FINM 3411
PAST FINAL EXAM QUESTIONS: Forwards and futures
Question 1: Forward/futures hedging [20 marks]
Suppose today is September 15. Your accounting staff have recently completed a cash flow analysis
for the next calendar year. A large receivable of around $3 million falls due at the end of March next
year. Also, your company will begin a new project at the end of June next year, which will require
an initial cash injection of about $3 million. Therefore, you have decided that you will invest the
surplus funds at the end of March. Your company’s investments earn the bank bill rate plus 100
basis points. You are concerned about interest rate risk and wish to put in place a risk management
procedure to hedge this risk. Describe how to do this and demonstrate that the hedge is successful
by considering cases where the 90-day BAB rate is 4% p.a. and 7% p.a. at the time the investment is
made. Be clear about what the cash flows are and when they will occur. Relevant financial
information appears in the table below.
Instrument
Current
Information
Current 90-day BAB Rate
5.0%
Current 180-day BAB Rate
5.2%
Current September BAB Futures Price
94.7
Current December BAB Futures Price
94.6
Current March BAB Futures Price
94.4
Current June BAB Futures Price
94.0
To hedge this risk we need to buy three March bank bill futures contracts. The following table
demonstrates the success of this hedging strategy:
Position
Interest on
loan
Futures
Payoff
Net
Position
BAB = 4%
3,000,000
3,000,000 
1  0.05 90
365
= 36,536
BAB = 7%
3,000,000
3,000,000 
1  0.0890
365
= 58,033


1,000,000
1,000,000

3


90
90
 1  0.04
1  0.056
365
365 

= 11,560


1,000,000
1,000,000
=
3


90
 1  0.07  90
1  0.056
365
365 

-10,042
48,096
47,991
1
Question 2 [20 Marks]
Part A [10 Marks]
Suppose today is September 15. Your accounting staff have recently identified that your firm will
have a cash flow shortfall of $2 million over the second quarter of next year. Your company borrows
at the bank bill (BAB) rate plus 200 basis points. You are concerned about interest rate risk and wish
to put in place a risk management procedure to hedge this risk. Describe how to do this and
demonstrate that the hedge is successful by considering cases where the 90-day BAB rate is 2% p.a.
and 5% p.a. at the time the loan is taken out. Be clear about what the cash flows are and when they
will occur. Potentially relevant financial information appears in the table below.
Current
Information
Instrument
Current 90-day BAB Rate
3.0%
Current 180-day BAB Rate
3.2%
Current September BAB Futures Price
96.7
Current December BAB Futures Price
96.6
Current March BAB Futures Price
96.4
Current June BAB Futures Price
96.0
Current September (next year) BAB
Futures Price
96.0
To hedge this risk we need to sell two March bank bill futures contracts. The following table
demonstrates the success of this hedging strategy:
Position
Interest on
loan
Futures
Payoff
Net
Position
BAB = 2%
BAB = 5%
2𝑚𝑚
− (2𝑚𝑚 −
90
1 + 0.04
365
= −19,533
-2(
1𝑚𝑚
90
1+0.02
365
−
1𝑚𝑚
90
1+0.036
365
)
)
2𝑚𝑚
− (2𝑚𝑚 −
90
1 + 0.07
365
= −33,935
-2(
1𝑚𝑚
90
1+0.05
365
−
1𝑚𝑚
90
365
1+0.036
= −7,783
= 6,760
-27,316
-27,175
)
)
2
Part B [5 Marks]
Briefly explain what you would do if your cash flow shortfall lasted until the end of September
rather than the end of June. Just explain what, if anything, you would do differently – no
calculations are necessary. Would you have a perfect hedge in this case?
Treat this as two three-month loans. We have already shown how to hedge the loan from March to
June. We would just do the same thing to hedge the ‘second’ loan from June to December. Thus,
in addition to what we have done above, we would also sell two June BAB futures contracts. There
will not be a perfect hedge because we are not borrowing at the BAB rate – the same small
discrepancy as above.
Part C [5 Marks]
Ignore Part B. Explain what you would do if your cash flow shortfall started and finished a month
earlier. Just explain what, if anything, you would do differently – no calculations are necessary.
Would you have a perfect hedge in this case?
In this case, the risk would finish at the end of May instead of at the end of June. Since there is no
May contract, we will have to use the June contract and close out early. This will not be a perfect
hedge for the same reason as above, plus there will be basis risk because we will be closing out the
futures contract a month before it expires.
3
Question 3. Forward/futures hedging. [Total of 20 Marks]
Your firm operates an oil refinery. You buy crude oil, process it, and sell unleaded gasoline. Assume
for this exercise that one gallon of crude oil produces one gallon of gasoline. You have just signed
a contract to deliver 126,000 gallons of unleaded gasoline to the operator of a bus fleet. Delivery is
to occur at the end of September and your customer will pay the going spot price on the day of
delivery. Assume that you will need to purchase the required amount of crude oil one month before
the unleaded gasoline is required – to allow sufficient time for production scheduling and processing.
This contract is outside your usual supply arrangements and you have no surplus storage capacity, so
you will purchase the crude oil on the spot market when it is required.
Explain how you would hedge the financial risk involved with this deal using the futures contracts
that are set out below (i.e., which contracts would you trade, how many, and would you buy or sell?)
Contract
Crude Oil Futures
Unleaded Gasoline Futures
Exchange
NYMEX
NYMEX
42,000 US Gallons
(1,000 barrels)
42,000 US Gallons
(1,000 barrels)
Futures Price
(per barrel = 42 gallons)
Futures Price
(per gallon)
June
$109
$3.24
July
$109
$3.22
August
$110
$3.21
September
$111
$3.20
October
$111
$3.18
November
$111
$3.17
December
$112
$3.17
Contract Size
Delivery month
Show that your proposed hedge works by examining cases where the relevant crude oil price is $80
per barrel and where it is $150 per barrel, and where the relevant unleaded gasoline price is $2.00
per gallon and where it is $4.00 per gallon.
Your contract is for 126,000 gallons, which amounts to three contracts. You will be buying crude oil
and selling unleaded gasoline, so you’ll need to take a long position in the crude oil contract and a
short position in the unleaded gasoline contract. You’ll need the crude oil at the end of August and
you’ll deliver the unleaded gasoline at the end of September, so your trades will be in the August and
September contracts respectively.
First, consider the purchase of the crude oil.
Crude oil price of $80 per barrel
4
Cash flow
Calculation
Value
Cost of crude
-3,000 × 80
-240,000
Futures payoff
+3(1,000)(80-110)
-90,000
Net payoff
-330,000
Crude oil price of $150 per barrel
Cash flow
Calculation
Value
Cost of crude
-3,000 × 150
-450,000
Futures payoff
+3(1,000)(150-110)
120,000
Net payoff
-330,000
Now consider the sale of the unleaded gasoline.
Unleaded gasoline price of $2 per gallon
Cash flow
Calculation
Value
Cost of crude
126,000 × 2
252,000
Futures payoff
-3(42,000)(2.00-3.20)
151,200
Net payoff
403,200
Unleaded gasoline price of $4 per gallon
Cash flow
Calculation
Value
Cost of crude
126,000 × 4
504,000
Futures payoff
-3(42,000)(4.00-3.20)
-100,800
Net payoff
403,200
5
Question 4: Forward/futures hedging [20 marks]
Your firm imports electronic components, processes them in Australia, and then exports the finished
product to Europe. It is currently November 1999, and you are concerned about foreign exchange
risk associated with a large project that you plan to undertake over the next year. You plan to import
a large shipment of electronic components from your Japanese supplier. The terms of the contract
require you to pay ¥750 million at the end of March 2000. You will spend six months processing
these components. At the end of September 2000, you will deliver the finished product to your
European customer. You will be paid 11 million Euros at the time of delivery. Current spot and
forward rates are:
Rate
Yen / $
Euro / $
Spot Rate
90
0.70
March 2000 Forward Rate
91
0.71
June 2000 Forward Rate
93
0.72
September 2000 Forward Rate
94
0.73
December 2000 Forward Rate
96
0.75
Describe precisely how you would hedge the foreign exchange risk in this case. Prove that your
proposed hedge works by showing that your net hedged position is the same in the following two
cases:

