Interest Rate Risk Management (1)

AFM · Chapter 20

Interest Rate Risk Management (1)

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1 Introduction

In this chapter we will consider the nature of interest rate risk and ways in which this risk can be managed.

Note that throughout this chapter we will be considering a company wishing to borrow money. All of the techniques dealt with are equally available for a company wishing to deposit money.

2 The nature of interest rate risk

Interest rates on borrowing have fluctuated greatly over the past. Companies can borrow money at either floating interest rates or at fixed interest rates. If they have floating rate borrowing, then clearly they are subject to the risk of future interest rate changes. We will consider the possible advantages and disadvantages of this form of borrowing later.

However, more important for the examination is fixed interest borrowing. It would appear that this carries no risk in that any later changes in the interest rate are irrelevant. However, there can still be a problem which is illustrated below.

Illustration

It is now 1 June. A company has decided that they will wish to take out a loan of £100,000 for six months, starting in 3 months time on 1 September.

If they were to take the loan today then the rate of interest that they would be charged is 10% p.a. (fixed).

The problem is that they are not taking the loan today but in 3 months time. If they do nothing then there is a risk that by the time they actually take the loan the rate of interest will have changed.

The risk that we are concerned about is therefore the risk of interest rates changing between now and the date the loan starts (not the risk of interest rates changing after the start of the loan – the loan will be taken at a fixed rate).

3 Methods of managing interest rate risk

The methods with which you must be familiar for the examination are the following:

forward rate agreements
interest rate guarantees
interest rate futures
interest rate options

The above are all ways of managing the risk involved with fixed interest borrowing, and will be dealt with in this chapter.

In addition you must be familiar with swaps, which are rather different (and deal with a somewhat different situation). These will be dealt with in the next chapter.

4 Forward rate agreements

A forward rate agreement (FRA) is the fixing of an interest rate now to apply to a loan starting at a fixed future date.

It is an OTC (over-the-counter) transaction and effectively involves asking the bank to quote an interest rate now to apply to a specified amount of borrowing, for a specified period, the loan to start at a specified future date. Once the interest rate has been agreed, then if the actual rate at the start of the loan is any different the bank and the company will settle up for the difference.

Terminology

If we ask the bank to quote an FRA 3-9 on £100,000 then it means that we want a fixed interest rate to be quoted for a loan of £100,000 starting in 3 months time and ending in 9 months time (i.e. for a 6 month loan).

It is now 1 June and X plc will need a fixed interest rate loan of £500,000 for 9 months starting on 1 September.

The bank quotes a rate of 10% p.a. to apply to the loan.

State what FRA is required
Calculate the result of the FRA and the effective interest rate if the actual interest rate for 9 month loans on 1 September is:
1. 13%
2. 8%

(a)	FRA 3–12 $500,000
(b)	(i)	Interest: 500,000 × ⁹/₁₂ × 13% =	48,750
		FRA: 500,000 × ⁹/₁₂ × (13% – 10%)	11,250
			37,500

(ii)	Interest: 500,000 × ⁹/12 × 8% =	30,000
	FRA: 500,000 × ⁹/12 × (10% – 8%)	7,500
		37,500

5 Interest Rate Guarantees

An interest rate guarantee (IRG) is an arrangement with the bank whereby the bank fix a maximum interest rate to be applied to a loan of a specified amount, for a specified period, starting on a specified future date.

It is effectively an option, in that if interest rates rise above the agreed rate then the company is protected whereas if interest rates should fall then the company gets all the benefit. Since the company can only benefit, and not lose, the bank will charge a premium for the IRG which is payable immediately, whether or not the option is eventually exercised.

It is an OTC instrument and can not be traded.

It is now 1 August and Y plc will need a fixed interest rate loan of $200,000 for 6 months starting on 1 December.

They ask the bank for an IRG at a rate of 12% p.a.. The bank quotes a premium of $1,500

Calculate the result of the IRG and the effective interest rate if the actual interest rate for 6 month loans on 1 December is:

13%
8%

(a)	Interest: 200,000 × 6/12 × 13% =	13,000
	IRG: 200,000 × 6/12 × (13% – 12%)	1,000
		12,000
	Premium	1,500
		13,500

(b)	Interest: 200,000 × 6/12 × 8% =	8,000
	IRG	–
	Premium	1,500
		9,500

6 Interest rate futures

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Interest rate futures operate in a similar way to currency futures in that they are instruments that change as interest rates change, that an investor can buy today and sell later (or sell today and buy later). At the end of the deal any profit or loss is calculated and settled between the investor and the dealer. A company intending to borrowing money on a future date can leave the borrowing at risk but use a futures ‘gamble’ to create an opposite risk that will net off against the risk of the underlying transaction.

