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B821 Financial Strategy

Block 4 Financial Risk Management

Unit 7

Risk Assessment and Interest Rate Risk Prepared by the Course Team

Masters



This publication forms part of an Open University course B821, Financial Strategy . Details of this and other Open University courses can be obtained from the Student Registration and Enquiry Service, The Open University, PO Box 625, Milton Keynes, MK7 6YG, United Kingdom: tel. +44 (0)1908 653231, email general [email protected]

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CONTENTS

1 Introduction 51.1 Introduction to Block 4 5

1.2 Introduction to Unit 7 8

2 Risk assessment 112.1 Defining risk 112.2 Risk mapping 132.3 Assessing the results 22

Summary 23

3 Interest-rate risk 253.1 Interest-rate risk 253.2 Quantifying interest-rate risk 29

Summary 32

4 Duration 334.1 So what is wrong with ‘ maturity ’ ? 334.2 A measure that works 354.3 Duration and quantifying interest exposure 41

4.4 Immunisation 444.5 Worked example of immunisation 46

Summary 49

5 Measuring and managing aggregate interest-rateexposure 515.1 Gap analysis and duration 515.2 Value at risk 60

Summary

666 Interest-rate risk management instruments:

FRAs and futures 67 6.1 Forward rate agreements 686.2 Interest-rate futures 71

Summary 79



7 Interest-rate risk management instruments: swaps 817.1 Defining and using interest-rate swaps 817.2 How can swaps save money ? 857.3 Using interest-rate swaps to trim borrowing costs 86

Summary 90Summary and conclusions 92

Answers to exercises 94

References and suggested reading 101

Acknowledgements 102



1 INTRODUCTION

1 INTRODUCTION

1 . 1 INTRODUCTION TO BLOCK 4

Units 7, 8 and 9 form a block that concentrates on a crucial aspectof running an organisation: risk and its management. Bearing inmind the aims of this course, you will not be surprised to find thatthe focus of the material in this block is on financial risks and how they can be managed.

For all organisations the need for effective risk management hasbeen visibly demonstrated in recent years by a series of highprofile financial calamities affecting major organisations around the world. These have included the demise of Barings Bank and Enronand the financial body blows experienced by the Allied IrishBank ’ s US subsidiary, Allfirst and by Orange County in California.In each case the problems these organisations got into were theresult of the inadequacy of their risk management practices.

This block will therefore explore each of the financial risks facingorganisations. In each case the approach will be to:l define the risk;l explain how the risk arises;l look at how the magnitude of the risk can be measured;l explore what can be done to manage (or ‘ hedge ’ ) the risk.

It is important that the individual risks are not looked at entirely inisolation from each other. Organisations may have small exposuresto the individual risks, but when these are aggregated they may have, in total, substantial financial risks that require carefulmanagement. Additionally, as we shall find out, there areinterrelationships between certain of the risks.

Consequently, we shall spend time at the start of the block (in Unit 7)looking at a framework with which organisations can assess theiroverall exposure to financial risk. This involves the subject of riskmapping. Then at the end of the block (in Unit 9) we shall look at how over arching risk management policies can be applied to managefinancial risks collectively and efficiently. When we do this we shalllook at some examples of how organisations actually apply riskmanagement policies.

Let us now introduce ourselves to these financial risks.

Unit 7 examines interest rate risk: the risk of financial loss causedby changes in interest rates. This is a form of risk to which almost

The problems encountered by Allfirst and Orange County, which perhaps are less

well known

than

those

experienced by Barings and Enron, are explained in two articles in the Course Reader. The article by Burke, ‘Currency exchange trading and rogue trader John Rusnak ’, looks in detail at Allfirst, while that by Culp, Miller and Neves, ‘Value at risk: uses and abuses ’, explores Orange County ’s financial calamity and also comments on the collapse

of Barings.

OU BUSINESS SCHOOL 5



UNIT 7 RISK ASSESSMENT AND INTEREST RATE RISK

all organisations will be exposed at some time or other. It can arise from the need to raise capital, but also from the management of ordinary operational cash flows. It is also a serious consideration when an organisation is investing surplus funds. As individuals, we are also intimately concerned with this topic when we consider our mortgages and savings, be these in the form of pension

contributions or other investments. We shall look carefully at the principal methods of measuring this type of risk – ‘ duration ’ and ‘ value at risk ’ . In doing this, we also undertake ‘ gap analysis ’ and apply discounted cash flow (DCF) analysis to the collective cash flows of an organisation. The subject matter is somewhat technical in places, but the coverage has been structured to ensure that the mathematics you will need to apply are not onerous. The unit concludes with an examination of some of the financial instruments available for managing interest risk.

The first part of Unit 8 examines foreign exchange risk. As you may know from reading the news over the past few years, mistakes in managing foreign exchange risk can cost a business substantial money – witness the losses of over US$780m incurred by the Allied Irish Bank ’ s US subsidiary, Allfirst. As you will see in the unit, it is not sufficient to claim that you are not exposed to foreign exchange risk simply because you are neither an exporter nor an importer. Where do your materials come from? Are they priced on an international market in, say, US dollars? Do your customers export your goods as subcomponents in their output? Who are your competitors and in what currency are their cost bases? Foreign

exchange (or

forex

or

FX)

risk

is

rather

more

pervasive

than

is

typically realised.

The second part of Unit 8 undertakes an analysis of contingent risk, the exposure to risks that arises if a particular event or sequence of events occurs. The unit explains how certain of these risks can be managed by the use of options. The growth of the options markets is one of the most important developments in finance over the past thirty years; it is also one of the least understood. In the course of their business, organisations often have to grant (to ‘ write ’ in the jargon) options to some of those with whom they transact. In the past, much of this was risk that could not be managed, merely assumed and borne. Options now provide a way of managing at least some risks.

It has to be admitted that the mathematics of option theory is fairly advanced and the adaptation of the theory to the complications of the real world is a matter of constant evolution. Nevertheless, the concepts underlying the calculations are intelligible, as are the techniques for using and managing options products. We have no need to follow every twist and turn of the theorists, but if any of you wish to, we shall point you in the right direction, with Vital Statistics being a good starting point.

Unit 9 analyses three further balance sheet risks.




1 INTRODUCTION

The activities of virtually all organisations expose them to some degree of credit risk, whether it be, for example, where a company finds that its business customers do not pay for the products supplied or where a bank finds that a company to whom it has lent money has gone bankrupt. As the collapse of the banking group BCCI in 1991 proved, you can even lose money if you put it

into a bank. Additionally, the large investment funds – including our own pension funds – are exposed to credit risk on the bonds and shares they purchase, since the issuers of these stocks could default.

We do not intend to turn everyone into a credit analyst, but the moment a business allows a customer ‘ normal trade terms ’ for payment, it has become a banker providing short term capital. It is, therefore, prudent for managers to have some exposure to the fundamentals of credit analysis, even if they are not employed in the banking and investment industry.

The unit then moves on to assess how companies should manage their liquidity risk – the risk that they do not have enough funds to meet payment obligations when they fall due. This is often a precursor to bankruptcy and liquidation. Failure to manage liquidity risk is ultimately terminal for a business: companies do not go bankrupt solely if they have mismanaged, for example, foreign exchange risk or interest rate risk. If they can pay for such losses and remain solvent they can continue in business. The problem arises when the money runs out and the business cannot refinance itself.

The unit then reviews operational risk. This is the risk that arises from the imperfect operation of controls, people or systems. You may think this is not directly related to financial risks, but it is. Operational controls are like the antibiotics prescribed to deal with a nasty infection! With good controls all the financial risks you examine in this block can be managed or contained. The failure of operational controls allows the infections of those financial risks to spread throughout the ‘ body corporate ’ hastening its demise. This may sound a bit dramatic, but if we go back to those corporate financial calamities that have hit the headlines in recent years (including Barings and Enron) the problems usually started because of the failure of operational controls, sometimes quite simple ones like the proper segregation of staff responsibilities.

Both Unit 9 and the block end with a return to the preoccupation of the early part of Unit 7: the strategic and tactical levels of the management of risk. To assist in this we undertake a review of the risk management policies applied by some leading companies.

By the time you reach this part of the block, you will have the tools both to be the strategist who designs the risk management systems and the technician who implements the strategy by

executing risk

management

transactions.

Consequently,

you

will

be

well placed to comment on the efficacy and prudence of these companies ’ risk management policies .





Benjamin Franklin said that nothing was certain except death and taxes; Merton Miller revised this in his work on capital structure to debt and taxes. I think they both left out one other certainty – risk, but at least we can sometimes do something about risk and not merely bow to the inevitable!

INTRODUCTION TO UNIT 7 1 . 2

The first topic in Unit 7 is a reassessment of our concept of risk. So far in this course you have encountered ways to assess the risk that is related to specific securities, such as to shares traded on the stock market. In this unit, we begin with a step back and offer a more general discussion about risk. We map what you have already learnt while, at the same time, introducing other types of risk that you might not have encountered.

You might find that this unit covers a lot of subject matter and that it can be technical in places, so please do take the time to go through the material in detail and try to engage with all the exercises and activities. One way to approach the content is to divide it into four parts (my suggestion would be Section 2; Sections 3 and 4; Section 5; Sections 6 and 7) taking at least a short break between studying each. By so doing, the material becomes easier to digest.

The reward for being able to carry out some of the technicalities in the unit is that, at the end, you will be conversant with the typical activities that take place in the treasury department of any type of organisation. The techniques described are not just the preserve of financial institutions. Public sector bodies, such as local authorities (and the managers of their pension funds), charities and mediumsized firms take active steps to manage their exposure to risk in ways similar to those we describe in this unit.

After having completed risk mapping at a strategic level, for the rest of the unit you will concentrate on interest rate risk. You will see how ‘ duration ’ and ‘ value at risk ’ offer ways to measure this risk. You will also be introduced to futures, forward rate agreements and interest rate swaps – these are known as ‘ derivatives ’ and they can be used to manage interest rate risk.

Learning outcomes

At the end of this unit, you should be able to: l understand the general implications of risk for an organisation; l categorise the forms of risk to which an organisation is subject; l plan and carry out a risk assessment exercise; l understand the concept of interest rate risk; l calculate ‘ duration ’ and understand its use for quantifying

interest rate risk;




1 INTRODUCTION

l produce a ‘ gap chart ’ for the purpose of measuring cash flows and understand how this can be used with discounted cash flow (DCF) analysis to manage interest rate risk;

l understand and use the concept of ‘ value at risk ’ ; l understand the concepts behind, and usage of, interest rate

products such

as

forward

rate

agreements,

futures

and

swaps.

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �





10 OU BUSINESS SCHOOL



2 RISK ASSESSMENT

2 RISK ASSESSMENT

In this first working section of the unit we begin by defining more clearly what we mean by ‘ risk ’ and we then categorise it into its main forms. We then proceed to consider how we might analyse risk – largely, but not exclusively, financial risk – for an organisation, through ‘ risk mapping ’ , a process known in some organisations as a ‘ risk audit ’ .

2 . 1 DEFINING RISK How do we define risk? You have already met a couple of empirical definitions in Unit 4, which introduced the concept of the variability of stock prices (measured either by the standard deviation, or the beta of the returns of the stock or portfolio) as the definition of risk in the context of portfolio theory. We now extend this into a more comprehensive definition.

The word ‘ risk ’ is thought to derive either from the Arabic word risq or the Latin word risicum (Kedar, 1970). The two possibilities quite neatly combine to give us the meaning for the English term

in our context. The Latin word originally referred to the challenge presented to seafarers by a barrier reef and so implied a possible negative outcome. The Arabic word, on the other hand, implies ‘ anything that has been given to you (by God) and from which you draw profit ’ and has connotations of a potential beneficial outcome.

A twelfth century Greek derivative of the Arabic risq related to chance outcomes in general with no positive or negative implications (Kedar, 1970). We can combine the above definitions to derive our concept of risk as being ‘ an uncertain future outcome that will improve or worsen our position. ’

There are two elements about this definition that should be noted.

1 It is probabilistic – the likely outcome can be assessed, but is not known with certainty.

2 It is symmetrical – the outcome may be pleasant or unpleasant.

Strictly speaking, the ‘ pleasant or unpleasant ’ aspect of the definition does not necessarily imply ‘ symmetry ’ , where the ‘ upside ’ and ‘ downside ’ are of an exact equivalent magnitude. For many financial matters, however, which are the main concern for this course, risk is more or less symmetrical. If you own shares, for

example, the

gain

or

loss,

relative

to

the

purchase

price,

is

the

same for a 1% change in the share price in either direction – before tax, at least. We shall thus keep the second point in the list.

As you have seen in Units 1 and 4, standard deviation is very often the key measure for financial risk.

The Arabic idea of risk is perhaps more suitable for buying financial options where, for a fee (or ‘premium ’), you can insure against the worst case scenario and be positioned to benefit from a positive scenario.





BOX 2.1

BUNGEE JUMPING IS RISKY!

This may not seem a very controversial idea, but bungee jumping can illustrate graphically the relevance of uncertainty to the

definition of ‘

risk’

that we shall use throughout the block.

If you attach a length of elastic to your ankles and jump off a very high bridge, it is a risky thing to do. The elastic may be too long; it may stretch excessively; it may snap; it may work as intended, giving you an adrenaline rush. In this last case the risk has been ‘managed ’.

