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Unformatted text preview: MACQUARI E )l
UNIVERSITY
This question paper may be retained by candidates SESSION 2 FORMAL EXAMINATIONS — NOVEMBERIDECEMBER 2014
EXAMINATION DETAILS: ACST201
FINANCIAL MODELLING Duration of exam
incL readin ﬁme if a “cable : 3 HOURS (PLUS 10 MINUTES READING TIME) Total no. of questions: 7 QUESTIONS
Total no. of pages
incl. this cover sheet : 10 INSTRUCTIONS: ANSWER ALL QUESTIONS. TOTAL MARKS AVAILABLE—100 ANSWER EACH QUESTION IN A SEPARATE BOOK THE EXAMINER WILL ONLY MARK THE FIRST QUESTION
ANSWERED. IN ANY EXAM. ANSWER BOOK. ALL OTHER
MATERIAL WILL BE IGNORED. MATERIALS PERMITTEDINOT PERMITTED: YOU MAY REFER TO THE SINGLE A4—SIZE SHEET OF PAPER
(WITH ANYTHING YOU LIKE WRITTEN/TYPED ON BOTH
SIDES) THAT YOU BROUGHT WITH YOU TO THE EXAM. YOU MAY TAKE THESE NOTES WITH YOU AT THE END OF
THE EXAM. PAPERBASED TRANSLATION DICTIONARIES PERMITTED NONPROGRAMMABLE CALCULATORS (NO TEXT RETRIEVAL
CAPACITY) PERMITTED  Candidates are required to obey all instructions provided by the Final Examination Supervisor and must refrain trom communicating in any
way with another student once they have entered the ﬁnal examination venue.
 Candidates may not write or mark the exam materials in any way durin reading time.  Candidates may only access authorised materials during this examination. A list of authorised material is available on this cover sheet. if it is alleged you have breached these nIles at any time during the examination. the matter may be reported to the University Discipline Committee
for deten'ninaticn. QUESTION 1 [15 marks] a. Agnes purchased an 180—day $1 000 000 bank bill 76 days ago for $985 900.28.
She sold it to Bertil today and receiVed $992 085.06. (i) [3 marks] Calculate the purchase yield (simple interest rate) and
sale yield (simple interest rate) of this bill (as a percentage, rounded
to 2 decimal places). (ii) [2 marks] Without any further calculations, explain how the sell—
ing price will change if Bertil accepts a lower yield. (iii) [2 marks] Calculate the capital gain or capital loss component of
Agnes’ investment (to two decimal places). (iv) [4 marks] Assuming Agnes borrowed to purchase the bill, what is
the break—even rate of interest of borrowing (simple interest, as a
percentage, rounded to 2 decimal places)? If the borrowing cost
rate is 12 basis points higher than the break—even rate, explain
whether Agnes will end up with aicash surplus or cash deﬁcit. b. A 6% pa. Treasury bond pays semiannual interest on 15 May and
15 November and is to be redeemed at par on 15 November 2018. (i) [3 marks] Find the price to yield 4% pa. (jg) on 1 October 2014. (ii) [I mark] Without doing any calculations, what will the approx—
imate price be to yield 6% pa? Provide a brief explanation of
how you arrived at your answer. Cease writing in your first booklet  Open your second examination booklet QUESTION 2 [14 marks] a. [4 marks] You have been asked to help ‘price a 21/2year 12% pa. Trea
sury bond at a yield of 8% pa. (jg) in Excel by a colleague.
 In cells A1 to A5 there are zeros. Cell A6 contains 100.
o In cell B1 there is a zero; in cells B2 to B6 6 appears. 0 In cell Cl is a zero. In cell (22 your colleague has typed =1/1.04.