The Yen/$ exchange rate turns out to be 102 at the end of March 2000 and the Euro/$
exchange rate turns out to be 0.81 at the end of September 2000.

The Yen/$ exchange rate turns out to be 92 at the end of March 2000 and the Euro/$ exchange
rate turns out to be 0.65 at the end of September 2000.
We need to buy Yen to deliver to our Japanese supplier at the end of March. Therefore, we BUY
YEN FORWARD. In particular, we need the MARCH 2000 contract and an amount of 750
million Yen.
We need to sell Euros to dispose of the payment from our European customer at the end of
September 2000. Therefore, we SELL EUROS FORWARD. In particular, we need the
SEPTEMBER 2000 contract and an amount of 11 million Euros.
Your strategy should be to:
1. Buy Yen forward to lock in the exchange rate for March 2000 at ¥91 / AUD$.
2. Sell Euros forward to lock in the exchange rate for September 2000 at Euro 0.73 / AUD$
The Yen / Dollar Hedge:

Case 1:
¥102 / AUD$
Cost of buying Yen
=
=
Payoff from forward contract =
¥750,000,000 / 102
$7,352,941.18
1
 1
750mm 


91 
 102
6
Total Cost

Case 2:
¥92 / AUD$
Cost of buying Yen
=
-888,817.07
=
$8,241,758.25
=
=
=
1
 1
750mm 


91 
 92
-89,584.33
=
$8,241,758.25
Payoff from forward contract =
Total Cost
¥750,000,000 / 92
$8,152,173.91
The Euro / Dollar Hedge:

Case 1:
Euro 0.81 / AUD$
Proceeds from selling Euros:
Payoff from forward contract
Total Revenue

Case 2:
Euro 0.65 / AUD$
Proceeds from selling Euros:
Payoff from forward contract
Total Revenue
=
=
11,000,000 / 0.81
$13,580,246.91
=
1 
 1
 11mm 


0.73 
 0.81
$1,488,246.24
=
AUD$ 15,068,493.15
=
=
11,000,000 / 0.65
$16,923,076.92
=
1 
 1

=  11mm 

0.73 
 0.65
=
-$1,854,583.77
=
AUD$ 15,068,493.15
7