If you do not jump off the high place, it is not risky – assuming you do not slip or suffer a dizzy spell while looking over the edge.

Consider another, rather unpleasant, alternative: jumping off the bridge without the bungee cord attached. This alternative is dire in its consequences, but it is not risky. There is no realistic uncertainty as to the outcome.




2 . 2 RISK MAPPING

An organisation ’ s attitude towards the various forms of risk to which it is exposed should be a direct interpretation of its business strategy. This has implications both ways: the strategy itself must address the appetite and capacity for risk within the business and

the systems and actions of the organisation regarding risk should seek to attain the goals envisaged by the strategy. This process of linking risk exposure and risk appetite to company policy is known as risk mapping .

Risk mapping is akin to an internal audit. This is distinct from the annual financial audit by external accountants, which is essentially a check that the company ’ s public financial statements are accurate, or ‘ true and fair’ . An internal audit is principally intended as an investigation of practice with a view to suggesting improvements. So, too, with a risk map.

The process can be divided into three sequential stages. 1 Determine which risk categories are involved.

2 Estimate the levels of exposure in terms of size or degree.

3 Rank the risks in terms of the importance they should be given when allocating the organisation ’ s risk capacity.

The third stage will usually necessitate an interrogation and interpretation of the overall strategy and may well also involve a reassessment of the strategy itself, given that the mapping process may well throw up aspects of risk not at present covered by policy.

Stage 1 What risk categories?

There is no single or definitive way to subdivide risk. The key point, however, is to ensure that the categorisation chosen covers each type of risk and is understood by all those using the results.

The approach taken here is to use four categories of risk as depicted in Figure 2.1 overleaf, namely: l Financial l Organisational l

Market l Environment.

Financial risk refers to possible changes to the monetary value of wealth because of variations in cash balances (that is, liquidity) or in resources. You have already examined some aspect of financial risk management. In Units 2 and 4 you learnt about ‘ gearing ’ or ‘ leverage ’ , which indicates the potential risk of future cash flows not being able to service debt. In this block you will learn about other potential sources of financial risk arising from interest rates, foreign exchange rates, credit exposures and organisational cash flows.

Organisational risk refers to such factors such as industrial relations, labour costs, skill requirements and other factors associated with ‘ personnel ’ . My definition would also include the quality and price

2 RISK ASSESSMENT





STEP = Social,

Technological, Economic and Political.

of materials, supplier power, potential disruption of supply and other issues associated with ‘ materials ’ . Additionally it includes ‘ research and development ’ (R&D) because this distinguishes the actual development of a product from the preceding marketing analysis that has identified the opportunity. Under the heading of organisational risk, I should include operational risk . This, as noted

in Section 1.1, relates to the risk of the imperfect operation of people, controls and systems and is a central element of the broad category of organisational risk.

�

�

�

�

Figure 2.1 Risk mapping categories

Market risk would be concerned with externally oriented factors that impinge directly on the sales of a business. The term should be seen as distinct from financial market risk, which we shall study later on in this block. The elements of this risk are commonly the responsibility of the marketing function of an organisation and appropriate subdivisions of this risk could be: ‘ market share ’ , ‘ total demand ’ , ‘ distribution ’ and ‘ product range ’ .

Finally, you could identify sources of risk that are industry specific through a formal analysis of the competitive environment . There is a logical and intentional similarity here with the headings you will have met in STEP analysis (or PEST, depending on the author)

earlier in your MBA studies. So there is no need for me to elaborate any further.




You will notice that much of your earlier study of strategy has a bearing upon the analysis of risk: for example, Porter ’ s five forces and value chain models help to illuminate an organisation ’ s risk profile.

Decisions about a company ’ s appetite for risk, both absolute and relative, are fundamentally a strategic function. The application of

risk management techniques

may

be

regarded

as

operational

or

tactical, but the goals derive directly from strategy.

Stage 2 Estimating exposure to risk

Having identified the categorisation appropriate to the organisation, the next task is to measure the assorted risks.

There are two main ways of thinking about the possible results of risk exposure. Either you can focus on the ‘ expected return ’ or on ‘ possible outcome versus return ’ . The expected return method is usually easier to use in a quantitative or comparative way. For example, assume you are faced with choosing between action A or action B each with the same level of risk. If it is possible to calculate the expected return of the alternatives then it is usually sensible to opt for whichever offers the better expected return.

How do you calculate expected return? As described in Unit 1, it is the sum of the values of the return of each possible outcome multiplied by its probability of occurrence. Formulaically this is represented as

=i n E(R) = ∑ p R i i

i=1

where

E(R) = expected return

R i = value of outcome i

pi = probability of outcome i.

This is the same definition as that for the mean return in statistics, which is fortunate since ‘ expected return ’ and ‘ mean return ’ are the same thing.

An important use for expected return is when considering avoidable risk: that is, risk to which the organisation can choose whether or not to be exposed. The simplest form of the rule is:

‘ only take on avoidable risk if the expected return is positive ’ . Similarly, if you have to decide between choices, the rule should be: ‘ choose the option with the highest expected return ’ .

You should immediately realise that either form of this rule is not yet complete as it does not address the balance between level of risk and level of return. Strictly speaking, satisfying the rule as so far stated is a necessary , but not a sufficient , condition for

accepting avoidable

risk.

Please

accept

this

for

the

moment

as

it

avoids judgements about ‘ acceptable ’ return for taking on risk: the simplification will allow us to investigate, in Box 2.2, another aspect of deciding on exposure to risk.

2 RISK ASSESSMENT

The expected return method is very much applicable and useful in finance – for instance, in your study of portfolio theory (see Unit 4).





BOX 2.2

WHEN SIMPLICITY IS NOT ENOUGH

You have the chance to play one of two coin tossing games. Whichever you choose to play, you will only have the chance to

toss once. Oh yes, notwithstanding the reputation of your opponent, the coin is fair! The probability of heads therefore equals the probability of tails, 0.5.

Game A If the coin lands on heads you will receive £12; if it comes up tails, you pay £10.

Game B If the coin lands on heads you will receive £12,500, if it comes up tails, you pay £10,000.

What should you do? First, calculate the expected return of each game.

Game A

E(R) = (+ £12 6 0.5) + ( – £10 6 0.5) = + £1

Game B

E(R) = (+ £12,500 6 0.5) + ( – £10,000 6 0.5) = + £1,250

So surely you play Game B? It offers £1,249 more expected return. It even offers a better percentage return, since for Game A

E(R)/Stake = £1/£10 = +10%

and for Game B

E(R)/Stake = £1,250/£10,000 = +12.5%

The simple decision rule is quite clear: play Game B.

But what if you lose on your one toss?

Personally, I could not afford the loss of £10,000 and I doubt if many of you could either. The possible negative outcome is not supportable, so I must decline to play Game B even though the expected return is more favourable.

The simple rule therefore needs to be extended to include checking that the downside possibilities are not ‘catastrophic ’ if

they actually occur. Now, I can afford to invest £10 in Game A ... .

This idea of avoiding catastrophic outcomes leads to the second factor we need to include when assessing risk: namely, ‘ possible outcome versus return ’ . This does not contradict the ‘ risk versus return ’ as epitomised by portfolio theory and the CAPM, but adds to it. ‘ Risk versus return ’ looks at the situation as a whole and judges whether on average the risk is worth accepting. This new

criterion says that for some sorts of risk it is necessary to consider whether some possible outcomes are so insupportable as to outweigh almost any level of average return.




2 RISK ASSESSMENT

Note that you have already met this idea of ‘ average risk ’ when studying portfolio theory and the CAPM. You measured it in terms of the standard deviations of the returns. The standard deviation is a way of condensing into a single number information about the average amount of scatter around the mean of a distribution. Since this represents uncertainty about the return received in any

particular period, it is truly a measure of risk as we have defined it. For some types of risk, however, it is not practical to calculate a proper statistical measure such as the standard deviation. Additionally, historic measures based on past returns may not capture ‘ discontinuities ’ that generate insupportable outcomes. For example, stock market declines, such as during 2001 – 2003, may be seen as included in, and allowed for, by standard deviation analysis, but crashes that happen in the space of a few days, such as in 1929 and 1987, reflect such radical and unusual changes as to preclude capture in such a measure.

In either situation, including a ‘

catastrophe avoidance’

criterion is not a rival to the standard deviation, but an adjustment to it. Figure 2.2 illustrates the idea, perhaps rather crudely.

Scenario A shows the value of a project for the whole range of possible outcomes: it is not a true ‘ distribution ’ in the proper statistical sense, but is meant to represent qualitatively the same sort of idea. The project is more likely than not to end up with a positive value, as implied by E(R) > 0. Furthermore, all the possibilities give relatively modest values, some positive, some negative, none extreme.

Scenario B, on the other hand, is expected to give a higher value than Scenario A, but there is a small chance of it ending up horribly negative – a ‘ catastrophic ’ outcome. While the expected return is better, we should also include in our consideration such a nasty possibility.

It is worth noting that the expected return system can encompass the ‘ possible outcome versus return ’ method. If you look at each of the terms in the E(R) summation, as well as the final result, then you can analyse the individual outcomes as required for this second method of assessing risk. Here you consider each potential

outcome and what would be the profit or loss should it actually occur. If one or more outcomes have an unacceptably large negative return, that is, a ‘ catastrophic ’ result, then this information should be taken into account.

A benefit of this ‘ summing over outcomes ’ method is that it forces us to think through the consequences of each possibility. Sometimes this is more important than calculating expected value. Also, it is much easier to apply this system where the assessment must be essentially qualitative, either in respect of the values or of the probabilities. However, this method has one significant

disadvantage: if

it

does

not

result

in

comparable

measures,

it

makes

assessing between options much more difficult, or, at the very least, less precise.





P r o j e c t v a l u e

Range of outcomes

Value for each possible outcome

Average value of project

P r o

j e c t v a l u e

Small chance of big negative value

Range of outcomes

Average value of project

Value for each possible outcome

Figure 2.2 ‘Expected return ’ and ‘possible catastrophe ’

ACTIVITY 2.1

The NPV rule of ‘ accept projects with positive NPV ’ seems to be an example of the naïve version of our risk rule: that is, it does not consider the level of return. Is this true?

No – providing the cost of capital has been correctly risk weighted. Assuming that this has been done, then a zero net present value means that the project is exactly ‘ fair ’ . In the terms of this discussion, the expected return is just enough to justify the risk. If, however, the calculation has been done with a company ’ s ‘ standard ’ or non-risk-weighted discount rate, the NPV rule has potentially been impoverished as a decision tool, especially if the proposed project is much riskier or much safer than the average for the business.

Risk mapping needs to show key areas of risk for the organisation in terms of danger and size of exposure. The aim is to provide data to enable informed strategic decision making about the allocation of the organisation ’ s risk capacity. Where possible, the mapping might include benchmarks for some types of risk. This is likely to be feasible for market oriented risks (for example, foreign




2 RISK ASSESSMENT

exchange, interest rate, commodity price and so on) as there is more chance of there being a published benchmark.

Box 2.3 shows the operational research technique of decision tree analysis, which can be useful for showing the links between choices and the risk implications of making those choices. Even if

you do

not

go

through

the

whole

process

of

estimation

and

‘

roll

back ’ , just drawing the tree will often clarify cause and effect.

BOX 2.3

THE CONCEPT OF A DECISION TREE

The principle in this operational research technique is to draw a graph of decision points and outcomes for a project or process, which forms the ‘tree ’ and its branches. In the full method, a monetary value and probability are assigned to each outcome and

then the tree is ‘

rolled back’

to work out the pathway through the project that offers the highest ‘expected monetary value ’ (EMV). An example is shown in Figure 2.3 for a television company deciding about producing a new series.

Series

Sell

1st series fails

1st seriessucceeds

2nd seriessucceeds

2nd seriesfails

Continue

Featurefilm

Major success

Minor success

Flop

Figure 2.3 An example of a decision tree

Often, just going through the process of drawing the tree is useful in itself. In particular, it helps clarify where our choices branch away from each other: in other words, if we choose to do X we have ‘burnt our boats ’ with respect to choices W, Y and Z. Clearly, the points at which

we cut ourselves off from possible courses of action are significant when thinking about the risks of a project. At times, this graphical approach can be a direct help in itself by showing us where, for example, re ordering of the project could serve to delay irreversible decisions – often an immediate aid to risk reduction. Adding in the values and probabilities is, in effect, providing the input for the calculation of an ‘expected return ’, but in a way which also takes into account the chronological sequence of events. Sometimes this adds little to our decision making, but often with more complicated projects (or strategic plans, if considering a whole organisation) it does improve the manager ’s knowledge to a worthwhile degree – and that

ought, on average, to lead to better choices being made.

See also Vital Statistics , Section 1.3.2.


Major success

Minor success

Flop




This ‘correlation of risk ’ is clearly akin to portfolio theory. However, because here we are considering a much broader range of risks it is not possible to be as mathematically precise as in portfolio theory – but the idea is the same.

So what should be the output from this second stage of the riskmapping process? Against each category chosen in Stage 1 there should be an analysis, probably containing both numeric and qualitative information, assessed in whatever way is appropriate for the particular type of risk. This should cover the following points.

