6

Part B

Family Name:.......SOLUTIONS.......... Q M Part 1 /50 Other Names:........................................................................ 21 /12.5 22 /12.5 Student Number:.................................................................. 23 /12.5 24 /12.5

Total

MURDOCH BUSINESS SCHOOL

BUS325 DERIVATIVE SECURITIES

IN-TERM TEST

FEBRUARY 2013

Time Allowed: One and one half hours.

Aids Allowed: To be supplied by Candidate: Calculator Attached to this paper: Formula Sheet

Format: This paper has two parts. Part A contains 20 multiple choice questions worth a total of 50 marks, and Part B contains 4 questions worth 12.5 marks each. Answer Part A on the answer sheet, and Part B on the question paper in the space provided. Show all calculations for Part B.

7

Part B Answer these questions on the question paper in the space provided.

21. Complete the table (below) of continuously compounded zero (spot) rates if the cash price of a bond that matures in exactly 18 months is $1,033.02. The bond has a face value of $1,000 and pays coupons semi-annually with a coupon rate of 8% p.a..

Maturity (months) Rate (% p.a.) 6

12 18 24

5.30 5.50

? 5.65

[12.5 marks]

0560.0)91943.0ln(5.1

1040/)21.81.7603.033,1(1040)9465.09738.0(4002.033,1

).40000,1(.40.4002.033,1).(..

3

3

5.1

5.1

5.11055.05.0053.0

.

3.

2.

1

3

3

3

332211

=

=

=

++=

+++=

+++=

r

r

e

e

eee

eFVCeCeCP

r

r

r

trtrtr

=> the eighteen-month spot rate is 5.60% p.a.

8

22. Suppose that it is February 23rd and the treasurer of an US firm realises that on August 23rd the firm will have to issue $3 million of commercial paper with a maturity of 180 days. If the paper were issued today, the firm would realise $2,892,000. September 91-day T-bill futures ($1million) are quoted at 92.00 on the CME. Describe the steps the treasurer should take to hedge the firms exposure?

[12.5 marks]

000,980)825.0100(000,10 ==F

902.525.0980000

5.02892000

=

=

=

F

S

DFDSN

February: Sell 6 September 90-day bank bill futures contracts

August: Buy 6 September 90-day bank bill futures contracts to close futures position, and issue (sell)

commercial paper with $3 million face value.

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23. On December 21st 2012, Eve entered into a one-year long forward contract to buy 100 ounces of gold for USD1,700.00/oz. Three months later (March 21st, 2013), she observes that the spot price of gold was USD1,620.00/oz, what is the value of her position on this date? Assume the only carrying cost associated with gold is the interest rate, which remains unchanged at 10% p.a. (continuous compounded) for all maturities.

[12.5 marks]

84.42$.17001620

.

)(

75.01.00

000

+=

=

=

==

e

eKSfhence

eSFandeKFf

rT

rTrT

Since Eve had a long position, she has made a gain (agreed to buy at a price below the new equilibrium futures price).

(Loss)

10

24. The continuously compounded dividend yield on the SPI is 3.0% p.a. and the risk-free rate of interest is 1.3% p.a. with continuous compounding for all maturities. If the five-month S&P500 share price index (SPI) futures price is 1,600 points, what will be the no-arbitrage value of the two-month index futures contract?

[12.5 marks]

16071

.11600

.11600

))((12

25.0017.0

)122125)).(030.0013.0(

12

=

=

=

=

F

eF

eF

TTqreFF

______________________________________________

END OF PAPER

11

Formulae you may require:

TqreSF )(00

=

TyceSF )(00

=

))((12

12 TTqreFF =

rTeFKf = )( 0

T)rr(00

fheSF =

)1ln(m

RmR mC +=

nn trn

trtrtreFVCeCeCeCP ..3

.

2.

1 ).(...... 332211 +++++=

tnt

ttntntntt TT

TRTRR

=

+

+++

..

,

RateDiscount 360

100PriceCash = n

==F

Sh

FF

SS

DVDVN

=

F

S

VVN =

=

=

Bec

tDiyt

in

ii

1

yDBB =

________________________________