Chapter 12: Interest rate risk

Chapter learning objectives

Upon completion of this chapter you will be able to:

  • describe and discuss gap exposure as a form of interest rate risk
  • describe and discuss basis risk as a form of interest rate risk
  • define the term structure of interest rates
  • explain the features of a yield curve
  • explain expectations theory and its impact on the yield curve
  • explain liquidity preference theory and its impact on the yield curve
  • explain market segmentation theory and its impact on the yield curve
  • discuss and apply matching and smoothing as a method of interest rate risk management
  • discuss and apply asset and liability management as a method of interest rate risk management
  • define a forward rate agreement
  • use a forward rate agreement as a method of interest rate risk management
  • define the main types of interest rate derivatives and explain how they can be used to hedge interest rate risk.

1 Interest rate risk

Financial managers face risk arising from changes in interestrates, i.e. a lack of certainty about the amounts or timings of cashpayments and receipts.

Many companies borrow, and if they do they have to choose betweenborrowing at a fixed rate of interest (usually by issuing bonds) orborrow at a floating (variable) rate (possibly through bank loans).There is some risk in deciding the balance or mix between floating rateand fixed rate debt. Too much fixed-rate debt creates an exposure tofalling long-term interest rates and too much floating-rate debt createsan exposure to a rise in short-term interest rates.

In addition, companies face the risk that interest rates mightchange between the point when the company identifies the need to borrowor invest and the actual date when they enter into the transaction.

Managers are normally risk-averse, so they will look for techniques to manage and reduce these risks.

Interest rate exposure

Interest rate risk refers to the risk of an adverse movement ininterest rates and thus a reduction in the company's net cash flow.

Compared to currency exchange rates, interest rates do not change continually:

  • currency exchange rates change throughout the day
  • interest rates can be stable for much longer periods

but changes in interest rates can be substantial.

It is the duty of the corporate treasurer to reduce (hedge) the company's exposure to the interest rate risk.

Gap exposure

The degree to which a firm is exposed to interest rate risk can beidentified through gap analysis. This uses the principle of groupingtogether assets and liabilities that are affected by interest ratechanges according to their maturity dates. Two different types of gapmay occur:

  • A negative gap occurs when interest-sensitive liabilities maturing at a certain time are greater than interest-sensitive assets maturing at the same time. This results in a net exposure if interest rates rise by the time of maturity;
  • A positive gap occurs is the amount of interest-sensitive assets maturing in a certain period exceeds the amount of interest-sensitive liabilities maturing at the same time. In this situation the firm will lose out if interest rates fall by maturity.

Practical examples of interest rate risk

The following are all practical examples of interest rate risk:

A company might borrow at a variable rate of interest, withinterest payable every six months and the amount of the interest chargedeach time varying according to whether short-term interest rates haverisen or fallen since the previous payment.

Some companies borrow by issuing bonds. If a company foresees afuture requirement to borrow by issuing bonds, it will have an exposureto interest rate risk until the bonds are eventually issued.

Some companies also budget to receive large amounts of cash, and sobudget large temporary cash surpluses that can be invested short-term.Income from those temporary investments will depend on what the interestrate happens to be when the money is available for depositing.

Some investments earn interest at a variable rate of interest ( in bank deposit accounts) and some short-term investments go upor down in value with changes in interest rates (for example, Treasurybills and other bills).

Some companies hold investments in marketable bonds, eithergovernment bonds or corporate bonds. These change in value withmovements in long-term interest rates.

Interest rate risk can be significant. For example, suppose that acompany wants to borrow $10 million for one year, but does not need themoney for another three weeks. It would be expensive to borrow moneybefore it is needed, because there will be an interest cost. On theother hand, a rise in interest rates in the time before the money isactually borrowed could also add to interest costs. For example, a riseof just 0.25% (25 basis points) in the interest rate on a one-year loanof $10 million would cost an extra $25,000 in interest over the courseof a year.

2 Why interest rates fluctuate

The yield curve

The term structure of interest ratesrefers to the way in which the yield (return) of a debt security orbond varies according to the term of the security, i.e. to the length oftime before the borrowing will be repaid.

The yield curve is an analysis of the relationship between the yields on debt with different periods to maturity.

A yield curve can have any shape, and can fluctuate up and down for different maturities.

There are three main types of yield curve shapes: normal, inverted and flat (or humped):

  • normal yield curve – longer maturity bonds have a higher yield compared with shorter-term bonds due to the risks associated with time
  • inverted yield curve – the shorter-term yields are higher than the longer-term yields, which can be a sign of upcoming recession
  • flat (or humped) yield curve – the shorter- and longer-term yields are very close to each other, which is also a predictor of an economic transition.