1 Why be exposed? – Is the exposure unavoidable? The analysis may show how certain risks can be avoided, or at least minimised, if different choices are made.

2 Size of exposure – This certainly needs to be assessed on a relative basis (that is, what proportion of the total risk does this element represent), but if an absolute value can be placed on it, so much the better. It is often as useful to senior management to use a rating scale (for example, highest = 1, next highest = 2, etc.), as opposed to specific numbers, for measuring relative risk exposures provided the scale is understandable and can be sufficiently discriminating.

3 Warnings – The analysis should flag any potential catastrophic outcomes arising from a particular risk element. Where feasible, it is helpful if the analysis shows what is currently done to avoid or ameliorate a risk. Alternatively, suggestions for future action can be included.

4 Cost of risk – If the risk is avoidable, or can be reduced, what would be the cost of avoidance or reduction? What is the potential benefit?

5 Correlation of risk – Many types of risk are interrelated. For key risk elements that are correlated, it is useful to make plain

the linkage where the importance of this is material. The overall goal for the mapping should be kept in mind: that is, to provide risk information to the organisation ’ s policy makers. As always, the objective is to end up with as succinct a report as is consistent with giving the senior management the input needed for them to produce an appropriate definition of corporate strategy.

Stage 3 Allocating risk capacity

We now rank the risks previously identified in

order to

facilitate

the

allocation

of

overall

risk

capacity. A useful rank order is as follows.

1 Unavoidable risk associated with coreactivities.

2 Risk unavoidable except by ceasingnon core activity.

3 Avoidable risk, core activities.4 Avoidable risk, non core activities.5 Selectable risk.

The intention

is

to

help

the

policy

makers

by

giving a sequence for consideration: that is, Group 1 ‘ uses up ’ some of the risk capacity before you can consider Groups 2 to 5, and so on.

‘ “ Be careful! ” All you can tell me is “ be careful ” !’




2 RISK ASSESSMENT

Group 5 needs some clarification. It is the set for types of risk where the degree of risk can be adjusted more or less voluntarily without changing the operations of the business. The classic example would be financial gearing – the management can, at least in the medium term, choose the debt/equity ratio without altering the company ’ s activities.

Some risk elements can appear in both Group 5 and elsewhere. For example, it may be necessary to accept some foreign exchange risk (forex risk) as a concomitant to doing business (Group 3). But the organisation could also take on forex risk that was essentially speculative – that part would be Group 5. In effect, Group 5 can be regarded as a ‘ balancing item ’ between the total risk represented by the main business and the capacity for risk decided upon as acceptable by the management.

It is a good idea, where possible, to rank the risk factors within the groups, but how possible this is depends on the measures used. If the expected value and standard deviation method is predominant, then ordering is feasible; most financial risks are amenable to this way of measuring risk/return, but whether the same is true of organisational, marketing and environmental risks is less certain. Ranking may also be possible with a scaled system, but this will often depend on the degree of discrimination the chosen scale allows. In general, the ordering is aiming to put at the top of each group ’ s list the factors with the best risk/return profile, and the worst at the bottom.

If two factors, A and B, have the same risk assessment, perhaps

measured by standard deviation, but A offers a better expected return, then the ordering is straightforward. It is less easy to be precise if A is also riskier. At this point the organisation ’ s particular attitude to risk becomes important. A very conservative business will require more return per unit of additional risk than will a more adventurous one, assuming the terms ‘ conservative ’ and ‘ adventurous ’ refer to the degree of risk aversion of the respective organisations. The rankings must reflect this attitude to risk.

Another way of partitioning within the groups is to treat linked risks together. For example, if there is a set of risks all associated

with operating in a particular country, report them together, on the premise that strategic level management may only be able to act on them as a group anyway. This form of partitioning can be used as well as, rather than instead of, the ranking procedure. It may add more complication than illumination to senior management ’ s interpretation, however, and can only be decided upon on a case by case basis.

By now you should have a sizeable report on the organisation ’ s overall risk profile – and hopefully a better understanding of that profile. It is time for decision making to take over from analysis.





ASSESSING THE RESULTS 2 . 3

Risk mapping is but one input to policy making. It is usually an important element, but can only be useful when put in context with other strategic requirements. In practice, risk is also a consequence of other policy decisions, and so should be seen

in this context rather than in isolation. It is reasonable to believe that an organisation has an intrinsic capacity for absorbing risk, dependent on such factors as its size, its economic and/or social role, the attitude of the owners and so on.

Unfortunately, it is seldom easy to put a figure on that capacity for any particular organisation, though there is often a consensus about the ‘ ballpark ’ area for the total. For example, most people would expect to see a biotechnology company accepting more risk than, say, a charity providing housing for disadvantaged people. Deciding

whether, for example, Macmillan Cancer Relief has more risk capacity than the British Heart Foundation, however, would be a much more difficult, if not impossible task.

In the corporate world – especially for exchange listed companies – although determining what is the risk capacity for a business is still fraught with difficulty, the market will be very clear if it thinks a company has got it wrong. Too much risk and the share price declines or even collapses; too little (that is, excessive unused capacity) and a take over bid may appear – nowadays, often a highly leveraged bid, using the excess risk capacity on offer.

Let us assume that the board of a company has, by some process (which will necessarily include evaluation of other strategic decisions already made), decided on an acceptable level of total risk. How should policy formulation in respect of risk allocation proceed?

It is important that risk allocation be seen as a constraint on the system, not a driver. By this we mean that it is the other inputs to strategy – corporate goals, market opportunities, core industry and so on – that should be promoting the direction of the organisation. The risk mapping and risk capacity calculations should be used to ‘ keep score ’ so that the organisation does not overstep the mark.

However, the effect of different parts of a business acting like a portfolio may mean that simply adding up the risks of individual aspects of the organisation may overstate the net risk. This can be allowed for in the mapping process (with some difficulty) or it may be accommodated in a less precise way by senior management taking an optimistic view of the total risk capacity of the business (that is, an overestimate of risk capacity compensating for an overestimate of the net risk).

In practice, the information made available by the risk mapping can help do more than just ensure that the business does not step over

the risk cliff into the chasm of destruction. Mapping can assist in




2 RISK ASSESSMENT

the choice of path so that the direction taken heads most swiftly towards the organisation ’ s goals, without smashing on the rocks or meandering inefficiently. By clarifying what dangers face the business, risk mapping better enables management to avoid them without having to leave an excessive ‘ margin for error ’ . The likelihood of optimising the risk to return equation is, therefore,

maximised.

SUMMARY

This section has been concerned with answering two questions: what types of risk and how much risk is an organisation exposed to?

In this context, risk can be described as an uncertain future outcome that will improve or worsen the organisation ’ s position. Risk can be expressed in probabilities of an upside or a downside outcome.

Risk mapping is the process whereby an organisation assesses the types and degrees of risk to which the business is exposed. Risk mapping can be broken down into three stages.

1 What risk categories?

2 Estimating exposure to risk.

3 Allocating risk capacity.

The risk categories include financial, organisational (operational), market and environmental.

There are two main ways of thinking about the possible results of risk exposure, either by focussing on the ‘ expected return ’ method or upon ‘ outcome versus expected return ’ . Expected return can be calculated by estimating the total of every outcome multiplied by its probability. This then allows the organisation to accept avoidable risk only if the expected return is positive. It also allows the organisation to choose the option with the highest expected return and to avoid, where possible, catastrophic outcomes.

This expected return analysis leads to the collection of data on: l

why the organisation is exposed and whether the risk is avoidable; l the size of the risk – graded perhaps from 1 to 10 (an exercise

that is admittedly difficult if you are solely relying on qualitative assessments);

l the warnings of possible catastrophic outcomes; l the costs of accepting or avoiding risks; l the identification of links to other risks.





The allocation of risk capacity can then be done by ranking risksas follows:1 unavoidable, core activities;2 risk unavoidable except by ceasing non core activity;3 avoidable risk, core activities;

4 avoidable risk, non core activities;5 selectable risk.

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3 INTEREST-RATE RISK


Having completed the strategic level risk mapping, in the rest of this block we move on to the tactical/operational level and concentrate on the category of risk which is the main concern of this course: financial risk.

Let us just remind ourselves of the six categories of financial risk and where in the block each will be covered. l Interest rate – Sections 3 to 7 of Unit 7 l

Foreign exchange – Unit 8 l Contingent – Unit 8 l Credit – Unit 9 l Liquidity – Unit 9 l Operational – Unit 9

3 . 1 INTEREST-RATE RISK

Interest rate risk is the risk of gain or loss from the rise or fall of

interest rates.

This

is

of

great

importance

as

all

organisations

are,

at some time or another, lenders or borrowers; in fact many businesses are both at all times.

An investor in debt instruments clearly has exposure to interest rates since these determine the return on the money that has been lent to the borrower. Equity investors, too, are concerned about interest rates, as one component in the estimation of a fair return on equity capital is the prevailing interest rate – remember the CAPM formula from Unit 4.

The users of capital are also fundamentally concerned about

interest rate risk as it affects the cost of raising funds. Granted, once a business has raised an amount of debt capital at a fixed rate, the service cost of that particular liability would not change for the life of the agreement, but what happens when the time comes to refinance the borrowing? Also, floating rate debt rates and the required rates of return for equity change as interest rates vary.

Interest rate risk also affects all investors. Most B821 students pay into a pension fund, or some other form of long term savings, which exposes them to interest rate changes. On the other side of the coin, many of us have exposure also as borrowers – particularly through the mortgages taken out to buy our homes.

So interest rate risk is a topic that should be of concern to all people. However, for much of this section we shall be analysing interest risk from the point of view of an investor in debt, particularly fixed rate debt, simply because the analysis is easier

within the

context

of

fixed

cash

flows

happening

at

preordained

times. While this takes us deep into the arena of financial markets, it should be appreciated that the concepts and methodology





covered relate to the financial assessments – specifically valuations – all organisations have to make.

Box 3.1 gives a reminder of the definition of a bond that you met in Unit 1, so it should be familiar to you.

A sterling bond with its interest coupons

In the US, short term (less than a year) government debt issues are called ‘T bills’. ‘T notes ’ are those with a medium term maturity (one to ten years) and ‘T bonds ’ are those with a long term maturity (more than ten years). The ‘T’ stands for the US

government ’s ‘Treasury Department ’.

BOX 3.1

WHAT IS A BOND?

In essence a bond is a medium or long term securitised evidence of indebtedness issued to raise funds by a state (called a ‘sovereign ’ or ‘government ’ bond), a supra national organisation, such as the World Bank or the Asian Development Bank (called a ‘supra ’ bond), a financial institution (‘financial ’ bond), a local authority (‘municipal ’ bond) or a non financial company (‘corporate ’ bond).

Typically, financial and corporate bonds will have an initial maturity of between one and fifteen years, and state issues between three and fifty years. For shorter maturities, other debt products are available and the upper limit is set by what

investors will

accept

rather

than

by

any

regulation.

For

example,

some United Kingdom government bonds are ‘perpetuals ’,





meaning they have no fixed repayment date, and in 1996 Disney Corporation issued a hundred year bond, though more for the publicity value than because they had a century long project in mind.

A majority of bonds are issued on a ‘fixed rate ’ basis, paying a known rate of interest throughout their life, but ‘floating rate ’ is also very common. The latter are called, quite logically, Floating Rate Notes or ‘FRNs ’. Some bonds even pay returns linked to a given indicator. For example, United Kingdom Index linked Government Bonds are calculated by reference to the Retail Price Index (RPI), although the United Kingdom now uses the Consumer Price Index (CPI) for the inflation target for monetary policy purposes.

‘Securitised ’ means the bond is issued in a freely transferable form, but this can either be ‘registered ’ or ‘bearer ’ in form. With the former, a registration of ownership (similar to the registration of

equities) is

maintained;

for

the

latter,

the

borrower

will

pay

interest

and principal to whomsoever turns up with the right piece of paper, giving anonymity to holders. There has been a movement in recent years towards registered form. In the US, for example, by law corporate bonds have to be registered.

In the markets and the press, bonds are usually described in a form similar to

Oval plc 6 3 / 4 2012

This is an Oval plc corporate bond paying 6.75% per annum interest, maturing in 2012. Most bonds repay all the principal on

maturity –

a ‘

bullet’

repayment. Fixed rate

bonds

pay

interest

either

annually (for example, Eurobonds) or semi annually (for example, US Treasuries). Floating Rate Notes normally pay interest quarterly on the dates when the interest rate for the next period is refixed.

Interest payments are called ‘coupons ’ because in the past, and even now on occasion, the bonds, if held in physical form, had tear off coupons that the investor presented to the issuer for each individual interest payment. In practice, this was done automatically by the investors ’ agents who kept the bonds in safe custody. For Eurobonds, very often the agent would be one of the two main clearing houses, Euroclear or Clearstream (previously known as

CEDEL). When buying or selling a Eurobond, more often than not both parties would maintain accounts with Euroclear or Clearstream and the transfer is simply a book entry.

All sorts of variants of this ‘classic ’ bond instrument are available. For example ‘equity warrants ’ may be attached, repayment may be in a different currency from the original loan, the date of repayment may be brought forward under certain circumstances – but the straightforward fixed rate, medium term bond is still immensely popular with both borrowers and investors.

United Kingdom Government Bonds are often referred to as ‘gilts ’ or ‘gilt edged stocks ’ due to the gilding that used to be applied around the edge of the bond certificates.