Interest rate futures are not quoted as actual interest rates, but as a number which is 100 – interest rate.

For example, a futures price of 92.00 is equivalent to an interest rate of 8% p.a.

Similarly, an interest rate of 12% p.a. has an equivalent future price of 88.00.

It is important to note two things.

Firstly, if a company is borrowing money, then they will suffer if interest rates rise between now and the date the loan will start. If interest rates do rise, then the futures price will fall. They need to make a profit from the future to cover against the increased interest, and the way in which they can make a profit from a falling futures price is to sell futures today and buy them back later at a lower price. A borrower will always SELL futures.

Secondly, the futures available are what are called 3 month futures. This means that any profit or loss is always calculated for 3 months even though the equivalent interest rate is quoted on a 12 month basis. This means that if the futures price changes by 2.00, this is equivalent to a change of 2% p.a., but any profit or loss is only calculated for a 3 month period and so will be 0.5% (2% divided by 4). This is always 3 months and has nothing to do with the length of the loan. It does however mean that we have to be careful to match the amount of the ‘gamble’ taking account of the length of the loan.

You will see how we deal with these two points in the following example. This example is intended to demonstrate how we use interest rate futures in a simple way – we will bring in the additional ‘rules’ afterwards.

Today is 3 October, and interest rates are 8% p.a.. X plc will wish to borrow $6M for 6 months starting on 1 January.

3 month January interest rate futures are available at 92.00.

Show how interest rate futures may be used to hedge the risk, and calculate the outcome on 1 January.

(Assume that on 1 January interest rates have changed to 10% and the futures price to 90.00)

Interest at current interest rates: 6M × 8% × ⁶⁄12 =	240,000
Futures ‘gamble’ required = 6M × ⁶⁄3 = 12M

On 1 January:

Interest 6M × 10% × 6/12 =	300,000
Profit in futures:	60,000
NET COST	240,000

Additional points:

Futures can only be dealt in contracts of fixed amounts – you will be told the contract size in the examination
In practice the change in futures prices will not exactly equate to the change in interest rates – the difference being the basis risk. If you are not told the futures price at the start of the loan then you will be expected to estimate it in the same way as we estimated the prices of currency futures – we assume that the basis risk falls linearly to zero over the life of the future.

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Barbara plc intends to borrow $40M for 6 months starting on 1 January.

Today is 1 November, LIBOR is 6% and Barbara can borrow at 1% above LIBOR.

Interest rate futures are available at the following prices: (contract size is $1M):

January	93.50
February	93.40
March	93.35

(The contracts expire at the end of the relevant month.)

Illustrate how futures may be used to hedge the interest rate risk.
(Assume that on 1 January LIBOR has risen to 9%.)
Calculate the effective interest rate

(a)	Interest at current interest rates: 40M × ⁶⁄12 × 7% =		£1,400,000
	Futures:	SELL
		January
		Contracts: 40M × ⁶⁄3 ÷ 1M =	80

Future price on 1 January:
	1 November	1 January	31 January
Interest	94.00	91.00
Futures	93.50	90.83
Difference	0.50	↱ 0.17	0

	Illustration on 1 January:
	Interest at current interest rates: 40M × ⁶⁄₁₂ × 10% =	$2,000,000
	Profit in futures:	534,000
	NET COST	1,466,000

7 Interest rate options

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In section 5 of this chapter we looked at Interest Rate Guarantees, which are effectively options but are OTC.

In this section we will look at traded options, which have the advantage that the premia are determined by market forces and therefore we can be more certain that we will be paying a ‘fair’ price. Also they have the advantage that they are traded and that therefore the options can be sold.

There is one enormous difference from currency options in that the options here are not on interest rates themselves, but are the option to buy or sell interest rate futures at a fixed price.

The option premia are given in the form of a table which you need to be able to interpret.

Dollar options. $500,000. Points of 100%

	Calls			Puts
Strike price	Sep	Dec	Mar	Sep	Dec	Mar
94.25	0.18	0.08	0.04	0.19	0.83	1.42
94.50	0.10	0.04	0.01	0.21	1.24	1.68
94.75	0.03	0.01	0.01	0.48	1.48	1.92

What does the strike price mean?
What do the headings ‘calls’ and ‘puts’ mean?
What do the months at the top of each column mean?
What does the ‘dollar options $500,000. Points of 100%’ mean?
What do the numbers in each column mean?

No answer

Agne intends to borrow $5.6M for 8 months starting in September, and wishes to protect herself against LIBOR rising above 5.75%.

LIBOR is currently 5% and Agne can borrow at 6.4%.

