ACTL2111/5102 2020 Term 2 Excel Assignment
Deadline: 3 August 2020 (Monday of Week 10) at 5pm sharp
Jackson is a fresh actuarial graduate who just started his rst full time job in a reputable insurance
company in Sydney on 3 January 2020. Upon the start of his job, Jackson also decided to make an
investment to accumulate a deposit to purchase his rst home in 10 years time. As a junior actuary who
passed Part I and Part II exams, Jackson has a personal preference of passive investment strategies,
that is, investments consisting of fund tracking well-diversi ed portfolios and government bonds only.
To make such important investment decision, he consulted a bank regarding his investment strategy.
You, a junior analyst in the bank, have received the case from your supervisor, with the following
information.
a. Salary:
(i) Jackson’s annual starting salary is $55,000 (after income tax) and it will increase by 4.5%
every year at the beginning of each year.
(ii) There are three actuarial exams Jackson will take. His salary will increase by 20% (i.e. 15.5%
extra compared to the regular increase described in part (i) above) at the beginning of the
year after he passes an exam. Since he is working full time, he will take only one exam every
year and his chance of passing each exam is 35%, independent of his performance in previous
exams (if there is any).
(iii) He receives his salary at the end of every fortnight on Friday, i.e. the rst payment will be
on 17 January 2020.
b. Savings: Jackson is very keen on saving as much as possible for his deposit, so he has decided that
each fortnight when he receives his salary, he will put 30% of it to his investment portfolio.
c. Investment options: After a meeting with Jackson, your supervisor has shortlisted the following
two investments for Jackson:
Option 1: 75% Vanguard Australian Shares Index Fund; 25% government (zero-coupon) bonds
maturing on 31 December 2029,
Option 2: 50% Vanguard Australian Shares Index Fund; 50% government (zero-coupon) bonds
maturing on 31 December 2029.
For example, in Option 2, Jackson will invest 15% of his total salary in government bonds and the
other 15% in the index fund every fortnight. The index fund does not pay dividends.
d. Bond return: Your colleague in the interest rate modelling team has given you the current spot
yield curve using the dynamic Nelson-Siegel model, where the (annual eective) -year spot yield
at time t is it; % with it; given by
it; = 1;t + 2;t
1 e
+ 3;t
1 e
e
; (1)
where = 0:6150 is a parameter. Here both t and are measured in years, where t is the amount
of time from 3 January 2020 (17th of Jan is t = 1=26, and 31st of Jan is t = 2=26 etc.) and is
the remaining time (counting from time t) until maturity. It is assumed that each year has exactly
52 weeks. (Note that it; will not be known before time t, and therefore from time 0’s perspective
it is modelled as a random variable.) The starting values of the ’s are given by
1;0 = 3:0
2;0 = 1:5;
3;0 = 2;
1
and then for subsequent values of t = 1
26 ; 2
26 ; :::; 925
26 ; 10 they satisfy the recursive relationship
1;t = 0:3 + 0:85 1;t 1
26
+ “1;t:
2;t = 0:25 + 0:65 2;t 1
26
“1;t;
3;t = 0:8 + 0:6 3;t 1
26
+ “2;t;
with
“1;t N(0; 0:10);
“2;t N(0; 0:19):
Here all “j;t’s are assumed to be independent (j = 1; 2 and t = 1
26 ; 2
26 ; :::; 925
26 ; 10).
*Note that negative interest rates are possible but rare, due to the dynamics of the ’s.
e. Return for the fund: the eective return rate for period [t; t + 1
26 ] is rt% with rt given by
it;1 + 5:5
26
+ Xt (2)
with
Xt N(0; 9);
where t is the beginning of a fortnight and the random variables Xt’s are independent.
f. Costs and fees and others: At this stage, your supervisor is going to present the two products
(described in c.) in preliminary form to Jackson so you do not need to consider the details such as
costs, fees, taxes on investment and reinvestment of the bond coupons.
