# Investment Management Assignment|Part

- The assignment should be completed individually.
- 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. - Due date: A hard copy of the assignment should be submitted in the assignment

box marked \Finance2″ located in Building 8, Level 5, by 5:00pm Friday 8

June 2018. Late submissions will not be accepted and no soft copy is required. - Complete a cover sheet (available on UTSOnline) with your signature and attach

it to a printout of your answers. - The assignment computations are to be done in Excel, but the solutions may be

pasted into Word and formatted for submission. You should provide explana-

tion and discussion to your work and answers. 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 10

pages in length.

Subject Coordinator: Tony He

In this assignment you will be computing bond prices, modied durations and holding period

returns. You will also implementing a hedging strategy for a stream of liabilities. In order

to help you do this you will nd an Excel workbook called AssignmentIIData2018.xlsx on

UTSOnline.

Data Description

In AssignmentIIData2018.xlsx, you can nd the coupon rate and maturity on 20 semi-

annual treasury bonds. You can also nd the zero-coupon yields (ZCYs) with dierent

maturities. Note that the ZCYs are expressed per annum with annual compounding.

Question 1 (Bond Pricing – 5 marks)

Upon graduation from the UTS Business School, you’re now working for a superannuation

fund. On your rst day at work, your boss has asked you to calculate the prices of the

treasury bonds that are currently traded in the market based on the current yield curve, and

also nd their yield-to-maturities (YTMs).

(a) Based on information provided for the treasury bonds and the ZCYs, plot the yield

curve and describe the general shape of the yield curve, and compute the bond prices

(accurate to 4 decimal places).

(1 mark)

(b) Based on the bond prices in part (a), calculate the yield-to-maturity (YTM) p.a.

(semi-annually compounded) for each of the treasury bonds. Plot the YTM curve with

respect to the maturity and comment on its relation to the yield curve in (a). Note:

you will need to use GoalSeek or Solver in Excel to nd the YTMs.

(2 marks)

(c) Suppose there is a zero-coupon bond (ZCB) with a face value of $100 and 2 years to

maturity, which currently trades at $95. Construct an arbitrage portfolio by trading

in the ZCB and also in the rst four treasury bonds to show how you can make an

arbitrage prot. You need to indicate your portfolio in terms of weights and dollar

amounts of the bonds and explain your answer.

(2 marks)

Question 2 (Holding Period Returns – 5 marks)

Now your boss is interested in investing in the long-maturity treasury bonds because of their

attractive yields, so you’re asked to analyse the risks that are involved in this investment.

(a) Suppose you decide to invest in treasury bond GSBE47 for 5 years. Assume coupons

can be reinvested at the current YTM of the bond, compute your holding period return

(HPR) p.a. (semi-annually compounded) if the YTM increases by 0, 25, 50, 75 and

100 basis points (bps), and if the YTM decreases by the same amount at the end of

year 5 when you sell the bond. Plot the relationship between HPR and changes in the

YTM and comment on your results.

(2 marks)

(b) Repeat part (a) assuming you now decide to also short-sell treasury bond GSBG25

with 5 years to maturity to fund your investment in treasury bond GSBE47.

(2 marks)

(c) Repeat part (a) assuming the YTM of the bond remains the same, instead the rein-

vestment yield of the coupons increases/decreases by 0, 25, 50, 75, and 100 bps. Plot

the relationship between HPR and changes in the reinvestment yield.

(1 mark)

Question 3 (Hedging interest rate risk – 5 marks)

Your boss is impressed with your work eciency and now the real challenging task comes

- you need to implement a hedging strategy to ensure that the fund has enough capital to

meet a liability. The superannuation fund will need to pay $100 million in 5 years’ time.

(a) Use the current yield curve to determine the present value and also the modied du-

ration of the liability.

(1 mark)

(b) Now, in order to hedge interest rate risk, you want to invest in a bond portfolio which

has the same modied duration as the liability. To accomplish this task, pick two of

the treasury bonds currently traded in the market, Bond A and Bond B, compute their

modied durations and determine the dollar amount that should be invested in each

bond. Note that you need to determine which two bonds are most suitable and explain

your choice. Also, assume the modied duration of your bond portfolio is given by

Dp = wADA + wBDB;

where wA and wB are the percentage weights invested in Bond A and Bond B respec-

tively.

(2 marks)

(c) Now suppose the entire yield curve shifts down by 100 bps. Calculate the percentage

change in the present value of the liability in part (a) and also of the value of the bond

portfolio in part (b). Comment on the eectiveness of the hedge.

(2 marks)