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
Sample Variance 1.26995E+19 1.47012E+19 0.000229 0.000663 0.000102 0.011207
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
Dissertation ISFA – Nguyen Quang Huy Page 86
The VaR of the profit margin of the portfolio at 99.5% is -5.69%
The ROI of the portfolio has the shape of normal distribution with the mean of 6.9% and standard
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]
The VaR of profit of each portflio at 99.5% confidence level is -14.2 billion VND (loss).
Under the extreme conditions of the stress test scenarios, the profitability criteria for par portfolio
may become very vulnerable.
Dissertation ISFA – Nguyen Quang Huy Page 87
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.
Dissertation ISFA – Nguyen Quang Huy Page 88
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
Dissertation ISFA – Nguyen Quang Huy Page 89
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
Dissertation ISFA – Nguyen Quang Huy Page 90
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%
Dissertation ISFA – Nguyen Quang Huy Page 91
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%
Dissertation ISFA – Nguyen Quang Huy Page 92
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
Dissertation ISFA – Nguyen Quang Huy Page 93
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
Dissertation ISFA – Nguyen Quang Huy Page 94
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
AGE CHILDProfit Margin
ROIAGE CHILD
BEYAGE CHILD
AG
E P
AR
ENT
AG
E P
AR
ENT
AG
E P
AR
ENT
Dissertation ISFA – Nguyen Quang Huy Page 95
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
AGE CHILDProfit Margin
ROIAGE CHILD
BEYAGE CHILD
AG
E P
AR
ENT
AG
E P
AR
ENT
AG
E P
AR
ENT
Dissertation ISFA – Nguyen Quang Huy Page 96
Appendix 5: Scenarios and Stress Test
Scenarios Test
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 2 Investment return is 6.0%/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 6 Lapse rate is 15%/year. Other assumptions keep unchanged as per best estimate
scenario.
Scenario 7 Commission and acquisition cost increase by 5.0%. Other assumptions keep
unchanged as per best estimate scenario.
Scenario 8 Commission and acquisition cost increase by 10%. Other assumptions keep
unchanged as per best estimate scenario.
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
best estimate scenario.
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 12 Investment return is 6.0%/year for the whole insurance period and Death Claim is
70% of the CSO1980. Other assumptions keep unchanged as per best estimate
scenario
Scenario 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.
Scenario 14 Investment return is 8.0%/year for the whole insurance period and lapse rates are
Dissertation ISFA – Nguyen Quang Huy Page 97
15%/year. Other assumptions keep unchanged as per best estimate scenario.
Scenario 15 Investment return is 8.0%/year for the whole insurance period and Death Claim is
70% of the CSO1980 and lapse rates are 15%/year. Other assumptions keep
unchanged as per best estimate scenario
Scenario 16 Investment return is 6.0%/year for the whole insurance period and Death Claim is
70% of the CSO1980 and lapse rates are 15%/year. Other assumptions keep
unchanged as per best estimate scenario
Stress Test
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
unchanged as per best estimate scenario
Scenario 18 Investment return is 5%/year for the whole insurance period and Death Claim is
120% of the CSO1980 and lapse rates are 30%/year. Other assumptions keep
unchanged as per best estimate scenario
Scenario 19 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
increase by 10%. Other assumptions keep unchanged as per best estimate
scenario
Scenario 20 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 acquisition cost increase
by 10%. Other assumptions keep unchanged as per best estimate scenario
Dissertation ISFA – Nguyen Quang Huy Page 98
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%
Profit MarginAGE CHILD
AG
E P
AR
ENT
ROIAGE CHILD
AG
E P
AR
ENT
Dissertation ISFA – Nguyen Quang Huy Page 99
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%
Profit MarginAGE CHILD
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%
Profit MarginAGE CHILD
AG
E P
AR
ENT
ROIAGE CHILD
AG
E P
AR
ENT
Dissertation ISFA – Nguyen Quang Huy Page 100
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%
Profit MarginAGE CHILD
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%
Profit MarginAGE CHILD
AG
E P
AR
ENT
ROIAGE CHILD
AG
E P
AR
ENT
Dissertation ISFA – Nguyen Quang Huy Page 101
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%
Profit MarginAGE CHILD
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%
Profit MarginAGE CHILD
AG
E P
AR
ENT
ROIAGE CHILD
AG
E P
AR
ENT
Dissertation ISFA – Nguyen Quang Huy Page 102
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%
Profit MarginAGE CHILD
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%
Profit MarginAGE CHILD
AG
E P
AR
ENT
ROIAGE CHILD
AG
E P
AR
ENT
Dissertation ISFA – Nguyen Quang Huy Page 103
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%
Profit MarginAGE CHILD
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%
Profit MarginAGE CHILD
AG
E P
AR
ENT
ROIAGE CHILD
AG
E P
AR
ENT
Dissertation ISFA – Nguyen Quang Huy Page 104
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%
Profit MarginAGE CHILD
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%
Profit MarginAGE CHILD
AG
E P
AR
ENT
ROIAGE CHILD
AG
E P
AR
ENT
Dissertation ISFA – Nguyen Quang Huy Page 105
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%
