THE UNIVERSITY OF NEW SOUTH WALES

SCHOOL OF RISK AND ACTUARIAL STUDIES

SESSION 1 2014

ACTL 3002: Life Insurance and Superannuation Models

Assignment

This is a Group Assignment.You will be assigned to Groups with others from your tutorial.Groups will normally be 4 or a maximum of 5 members.You should review the Student Guide to Learning in Groups.

Marks total 100 for all of the Group Assignment tasks and the Group Assignmentis 15% of total assessment.The Group Assignment consists of 3 components:

Part (a): worth 25 marks of the Assignment total Part (b) - (i): worth 40 marks of the Assignment total Part (b) - (ii): worth 35 marks of the Assignment total - peer and self assess-

ment (details in separate document)

Part (a) In this part you will need to submit a written Group report and youwill be assessed on your written communication skills.You will be given feedback to assist you improve for the submission of your GroupReport in Part (b) - (i).Due 8.55am 25 March 2014

Part (b) - (i) In this part you will need to submit a written Group report andyou will be assessed on your written communication skills.Due 8.55am 29 April 2014

Instructions

The font size of the main body of your assignment must be 12pt. The assignment you submit must be in this order: Cover Page, the report and

the appendices.

Assignments must be submitted via the Turnitin submission box that isavailable on the course website. As long as the due date has not been reached,you can resubmit your work: the previous version of your assignment will bereplaced by the new version.

All parts of your assignment must be uploaded as a unique pdf document.

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Please note that it is School policy that late assignments, even by oneminute, will not be marked. Assignments MUST be submitted prior to thedue time and date.

Students are reminded of the risk that technical issues may delay or evenprevent their submission (such as internet connection and/or computer break-downs). Students should then consider either submitting their assignmentfrom the university computer rooms or allow enough time (at least 24 hoursis recommended) between their submission and the due time. The Turnitinmodule will not let you submit a late report. No paper copy will be eitheraccepted or graded.

Marks will be given for the written presentation of your results. A clear andprecise presentation is expected in the main body of your assignment. Youshould use graphs and tables as appropriate. Full assessment criteria are givenin the Writhen Communication Assessment Rubric.

Programming code or spreadsheets should not appear in the main body. Theymust be provided as appendices at the end of your assignment.

The font size requirement does not apply to the appendices.Assignment details follow over page.

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Product InformationYou are the actuarial team in a life insurance company. Your team is assessingthe design, pricing and risks of an annual premium deferred annuity contract. Thedeferred annuity commences at age 65. Premiums are level annual and paid fromissue date to age 65. Premiums net of expenses are invested in the insurance fundand this fund earns interest. The accumulated premiums net of expenses is used topurchase an annuity at age 65. The annuity is payable monthly in arrears. You areassessing premiums for male lives.The features of the product are:

There is a guaranteed minimum accumulation amount at age 65 for the pre-miums net of expenses. This is based on a guaranteed interest rate of 4%p.a.

On death of the policyholder, there is a benefit payable at the end of the policyyear of death of the return of the gross premiums with no interest.

The policyholder may surrender the policy only up to age 65. The surrenderbenefit is the accumulation of the premiums net of expenses at an interest rateof 2% p.a..

Level annual premiums are payable in advance until age 65 earlier death. The deferred annuity is guaranteed to be a minimum of the annuity that would

be paid based on the accumulated premiums net of expenses with an interestrate of 4% p.a.and mortality of 45% of PMA92 from 65 onwards.

Part (a) (25 marks)Page limit for this Part(a): maximum of 2 A4 pages including figures, graphs andtables.

You have to prepare a report for the Group Actuary that presents and discussesthe cash flow profile of the product.

Your report will need to present and discuss the cash flows including premiums(for a range of typical amounts), investment returns, expenses, expected death andsurrender payments, accumulation amounts, annuity payments, and profit and riskmargins.

You need to think carefully about how to present this information.What premium amounts and ages should be used? How should the cash flows bepresented? Can you use graphics and figures effectively? What are the key featuresof the product cash flows you will need to emphasize and why? Can you quantifyuncertainty in cash flows using variance?

Assumptions The following should be assumed:

Current interest rate earned on the life insurance fund is 5% p.a.

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Initial Expenses: $600 per policy before ag 65; Renewal Expenses: $100 at the start of each of year starting from the second

year until death;

Initial Commission: 20% of the first premium at the start of the first year; Renewal Commission: 2.5% of the premium at the start of each year starting

from the second year;

Profit and risk margin of 17% of the gross premiums and 10% of the annuitypayments.

Mortality: Life table (75% of the mortality in ELT15 (males) prior to age 65and 55% of PMA92 from 65 onwards)

Rate of surrender: 5% pa; Proportion of policyholders using the accumulated premiums to purchase an

annuity 35%.

Assignment details continue over page.

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Part (b) (40 marks)Page limit for this Part(a): maximum of 4 A4 pages including figures, graphs andtables.

You have to prepare a report that discuses the risks of the product from uncer-tain future interest rates and mortality.

This should be based on a sensitivity analysis to see the impact on the profitmargin of changes in the interest rate and mortality assumptions. You will need toinclude both increases and decreases in these assumptions and use both reasonableand extreme changes to give stress tests. Your results should be related to theirimpact on profit margins. You should also allow for and discuss the product guar-antees explicitly.

(You should search and read some relevant academic reports and/or articles tohelp you answer this question. The Journal of Risk and Insurance has many papersthat may be useful. For the uncertainty of the growth rate and interest rate, youcan start with the article titled Why not random interest published by Society ofActuaries and the references therein. The above article can by found by Googlingthe title. For any article you intend to read, go through the abstract first to seewhether it is relevant and then decide whether to read the full content. You canaccess most of the academic papers through UNSW network. You can also seek helpfrom library staff with finding references.)

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