An ‘equity warrant ’ is an option giving the right, but not the obligation, to buy shares at a fixed price up to a stated date. We discuss options in Unit 8.





The calculations to find

the yield

to

maturity

are

in

Section 5.4.1 of Vital Statistics .

How is a fixed rate bond valued? It consists of a known set of cashflows payable at known dates, so the price of a bond is simply the value today of the sum of its future cash flows: its present value. Additionally, you can look at the percentage return offered by thebond, for which the internal rate of return (IRR) is used. This iscalled the yield to maturity (YTM) or redemption yield for the

bond.Note that the formula for the discounted cash flow (DCF) for abond can only have one real IRR (because it consists, for investors,simply of an initial negative and then several positive cashflows) – so one important worry about IRR is not relevant here.

Prices are usually quoted with 100 representing 100% of face value,so if a bond with a face value of £1,000 is priced at 100 (known as‘ par value ’ ) it will cost £1,000 to buy, excluding transaction costs. If it is priced at 95, the £1,000 face value bond will cost £950; if theprice is 110, the cost will be £1,100 and so on. If the coupon onthe bond is lower than current interest rates then the bond will be valued ‘ below par ’ and the price will be quoted as less than 100.Conversely, if the bond offers a coupon higher than current rates,buyers will have to pay ‘ above par ’ – greater than 100 – topersuade the owner to sell.

To explain this further, look at a £100 two year bond that has anannual coupon of 6% per annum – or in the abbreviated form weshall use in the rest of the block – 6% p.a. The cash flows wouldbe as follows:

Year 1 Year 2

£6 coupon £6 coupon plus £100 principal = £106

If the yield to maturity was 4% the present value of these cash flows – using the discount factors for 4% yields for cash flows at years 1 and 2 – would be

Year 1 Year 2

Cash flow £6 £106

Discount factor 0.962 0.925

Present value £6 6 0.962 = £5.77 £106 6 0.925 = £98.05





The current price would be the total of these present values

£5.77 + £98.05 = £103.82

The bond has a price above the ‘ par ’ price of £100 since with current interest rates at 4% p.a. an investor selling the bond would want a fair value for an asset offering an annual coupon of 6% p.a.

compared with the lower current rates of returns.

BOX 3.2

Interest rates are expressed on a per annum (p.a.) basis. ‘Per annum ’ is the Latin phrase ‘for a year ’, so if you invested E 100 at 6% p.a. for one year you would get E 6 in interest. For six months you would receive half the p.a. amount – E 3. For two years you would get the p.a. amount of E 6 twice, giving total interest of E 12; for three years you would get E 18 and so on. Note that in the two and three year examples it is assumed that the interest paid each year is not

reinvested. We are therefore looking at ‘simple interest ’ rather than ‘compound interest ’ here.

EXERCISE 3.1

A corporate bond with a face value of £100 and a coupon rate of 5% matures in two years with a bullet repayment. What is the price of the bond if the yield to maturity is:

(a) 5% p.a. (b) 3% p.a.

(c) 8% p.a.?

QUANTIFYING INTEREST-RATE RISK 3 . 2

In the previous section we looked at the relationship between bond values and interest rates. We found that we are ‘ at risk ’

if interest rates vary. We now need to examine further the methodology used by looking at the impact on a single cash flow of a change in interest rates. The exercise will also require you to learn more about the levels of interest rates for different periods to maturity – or, to put it another way, the structure of ‘ yield curves ’ – and the choice of precisely which interest rates to use to undertake the measurement of interest rate risk.

Assume we are due to receive an inward cash flow of £1m in two years’ time. What is the worth of this asset? It is the present value, discounted for two years at an appropriate discount rate. For

‘Bullet ’ repayment means that all the principal sum is repaid in one amount

on the maturity date of the bond.





the sake of simplicity, assume that this cash flow comes from a debt instrument (for example, a fixed rate bond) and therefore that the relevant two year interest rate would be the appropriate discount rate. To grasp fully this process of valuation and to understand both the different types of interest rates and the concept of a ‘ yield curve ’ please read Box 3.3.

The yield to maturity (and hence the value of the bond in the secondary market) will change following variations in the reference rate adopted.

BOX 3.3

SPOT RATES, TERM RATES AND THE YIELD CURVES

In the preceding paragraph we calmly talk about ‘the two year interest rate ’ for an inward cash flow of £1m, but what do we mean by this?

Part of the answer to that question lies in the idea of ‘basis ’. ‘Basis ’ simply means the key factors that define how interest will

be calculated. For example, are we talking about fixed rate or floating rate debt? Is it for secured or unsecured debt? Is it for a ‘bullet ’ loan or an ‘amortising ’ one (‘bullet ’ simply means the principal is paid in one lump at maturity; ‘amortising ’ that repayment is spread over the life of the loan according to a pre arranged pattern)? What is the reference rate to be used? Usually rates are set by reference to a ‘benchmark ’: for fixed rate debt, this is typically the interest rate for domestic government debt in that currency for the appropriate length of time. For floating rate debt, reference may usually be made to the interbank rate or sometimes to a domestic ‘official rate ’, such as the European

Central Bank

(ECB)

rate

or,

alternatively,

to

bank

‘

base’

rates

(United Kingdom) or ‘prime ’ rates (US).

We must choose our ‘basis ’ to be the two year fixed rate United Kingdom government debt. A two year United Kingdom government bond will not only pay out money at maturity, but also interest every six months (the ‘coupons ’). Thus the so called two year rate is a blend of rates based on cash flows in forward periods of six months, one year, eighteen months and two years. Granted, this blend will be heavily weighted towards the end because the final cash flow of principal plus interest is so much larger than the other amounts. So, the bald ‘two year rate ’, or ‘yield ’, seen in

newspapers or on dealers ’ screens is not strictly accurate for our £1m to be received in one ‘lump ’ in two years ’ time.

What we require is the interest rate from now stretching out to two years with no intervening cash flows. This is called the spot rate of interest or zero-coupon rate or, simply, zero rate since it is the rate for a single cash flow with zero intervening cash flows. It turns out that spot rates such as this are useful and important in debt (and other) valuations.





Yield curves are the depiction of interest rates for different forward periods and are commonly shown graphically as in Figure 3.1.

I n t e r e s t r a t e ( r )

%

4.0

4.5

5.0

5.5

Term to maturity (years)1 2 3 4 5 6 7

Figure 3.1 Yield curve

The consequence of having both ‘zero rates ’ for rates applying to a specific single cash flow and ‘yield to maturity ’ which accommodate a blend of cash flows over the life of a debt instrument is that we must be careful when using yield curves to analyse interest rates for given terms. Some yield curves are zero coupon curves showing the zero rates applying for a range of maturities. Other yield curves show rates for which intervening cash flows are assumed: for example, an annual yield curve will show rates for one year, two years, three years and so on, with the assumption, in each case, that interest is paid once a year.

Note as well that yield curves of whatever basis (zero, semi annual and so on) are individual to each issuer. The yield curve for the debt of the French Government will be different from that prevailing

for a

French

bank

or

a

French

industrial

company

and

all

will

be

different from the curve for, say, an Italian company, despite the fact that all will be issuing in euros. Yield curves are individual to each organisation since the rate at which each issue at will reflect their credit quality and this will vary between them.

Noting the information in Box 3.3, assume that the two year spot rate is currently 6% p.a. The worth of our right to receive £1m in two years’ time is therefore

£1m/(1 + 0.06)2

= £889,996.44

What will happen to the value if the two year spot rate rises by, say, 1% p.a.? The asset will now be worth

£1m/(1 + 0.07)2 = £873,438.73

a fall (or loss) of about 1.86%.

On the other hand, if interest rates had fallen by 1%, the value of the asset would have risen by a similar magnitude.

Do not confuse the term spot rate of interest (which means the rate of interest ‘now ’ or ‘on the-spot ’) with the term ‘spot exchange rate ’ that you will meet in Unit 8. The latter is simply the exchange rate for the sale or purchase of a currency to be settled, usually, two working days ahead.





We can generalise this idea by saying:

interest rate risk is the change in the present value of a set of cash flows for a given change in the relevant interest rate(s).

This is the quantified version of our basic definition of interest rate risk. Now that we at least know what we are talking about, it is

time to begin considering how to measure in a practical and systematic way the extent of exposure to this form of risk.

SUMMARY

In this section we have defined what is meant by interest rate risk. Initially, we described it in a qualitative way as the gain or loss sustained as interest rates change.

Later you were able to quantify this definition as the change in the present value of the cash flows for a particular change in interest

rates. In the middle of the section we recapped on what is meant by a ‘ bond ’ , an instrument you met first in Unit 1. We also investigated the idea of spot rates, zero rates and yield curves – subjects we shall meet again later in this unit.

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4 DURATION

4 DURATION

We saw in the previous section how a bond ’ s price changes with a change in interest rates. We now need to look at how individual bonds vary in their sensitivity to changes in interest rates. For this we need an actual measure with which we can say Bond A is more or is less exposed to movements in interest rates than Bond B. For this we need to investigate the concept of duration.

The concept of duration was invented by F. R. Macaulay who, in a book written in 1938, introduced the term, which is also referred to as Macaulay ’ s duration . An important further step was taken by F. M. Reddington in the 1950s, who used duration to develop ‘ immunisation ’ strategies against interest rate risk.

4 . 1 SO WHAT IS WRONG WITH ‘ MATURITY ’ ?

An important question which we need to answer is: why go to the trouble of calculating this duration measure? Why not just use

maturity –

which is

usually

a

lot

easier

to

ascertain

– to

compare

two bonds and estimate their exposure to interest rate movements?

The simple answer to this is that while maturity provides a guide to interest rate exposure, it is by no means sufficient or complete. Let us use an example to demonstrate this.

Take two bonds, A and B. Both will mature in five years. Bond A pays a coupon of 3% p.a., Bond B pays a coupon of 10% p.a. They are both issued by the same borrower (so there is nothing to choose between the bonds when it comes to the creditworthiness of the issuer) and both have a yield to maturity of 7% p.a. Note that

the yield to maturity is the market’

s current rate of investment return on lending to this borrower.

Let us have a look at the way the two bonds change in value as the required yield rises or falls from the current 7% p.a. Remember, the value of a bond is simply the present value of the stream of cash flows it represents. Of course, while the yields are the same in each case, since Bond B actually pays out a lot more cash than Bond A, the prices of the two bonds will be very different. We are really concerned, though, about the percentage change in each price as rates change.

The values for Bonds A and B for yield to maturity (YTM) of between 3% p.a. and 10% p.a., on the basis of a face value for each of £100, are shown in Table 4.1. The table also gives

A common misconception of B821 students is to

think that

duration

only

applies to bonds. In fact, duration applies to any series of cash flows.

See Exercise 3.1 to remind yourself how to calculate the price of a bond as the yield to maturity varies.





the percentage price change compared with the initial price when the yield to maturity was 7% p.a.

Refer to

Vital Statistics ,

Section 5.4 to see how to calculate the prices of Bonds A and B.

Table 4.1 Comparison of Bonds A and B fo r different YTMs

YTM

(%) Price of

A

(£) Change

(%) Price

of

B

(£) Change

(%)

3 100.00 +19.62 132.06 +17.60

5 91.34 +9.26 121.65 +8.33

7 83.60 0.0 112.30 0.0

10 73.46 – 12.13 100.00 – 10.95

Notice that

when

the

yield

to

maturity

for

the

bond

is

the

same

as

the coupon rate then it is valued at its face value of £100. For example, Bond A is priced at £100 when the yield to maturity is equal to its 3% p.a. coupon and Bond B is priced at £100 when the yield to maturity is equal to its 10% p.a. coupon. Note also that, even if the face value of the bond is not £100, it is conventional to value bonds in ‘ lumps ’ of 100.

Note also that the coupon rate is fixed at the time of issue. Depending on subsequent changes in market interest rates the value of a bond will move in price to offer the required YTM for these changed market conditions (see the YTM column). This results in YTMs varying from the fixed coupon rate. Consequently, the value of a bond will fluctuate above or below the original issue price (see the Change column).

It is important to note that, for both Bonds A and B, value falls as interest rates and hence the yield to maturity rise . This follows directly from the definition of bond value as being the present value of the cash flows. In any discounted cash flow calculation, the present value falls as the discount rate rises.

We can see that Bond A is more susceptible to changes in interest

rates than

Bond

B,

even

though

they

are

for

the

same

maturity.

We can straight away conclude that maturity alone is not a good enough measure to tell us what we need to know about exposure to interest rate risk.

What is the difference between the two bonds? They have the same credit quality, the same yield to maturity and the same maturity but differing cash flow sequences. It is obvious, therefore, that our measure must take into account the cash flows of our instrument and their timings, combining them neatly into a single number. Duration does this for us.




3

4 DURATION

A MEASURE THAT WORKS 4 . 2

Duration, in simple language, is an average measure of the time you have to wait to receive the cash flows from a bond. Let us take three examples.

1 A four year bond which has a zero coupon rate (0% p.a.): it

pays no interest coupons, just a bullet sum on maturity.

Year 0 Year 1 Year 2 Year 3 Year 4

– – – – 100

All the cash flow arises in Year 4. Therefore, the duration must befour years.2 A four year bond that has a 5% p.a. coupon rate.