Profit MarginAGE CHILD
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%
Profit MarginAGE CHILD
AG
E P
AR
ENT
ROIAGE CHILD
AG
E P
AR
ENT
Dissertation ISFA – Nguyen Quang Huy Page 106
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%
Profit MarginAGE CHILD
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%
Profit MarginAGE CHILD
AG
E P
AR
ENT
ROIAGE CHILD
AG
E P
AR
ENT
Dissertation ISFA – Nguyen Quang Huy Page 107
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%
Profit MarginAGE CHILD
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%
Profit MarginAGE CHILD
AG
E P
AR
ENT
ROIAGE CHILD
AG
E P
AR
ENT
Dissertation ISFA – Nguyen Quang Huy Page 108
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%
Profit MarginAGE CHILD
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%
Profit MarginAGE CHILD
AG
E P
AR
ENT
ROIAGE CHILD
AG
E P
AR
ENT
Dissertation ISFA – Nguyen Quang Huy Page 109
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%
Profit MarginAGE CHILD
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%
Profit MarginAGE CHILD
AG
E P
AR
ENT
ROIAGE CHILD
AG
E P
AR
ENT
Dissertation ISFA – Nguyen Quang Huy Page 110
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%
Profit MarginAGE CHILD
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%
Profit MarginAGE CHILD
AG
E P
AR
ENT
ROIAGE CHILD
AG
E P
AR
ENT
Dissertation ISFA – Nguyen Quang Huy Page 111
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%
Profit MarginAGE CHILD
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%
Profit MarginAGE CHILD
AG
E P
AR
ENT
ROIAGE CHILD
AG
E P
AR
ENT
Dissertation ISFA – Nguyen Quang Huy Page 112
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%
Profit MarginAGE CHILD
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%
Profit MarginAGE CHILD
AG
E P
AR
ENT
ROIAGE CHILD
AG
E P
AR
ENT
Dissertation ISFA – Nguyen Quang Huy Page 113
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%
Profit MarginAGE CHILD
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%
Profit MarginAGE CHILD
AG
E P
AR
ENT
ROIAGE CHILD
AG
E P
AR
ENT
Dissertation ISFA – Nguyen Quang Huy Page 114
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%
Profit MarginAGE CHILD
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%
Profit MarginAGE CHILD
AG
E P
AR
ENT
ROIAGE CHILD
AG
E P
AR
ENT
Dissertation ISFA – Nguyen Quang Huy Page 115
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%
Profit MarginAGE CHILD
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%
Profit MarginAGE CHILD
AG
E P
AR
ENT
ROIAGE CHILD
AG
E P
AR
ENT
Dissertation ISFA – Nguyen Quang Huy Page 116
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%
Profit MarginAGE CHILD
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%
Profit MarginAGE CHILD
AG
E P
AR
ENT
ROIAGE CHILD
AG
E P
AR
ENT
Dissertation ISFA – Nguyen Quang Huy Page 117
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%
Profit MarginAGE CHILD
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%
Profit MarginAGE CHILD
AG
E P
AR
ENT
ROIAGE CHILD
AG
E P
AR
ENT
Dissertation ISFA – Nguyen Quang Huy Page 118
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
Death/ TPD benefit of the
child (before age of 18) N/A 150M
Death/ TPD benefit of the
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%
Dissertation ISFA – Nguyen Quang Huy Page 119
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
Death/ TPD benefit of the
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
Death/ TPD benefit of the
child (before age of 18) N/A 100.5M
Death/ TPD benefit of the
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%
Dissertation ISFA – Nguyen Quang Huy Page 120
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
Dissertation ISFA – Nguyen Quang Huy Page 121
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.8419
R Square
0.7088
Adjusted R Square
0.7082
Standard Error
0.0049
Observations 499
ANOVA
df SS MS F Significance F
Regression 1 0.02856128 0.02856128 1209.66441 3.046E-135 Residual 497 0.01173462 2.3611E-05
Total 498 0.04029591
Coefficients Standard Error t Stat P-value Lower 95%
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%
Lapse vs Profit Margin
Dissertation ISFA – Nguyen Quang Huy Page 122
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.9272 R Square 0.8598 Adjusted R
Square 0.8595 Standard Error 0.0057 Observations 499 ANOVA
df SS MS F Significance F
Regression 1 0.0985
0.0985
3,047.74 0.0000
Residual 497 0.0161
0.0000
Total 498 0.1146
Coefficients Standard Error t Stat P-value Lower 95%
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
Dissertation ISFA – Nguyen Quang Huy Page 123
B. For Par Product
SUMMARY OUTPUT
Regression Statistics
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
Dissertation ISFA – Nguyen Quang Huy Page 124
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.8258
R Square
0.6820
Adjusted R Square
0.6814
Standard Error
0.0021
Observations 499
ANOVA
df SS MS F Significance F
Regression 1
0.0046
0.0046
1,065.9021 9.744E-126
Residual 497
0.0022
0.0000
Total 498
0.0068
Coefficients Standard Error t Stat P-value Lower 95%
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%
Lapse vs Profit Margin
Dissertation ISFA – Nguyen Quang Huy Page 125
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.9216
R Square
0.8493
Adjusted R Square
0.8490
Standard Error
0.0024
Observations 499
ANOVA
df SS MS F Significance F
Regression 1
0.0159
0.0159
2,801.1170 2.21E-206
Residual 497
0.0028
0.0000
Total 498
0.0187
Coefficients Standard Error t Stat P-value Lower 95%
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