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

MID-SEMESTER TEST

JUNE 2012

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. The cash price of a $1,000 bond that paid coupons semi-annually with a coupon rate of 7% p.a. that matures in exactly 18 months is $1,017.34.

The continuously compounded zero rates are as follows:

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

12 18 24

5.3 5.5 ?

5.9

What is the missing zero (spot) rate? [12.5 marks]

057.0)918.0ln(5.1

1035/)21.6734.017,1(1035)9465.09738.0(3534.017,1

).35000,1(.35.3534.017,1).(..

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 5.7% p.a.

8

22. On June 1, the treasurer of a US firm decides to hedge the planned issue of corporate bonds against further interest rate increases. On current forward interest rates, the August bond issue would realise $1.89 million. The bonds would have a total face value of $2.0 million and a duration of 6.6 years. The September Treasury bond futures price is currently 94-08 and the cheapest-to-deliver bond will have a duration of 8.7 years at maturity. How should the treasurer hedge against changes in interest rates over the next two months?

[Note: T-bond futures have $100,000 face value.] [12.5 marks]

2.157.8250,94

6.6000,890,1

=

=

=

FF

SS

DVDVN

i.e. SHORT 15 December contracts.

9

23. Assume the only carrying cost associated with gold is the interest rate, which remains unchanged at 10% p.a. (continuous compounded) for all maturities. Suppose that on March 16th 2012, Jill had entered into a one-year short forward contract to sell 100 ounces of gold for USD1,700.00/oz. If three months later (June 16th, 2012), she observed that the spot price of gold was USD1,838.00/oz, what would be the value of her position on this date?

[12.5 marks]

84.260$1838.1700

.

)(

75.01.00

000

=

=

=

==

e

SeKfhence

eSFandeFKf

rT

rTrT

Since Jill had a short position, she has made a loss.

(Loss)

10

24. The five-month S&P500 share price index (SPI) futures price is 1,400 points. If 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, what will be the no-arbitrage value of the two-month index futures contract?

[12.5 marks]

14061

.11400

.11400

))((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 =

________________________________