– 5 5 5 105

The average time we have to wait to get our cash flows is less than four years, as some of the cash flows are received in Years 1 – 3.

A four year bond that has a 20% p.a. coupon rate.


– 20 20 20 120

The average time we have to wait to get our cash flows is much

less than four years, as a significant proportion of the cash flows are received in Years 1 – 3.

To be able to calculate the average time, or duration, precisely we need to look at the mathematics behind it.

Duration is, therefore, the weighted average maturity of the cash flows. The weighting for each time period is the present value of the cash flow occurring in that time slot expressed as a percentage of the total present value or value of the bond.

By using the present values of the relevant cash flows in the

weightings for

each

term

or

time

period,

t

i

, we

ensure

that

the

overall measure correctly reflects the relative importance of each time period in the overall result. The equation may, at first glance,





Weighted average is discussed in Section 3.2.7 of Vital Statistics . The proof of this duration formula is given in Section 5.4.2 of Vital Statistics .

look complex, but it is simply condensing into figures the idea of a weighted average maturity.

So the calculation of duration requires each individual discounted cash flow to be multiplied by the term applicable to it, aggregated and divided by the prevailing bond price. Thus

1 ⎡ CF1 CF2 CFn ⎤D = ⎢t 1 + t 2 + " + t n ⎥P ⎣ (1 + r ) t 1 (1 + r ) t 2 (1 + r ) t n ⎦

where

D = duration

P = price of the bond

CFi = cash flow taking place at time t i t i = time receipt (or payment) of CFi

r = discount rate.

To see that this equation really does represent a true weighted average, note that the definition of the price (P), is the sum of the present values of each cash flow (CF). Since we are dividing all the terms by P, the equation is of the form

D = ×t 1w1 t 2

w2 + " t n wn+ × + ×

P P PCFi where each term has been represented by wi(1 + r ) t i

and P = w + + " +w1 w2 n

This is the normal form for a weighted average.

You may find it easier to understand the formula if you look at it with t 1, t 2 , ..., t n replaced by 1, 2, ..., n . In other words, with the cash flows taking place at exact numbers of years in the future. Never forget, however, that in reality t can represent any length of time. For example, if you are dealing with bonds or their equivalents, the annual periods are only whole numbers of years one day out of 365. In other words, on a coupon payment day it is exactly one year until the next interest payment, but for every other day it will be only a fractional part of a year to the next cash flow. Thus, as an example, two months after the last interest payment it will be 10 /12 of a year to the next coupon date, 110 /12

years to the one after that and so on.




4 DURATION

The durations for Bonds A and B from Section 4.1 are calculated in Table 4.2.

Table 4.2 Durations of Bonds A and B

Year CFA PV (CFA) t 6 PV (CFA)

1 3 2.80 2.80

2 3 2.62 5.24

3 3 2.45 7.35

4 3 2.29 9.16

5 103 73.44 367.20

83.60 391.75 Duration A = 391.75/83.60 = 4.69 years

Year

CFB PV (CFB )

t 6 PV

(CFB )

1 10 9.35 9.35

2 10 8.73 17.46

3 10 8.16 24.48

4 10 7.63 30.52

5 110 78.43 392.15

112.30 473.96 Duration B = 473.96/112.30 = 4.22 years

=r 7% p.a. for duration calculation (i.e. the yield to maturity)

You can now see the difference between the two bonds. Bond A, which is more volatile with respect to interest rates, has a longer duration than Bond B. Our new measure is therefore an improvement: it distinguishes between instruments with the same maturity, but different exposure to interest rate changes.

EXERCISE 4.1 Calculate the duration of the three bonds introduced at the start of this section.

(a) Four-year (0% p.a.) zero-coupon bond

(b) Four-year 5% p.a. coupon bond

(c) Four-year 20% p.a. coupon bond

The yield to maturity is 10% p.a. and each bond has a face value of £100.





BOX 4.1

MATURITY WRONG, DURATION RIGHT

We can show that sometimes maturity points the wrong way, but duration always shows which bond is more exposed to interest rate

movements.

Compare Bond A with another bond, Bond C. Again, they have the same issuer, but this time Bond C has six years to maturity and pays a coupon of 15% p.a.

Looking at the maturity, we might assume Bond C was more volatile with respect to interest rates. In fact, as can be seen from the following table, Bond C is a little bit less susceptible to rate changes than Bond A.

YTM

(%)

Price of A

(£)

Change

(%)

Price of C

(£)

Change

(%) 3 100.0 +19.62 165.01 +19.46

5 91.34 +9.26 150.76 +9.14

7 83.60 0.0 138.13 0.0

9 76.66 – 8.30 126.92 – 8.12

10 73.46 – 12.13 121.78 – 11.84

So what is the duration of Bond C? At 7% p.a. yield to maturity, it

is 4.60 years – calculate this if you wish using the methodology you applied for Exercise 4.1. This duration is, indeed, slightly shorter than Bond A’s at 4.69 years. For example, when the yield to maturity changes from 7% p.a. to 10% p.a. we can see that the price of Bond A changes more in percentage terms than the price of Bond C.

Duration is, ultimately, a measure of how sensitive the present value of a series of cash flows is to a change in the discount rate.

In general we can say: l the longer the duration, the higher the exposure to interest rate

risk; l any sequence of cash flows with a duration of n years will have

exactly the same volatility with respect to interest rates as any other sequence with an equal duration of n years.

Duration therefore shows us that the workings of compound interest mean that a cash flow of a given size, say £1,000, will be more exposed to interest rate changes the further in the future is its payment date. This is simply saying that interest rates have more time to have an impact on the value of a cash flow a long time in the future than on one due for payment shortly. Table 4.3 shows

the change in present value for different interest rates of a payment of £1,000 in one, five and ten years.





BOX 4.2

ZERO-COUPON BONDS

Since the last cash flow for a bond includes the principal payment, this cash flow item will dominate the calculation and make the

duration less than, but reasonably close to, the maturity of the bond for shorter maturity bonds.

For long lived bonds paying coupons, the difference between maturity and duration can become surprisingly large. The US Treasury ‘long bond ’ has a thirty year maturity, but depending on the prevailing level of interest rates its duration is typically only around fifteen to eighteen years – little more than half its maturity term. What is happening is that, while the final principal repayment is still ten or twenty times larger than any one of the yearly interest flows, all those coupon payments (thirty of them) mean that the relative importance of the final cash flow is lessened.

However, investors with long term liabilities, such as pension funds or life insurance companies, need assets that are equivalently long term.

The duration of a bond can never exceed its maturity, but what kind of instrument will have the longest possible duration?

We can see from the earlier examples that the smaller the coupon, the longer the duration. The final payment becomes relatively more important the smaller the intervening cash flows. The ultimate version of this is where the bond pays no coupons, just a lump sum at maturity. These are, quite logically, called zero-coupon bonds , often abbreviated to ‘zeros ’. They are the only type of bond where the duration is equal to the maturity. So a thirty year zero coupon bond is an asset with a really long life.

‘Gilt strips ’ are examples of zero coupon bonds. These are United Kingdom government bonds which can be stripped into their individual cash flow components – namely the coupon (or interest) strips and the principal strip (on maturity), in effect, creating a number of zero coupon bonds from one conventional bond with a semi annual coupon. Introduced in 1997, these strippable gilts help pension and investment funds with their need for assets that match

precisely their

liabilities

to

those

investing

in

the

funds.

Such matters may seem to be of interest only to fund managers, but think back to Box 3.3 concerning spot rates. What we had there was the need to find an interest rate that was correct for a single cash flow at a particular future time, with no intervening flows.

That is exactly what we see with zero coupon bonds. Indeed, what we refer to as a spot interest rate would typically be called the zero coupon rate (or the zero rate) by a financier. Same thing, different label.




4 DURATION

ACTIVITY 4.2

Try to estimate what the duration of a ‘ century bond ’ , like the one issued by The Disney Corporation in 1996, would be. Let it have a 5% p.a. coupon, and a 5% p.a. yield to maturity. The maturity term is obviously 100 years.

Either use your spreadsheet to calculate the answer (if you use the ‘ Fill Right ’ function of Excel it is surprisingly quick and simple to do) or try to guess a ‘ ball-park ’ answer if your PC is not nearby.

My spreadsheet gives a duration just short of twenty-one years. Quite a difference from a maturity of a hundred years.

DURATION AND QUANTIFYING

INTEREST EXPOSURE 4 . 3

The duration formula we have seen so far provides us with a good measure with which we can compare portfolios of cash flows. The criterion is simple: the longer the duration, the greater the interest exposure.

We can use another version of the duration formula, derived directly from the present value equation, that will give us even

more information: namely, an estimate of the amount a portfolio will change in value for a given change in interest rates. This is clearly useful. The relevant formula is

1ΔP = −D ×P × × Δr (1 + r )

where

ΔP = change in price (or value)

D = duration

P = price

r = interest rate D r = change in interest rate or yield to maturity.

Alternatively, if we want the percentage change in price, as was calculated in Table 4.1, then the formula is even more convenient as it does not depend upon the current price (though it is needed to calculate D). Note that D P/P should be expressed as a percentage.

ΔP 1= −D × × Δr ×100P (1 + r )

For example, if we take Bond A from Table 4.2 we know that with a yield to maturity of 7% p.a. it has a price of £83.60 and

For further discussion of this formula, see Section 5.4.2 of Vital Statistics .





a duration of 4.69 years. The effect of a 1% rise in interest rates on the price of the bond would be:

ΔP 1= −4 69 × × . ×. 0 01 100P ( + . )1 0 07

= −4 38. %

In other words, the duration formula has shown that, for a 1% rise in yield to maturity, the price of the bond would fall by 4.38%. The bond price therefore falls by £83.60 6 4.38% = £3.66. This reduces the bond price to £83.60 – £3.66 = £79.94.

We can check this estimate of a new price for Bond A by recalculating its value using discounted cash flow and a discount rate of 8% (the new yield to maturity). If we do this, the value of Bond A becomes £80.04, slightly above the estimate using the duration formula of £79.94. The difference is due to the fact that

the duration

formula

is

an

approximation

of

the

price/yield

relationship. It assumes a straight line relationship (for small changes in yield) rather than the curve it actually is. The difference is called ‘ convexity ’ and this is discussed in more detail in Vital Statistics , Section 5.4.3. For the mathematically minded, the duration equation is a first order estimate of the impact of a change in yield on a bond price. As we can see from the example, it is a quite accurate estimate and, in practice, in fast changing markets, it is easier to estimate changes using duration than to recalculate bond values using discounted cash flow (DCF) analysis.

EXERCISE 4.2

Calculate the percentage change in price of a bond for a 1% fall in interest rates if the bond has a yield to maturity of 6% and a duration of three years. What would the price move to if the prevailing price was £100.00?

This graphical idea is also discussed in Section 5.4.3 of Vital Statistics , and the coverage is also continued into the idea of convexity.

BOX 4.3

WHAT DOES THE EQUATION MEAN?

We have a formula that relates the change in the value of a bond to duration and interest rates. Does it represent anything realistic? Actually, it does.

If we drew a graph of value against interest rate (that is, with value plotted up the y axis and interest rate along the x axis), what would we be showing? The graph would show the result of the price equation for each rate of interest. It would look something like Figure 4.1.




4 DURATION

P

r

Figure 4.1

For a small change, D r , in the interest rate we can approximate the curve by a straight line tangential to the curve at the point (r , P), as shown in Figure 4.2. The equivalent change, D P, in value will be given by

D P = Gradient of straight line 6 D r

P

dr

dP

r

Figure 4.2

This gives us the formula

Δ ΔP

D P= − × × +

r r ( )1





The mathematical derivation of the equation is not required for B821, as long as you understand the graphical idea it comes from. For those who prefer to see the mathematics, it is shown below. You do not have to remember it!

The gradient of the line is given by the first derivative of the present value equation, so

CF1 CF2 CFn P = + + " +(1+ r )t 1 (1+ r )t 2 (1+ r )t n

dP CF CF CF= −t 11t 1+11)

− t 2 (2t + )

" − t n n (t n +1)d r (1+ r )( (1+ r ) 2 1 (1+ r )

1 ⎡ CF1 CF2 CFn ⎤= − t ++ t " + t 1+ r ⎢⎣

1(1+ r )t 1

2(1+ r )t 2

n (1+ r )t n

⎥⎦

1= − × ×D P

(1+ r

)

Therefore

1Δ D × × Δr P = − P(1+ r )

Now we know it does come from something sensible, we can use the formula without worrying further about its origin.

Now that we understand duration we can use the concept to help manage an organisation ’ s interest rate exposure. We shall see how duration can be used to ‘ immunise ’ against interest rate risk by matching the risk on an organisation ’ s assets against the risk on its liabilities.

IMMUNISATION4 . 4

The concept of duration was first applied to the assets and liabilities of life insurance companies. If such a company is large

enough, its liabilities – that is the life insurance repayments it will have to pay out – are predictable to a high degree of accuracy. To make sure it can meet these commitments, the life insurance company will seek to ensure that the premiums it receives (after expenses and profit) are invested in assets (in practice often instruments of high credit quality, such as government bonds) that have the same present value as that of the liabilities. Will the two sets still match when interest rates change?

