Finance Discipline Group

UTS Business School

25503 Investment Analysis

Assignment—Part II

Autumn 2016

1. The assignment should be completed in groups of 3–4 students. Your group should

be the same as for the first part of the assignment (unless explicit permission has

been granted from the subject coordinator). All group members receive the same

mark.

2. Help: For consultation times, please check UTSOnline and the subject outline.

Note that email is not an efficient 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 5” located in Building 8, Level 5, by 5:00pm Wednes-

day 8 June 2016. 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.

5. The assignment computations are to be done in Excel, but the solutions may be

pasted into Word and formatted for submission. The final report, including all

text, tables and figures should be printed out on A4 paper with a minimum font

size of 12. Also, the final report (excluding the cover sheet) should not exceed 12

pages in length.

Subject Coordinator: Kristoffer J. Glover

In this assignment you will implement an index tracking investment strategy as well as

construct an immunized bond portfolio. In order to help you do this you will find an Excel

workbook called AssignmentData2.xlsx on UTSOnline. It contains weekly stock price data

for the six largest capitalised companies on the Australian stock market along with the levels

of the All Ordinaries index for the last three years.

1

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 first 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 offerings and

your boss wants you to investigate the different 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 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 re-

turns for the six stocks, as well as the variance-covariance matrix of these returns.

These expected returns etc. should be annualized (i.e., in annual units).

(c) Using the All Ordinaries index as a proxy for the market portfolio (MP), estimate

and report the betas of the six stocks.

(d) Decompose the total risk (variance) of each asset into its systematic and un-

systematic components, i.e., report all three values (variance, systematic risk,

unsystematic risk) along with the diversification ratio (R2) for each stock and the

index.

(e) Assuming risk-free borrowing and lending at rF = 2% per annum, plot the capital

market line (CML), and indicate the positions of the six stocks as well as the MP.

(f) Plot the security market line (SML), and indicate the positions of the six 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 All Ordinaries index is not traded, you wish to construct a portfolio out of the six

stocks that ‘tracks’ the index as close as possible (in some sense). Your boss asks you to

propose at least two different 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 six 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 six stocks) of the portfolio that minimises the variance

of the difference in weekly returns between the portfolio and the AORD index.

More specifically, let r1, . . . , rT be the vector-valued sample returns of the six

stocks, for t = 1, . . . , T weeks. Similarly, let rI,1, . . . , rI,T denote the sample

returns of the index. Then you want to find the vector of portfolio weights that

2

solves the following minimisation problem:

min

x

Var x

⊤

rt − rI,t .

Again you should describe in words what you have done in Excel as well as report

the minimum value achieved for the variance of the differences.

(c) Report the expected return, variance, beta and R2 for your two tracker portfolios

constructed above. Which method do you recommend to your boss and why?

You present this evidence to your boss, who, after careful consideration, asks you to construct

and implement a completely different method of her own! Oh well, at least you learnt

something.

Since the tracking portfolio is a passive strategy, there is not much work to do on it once it

has been constructed. The next morning, when your boss realises this she decides to loan you

to one of the other partners who specialises in the company’s fixed-income offerings. Within

five minutes of arriving at his desk you are asked to help with an urgent bond portfolio

immunization in which you need to perform the following tasks and have the results on your

new supervisor’s desk in two hours:

3. A firm has a liability, L, which requires a payment of $25,000 per year (paid annually

at the end of the year), for 15 years, plus a final payment of $1,000,000 at the end of

the 15th year. The following semi-annual coupon-bearing bonds, with a face-value of

$1,000, are available for investment:

Bond Maturity (Years) Coupon

1 20 6%

2 15 7%

3 5 8%

Assume that the market YTM is a flat 7% per annum, with semi-annual compounding.

(a) Construct an immunizing portfolio for L with 50% invested in Bond 1 and 50%

invested in Bonds 2 and 3 combined. Report the portfolio weights and show your

workings.

(b) Assess the effectiveness of your immunizing portfolio if the market YTM increases

by 0.5%.

(c) What would the coupon rate need to be on Bond 1 for the immunization to be

done by simply investing 100% in this (20 year) bond?

With more than an hour to spare, you finish the last calculation and hand the results to

your new supervisor. He’s impressed. So much so that he offers to take you for lunch on

expenses. As you tuck into your rib eye at Rockpool you start to realise that maybe all your

hard work in 25503 Investment Analysis was worth it after all!

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