ACST201 Financial Modelling
Question 1 [4 marks]
Linze bought a $1 000 000 90-day bank bill on 5 August 2014 at a yield of
2.65% p.a. He sold the bond on 17 October 2014 at a yield of 2.71% p.a.
a. [2 marks] What is Linze’s annualised yield over this holding period?
b. [2 marks] Decompose Linze’s dollar yield on this transaction into an
interest rate component and a capital gain/loss component.
Question 2 [5 marks]
In OLQ2 and GSPT1 you did numerous duration calculations for a variety
of bonds. Examining your results, explain how your results illustrate the
following claims (from slides 41–42 of your week 06 lecture).
a. [1 mark] For two bonds with the same coupon rate and yield to maturity,
the one with the longer term to maturity has a higher duration.
For two bonds with the same term to maturity and yield to maturity,
the one with the lower coupon rate has a higher duration.
b. [1 mark] For two bonds with the same term to maturity and coupon
rate, the one with the lower yield to maturity has a higher duration.
For two bonds with the same coupon rate and yield to maturity, the
one with the shorter term to maturity has a lower duration.
c. [1 mark] For two bonds with the same term to maturity and yield to
maturity, the one with the higher coupon rate has a lower duration.
For two bonds with the same term to maturity and coupon rate, the
one with the higher yield to maturity has a higher duration.
Gordo, the owner of a gold mine, estimates the net cash flow from his mining
operations will be as follow.
Time (years) Net cash flow ($)
1 500 000
2 400 000
3 300 000
4 200 000
5 100 000
d. [2 marks] Calculate the duration of the project at an interest rate of 4% p.a.
Question 3 [12 marks]
In the distant land of Imbroglio, Syed is considering buying corporate bonds.1
He has formed the view that there is a constant probability of default of 0.075
in any half year. Syed knows that if the bond defaults he will receive no
further payments at all from the bond.
a. [3 marks] Draw a detailed contingent cash flow diagram, from Syed’s
perspective, that models the possible financial outcomes.
b. [3 marks] What price should Syed pay for a 5-year 6% bond to earn
a yield of 8% p.a.? Carefully set out all your working.
Prior to Syed’s purchase, the government of Imbroglio introduces a program
of quantitative easing. Syed’s analysis of the program suggests that, for
those firms that default in the next six months, each will have a probability
of recovering and paying coupon of 0.5 (and 0.5 of remaining in default) in
the next six month period. Thereafter, the program will have no effect, and
all defaulting firms will remain in default. The probability of a solvent firm
moving into default remains at 0.075.
c. [3 marks] Draw a detailed contingent cash flow diagram, from Syed’s
perspective, that models these revised possible financial outcomes.
d. [3 marks] What price should Syed pay for a 5-year 6% bond to earn
a yield of 8% p.a. under these new circumstances? Carefully set out
all your working.
Question 4 [8 marks]
Johno, a jeweller, has won the contract from the NRL to design and build a
new trophy. He will need a kilogram of gold on 1 March 2015 to start work
on his project. Johno’s daughter is doing the HSC at the moment, and he’s
got marital problems. He’s got enough stress in his life, and is worried that
the price of gold will rise over the next few months.
Gordo, a gold miner, will easily have this supply of gold available for
sale on 1 March 2015.
Silvio, Johno’s brother-in-law, runs a security firm. He is able and willing
to store gold for Johno for no cost—and at no risk of loss or theft.
Johno is aware that he could buy the gold forward—that is, negotiate a
price now with Gordo for the delivery of the gold on 1 March 2015. Then
he wouldn’t have to worry about any rises on the price of gold over the next
few months.
a. [3 marks] By using two carefully labelled cash flow diagrams in your
answer, setting out the cash flows associated with the forward contract
and the replicating portfolio, explain how you can determine the
arbitrage-free forward price of gold for the forward contract between
Johno and Gordo.
In your solution, take the current date as 23 October 2014 and the
current price of gold per kilo as AUD$45 561.78. Also, take the current
simple interest rate for all loans up to 180 days duration as 2.9% p.a.
Johno and his wife have just had a huge row, and have decided to get
divorced. Silvio is not speaking to Johno any more, so Johno will have to
re-price his forward contract.
b. [6 marks] Using the details given above, but now factoring in a cost
of secure storage of $50 for terms up to 180 days, and an insurance
cost of $20, repeat a. above.
Question 5 [0 marks]
Consider the following floating rate bond: it has a face value of $100. Each
half year it pays coupon based on the current market returns over the half
year that has just ended. That is, if the market returns 3% from 15 January
to 15 July then the bond pays $3.
The bond matures in 10 years’ time, at which point the $100 face value
is returned to the purchaser.
How much would you pay for this floating rate bond? Why?
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