If it could purchase bonds that had exactly the same maturities as the liabilities and paid no intermediate coupons that would need to be reinvested at uncertain future interest rates, the life insurance company would have no difficulty in meeting its liabilities, since




4 DURATION

each bond could be held to maturity when it would pay off aknown amount. In real life, however, only bonds of certainparticular maturities are available and most do pay coupons.

Reddington (1952) suggested that if:l the present value of the assets is equal to that of the liabilities

andl the duration of the assets is equal to that of the liabilities the

portfolio would be immunised .

Immunisation means that the present value of the assets continue to match that of the liabilities even if interest rates changed . In other words, the assets would provide sufficient funds to meet the liabilities irrespective of movements in interest rates.

By matching present values and duration the insurance company would have removed its exposure to interest rate risk by ensuring

that the

overall

value

of

its

assets

always

matched

that

of

its

liabilities, even as rates changed. The important point to note is that this would be true even though the individual cash flows and timings differed dramatically between the constituent assets and liabilities.

How this works you will see shortly, but it is worth keeping in mind this practical use of the concept of duration. The concept of immunising a sequence of cash flows can and is applied much more widely than just to managing life insurance portfolios. Note, though, that immunisation is not a one off exercise. Each day and as interest rates move, the immunisation process should be checked and, if necessary, recalibrated.

ACTIVITY 4.3

Equities are usually deemed to be inappropriate for immunising short-term liabilities. Why do you think this is the case?

Equities typically have a low dividend yield and no fixed maturity. Consequently, the forecast duration for equities is akin to that of a very-long-term bond with a low coupon: that is, they have a very long duration and, hence, are not good assets to immunise short-term liabilities

This description of immunisation implies that insurance companies invest mainly in debt instruments such as government, financial or corporate bonds. While they do invest in bonds to a significant extent, they hold large amounts of other assets, such as equities, property and so on, in their portfolios. Provided you can make reasonable predictions about the future cash flows expected to be

generated by such assets – for example, the dividends for equities, the rentals for property – you can make use of the duration and




4 DURATION

the £100m liability at the appropriate time and, to be able to do this, it decides to invest in bonds.

It chooses two bonds in which to invest. In both cases their next coupons are due in exactly six months. l Bond A is a four year 10% p.a. coupon bond with a face value

of £1,000 paying annual coupons. With a yield to maturity of 8% p.a. and maturity 3.5 years away, the current price is 110.81. The duration is 3.00 years.

l Bond B is a six year 3% p.a. coupon bond with a face value of £1,000 paying annual coupons with maturity 5.5 years away. The current price with a yield to maturity of 8% p.a. is 79.90. The duration is 5.01 years.

Since the duration of the future liability is 3.5 years, the mixture of bonds purchased has to have a duration of 3.5 years as well. We therefore need to define the proportions of Bonds A and B that

have a weighted average duration of 3.5 years. If we define a as the proportion of the £100m invested in Bond A then (1 - a ) must be the proportion to be invested in Bond B, since

a + (1 - a ) = 1

that is, the whole of the £100m.

We know the duration of Bond A is 3.0 years and that of Bond B is 5.01 years. The duration of the liability is 3.5 years, therefore

[a 6 3.00] + [(1 – a ) 6 5.01] = 3.5

Solving this equation for a

a ×3 00 + 5 01. − a ×5 01. = .. 3 5a × ( .3 00 − 5 01) + 5 01 = .. . 3 5

− . a + 5 01 = 3.552 01 .. + 2 015 01 = 3 5. . a

5 0 1 3 5. − . = 2 01. a

1 51. = 2 01. a

1 51. = a

2 01.

a = 0 751.

Hence, the proportion invested in Bond B is

b = ( � )a 1 0 751. .1 = ( � )= 0 249 .

This gives the proportion to be invested in Bond A as 0.751, with the balance of 0.249 to be invested in Bond B.

You can check the figures if you wish by looking at the Excel spreadsheet RISKPLC.XLS on

CD ROM 2.





The total investment has to be the present value of £100m in 3.5 years ’ time, discounted at 8% a year. That is, the present value is

PV = £100m/1.08 3.5 = £76.387m

Thus the investments are

Bond A

0.751

6 £76.387m

=

£57.367m

Bond B 0.249 6 £76.387m = £19.020m

Finally, we need to work out how many bonds of each type we need to purchase to give the right amount of investment in each. These bonds have a face value of £1,000, and the current prices of Bonds A and B are 110.81 and 79.90, respectively. Remember that according to the pricing convention for bonds, those prices mean that a £1,000 face value bond will cost £1,108 and £799. Thus the holdings should be

Bond A 57,367,000/1,108 = 51,775 bonds

Bond B 19,020,000/799 = 23,805 bonds

To confirm that the immunised portfolio does remove the risk of interest rate movement from Risk’ s ability to meet the liability, let us see what happens to the value of the liability and of the portfolio if interest rates change immediately after purchasing the portfolio. This is, of course, the most extreme possibility, so if rates actually vary later on – which is more likely – then we know that this is covered by considering the ‘ immediate movement ’ scenario.

Table 4.5 An immunised liability and asset portfolio

r %

PV (liability) £m

PV (assets) £m

PV (assets) – PV (liability) £000

Mismatch as % of PV assets

1 96.577 97.001 424 0.437

3 90.172 90.376 204 0.226

5 84.302 84.375 73 0.087

7 78.914 78.927 13 0.016

8 76.387 76.387 0 0.000

9 73.962 73.969 7 0.009 10 71.635 71.656 21 0.029

15 61.314 61.531 217 0.353

20 52.828 53.368 540 1.012

Looking at Table 4.5, this is quite an impressive result. For a change in interest rates of 12% (from 8% to 20%), the portfolio has drifted

away from

the

liability

value

by

just

1%.

In

practice,

Risk

plc

would




4 DURATION

have been able to adjust the portfolio well before rates moved so much. More representative would be that, for a plus or minus 1% shift, the drift in this hedged portfolio would be less than 0.02%.

SUMMARY

Duration is a measure that has been known for a long time – Macaulay introduced it in the 1930s and Reddington used it in the 1950s – but it became a widely usable technique when personal computers reached the manager ’ s desk. If you can create a DCF spreadsheet for NPV or IRR, you can make it calculate duration at the same time; it effectively just requires adding one more row or column to multiply each PV (cash flow) by the time at which the flow occurs.

Duration gives us a measure that accurately reflects a portfolio of cash flows ’ exposure to movements in interest rates, unlike maturity, which is an insufficient discriminator and ignores the effect of coupons on interest rate risk. Indeed, maturity can actually imply that ‘ A ’ is more exposed to interest rate movement than ‘ B’ when in reality it is the other way round. Duration takes both maturity and coupon payments into account and can be used to give the actual amount by which a bond or portfolio will change in value for a given change in interest rates.

The duration measure is not perfect, because it approximates the curve of portfolio value against interest rates with a straight line. Thus, it is only accurate for reasonably small movements in interest rates: in practice, duration is typically good enough for a rise or fall of one or two percentage points in interest rates.

Lastly, remember that, as already mentioned in the section, the methods of duration and immunisation can be applied to any known sequence of cash flows. Duration as a measure of interestrate risk and as an immunisation tool is most often applied with debt instruments such as fixed rate bonds, but the method ’ s applicability is not confined to such a restricted use.

We now turn to two other methods for analysing exposure to interest rate risk: ‘ gap analysis ’ and ‘ value at risk ’ .

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �




5 MEASURING AND MANAGING AGGREGATE INTEREST-RATE EXPOSURE


In the previous two sections we learnt how interest rate risk onbonds can be measured and discussed the importance of duration. We now have to look at how these and other analytical tools canbe employed to measure the aggregate interest exposure of anorganisation, thereby providing managers with summary information with which to make decisions about risk positioning. As already mentioned, interest rate risk applies to any set of cashflows – not just the cash flows arising from bonds. Since all

organisations have cash flows, every organisation has exposure tointerest rate risk. Consequently, all organisations should measurethis exposure and manage it.

The two techniques we shall look at in this section are:l gap analysisl value at risk.

Dennis Weatherstone, the former chairman of the US investmentbank J.P. Morgan, once demanded of his executives ‘ ... at the closeof business each day tell me what the market risks are across all

businesses’

. The

request

effectively

required

one

number,

in

USdollars, to be provided each evening which showed J.P. Morgan ’ s

aggregate market risk exposure. Let us see if we could have helpedmeet Mr Weatherstone ’ s demand!

5 . 1 GAP ANALYSIS AND DURATION

You should now be able to calculate the duration of a single bond and, through the analysis of immunisation in Section 4, you should be able to calculate the duration of a small portfolio of bonds.

The purpose of this section is to take the analysis a stage further and show how discounted cash flow (DCF) analysis of an organisation ’ s projected cash movements can produce an aggregate measure of sensitivity to interest rate risk. In this way a tool is created for managers to understand the total amount of interest rate risk being run and thereby provide a means of ensuring that the quantum of this risk is within an acceptable level.

Again I want to stress that this is not an academic exercise or one applying only to participants in the financial markets. All organisations have interest rate exposure arising from their cash

flows. Indeed, one of my first jobs involved managing the interest exposure of a United Kingdom local authority. This required detailed analysis of the authority ’ s cash flows arising from anything from local tax receipts and salary payments to contractual payments





on infrastructure projects and interest and principal payments on the authority ’ s debt.

In Table 5.1, the forward cash flows of an organisation are laid out. You should take note of the following points.

l There are flows which arise from core business activities,

including running costs, earnings from sales, tax payments and other transfers and the payment of bank charges. In each case they are cash flows and not accounting movements.

l There are, naturally, both inflows to, and outflows from the organisation during the period. In this case, cash flows cover a five year forward period. This is deemed to be the maximum forward planning horizon for the organisation in question and for the purposes of this exercise we shall assume there are no net cash flows beyond Year 5. In reality, the planning horizon would depend upon the nature of the organisation ’ s business, with capital intensive organisations having longer planning horizons than those employing assets with a shorter life span. Certainly, accurate gap analysis requires the time period to extend to encompass all known future cash flows.

l The cash flows are divided into six month periods in our example. Alternative periods, say of three months or one year, could be chosen. The choice would depend on just how precise you want your analysis of interest rate exposure to be: the greater the precision desired, the shorter would be the periods you would choose.

l The net cash flow in each period, be it net inflow or net

outflow, is the ‘ gap ’ . l If the organisation is operating in a multi currency environment,

it would have to produce cash flow analyses for each currency, particularly since different interest rate levels apply to different currencies.

l The flows from the investments held as liquid assets by the organisation are also shown. In the example, we have £200m invested, in each case, in a two year and a five year government bond. Both bonds pay 3% p.a. with interest paid semi annually. £100m is also on deposit for one year at 4% p.a.

paid semi annually.





T a b l e 5

. 1

F o r w a r d

p e r i o d

0 –

6 m t h 6

–

1 2 m t h

1 2

– 1 8 m t h

1 8

– 2 4 m t h

2 4

– 3 0 m t h

3 0

– 3 6 m t h

3 6

– 4 2 m t h

4 2

– 4 8 m t h

4 8

– 5 4 m t h

5 4

– 6 0 m t h

C a s h i n f l o w s ( £ m )

E a r n i n g s

7 3

8 0

8 5

9 0

9 5

1 0 0

1 0 5

1 1 0

1 1 5

1 2 0

I n v e s t m e n t s

d e p o s i t s

2

1 0 2

b o n d s

6

6

6

2

0 6

3

3

3

3

3

2 0 3

C a s h o

u t f l o w s ( £ m )

R u n n i n g c o s t s

- 6 0

- 6 5

- 7 0

- 7 5

- 8 0

- 8 5

- 9 0

- 9 5

- 1 0 0

- 1 0 5

T a x a t i o n

- 1 0

- 1 0

- 1 0

- 1 0

- 1 0

C a p i t a l

e x p e n d i t u r e

- 3 5

- 2 0

- 4 0

- 1 0

B a n k c h a r g e s / o t h e r c o s t s

- 5

- 5

- 5

- 5

-

5

N e t c a s h f l o w : t h e

‘

g a p

’

- 1 9

9 3

1 6

1

7 1

1 3

8

3

8

1 3

2 0 8





If you are still unsure about the terms ‘zero rate ’

and ‘

zero coupon’

rate read Box 4.2 again.

We have now established the ‘ gaps ’ – the net inflows and outflows in each of the forward maturity periods. The summation provides a snapshot of the cash movements the organisation will experience during the course of the forward five year period.

Based upon this information, we can now calculate the net present

value of

the

organisation

’

s cash

flow

by

discounting

back

to

the

present value each of the ‘ gaps ’ . To do this, the discount rate to be applied should be the appropriate zero coupon rate for the mid point of each of the forward maturity periods. Although this is a bit of an approximation, since not all the cash flows in each period will occur at this half way point, it is sufficiently accurate for this analysis. Effectively, each gap can be seen as a single cash flow to de discounted by the market rate for a single cash flow bond with the same term to maturity – the zero coupon rate.

Based upon these zero coupon rates, the net present value of the gaps is shown in Table 5.2.

Simply adding the net present values of the gaps gives a measure of the net worth of the organisation ’ s cash flows based on the five year planning profile. Currently this is £449.7m .