You need to perform the following analysis for your supervisor to present to Jackson:
1. Project Jackson’s salary payments over the next 10 years (from the rst payment on 17 January
2020 to the last payment in 2029), under the following scenarios:
(i) He passes the three exams in 2022, 2025 and 2028 (average scenario);
(ii) He passes the three exams in 2020, 2021 and 2022 (best scenario);
(iii) He passes the three exams in 2024, 2028 and does not pass the last exam before 2030 (bad
scenario).
Also calculate the probability of each of the scenarios (i)-(iii).
2. Interpret the terms in (1). Via simulation, plot the spot yield curves at 1 January 2027 and 1
January 2029 respectively, for 0 10, i.e. the yield curve for the next 10 years starting at
1 January 2027 and another yield curve for the next 10 years starting at 1 January 2029. (Hint:
You only need to simulate one trajectory when plotting the two yield curves, and the yield
curves are dependent.) Explain the shape of the curves. Also interpret the formula (2).
3. For each of the options in the average scenario, run 100 simulations on the terminal value of
Jackson’s investments and calculate relevant summary statistics including the mean, standard
deviation, minimum, maximum, median. Plot the histograms for the terminal values of the two
options in the same graph.
*Hint: You may want to create a new worksheet and use VBA to copy your answer in each
simulation to the new worksheet.
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4. Provide a brief recommendation to Jackson based on your analysis (max. 250 words). This
should be placed in a separate sheet within the same EXCEL le.
Please note all workings used to arrive at any conclusions must be presented in your
workbook in a logical and coherent manner. This includes any macros you write
and excel formulas you have used. Any macros and formulas used must work when
the marker runs them. You will be marked on your presentation and readability.
Assignment submission procedure
Your assignment must be uploaded as a unique EXCEL document. As long as the due date is still
future, you can resubmit your work; the previous version of your assignment will be replaced by the
new version.
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regard to other sources (such as the internet or all assignments submitted all around the world via
Turnitin). More information is available at: [click]. Please read this page, as we will assume that you
are familiar with its content.
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within the submission system as the system may not support viewing Excel le. This will not be
a problem because the grader will download your Excel le for grading purposes. After submission,
please download the le from the system to make sure that (1) it is the right le (as students usually
have saved multiple versions of the le in their own computer); and (2) you can view the downloaded
le in your computer (in case the le is corrupted possibly due to e.g. internet disruption during le
upload).
Please note that the School of Risk and Actuarial Studies will apply the following policy on late
assignments. A penalty of 25% of the mark the student would otherwise have obtained, for each
full (or part) day of lateness (e.g., 0 day 1 minute = 25% penalty, 2 days 21 hours = 75% penalty).
Students who are late must submit their assessment item to the LIC via e-mail. The LIC will then
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Plagiarism awareness
Students are reminded that the work they submit must be their own. While we have no problem with
students discussing assignment problems if they wish, the material students submit for assessment
must be their own. In particular, this means that any code you present are from your own computer,
which you yourself developed, without any reference to any other student’s work.
While some small elements of code are likely to be similar, big patches of identical code (even with
dierent variable names, layout, or commentsTurnitin picks this up) will be considered as plagiarism.
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The best strategy to avoid any problem is not to share bits and pieces of code with other student
outside your group.
Note however that you are allowed to use any EXCEL les that were made available during the course
(either from the lectures or developed in the lab tutorials). You don’t need to reference them formally,
and this will not be considered as plagiarism.
Students should make sure they understand what plagiarism iscases of plagiarism have a very high
probability of being discovered. For issues of collective work, having dierent persons marking the
assignment does not decrease this probability. For more information on plagiarism, see [click].
Students may consult the Write well; Learn deeply” website [click] and consult the resources provided
there. In particular, all students should do the quiz about plagiarism to make sure they know how to
avoid any issue. For instance, did you know that sharing any part of your work with other students
(outside your group) before the deadline is already considered as plagiarism? 1
Assessment criteria
Please see the le Rubric”.
1Yes, that’s right, just sending it, even if the third party promises not to copy, is already plagiarism in the UNSW
policy!
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