Semester 2 – End of Semester, 2020 STAT3038/6045 Actuarial Techniques

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Research School of Finance, Actuarial Studies & Statistics

FINAL EXAMINATION
Semester 2 – End of Semester, 2020

STAT3038/6045 Actuarial Techniques

Writing Time: 150 minutes
Reading Time: nil

Exam Conditions:
Central Examination
Students access this exam paper via a link from a Wattle quiz invigilated by Proctorio
This examination paper is not available to the ANU Library archives

Materials Permitted In The Exam:
Computer utilizing only Wattle, Excel, Word, Adobe PDF Reader (and email if required – see below)
Files saved locally on the computer may be accessed during the exam
Paper-based Dictionary
Calculator (programmable allowed)

Instructions to Students:
• The exam contains one question only which you must answer. Your submission must consist
of a maximum of one Excel file and a maximum of one Word file.
• You MUST use “Final Exam Template” on Wattle as the starting point for the Excel work
required in this question. Marks will be deducted from the final exam score for not following
this instruction.
• You MUST start your Word work in this question from a blank document. Marks will be
deducted from the final exam score for not following this instruction.
• Students have been previously advised in Lesson 1.7 and Lesson 2.6 of the Proctorio
requirements of this exam and have been given an opportunity to download the necessary
software and practice submission via Proctorio before this exam.
• You have 150 minutes to upload your solution to the exam. This time starts from when you
have completed the Proctorio pre-checking and are able to access the exam. A countdown
timer can be found in the activity from which you access the exam. Make sure you leave
sufficient time to upload your solutions within the 150 minute period. It is strongly
recommended you finish the exam 10 minutes before the end of the 150-minute period to
give yourself sufficient time.
• The latest possible time to submit the exam is 160 minutes after the scheduled start of the
exam, although the 150 minute time limit described above still applies. Hence you have 10
minutes from the scheduled start of the exam to complete the Proctorio pre-checking and
access the exam. If you take longer than 10 minutes to complete the pre-checking you will
have less than 150 minutes to upload your solution to the exam.
• The course convener will be available on Zoom and by email if required during the exam. A
link to the Zoom meeting is available in the Proctorio examination area.


Semester 2 – End of Semester, 2020 STAT3038/6045 Actuarial Techniques

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Instructions to Students (continued):
• If the course convener needs to contact all students they will do so via a forum post linked in
the Proctorio examination area as “Messages to all students from course convener”. Make
sure to check this document occasionally during the exam, and click on the link at least once
every two hours to ensure you are not logged out of Wattle before uploading your solution.
• For any technical issues during the exam, you can contact Wattle help via +61 2 6125 4321
(opt 1, opt 5) or wattle.support@anu.edu.au.
• When you have completed your attempt, you must upload both your Excel and Word files to
the quiz activity from which you accessed this exam paper. After this, you must also
immediately upload your Excel file to the “Upload Final Exam Solution Excel Submission”
assignment activity on Wattle and your Word file to the “Upload Final Exam Solution Word
Submission” Turnitin activity on Wattle. In the unlikely event of an issue with uploading
solutions you will be able to submit a soft copy of your Excel and Word work by email to the
course convener. Ensure that any submission occurs before the completion of your 150
minute time limit. Late submissions will not be accepted.
• Ensure that you save your work regularly. This is your responsibility and no allowance will be
made for forgetting to save your work.
Semester 2 – End of Semester, 2020 STAT3038/6045 Actuarial Techniques

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Question

BMZ is investigating entering into an arrangement with another financial services institution,
Eastcap, where Eastcap would share some of the obligations of the BMZ Superannuation
Scheme. How this arrangement would work is as follows:

Option 1
• At the start of each year (1 July), the Scheme would pay Eastcap a premium of $(Z%
x Expected Withdrawal Payments).
• The Expected Withdrawal Payments are calculated by aggregating the following
across all active members of the Scheme:

Leaving Service Benefit of the member at that 1 July; multiplied by the probability
that the member will withdraw at the next 30 June.

• Upon voluntary departure of a member, the Scheme would pay (1 – Z%) of the
withdrawal benefits payable, with Eastcap paying the remaining Z% of the withdrawal
benefits payable.

Option 2
• At the start of each year (1 July), the Scheme would pay Eastcap a premium of $(Y%
x Expected Death Payments).
• The Expected Death Payments are calculated by aggregating the following across all
remaining members of the Scheme:

Death Payment that the member is eligible for at the next 31 December; multiplied by
the probability that the member will die at the next 31 December.

• Upon death of a member, the Scheme would pay (1 – Y%) of the death benefits
payable, with Eastcap paying the remaining Y% of the death benefits payable.

You are the actuarial consultant to the Scheme. The Chief Finance Officer (CFO) of BMZ
would like some analysis of the potential effect of these arrangements on the funding level
of the Scheme for the next 10 years.

Prepare a note to the CFO, of no more than 3 pages in Word, which includes the following:
• A brief scope of your task.
• A graphical comparison of the median and 15th/85th percentile Funding Level over
each of the next 10 years, for Z% = 0%, 50% and 100%. Keep Y = 0%.
• A graphical comparison of the median and 15th/85th percentile Funding Level over
each of the next 10 years, for Y% = 0%, 50% and 100%. Keep Z = 0%.
• Descriptions and reasons for the results of the above comparisons, including any
additional analysis that assists in explaining the results.
The document is not required to have any details on the underlying model used and must be
able to be read on its own without reference to the Excel workbook.

Note that the premium paid by the Scheme is not to be included in the Funding Level
calculation at the same 1 July. For example, the Funding Level at 1 July 2020 is unchanged
at 120.2%, with the premium being deducted from the Scheme Assets after the Funding
Level is calculated.
Semester 2 – End of Semester, 2020 STAT3038/6045 Actuarial Techniques

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Question…continued

Recall that the benefits of the Scheme are calculated as follows:

Reason for departure

Benefit paid

Leaving service (voluntarily)

0.015 x (65 – Age at date of leaving service) x Member
Account;

plus

(1 – 0.015 x (65 – Age at date of leaving service)) x 23% x
Years of membership at date of leaving service x Annual
Salary at the date of leaving service

Death (paid to dependents)

23% x (65 – Age at date joined the scheme) x Annual Salary
at the date of death


Further instructions
Use “Final Exam Template” as a starting point for the Excel work required in this question.
You may assume that all assumptions and other components in “Final Exam Template” are
correct and do not require any updating beyond any requirements described in the question.
You should do the following when creating the revised Excel workbook:
• Output from different scenarios that are needed for graphing purposes should be
pasted in the “Key Results” worksheet as values. Any graphs you generate to
answer the question should be placed in this worksheet.
• Any new worksheets you create should have their worksheet tabs highlighted in light
blue.
• Any worksheets that have additions or changes made to them should have their
worksheet tabs highlighted in light blue. Any cells in these worksheets that have
been created or changed should be highlighted in light blue.
• You should design the changes in such a way that the Options and Z/Y values to be
compared in the question can easily be switched between by changing as few cells
as possible. Your submitted Excel workbook should include the calculations from the
revised cash flow structure with Z = 50% and Y = 0%.

The weighting of each component of this task towards the mark for this question is as
follows:
• Calculation of output elements required by the question in Excel = 40%
• Following the instructions above in designing the Excel workbook = 5%
• Appropriate description of scope of task in Word document = 5%
• Presentation of results given the requirements of the stakeholder = 20%
• Description and reasons for the results in the Word document = 25%
• General structure and coherence of the Word document = 5%

END OF EXAMINATION

























































































































































































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