How does the net present value of the cash flow help management measure and control the organisation ’ s exposure to interest rate risk? What is the organisation ’ s exposure? In some ways, the answer to this is ‘ how long is a piece of string ’ , since the exposure any individual or entity has to interest rate movements – even if we know the exact current composition of their cash flows – depends

on how

far

interest

rates

move.

A

5%

p.a.

movement

in

rates

will

be five times as beneficial or costly than if rates move by 1% p.a.

There are more complications. What if short term rates rise by 3% p.a., but long term rates from two years onwards remain unchanged? The shapes of yield curves can, and do, alter over time and in such circumstances the impact of rate movements will particularly hinge on the maturity profile of the gaps.

Sophisticated measurement and management of risk would assess the impact on the organisation ’ s net present value under a variety of changing interest rate scenarios. To provide a simple tool for

management, however,

the

company

could

produce

a single

measure showing the impact on the value of the company under extreme interest rate movements. Let us call this a ‘ maxishock ’ – perhaps akin to a ‘ catastrophe ’ if we think back to the work done earlier in this unit on risk mapping. Management could then consider if the impact of this maxi shock was tolerable. If it was tolerable (that is, the organisation could comfortably survive it) then the management would then be happy to live with its interestrate position, since logically all other more likely movements in interest rates would be more tolerable and perhaps beneficial.

But before making this assessment it is necessary to determine what constitutes a maxi shock. This could be done by assessing historical movements in interest rates – both long term and short term – in the currency in question. Clearly, a currency that has


http://slidepdf.com/reader/full/%E3%B4%B49.7m





T a b l e 5

. 2

F o r w a r d

p e r i o d

T o t a l

£ m

0 –

6 m t h

6

–

1 2 m t h

1 2

– 1 8 m t h

1 8

– 2

4 m t h

2 4

– 3 0 m t h

3 0

– 3 6 m t h

3 6

– 4 2 m t h

4 2

– 4 8 m t h

4 8

– 5 4 m t h

5 4

– 6 0 m t h

M i d - p o i n t

3 m t h

9 m t h

1 5 m t h

2 1 m t h

2 7 m t h

3 3 m t h

3 9 m t h

4 5 m t h

5 1 m t h

5 7 m t h

Z e r o - c o u p o n r a t e

( % p . a . )

3 . 0 0 %

3 . 2 5 %

3 . 5 0 %

3 . 7 5 %

4 . 0 0 %

4 . 2 5 %

4 . 5 0 %

4 . 7 5 %

5 . 0 0 %

5 . 2 5 %

D i s c o u n t f a c t o r

0 . 9 9 2

0 . 9 7 6

0 . 9 5 8

0 . 9 3 8

0 . 9 1 6

0 . 8 9 2

0 . 8 6 7

0 . 8 4 1

0 . 8 1 3

0 . 7 8 5

G a p ( £ m )

- 1 9

9 3

1 6

1 7 1

1 3

8

3

8

1 3

2 0 8

N P V o f g a p ( £ m )

( = G a p

6

D i s c o u n t

f a c t o r )

4 4 9 . 7

- 1 8 . 8

9 0 . 8

1 5 . 3

1 6 0 . 3

1 1 . 9

7 . 1

2 . 6

6 . 7

1 0 . 6

1 6 3 . 2

T h e z e r o - c o u p o n r a t e u s e d

( r a n g i n g f r o m 3 %

f o r 3 m

o n t h s t o 5 . 2 5 %

f o r 5 7 m o n t h s ) a r e t h e p r e v a i l i n g

i n t e r e s t r a t e s a t t h e t i m e t h e o r g a n i s a t i o n u n d e r t a k e s

i t s g a p a n a l y s i s .

T h e r a t e s

a r e b a s e d u p o n t h e

g e n e r a l l e v e l o f

i n t e r e s t r a t e s

i n t h e m a j o r g l o b a l e c o n o m

i e s a t t h e t i m e o f w r i t i n g .





You may want to refer to the coverage of normal distribution curves in

Section 3.3.3

of

Vital

Statistics to assist in you understanding of standard deviations.

experienced more interest rate volatility will be more likely, on the basis of its history, to give the organisation a bigger maxi shock than a currency whose interest rate volatility has been low.

Statistical techniques can be applied here. The organisation could assess the mean movement of interest rates over different time

periods, say

over

the

past

ten

years,

and

compute

their

standard

deviation. If we assume these rate movements are normally distributed, the maxi shock levels could then be set at a defined standard deviation from the mean. For example, at 1.65 standard deviations the maxi shock would capture the worst 5% of adverse rate movements.

Other, simpler, techniques could be used. For instance, the most extreme movement in rates experienced in any short term period, say three months, within past history could be ascertained. It is very much the scale of these rapid movements in rates (that is, those which arise before much can be done to alter its gap profile) that the organisation should be most concerned about.

Historically, short term interest rates have, at least in the United Kingdom, been more volatile than long term yields, so the characteristics of the maxi shock could be tapered from the short to the long term.

After making its assessment, let us say that the organisation determines that a maxi shock comprises an immediate move in rates of +3% p.a. from short term rates tapering in a linear manner to +2% p.a. for five year rates. The organisation can now ‘ shock ’ its

gaps by

these

movements

in

rates.

Table

5.3

shows

the

movement

in the net present value of the organisation ’ s gaps arising from the maxi shock. This is calculated by multiplying the value of the gaps by the difference between the discount factors for the current level of interest rates and the discount factors for the ‘ shocked ’ level of rates.

The data in Table 5.3 show that the maxi shock would lose the organisation £26.6m in value. The organisation has to consider if this is a survivable shock.

Again the factors explored when we looked at risk mapping are

relevant here.

Since

the

extent

to

which

an

organisation

is

prepared

to be exposed to risk will depend on its risk capacity and risk appetite.

If the organisation decides that the limit on interest rate risk should be set at £50m, the interest rate position held is within the limit – the ‘ maxi shock’ can be absorbed. If, however, the organisation is more averse to risk and sets a limit of £10m then the position is outside the limit and action would have to be taken to reduce the risk of loss in the event of a maxi shock. This could be done by taking action to revise its gap profile. One way to do this would be to reduce the duration of its investments in liquid assets – since little seems able to be done to change the profile of the company ’ s other





T a b l e 5

. 3

F o r w a r d

p e r i o d

T o t a l

£ m

0

– 6 m t h

6

– 1 2 m t h

1 2

– 1 8 m t h

1 8 –

2 4 m t h

2 4

– 3 0 m t h

3 0

– 3 6 m t h

3 6

– 4 2 m t h

4 2

– 4 8 m t h

4 8

– 5 4

m t h

5 4

– 6 0 m t h

M i d - p o i n t

3 m t h

9 m t h

1 5 m t h

2 1 m t h

2 7 m t h

3 3 m t h

3 9 m t h

4 5 m t h

5 1 m

t h

5 7 m t h

Z e r o - c o u p o n r a t e ( %

p . a . )

3 . 0 0 %

3 . 2 5 %

3 . 5 0 %

3 . 7 5 %

4 . 0 0 %

4 . 2 5 %

4 . 5 0 %

4 . 7 5 %

5 . 0 0 %

5 . 2 5 %

D i s c o u n t f a c t o r , D F 1

0 . 9 9 2

0 . 9 7 6

0 . 9 5 8

0 . 9 3 8

0 . 9 1 6

0 . 8 9 2

0 . 8 6 7

0 . 8 4 1

0 . 8 1 3

0 . 7 8 5

S h o c k e d z e r o - c o u p o n

r a t e ( %

p . a . )

6 . 0 0 %

6 . 1 5 %

6 . 3 0 %

6 . 4 5 %

6 . 6 0 %

6 . 7 5 %

6 . 9 0 %

7 . 0 5 %

7 . 2 0 %

7 . 3 5 %

D i s c o u n t f a c t o r , D F 2

0 . 9 8 5

0 . 9 5 6

0 . 9 2 7

0 . 8 9 7

0 . 8 6 6

0 . 8 3 6

0 . 8 0 5

0 . 7 7 5

0 . 7 4 5

0 . 7 1 5

D F 2

- D F

1

- 0 . 0 0 7

- 0 . 0 2 0

- 0 . 0 3 1

- 0 . 0 4 1

- 0 . 0 5 0

- 0 . 0 5 6

- 0 . 0 6 2

- 0 . 0 6 6

- 0 . 0 6 8

- 0 . 0 7 0

G a p ( £ m )

- 1 9

9 3

1 6

1 7 1

1 3

8

3

8

1 3

2 0 8

N P V o f ‘ s h o c k ’ ( £ m )

( g a p 6

( D F

2 –

D F 1

) )

- 2 6 . 6

0 . 1

- 1 . 9

- 0 . 5

- 7 . 0

- 0 . 7

- 0 . 4

- 0 . 2

- 0 . 5

- 0 . 9

- 1 4 . 6





T a b l e 5

. 4

F o r w a r d

p e r i o d

T o t a l

£ m

0

– 6 m t h

6

– 1 2 m t h

1 2

– 1 8 m t h

1 8 –

2 4 m t h

2 4

– 3 0 m t h

3 0

– 3 6 m t h

3 6

– 4 2 m t h

4 2

– 4 8 m t h

4 8

– 5 4

m t h

5 4

– 6 0 m t h

M i d - p o i n t

3 m t h

9 m t h

1 5 m t h

2 1 m t h

2 7 m t h

3 3 m t h

3 9 m t h

4 5 m t h

5 1 m

t h

5 7 m t h


p . a . )

3 . 0 0 %

3 . 2 5 %

3 . 5 0 %

3 . 7 5 %

4 . 0 0 %

4 . 2 5 %

4 . 5 0 %

4 . 7 5 %

5 . 0 0 %

5 . 2 5 %

D i s c o u n t f a c t o r , D F

1

0 . 9 9 2

0 . 9 7 6

0 . 9 5 8

0 . 9 3 8

0 . 9 1 6

0 . 8 9 2

0 . 8 6 7

0 . 8 4 1

0 . 8 1 3

0 . 7 8 5


r a t e ( %

p . a . )

5 . 0 0 %

5 . 2 5 %

5 . 5 0 %

5 . 7 5 %

6 . 0 0 %

6 . 2 5 %

6 . 5 0 %

6 . 7 5 %

7 . 0 0 %

7 . 2 5 %


2

0 . 9 8 8

0 . 9 6 2

0 . 9 3 5

0 . 9 0 7

0 . 8 7 7

0 . 8 4 6

0 . 8 1 5

0 . 7 8 3

0 . 7 5 0

0 . 7 1 7

D F

2 -

D F 1

- 0 . 0 0 4

- 0 . 0 1 4

- 0 . 0 2 3

- 0 . 0 3 1

- 0 . 0 3 9

- 0 . 0 4 6

- 0 . 0 5 2

- 0 . 0 5 8

- 0 . 0 6 3

- 0 . 0 6 8

G a p ( £ m )

- 1 9

9 3

1 6

1 7 1

1 3

8

3

8

1 3

2 0 8

N P V o f ‘ s h o c k ’ ( £ m )

- 2 3 . 4

0 . 1

- 1 . 3

- 0 . 4

- 5 . 3

- 0 . 5

- 0 . 4

- 0 . 2

- 0 . 5

- 0 . 8

- 1 4 . 1





Markowitz ’s portfolio theory was covered in Unit 4.

Mixing gap analysis with DCF techniques and shock testing the gaps arising from the cash flows is one way to provide the answer to the challenge laid down by Dennis Weatherstone at the start of this section – the provision of a single measure of market risk. Note, though, that: l we only get to that number by making assumptions about the

potential scale of future rate movements; l once we arrive at that single number the organisation must

make a decision – based in part on subjective criteria – as to whether the risk is tolerable;

l the measurement of risk, and the appetite for it, should reflect the nature of the organisation and its financial strength;

The final thought you are, perhaps, left with is that interest risk management is not just down to computers – there is considerable scope for human intervention. Computers have not taken over the thinking process ... well not quite yet, anyway!

VALUE AT RISK 5 .2

The previous sub section took us two steps forward in understanding how to manage interest rate risk by: l deriving (albeit on the basis of considered assumptions)

a single, clear, measure of exposure to risk; l comparing that exposure to risk with a limit for the risk.

This idea of a single readily understandable measure brings us to one of the most popular methods currently in use for managing interest rate risk – value at risk or VaR . While we look at ‘ value at risk ’ here in the context of interest rate risk, the methodology can be adopted to assess the risk arising from the price movements of any instrument or commodity.

The origins of this measure can be traced to Harry Markowitz ’ s paper on ‘ Portfolio selection ’ (1952), where the measure was applied to techniques of portfolio optimisation. In the 1980s the US Securities and Exchange Commission (SEC) used a value at risk

measure to assess the risk on bank securities portfolios. It was not until the 1990s, though, that value at risk really came to the fore as a risk management measure. In 1994 the investment bank JP Morgan launched its Risk Metrics service which promoted the use of value at risk among its institutional clients. In 1995 the Basle Committee on Banking Supervision introduced market risk capital requirements for banks based upon value at risk measures.

These developments in the mid 1990s coincided with a number of episodes in the financial markets, which heightened institutional concerns about market risks, including the collapse of Barings Bank

in 1995, the bankruptcy of the Californian municipal authority Orange County in 1994 and the losses on market trading incurred by the German bank Metallgesellschaft in 1993.





