Interest Rate Futures
Mark Fielding-Pritchard of mefielding.com
ACCA p4 , also CFA, ICAS, ICAEW
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The question is based on ACCA P4,
Phobos from 12/08

Please download the question, it is on our website

Key information

Now is 1 January, loan will be taken out 1 March, the
loan is for £30m for a period of 4 months

Assumption: when the loan is taken out it is fixed
rate
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3 Questions

1) Do I buy (calls) or sell (futures)?
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The theoretical value of a future is 100 – LIBOR

Therefore if interest rates are 5%, value is 95

If interest rates rise to 6%, value falls to 94
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If we are hedging rising interest rates we sell.
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Sell at 95

Buy at 94
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Gain
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What does gain or loss mean?
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A contract has a standard value of £500,000
for 3 months

A gain of 1 = 1%x 500000 x 3/12 = £1250

In the question they give you tick value, 1 tick
= 0.01% = 12.50. 100 ticks = 1% = £1250
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3 Questions

Question 1, do we buy or sell. We sell because the company has
a rsik of rising interest rates

Question 2, how many?

1 contract will hedge £500000 for 3 months.

If your loan will be 1 million for 3 months you need 2 contracts
because your interest is twice as much

Similarly if your loan is £500000 for 6 months you will need 2
contracts because your interest will be twice as much.
Remember the loan is fixed interest when taken out so don’t
think about changing rates or anything, just simple maths.
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Question 2- How many contracts

Easy Formula

Number of contracts =

In our example =

= 80
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𝑥
3
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑜𝑛𝑡ℎ𝑠 𝑜𝑓 𝑟𝑖𝑠𝑘
𝑠𝑢𝑚 𝑜𝑓 𝑙𝑜𝑎𝑛
𝑥
3
500000
30𝑚
500000
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Question 3 Which Month

Assume in these questions that securities close at the end of the
month

Futures price will not = 100- LIBOR

The difference is called basis risk. This arises for a lot of
reasons, expectations, volatility, changes in interest rates etc.
The longer the futures ha to go until closure the greater will be
that basis risk

Therefore we choose the future that closes first after our risk
ends, our risk ends when we take out a fixed rate loan (1 March)
therefore we chose March futures

If we look at our March future he price is 93.88 which implies a
Libor of 6.12%. Libor is actually 6% so basis risk is 0.12% or 12
ticks and the market is expecting a rise in interest rates
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Our Hedging Strategy

Therefore bring together the elements of the 3
questions.

On 1 January we will sell 80 March futures

On 1 March we will close our position by
buying 80 March futures
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Illustration of effect
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The examiner wants you to show what happens if interest rates rise and fall

So lets take 5 & 7% (Currently 6%)

Interest on the loan

30m x 4/12 x 7%= 700000

30m x 4/12 x 5%= 500000

Benchmark

30m x 4/12 x 6%= 600000
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Effect of the future 1

7%
5%

Sold
93.88
93.88

Buy
92.96
94.96

Difference
0.92

Where does 92.96 come from?

Basis risk on 1 January was 94-93.88= 12 basis points

Basis risk declines evenly so on 1 March 2/3 will have disappeared,
therefore 1/3 or 4 basis points remains. And it is above LIBOR so
LIBOR of 7% gives an implicit rate in the future of 7.04%
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(1.08)
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Effect of the future 2

So at 7% interest rate we had again of 0.92 % or 92 ticks
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0.92%x 500000x 3/12x 80 = 92000, or

92x 12.5x 80 = 92000

So at 7% our additional interest was 100000 minus our future gain of 92000
gives us a loss of 8000 and hedge efficiency of 92%

If rates fall to 5%

We save 100000 on interest but we lose 108000 (108x12.5x80)
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Net loss is 8000 as before, hedge efficiency is 100/108 (92.6%)

Loss has arisen because of 8 ticks of basis risk (8x12.5x80) disappearing
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Problems with futures
 Cost
 Deposits
 Margin
calls
 Market
sentiment
 Open
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