The slope of the yield curve is also seen as important: the greaterthe slope, the greater the gap between short- and long-term rates.

The yield curve

Analysis of term structure is normally carried out by examiningrisk-free securities such as UK government stocks (gilts). Newspaperssuch as the Financial Times show the gross redemption yield (i.e.interest yield plus capital gain/loss to maturity) and time to maturityof each gilt on a daily basis.

The return for each instrument is plotted on a graph where the yaxis represents the annual return and the x axis represents theinstrument's remaining term to maturity. The points plotted on the graphare then joined up to produce a yield curve.

This term structure of interest rates might be shown as a yield curve, as follows.

The redemption yield on shorts is less than the redemption yield ofmediums and longs, and there is a 'wiggle' on the curve between 5 and10 years.

A yield curve can have any shape, and can fluctuate up and down for different maturities.

Generally however, yield curves fall into one of three typical patterns.

Normal. A normal yield curve is upward sloping, so that theyield is higher on instruments with a longer-remaining term to maturity.The higher yield compensates the investor for tying up capital for alonger period. Although the yield curve slopes upwards, the gradient ofthe curve is not steep. A normal yield curve might be expected wheninterest rates are not expected to change.

Inverse. An inverse yield curve is downward sloping, so thatthe yield is lower on instruments with a longer-remaining term tomaturity. An inverse yield curve might be expected when interest ratesare currently high but are expected to fall.

Steep upward-sloping curve. When interest rates are expectedto rise, the yield curve is likely to have a steep upward slope, withyields on longer-term investments much higher than the yield onshorter-dated investments.

Yield curves are usually drawn for 'benchmark' investments that areeither risk free (government securities) or low risk (such as yields oninterest rate swaps). However, they are representative of the slope ofthe yield curve generally for all other financial instruments, such asinter-bank lending rates and corporate bond yields.

The shape of the yield curve at any point in time is the result of the three following theories acting together:

  • liquidity preference theory
  • expectations theory
  • market segmentation theory.

Liquidity preference theory

Investors have a natural preference for more liquid (shortermaturity) investments. They will need to be compensated if they aredeprived of cash for a longer period.

Expectations theory

The normal upward sloping yield curve reflects the expectation thatinflation levels, and therefore interest rates will increase in thefuture.

Market segmentation theory

The market segmentation theory suggests that there are differentplayers in the short-term end of the market and the long-term end of themarket.

If there is an increased supply in the long-term end of the marketbecause the government needs to borrow more, this may cause the price tofall and the yield to rise and may result in an upward sloping yieldcurve.

Factors affecting the shape of the yield curve

The shape of the yield curve at any particular point in time isgenerally believed to be a combination of three theories actingtogether:

  • liquidity preference theory
  • expectations theory
  • market segmentation theory.

Liquidity preference theory

Investors have a natural preference for holding cash rather thanother investments, even low-risk ones such as government securities.They therefore need to be compensated with a higher yield for beingdeprived of their cash for a longer period of time. The normal shape ofthe curve as being upwards sloping can be explained by liquiditypreference theory.

Expectations theory

This theory states that the shape of the yield curve variesaccording to investors' expectations of future interest rates. A curvethat rises steeply from left to right indicates that rates of interestare expected to rise in the future. There is more demand for short-termsecurities than long-term securities since investors' expectation isthat they will be able to secure higher interest rates in the future sothere is no point in buying long-term assets now. The price ofshort-term assets will be bid up, the price of long-term assets willfall, so the yields on short-term and long-term assets will consequentlyfall and rise.

A falling yield curve (also called an inverted curve, since itrepresents the opposite of the usual situation) implies that interestrates are expected to fall.

In the early 1990s interest rates were high to counteract highinflation. Everybody expected interest rates to fall in the future,which they did. Expectations that interest rates would fall meant it wascheaper to borrow long-term than short-term.

A flat yield curve indicates expectations that interest rates are not expected to change materially in the future.

Market segmentation theory

As a result of the market segmentation theory, the two ends of thecurve may have different shapes, as they are influenced independently bydifferent factors.

  • Investors are assumed to be risk averse and to invest in segments of the market that match their liability commitments, e.g.
    • banks tend to be active in the short-term end of the market
    • pension funds would tend to invest in long-term maturities to match the long-term nature of their liabilities.
  • The supply and demand forces in various segments of the market in part influence the shape of the yield curve.