It is now 13 August, and options are available at the following prices:

Short Dollar options. $500,000. Points of 100%

	Calls			Puts
Strike price	Sep	Dec	Mar	Sep	Dec	Mar
94.25	0.18	0.08	0.04	0.19	0.83	1.42
94.50	0.10	0.04	0.01	0.21	1.24	1.68
94.75	0.03	0.01	0.01	0.48	1.48	1.92

Futures prices on 13 August are:

September	94.30
December	94.20
March	94.10

Show how the options can be used to hedge against the risk.
Show the outcome of the hedge if the loan is negotiated on 18 September and LIBOR is 6.5% on that date.
Calculate the effective interest rate.

(a)

PUT
September
Strike price 94.25
Contracts: 5.6M × 8⁄3 ÷ 0.5M = 30
Premium

(b)	On 18 September
		13 August	18 September	30 September
	Interest	95.00	93.50
	Futures	94.30	93.32
	Difference	0.70	↱ 0.18	0

	Interest on loan: 5.6M × 7.9% × 8/12 =	294,933
	Profit on options:	34,875
		£260,058
	Premium	£7,125
	Net payment	£267,183
(c)

8 Interest Rate collars

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As you have seen in the previous sections, if we are borrowing money, then we can fix a maximum interest rate by buying a put option.

So, for example, if we buy a put option at a strike price of 92.00 then we will be fixing a maximum interest rate of 8%.

So…. if the actual interest rate turns out to be only 5% we do not exercise the option and we just pay 5%. But if the actual interest rate turns out to be 10% then we pay the interest at 10% but exercise the option and effectively ‘claim back’ 2% from the seller of the option. (For details of how exactly this works see the Course Notes and lectures on options).

The benefit of buying the option is obvious – we fix a maximum rate but we get the benefit if rates are lower. However the downside is that we have to pay a premium for the option – whether or not we end up exercising it.

Similarly, there are people who are depositing money and therefore will be wanting to fix a minimum interest rate. They will buy a call option. If the interest rate falls then they will ‘claim’ from the seller of the option, but if the interest rate rises then they will get the benefit of the higher rates and will not exercise the option.

Back to the borrower!

They fix a maximum rate, but the downside is they have to pay the premium.

What they can do to reduce the cost is to also sell a call option (effectively becoming a dealer) and will therefore receive a premium from the person buying it.

This means they still have the benefit of fixing a maximum rate (a ‘cap’) but the net cost of it is reduced because although they still pay the premium for the put option, they will also be receiving a premium from selling the call option.

However, selling a call option will mean that they are accepting a minimum interest rate (a ‘floor’).

Illustration

Suppose we buy a put option with a strike price of 92.00 (fixing a maximum interest rate of 8%).

Suppose we also sell a call option with a strike price of 96.00 (fixing a minimum interest rate for the buyer of 4%).

Let us see what happens for different actual interest rates that might apply when they actually start the loan.

Suppose the actual interest rate turns out to be:

a) 10%; b) 6%; and c) 3%

Solution

If the actual interest is 10% then we will ‘claim’ on the put option and get 2% back from the seller. The person who bought the call option will not ‘claim’ because they are getting higher interest on their deposit. So the net cost to us is 8% – this is the most we will ever end up paying.
If the actual interest is 6% then we will not ‘claim’ on the put option. Also the person who bought the call option will not ‘claim’ from us. So we will end up paying 6% – we have got the benefit of the lower rate.
If the actual interest is 3% then we will not ‘claim’ on the put option. However, the person who bought the call option from us (because they wanted to fix a minimum interest rate on their deposit of 4%) will ‘claim’ 1% on us because we sold it to them. So we will end up paying 4% in total (3% on the loan, and 1% to the buyer of the call option).

The end result means that whatever the interest rate turns out to be, the maximum that we will end up paying will be 8% (fixed by buying the put option of 92.00), but it will also mean that the minimum we will end up paying is 4% (fixed by selling the call option at 96.00).

The reason that we might wish to do this is that we are still able to fix the maximum interest we will pay, but by accepting a minimum interest the net cost of the premium will be reduced (we pay for the put option, but receive a premium from selling the call option).

Having a maximum rate is a ‘cap’. Having a minimum rate is a ‘floor’.

Having a maximum and a minimum is a ‘collar’.

Everything in this chapter is worked for a borrower, but deposits are examined too, and a deposit is the mirror image. A depositor loses if rates fall, so buys futures rather than selling them, buys call options to fix a minimum rate, and builds a collar by buying a call and selling a put. The number of contracts still follows the period at risk, not the three months of the contract: a four-month deposit needs the amount × 4/3 ÷ the contract size, just as Barbara's six-month loan in Example 4 needed 40M × 6/3 ÷ 1M = 80.

Use the previous example (example 6) to show how Agne could use a collar to hedge her borrowing.