In cell CS, =1/1.04“2. In cell 04, =1/1.04“3, and so on—cell CS
contains =1/1.04“5. Please turn over Your colleague has asked you to type in a formula to value the bond in
cell D1. What will you type? b. [4 marks] The following data appears in cells A3 : C40 in an Excel spread
sheet. Coupon Yield Price (5'2) (32) 2% 100.000
2% 91.017
2% 82.940
2% 75.667
2% 69.113
2% 63.200
2% 57.859
2% 53.029
2% 48.659
2% 44.699 Explain how you would graph prices (against yields) in Excel. Price
should be on the vertical axis of your graph. You should label the curve
you have plotted as “2% coupon”. c. [6 marks] A part of question 2 of your take—home quiz 1 read as follows. Belinda, who has just turned 25, will invest $1 500 every year
on her birthday for the next 40 years. How large will this retirement fund be on her 65th birthday—
immediately after making her annual payment—if her invest
ment earns o 10% p.a. in years 1—51 0 8% p.a. in years 6—15, I 9% pa. in years 16—30, and o 3% pa. in years 31—40? A student’s answer to this part of the question is given below. 1.15 — 1 m 15 . 9 1.0810 — 1
. . . 1 ——
01 (1 08) (1 09) (1 03) + 500 0.08 1.0915 — 1 9 1.039 4 1
—— . ——— 1
+1500 009 103 +1500 (103 + 500 = 939623970 + 103.273.5471 + 574640042 + 15238.6592 + 1500
= 271 438.61 1500 (1.09)15(1.03)9 Please turn over The correct answer was $279 536.77. What errors has this student made? Write out the correct expression. Cease writing in your second booklet a Open your third examination booklet QUESTION 3 [16 marks] An investor bought a 3~year 6% Treasury bond on 15 June 2014 at a yield of
jg = 4% pa. The investor will reinvest all coupons over the life of the bond
at jg = 3.2% p.a. The bond will be redeemed at par on the maturity date
(face value $100). 7 a. [2 marks] Calculate the total accumulated value of the cash ﬂows gen
erated by this bond at maturity, assuming the investor holds it to
maturity. b. [2 marks] Calculate the total realised compound yield (TROY) of this
bond under the circumstances given in a. c. [2 marks] Decompose the total accumulated value generated by this
bond (if it is held to maturity) into: original purchase price, coupons,
interest on coupons, and capital gain/ loss. ‘ d. [2 marks] If the investor holds the bond for 1 1/2 years and sells it for a
yield of jg = 3.8% p.a., calculate the holding period yield (HPY). e. [4 marks] At the original purchase date, what was the duration of this
bond? f. [2 marks] As at 15 June 2014, use the concept of modiﬁed duration to
estimate the price of the bond if the yield to maturity falls to jg =
3.9% p.a. immediately after the investor buys the bond. g. [2 marks] What are two major factors affecting duration of a Treasury
bond? In which direction do they affect duration? Cease writing in your third booklet Please turn over a Open your fourth examination booklet QUESTION 4 [14 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 0.05
in any half year. Syed knoWs that if the bond defaults he will receive no
further payments at all from the bond. 3.. [3 marks] Draw a detailed contingent cash ﬂow diagram, from Syed’s
perspective, that models the possible ﬁnancial outcomes of purchasing
a 4—year 4% bond (jg rates). b. [3 marks] What price should Syed pay for a 4year 4% bond to earn a
yield of 5% pa? 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 0.6
of recovering and paying coupon (and 0.4 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 0.05. In summary, then, (with all times in
years): 0 From t = 0 to t = 0.5, the probability a solvent ﬁrm will default is 0.05,
and the probability a defaulted ﬁrm will return to solvency is 0.0. a From t = 0.5 to t = 1.0, the'probability a solvent ﬁrm will default is 0.05, and the probability that a defaulted ﬁrm will return to solvency
is 0.6. a From t = 1.0 to t = 1.5, the probability a solvent ﬁrm will default is 0.05, and the probability that a defaulted ﬁrm will return to solvency
is 0.0. a From 15 = 1.5 to t =‘ 2.0, the probability a solvent ﬁrm will default is 0.05, and the probability that a defaulted ﬁrm will return to solvency
is 0.0. 0 From 75 = 2.0 to t = 2.5, the probability a solvent ﬁrm will default is 0.05, and the probability that a defaulted ﬁrm_will return to solvency
is 0.0. 1Assume that the corporate bonds of Imbroglio have patterns and valuation rules iden
tical to Australian Treasury bonds. Please turn over 0 And so on. c. [.4 marks] Draw a detailed contingent cash ﬂow diagram, from Syed’s
perspective, that models these revised possible ﬁnancial outcomes. (:1. [4 marks] What price should Syed pay for a 4year 4% bond to earn a
yield of 5% pa. under these new circumstances? Carefully set out all
your working. Cease writing in your fourth booklet Please turn over a Open your fifth examination booklet QUESTION 5 [14 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 April 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 further 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 April 2015. Silvio, Johno‘s brotherin—law, runs a security ﬁrm. He is able and willing
to store gold for J ohno 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 April 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 con
tract and the replicating portfolio, explain how you can determine the arbitragefree forward price of gold for the forward contract between
Johno and Gordo. In your solution, take the current date as 25 November 2014 and the
current price of gold per kilogram as AUD$46 711.42. Also, take the
current simple interest rate for all loans up to 180 days duration as
2.8% p.a. J ohno and his wife have just had a huge row, and have decided to get di
vorced. Silvio is not speaking to Johno any more, so Johno will have to
re—price his forward contract. b. [5 marks] Using the details given above, but now factoring in a cost of
secure storage of $40 for terms up to 180 days, and an insurance cost
of $16, repeat a. above. Immediately after concluding his deal with Gordo (i.e., the same day, when
the market price of gold is $46 711.42 per kilogram), Johno meets Wacka.