Market segmentation theory explains the 'wiggle' seen in the middleof the curve where the short end of the curve meets the long end – itis a natural disturbance where two different curves are joining and theinfluence of both the short-term factors and the long-term factors areweakest.

The significance of the yield curve

Financial managers should inspect the current shape of the yieldcurve when deciding on the term of borrowings or deposits, since thecurve encapsulates the market's expectations of future movements ininterest rates.

For example, a normal upward sloping yield curve suggests thatinterest rates will rise in the future. The manager may therefore:

  • wish to avoid borrowing long-term on variable rates, since the interest charge may increase considerably over the term of the loan
  • choose short-term variable rate borrowing or long-term fixed rate instead.

The significance of yield curves

Expectations of future interest rate movements are monitoredclosely by the financial markets, and are important for any organisationthat intends to borrow heavily or invest heavily in interest-bearinginstruments. A company might use a 'forward yield curve' to predict whatinterest rates might be in the future. For example, if we know thecurrent interest rate on a two-month and a six-month investment, it ispossible to work out what the market expects the four-month interestrate to be in two months' time.

A corporate treasurer might analyse a yield curve to decide for howlong to borrow. For example, suppose a company wants to borrow $20million for five years and would prefer to issue bonds at a fixed rateof interest. One option would be to issue bonds with a five-yearmaturity. Another option might be to borrow short-term for one year,say, in the expectation that interest rates will fall, and then issue afour-year bond. When borrowing large amounts of capital, a smalldifference in the interest rate can have a significant effect on profit.For example, if a company borrowed $20 million, a difference of just 25basis points (0.25% or one quarter of one per cent) would mean adifference of $50,000 each year in interest costs. So if the yield curveindicates that interest rates are expected to fall then short-termborrowing for a year, followed by a 4-year bond might be the cheapestoption.

3 Hedging interest rate risk

Forward rate agreements (FRAs)

The aim of an FRA is to:

  • lock the company into a target interest rate
  • hedge both adverse and favourable interest rate movements.

The company enters into a normal loan but independently organises a forward rate agreement with a bank:

  • interest is paid on the loan in the normal way
  • if the interest is greater than the agreed forward rate, the bank pays the difference to the company
  • if the interest is less than the agreed forward rate, the company pays the difference to the bank.

Test your understanding 1 – FRAs

Enfield plc's financial projections show an expected cash deficitin two months' time of $8 million, which will last for approximatelythree months. It is now 1 November 20X4. The treasurer is concerned thatinterest rates may rise before 1 January 20X5. Protection is requiredfor two months.

The treasurer can lock into an interest rate today, for a futureloan. The company takes out a loan as normal, i.e. the rate it pays isthe going market rate at the date the loan is taken out. It will thenreceive or pay compensation under the separate FRA to return to thelocked-in rate.

A 2-5 FRA at 5.00 – 4.70 is agreed.

This means that:

  • The agreement starts in 2 months time and ends in 5 months' time.
  • The FRA is quoted as simple annual interest rates for borrowing and lending, e.g. 5.00 – 4.70.
  • The borrowing rate is always the highest.


Calculate the interest payable if in two months' time the market rate is:

(a)7% or


Test your understanding 2 – FRAs

Able Plc needs to borrow £30 million for eight months, starting in three months' time.

A 3-11 FRA at 2.75 – 2.60 is available.

Show the interest payable if the market rate is (a) 4%, (b) 2%.

Interest rate guarantees (IRGs)

An IRG is an option on an FRA. It allows the company a period of timeduring which it has the option to buy an FRA at a set price.

IRGs, like all options, protect the company from adverse movements and allow it to take advantage of favourable movements.

Decision rules:

IRGs are more expensive than the FRAs, as one has to pay for theflexibility to be able to take advantage of a favourable movement.

If the company treasurer believes that interest rates will rise:

  • he will use an FRA, as it is the cheaper way to hedge against the potential adverse movement.

If the treasurer is unsure which way interest will move:

  • he may be willing to use the more expensive IRG to be able to benefit from a potential fall in interest rates.

Interest rate futures

Interest rate futures work in much the same way as currency futures. The result of a future is to

  • lock the company into the effective interest rate
  • hedge both adverse and favourable interest rate movements.

Futures can be used to fix the rate on loans and investments. We will look here at loans.

How they work

As with an FRA, a loan is entered into in the normal way. Suitablefutures contracts are then entered into as a separate transaction.

A futures contract is a promise, e.g.:

  • if you sell a futures contract you have a contract to borrow money – what you are selling is the promise to make interest payments.

However the borrowing is only notional.

