Midterm sample paper

BUS333 DERIVATIVE SECURITIES

MID-TERM TEST - PREVIOUS QUESTIONS

SOLUTIONS

1. The continuously compounded zero rates are as follows:

Maturity (months) Rate (% p.a.)
6 5.0
12 5.2
18 5.4
24 5.6

a) What will be the 6-month zero rate 18 months forward?

Rt  n .Tt  n  Rt .Tt
Rt ,t  n 
Tt  n  Tt
5.6  2  5.4 1.5

2  1.5
 6.2%
b) What will be the cash price of a $1,000 bond that matures in exactly 18 months and pays
coupons of $30 every six months?
P  C1.e r1 .t1  C2 .e  r2 .t2  C3 .e  r3 .t3  ...  (Cn  FV ).e  rn .tn
 30.e0.0500.5  30.e0.0521  1, 030.e0.0541.5
 30  0.9753  30  0.9493  1030  0.9222
 $1007.60
c) What is the 12-month par yield?

P  C1.e  r1 .t1  C2 .e  r2 .t2  C3 .e  r3 .t3  ...  (Cn  FV ).e  rn .tn
1, 000  C .e0.0500.5  C .e0.0521  (1, 000  C ).e 0.0541.5
1, 000  C.(0.9753  0.9493  0.9222)  1000  0.9222
1, 000  2.8468  C  922.2
C  27.33

, 2. The risk-free rate of interest is 4.3% p.a. with continuous compounding for all maturities,
and the continuously compounded dividend yield on the All-Ordinaries share price index
(SPI) is 2.3% p.a. The two-month SPI futures “price” is 4,800 points. What must the value
of the five-month index futures contract be if there is no arbitrage opportunity?

(r q)(T2 T1 )
F Fe
2 1
( 0.043 0.023)).( 5  2 )
 4800.e 12 12


 4800.e0.020.25
 4824

3. a) Compare and contrast a ‘rolling’ (stacking) hedge with a ‘strip’ hedge. Identify the
considerations that may favour the use of one over the other.

b) What is a ratio hedge? What advantages does it have over a naive hedge?

c) Describe the operation of a margin account. What is the purpose of a margin deposit, and
why is one required for buyers and sellers of futures contracts but only for sellers of options
contracts?


4 On September 25th, an investor holds 50,000 ANZ shares with a price of $28 and beta of 0.9.
The investor believes that for the next month, the market will exhibit continued nervousness
over US sub-prime lending, and decides to hedge using ASX SPI 200 contracts. October,
November and December contracts are currently priced at 6,250, 6,265 and 6,280
respectively, and one contract is for $25 times the index. What futures trading strategy would
hedge the investor’s position?

S  50, 000  $28  $1.4m
F  6265  $25  $156, 625

S
N  .
F
1.4m
 0.9
156, 625
 8.04
Therefore Sell (short) 8 November SPI200 contracts in September and close these out after
the volatility has passed in October (25th).




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