Wacka is prepared to buy or sell a kilogram of gold from, or to, Johno in a forward contract with a forward price of gold of $47 500 per gram on 1 April
2015. c. [3 marks] Explain how Johno could make an arbitrage proﬁt in these
circumstances. Please turn over d. [3 marks] How much proﬁt could Johno make on one such (one kilo
gram) forward contract? Illustrate your answer with a carefully labelled
cash ﬂow diagram. Cease writing in your fifth booklet 0 Open your sixth examination booklet QUESTION 6 [16 marks] Linze is thinking of buying a European call option on shares in Echidna
Pty. Ltd. He is trying to price the option using a simple (binomial) model,
assuming monthly price increases of 10% on the current price, or decreases
of 5% on the current price. The current price of one Echidna share is $28.
The European call option will expire at the end of one month. The strike
price is $29. The share will not pay any dividends during the few months.
Linze can borrow money today for one month at the rate of 312 = 6% p.a. a. [4 marks] Consider the replicating portfolio (i.e., the investment strat
egy which will give identical payoffs, at the end of one month, to the
call option) thatinvolves buying h shares in Echidna Pty. Ltd. today,
and borrowing $3 for one month. Find the values of h and B. b. [2 marks] What is the initial cost (i.e., net outlay) today of investing
in the replicating portfolio? c. [1 mark] What is the fair price (premium) for the call option, using the
arbitrage—free pricing method? 7 d. [3 marks] The contingent payments method will give the same option
value as the arbitrage pricing method, as long as the appropriate value
is used for p (the probability of an upward price movement). Find the
appropriate value of p in this case. Suppose Linze decides on buying a European call option that expires in two
months, instead. Use the characteristics mentioned above, a monthly price increases of 10% are possible,
a monthly price decreases of 5% are possible,
0 a strike price of 29, and o the same interest rate given above, to answer the following. Please turn over e. [3 marks] Draw a contingent cash ﬂow diagram representing the payoffs
associated with this call option. f. [3 marks] Calculate the price of this call option. Cease writing in your sixth booklet Please turn over a Open your seventh examination booklet QUESTION 7 [11 marks] Consider the following ﬂoating rate bond: it has a face value of $100. Each
half year it 'pays a coupon based on the current market returns over the half
year that has just ended. That is, if the market returns 6% from 15 January
to 15 July then the bond pays $6. ‘ The bond matures in 10 years’ time, at which point the $100 face value
is returned to the purchaser. a. [2 marks] How much would you pay for this ﬂoating rate bond? Why? Carsten had a serious motorcycle accident a number of years ago, greatly
reducing his earning capacity. Shortly afterwards, he invested his savings
in a ﬂoating rate bond. While he is conﬁdent the issuer is solvent, he is
concerned that the bond returns may be low and volatile over the next eight
years. He wants stable returns over the next eight years to ensure he can pay
his annual bills (electricity, water, council rates and so on). o The current annual term structure of interest rates (3'1 rates) is (0.024,
0.025, 0.026, 0.028, 0.029, 0.030, 0.031, 0.032). 0 An eight year AAA corporate bond paying annual coupon (5h rate) at
3% pa. is currently priced at $98842 per $100 nominal. What stable rate of return could Carsten enjoy over the next eight years with
an interest rate swap?
In answering this question ensure you do the following. b. [3 marks] Draw a cash ﬂow diagram indicating how the interest rate
swap works. c. [6 marks] Write out, and solve, anequation of value for the desired
stable rate of return (to two decimal places). Relate your equation of
value to your cash ﬂow diagram. Cease writing in your seventh booklet . End of paper 10 ...
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