  • We close out the position by reversing the original deal, before the real borrowing starts, i.e. before the expiry date of the contract.
  • This means buying futures, if you previously sold them, to close out the position. The contracts cancel each other out, i.e. we have contracts to borrow and deposit the same amount of money.
  • The only cash flow that arises is the net interest paid or received, i.e. the profit or loss on the future contracts.

As with all futures (as we saw in the previous chapter), eachcontract is for a standardised amount with a set maturity date. A wholenumber of contracts must be dealt with.

The price of futures moves inversely to interest rates therefore:

Basis risk

The gain or loss on the future may not exactly offset the cash effectof the change in interest rates, i.e. the hedge may be imperfect. Thisis known as basis risk.

The risk arises because the price of a futures contract may bedifferent from the spot price on a given date, and this difference isthe basis. This is caused by market forces. The exception is on theexpiry date, when the basis is zero.

The other main reason why a hedge may be imperfect is because thecommodity being hedged (be it currency or interest) must be rounded to awhole number of contacts, causing inaccuracies.


Borrowers may additionally buy options on futures contracts. Theseallow them to enter into the future if needed, but let it lapse if themarket rates move in their favour.


An interest rate swap is an agreement whereby the parties agree toswap a floating stream of interest payments for a fixed stream ofinterest payments and vice versa. There is no exchange of principal.

Swaps can be used to hedge against an adverse movement in interestrates. Swaps may also be sought by firms that desire a type of interestrate structure that another firm can provide less expensively.

Say a company has a $200 million floating loan and the treasurerbelieves that interest rates are likely to rise over the next fiveyears. He could enter into a five-year swap with a counter-party to swapinto a fixed rate of interest for the next five years. From year sixonwards, the company will once again pay a floating rate of interest.

Illustration 1 – Interest rate swaps

Company A wishes to raise $6m and to pay interest at a floatingrate, as it would like to be able to take advantage of any fall ininterest rates. It can borrow for one year at a fixed rate of 10% or at afloating rate of 1% above LIBOR.

Company B also wishes to raise $6m. They would prefer to issuefixed rate debt because they want certainty about their future interestpayments, but can only borrow for one year at 13% fixed or LIBOR + 2%floating, as it has a lower credit rating than company A.


Calculate the effective swap rate for each company – assume savings are split equally.


In addition to a basic swap, counterparties can also agree to swapequivalent amounts of debt in different currencies. This is knows as a currency swap.

The principal is not transferred and the original borrower remains liable in the case of default.

Other practical ways to manage risk

Cash flow matching

An effective, but largely impractical, means of eliminating interest rate risk.

Stated simply, interest rate risk arises from either positive (invested) or negative (borrowed) net future cash flows.

The concept of cash matching is to eliminate interest rate risk by eliminating all net future cash flows.

A portfolio is cash matched if :

  • every future cash inflow is balanced with an offsetting cash outflow on the same date
  • every future cash outflow is balanced with an offsetting cash inflow on the same date.

The net cash flow for every date in the future is then zero, and there is no risk of interest rate exposure.

Whilst clearly not achievable, it does provide a broad goal that businesses can work towards.

Asset and liability management

Problems arise if interest rates are fixed on liabilities for periods that differ from those on offsetting assets.

Suppose a company is earning 6% on an asset supported by aliability on which it is paying 4%. The asset matures in two years whilethe liability matures in ten.

  • In two years, the firm will have to reinvest the proceeds from the asset.
  • If interest rates fall, it could end up reinvesting at 3%. For the remaining eight years, it would earn 3% on the new asset while continuing to pay 4% on the original liability.

To avoid this, companies attempt to match the duration of their assets and liabilities.

Chapter summary

Test your understanding answers

Test your understanding 1 – FRAs

In this case the company is protected from a rise in interest ratesbut is not able to benefit from a fall in interest rates – it islocked into a rate of 5% – an FRA hedges the company against both anadverse movement and a favourable movement.


  • The FRA is a totally separate contractual agreement from the loan itself and could be arranged with a completely different bank.
  • They can be tailor-made to the company's precise requirements.
  • Enables you to hedge for a period of one month up to two years.
  • Usually on amounts > £1 million. The daily turnover in FRAs now exceeds £4 billion.

Test your understanding 2 – FRAs

Created at 5/24/2012 4:16 PM  by System Account  (GMT) Greenwich Mean Time : Dublin, Edinburgh, Lisbon, London
Last modified at 5/25/2012 12:54 PM  by System Account  (GMT) Greenwich Mean Time : Dublin, Edinburgh, Lisbon, London

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