Finance Discipline Group
UTS Business School
25503 Investment Analysis
Assignment|Part II
Autumn 2018
1. The assignment should be completed in groups of 3{4 students. If you are satis ed
with the performance of your group for the Assignment Part I, your group may
remain the same. If your submitted Group Work Declaration Forms indicate that
all members of the group have contributed fairly to this assignment, each member
will receive the same mark for the assignment.
2. Help: For consultation times, please check UTSOnline and the subject outline.
Note that email is not an ecient way for asking questions about the assignment;
please post any questions on the UTSOnline discussion board.
3. Due date: A hard copy of the assignment should be submitted in the assignment
box marked FINANCE 3″ located in Building 8, Level 5, by 5:00pm Wednes-
day 6 June 2018. Late submissions will not be accepted and no soft copy is
required.
4. Complete a cover sheet (available on UTSOnline) with all the signatures from your
group members and attach it to a printout of your answers. Please note the in-
structions regarding Group Work Declaration Forms.
5. The assignment computations are to be done in Excel, but the solutions may be
pasted into Word and formatted for submission. The nal report, including all
text, tables and gures should be printed out on A4 paper with a minimum font
size of 12. Also, the nal report (excluding the cover sheet) should not exceed 12
pages in length.
Subject Coordinator: Vitali Alexeev
In this assignment you will implement an index tracking investment strategy. In order to help you
do this you will nd an Excel workbook called AssignmentData2.xlsx on UTSOnline. It contains
weekly stock price data for twelve companies listed on the Australian Security Excahnge along
with the levels of the ASX200 index. The `Sample Data’ will be used for Questions 1 and 2 and
the `Out-of-Sample Data’ will be used for Question 3.
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It has been over a month since you started working for the small asset management company (see
Part I) and in that time your boss agreed to implement the portfolio you constructed on your very
rst day on the job (after some more minor `tweeks’). You have now just returned from the break
and your boss has set you on your next project!
The company is thinking of adding an index tracking fund to their investment o erings and your
boss wants you to investigate the di erent methods of constructing such a tracking portfolio. To
do this you should perform the following preliminary analysis:
1. (a) Transform the stock prices and index values in the `Sample Data’ tab into continuously
compounded returns (you do not need to report these in your submission).
(b) Using the resulting returns data, estimate (and report) the vector of expected returns
for the twelve stocks and the index. You should also report the variance-covariance
matrix for the twelve stocks as well as the variance of the index. The expected returns
etc. should be annualised (i.e., in annual units).
(c) Using the ASX200 index as a proxy for the market portfolio (MP), estimate and report
the betas of the twelve stocks.
(d) Decompose the total risk (variance) of each asset into its systematic and unsystematic
components, i.e., report all three values (variance, systematic risk, unsystematic risk)
along with the diversi cation ratio (R2) for each stock and the index.
(e) Assuming risk-free borrowing and lending at rF = 1% per annum, plot the capital
market line (CML), and indicate the positions of the twelve stocks as well as the MP.
(f) Plot the security market line (SML), and indicate the positions of the twelve stocks as
well as that of the MP. Based on this graph, discuss which stocks look over-valued, and
which stocks look under-valued?
Since the ASX200 index is not traded, you wish to construct a portfolio out of the twelve stocks
that `tracks’ the index as close as possible (in some sense). Your boss asks you to propose at least
two di erent methods for constructing such a tracker portfolio. After some careful research you
come up with two possible methods and to implement these you must perform the following tasks
(Hint|you will need to use Solver):
2. (a) Report the weights (in the twelve stocks) of the portfolio whose variance is minimised
but whose exposure to the index is exactly one, i.e., that has P = 1. You should
describe in words what you have done in Excel and report the value of your portfolio’s
(minimised) variance.
(b) Report the weights (in the twelve stocks) of the portfolio that minimises the Root-
Mean-Square Error (RMSE) of the di erence in weekly returns between the portfolio
and the ASX200 index. More speci cally, let r1; : : : ; rT be the vector-valued sample
returns of the twelve stocks, for t = 1; : : : ; T weeks. Similarly, let rI;1; : : : ; rI;T denote
the sample returns of the index. Then you want to nd the vector of portfolio weights
Note you should use the variance-covariance matrix to calculate the portfolio’s variance.
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that solves the following minimisation problem:
min
x
vuut
1
T
XT
t=1
(x>rt ? rI;t)2:
Again you should describe in words what you have done in Excel as well as report the
minimum value of the RMSE achieved.
(c) Report the expected return, variance, beta and R2 for your two tracker portfolios con-
structed above. Which method do you recommend to your boss and why?
You present this evidence to your boss, who, after careful consideration, decides to implement the
tracking portfolio you constructed in 2(b).
Since the tracker portfolio is a passive strategy, your boss moves you on to other projects. However,
10 months have now passed and your boss asks you to look into the performance of the tracker
portfolio. The portfolio was constructed on June 30, 2017 (seconds before the market closed for the
day at 4pm) using the portfolio weights found in 2(b) and with an investment amount of $1,000,000.
You should assume that this was done without any transaction costs at the prices quoted on that
date in the `Out-of-Sample’ tab and that any fraction of a share can be purchased. You should
also assume that the portfolio was held, without any further transactions, until April 27, 2018 (i.e.,
the portfolio was not re-balanced). To assess the performance of the tracking portfolio you need
to perform the following tasks:
3. (a) Calculate and report a time-series plot of the tracker portfolio value from June 30, 2017
to April 27, 2018, along with the performance of the ASX200 index, clearly indicating
which series is which. You should also normalise the values of both time series so that
their values are 100 on June 30, 2017.
(b) Report the simple annualised return of the tracker portfolio and the ASX200 index over
the investment period.
(c) Using the weekly continuously compounded returns for the tracker portfolio and the
index, report the beta, R2, and RMSE for the tracker portfolio over the investment
period. Comment on how close these values are to the values found for the tracker
portfolio `in sample’ from Questions 2(b/c).
You put some nishing touches to the report, print it, and take it to your bosses oce. She
scans over the documents brie y, clearly impressed by the level of detail and rigour of your analysis.
So much so that she o ers to take you to lunch on expenses! As you tuck into your rib-eye steak
at Cafe Sydney looking out across the harbour, you start to realise that maybe all your hard work
in 25503 Investment Analysis was worth it after all!
The End.
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