Market risk management became a priority for organisation ’ s and their treasury departments, with value at risk rapidly becoming the tool of choice for risk managers – and indeed for some regulators who were keen to see its adoption by the organisations they regulated.

ACTIVITY 5.2

When you have finished this section it would be useful for you to read (if you have not done so already) the article in the Course Reader by Culp, Miller and Neves on ‘ Value at Risk: Uses and Abuses ’ . In particular, the article assesses how useful value at risk techniques would have been in preventing the problems encountered by Barings, Orange County and Metallgesellschaft.

So what is value at risk or VaR?

VaR is a measure of risk. Using observations of market volatility – inour case the volatility of interest rates – VaR provides a probabilisticmeasure of the future value of financial assets.

VaR estimates:l the maximum loss that is expected with a defined amount of

confidence (for example, 99%) over a defined forward period (for example, 1 day); or

l the likelihood of a loss greater than a defined amount in value over a given forward period.

Both of these measures are really different ways of expressing the same information and both employ the standard VaR parameters: l what maximum loss?l over what period?l with what degree of confidence?

There are three main ways in which VaR can be computed.

1 The historical method which analyses actual interest rate

movements seen in the past. 2 The variance method, which assumes interest rate movements

are normally distributed.

3 The Monte Carlo simulation method , which is based on random samples of interest rate movements.

We do not need to get immersed here in the mathematics used to compute VaR – further details are, in any case, provided in the article in the Course Reader by Culp, Miller and Neves on VaR. In this section we keep things a little simpler by analysing the summary information provided by the VaR mathematics.

Let us look at an example. Figure 5.1 shows the current value of a bond portfolio (£500m) and the probability of its value one day forward, shown as a normal distribution curve around the current





value. This distribution has been derived from looking at the past history of the portfolio ’ s valuation arising from daily movements in interest rates – as you already know when rates rise, the value of a portfolio of bonds will fall and vice versa.

F r e q u e n c y

( d a y s )

0

50

100

150

200

250

300

Lowest 5%of valuations

485 515 530 545Valuation (£m)

470 500

Figure 5.1 Value at risk diagram

There are a variety of measures the risk manager of the

organisation might take from the VaR diagram. They could, for example, measure the valuation of the portfolio at a defined point – say, at the point which cuts off the 5% lowest expected valuations. Here the value is £485m: that is, 95% of the expected valuations one day forward exceed £485m.

The risk manager can then report that: l with 95% confidence, the maximum expected loss tomorrow

will not exceed £15m (£500m minus £485m); l the risk of losing £15m or more tomorrow is 5% (or that losing

£15m or more is a one day in twenty chance).

Note that the VaR methodology does not define an exact loss – rather it defines the minimum expected loss. The portfolio could lose £50m in value tomorrow, but this does not invalidate the statement that the portfolio has a 5% chance of losing £15m or more – it just means that this one day in twenty has been a particularly bad one day in twenty.

What happens next takes us back to the last section on gap analysis.

Are the levels of risk defined by the VaR analysis acceptable to the

organisation? Do they conform to the risk capacity and risk appetite levels set by the organisation? If they do, the portfolio does not have to be altered – at least not today. If the risk is beyond





the parameters set by the organisation then the portfolio will immediately have to be made less risky by reducing exposure to adverse rate movements.

There is a simplicity in respect of the probabilistic statements that result from VaR that is attractive to management. If the limit on

daily losses

on

the

portfolio

is,

say,

£25m

and

the

VaR

measure

shows that this or a greater sum will only be lost one day in every 100 (that means the 1% one day VaR is £25m or, with 99% confidence, the expected loss tomorrow will not exceed £25m) then the organisation ’ s managers can go to bed that night knowing that, probabilistically, there is a 99% chance of them not having a bad day tomorrow!

There are many variations that can be applied to VaR measures simply by changing the forward period. Based upon probabilistic movements in interest rates, the value distribution of a portfolio will normally have a greater spread the longer the forward period. Organisations may be focused on what can happen over a week or a month or longer at least to the same degree that they are concerned about tomorrow.

So with VaR analysis you can derive measures for a variety of forward periods including one week, one month and one year. The choice about which VaR to focus on should be up to each organisation and its decision should be shaped by the nature of its business and its appetite for risk. A bank operating a trading fund will always be sensitive to short term VaRs and will commonly have limits on the one day VaR. A non financial services organisation

with a small investment portfolio may not be hugely exposed to changes in the portfolio ’ s valuation and could content itself by monitoring a limit based on the ninety day or 180 day VaR.

Additionally, individual VaRs should be produced for each currency in the same way as in gap analysis.

While VaR has many virtues as an effective risk management tool the methodology does have some limitations. l The probabilistic measures are usually drawn from historic rate

patterns. Each day of activity in the market adds to that history so that, if the duration of the portfolio is unaltered from Day 1 to Day 2, the VaR measures for the two days may differ. Having a risk position within your risk limit today does not mean you will not have to take action to alter your portfolio to stay within that limit tomorrow.

l There is nothing to stop a portfolio, managed by reference to a VaR limit, losing substantial value over a sustained period. The one day in a hundred VaR – although statistically unlikely – could repeat itself on a number of consecutive or non consecutive days generating substantial losses.





BOX 5.2

VAR AND THE ENERGY TRADERS

There is the risk that the underlying assumptions upon which VaR calculations are based are incorrect, particularly when tested in

volatile market conditions. Energy traders in the US experienced a classic example of this in 2001 and 2002. These traders employed VaR techniques to measure their exposures, using their own assumptions about the yield curves for financial hedging instruments for the energy products. These assumptions had to be made because the market in these energy products was illiquid and could not, therefore, provide usable pricing information. When the US energy company Enron collapsed in 2001 the assumptions that the energy traders had been using were proved to be inaccurate. The VaRs they actually had were far higher than they believed them to be, with the result that unexpectedly large losses

were incurred by many traders. The case also proves a key point that you need to be very careful valuing your assets when the market for those assets is illiquid. Markets that are illiquid only provide indications of what you might get if you sold your assets – not a measure of what you would definitely get.

Proof of the attractiveness of VaR as a management control tool is reflected in how many banks now report their VaR levels with the

rest of their financial results. In September 2003, the US investment bank Goldman Sachs commented in its quarterly results that its one day VaR had risen over the previous year from $47m to $64m. This invoked some concern with analysts expressing reservations about the bank ’ s preparedness to take large trading positions in the financial markets. Indeed, as the extract from the Financial Times in Box 5.3 relates, most of the world ’ s leading banks increased their VaR in 2003.

BOX 5.3

RISKY BUSINESS

Filings for 2003 indicate that, almost without exception, the world ’s leading wholesale banks increased average daily VaR last year.

For some, the increased willingness to take on trading risk has been sizeable. Average VaR at Goldman Sachs and Citigroup stood 21 per cent higher in 2003 than in 2002, and 46 per cent higher at JP Morgan Chase. Morgan Stanley and HSBC produced more modest rises in average VaR ... . The Swiss banks also





reported significantly higher average value at risk in 2003, and UBS announced that it planned to increase its VaR limit by a third.

The VaR methodology, however, has limitations. Historical market data, as Morgan Stanley dryly observes in its annual report, ‘may provide only limited insight into losses that could be incurred under market conditions that are unusual relative to the historical period used ’. One day VaR ... may be particularly inadequate when market liquidity suddenly dries up, so positions cannot be closed.

Taking on additional risk may be a reasonable business decision but regulators are starting to raise eyebrows.

Susan Schmidt Bies, a Federal Reserve governor, warned recently that today ’s historically low interest rates ‘are not within the work experience of many investment and risk managers ’, and urged caution at times when the business and interest cycles may be turning.

(Financial Times , 2004)

ACTIVITY 5.3

Why do you think many of the world ’ s leading banks increased their VaR in 2003? What financial and economic factors would have encouraged them to do so?

There is

no

single

explanation

for

the

enlargement

to

banks

’ risk appetite in 2003. The most probable explanation was that, with earnings from equity markets poor and with interest rates low, thereby offering low returns from new investments in the bond markets, banks may have felt in 2003 that to make greater returns they had to take greater risks.

Other factors contributed to the decision. Globally, banks had experienced good business conditions and profitability – and had consequently strengthened their capital position – in the years before 2003. Consequently, there was, perhaps, an increased preparedness to take on risk since losses, if they materialised, could be more readily borne.

It is also likely, though, that some banks were simply taking on more risk because that is what they perceived other banks as doing ... and in banking, as in other aspects of life, you can feel exposed if you are not doing what everyone else is.





FRAs are forward contracts on interest rates. In Unit 8 you will come across forward contracts on foreign exchange which are known more simply as ‘forwards ’. ‘Notional principal ’ is not

itself an actual cash flow. Rather, it is the amount (say, E 100m) that is used to determine the actual cash flows between counterparties that arise from a derivatives contract.

As with all over the counter versus exchange traded decisions, the choice is usually to balance convenience against cost. To use a clothing analogy, the exchange traded alternative is like ‘ ready to- wear ’ – cheaper, but may not fit exactly. The over the counter deal can be customised – tailored, to maintain the analogy – to match specific requirements, but you pay a (marginally) higher price for it.

FORWARD RATE AGREEMENTS 6 . 1

A forward rate agreement , or FRA , is a contract between two parties which determines the interest rate that will apply to a notional cash flow (known as the ‘ notional principal ’ ) for a specified forward period from a defined future date. It does not necessarily involve either a loan or a deposit and is simply a formal promise between two parties for one to compensate the other for the difference between the agreed rate and the relevant market

interest rate at the start of the notional transaction. For this reason FRAs and other similar types of transactions are often referred to as ‘ contracts for differences ’ .

FRAs can be written in many different currencies, but the largest markets are in US dollars, euros, sterling, Swiss francs and Japanese yen.

FRAs are quoted in terms of the contract period. For example, ‘ three against six months ’ or ‘ 3’ s : 6’ s’ (or ‘ 3v6’ ) will refer to a three month period starting in three months ’ time; ‘ 9’ s:15’ s’ refers to a six month period starting in nine months ’ time.

EXAMPLE 6.1

The Quancrete company finds that credit extended to a major customer is longer than that obtained from suppliers. In three months ’ time, the company will need working capital for a further three months. On 12 February, the BB Bank sells or ‘writes ’ an FRA to Quancrete for ‘three against six months ’ (or ‘3v6 ’) at 5% p.a. Settlement date is 12 May. Compare the following outcomes.

On 12 May, the three-month market rate is 6% p.a.

Quancrete borrows at the market rate 6% p.a.

BB Bank pays the difference between 6% p.a. and 5% p.a. – 1% p.a.

The actual rate incurred by Quancrete is 5% p.a.

On 12 May, the three-month market rate is 4% p.a.

Quancrete borrows at the market rate 4% p.a.

Quancrete pays BB the difference between 4% p.a. and 5% p.a.

+1% p.a.

The actual rate incurred by Quancrete is 5% p.a.





( . − 0 0530. ) × / × £10 000 000, ,0 0625 92 365 = £ ,23 57 3 843.1+ (0.0625 × 92 365 / )

That is, the bank paid Widgets plc £23,573.84 . This compensated the company for the extra borrowing costs it incurred over and

above 5.30% p.a. when using the actual market rate of 6.25% p.a. at the actual time of borrowing.

Note that in its actual borrowing, Widgets will pay its normal spread (or ‘ margin ’ ) above LIBOR, the size of which is determined by its credit status.

The main advantages of FRAs can be summarised as follows: l Future interest rate exposure can be hedged without

commitment to

a

specific

borrowing

or

deposit.

l Transactions can effectively be reversed at any time before the

settlement of the FRA by taking out an equal and opposite FRA, Off setting positions are known as an ‘ off setting position ’ . Alternatively, the contract can, key to understanding how with the agreement of both parties, either be cancelled or can people enter and exit derivative markets. be ‘ assigned ’ (sold on) to another party. If interest rates have

changed since the original FRA was transacted, however, such cancellations, assignments and reversals will result in gain or loss. If an off setting position is used to achieve a reversal, both contracts remain on the books of the transactors until they mature. In other words, matching FRAs are equal and opposite,

but do not eliminate each other, unlike a pair of opposite futures contracts, as you will see shortly.

l FRAs are usually tailored by banks to meet the specific requirements of organisations in terms of both dates and amounts. Contracts covering a three month period are particularly common since they match the custom on floatingrate debt of having quarterly interest rate refixings.


http://slidepdf.com/reader/full/%E3%B2%B3,573.84

http://slidepdf.com/reader/full/%E3%B2%B3,573.84



6 INTEREST-RATE RISK MANAGEMENT INSTRUMENTS: FRAs AND FUTURES

EXERCISE 6.1

A company, Wembley Wheels, owns a network of car showrooms. The company always has a peak borrowing requirement in June, July and August, reflecting the seasonal demand for new cars. In April the base rate was at a relatively

low level of 4% p.a. The finance director was concerned that the rate might rise before she needed to increase her seasonal borrowing and wanted to protect Wheels ’ costs against such an eventuality.

At that time, she was uncertain as to the exact timing and extent of the borrowing. However, her projections showed an average requirement of £1m over the three-month period, with a peak borrowing of £2m. She therefore bought a £1m FRA from the bank, fixing three-month LIBOR at 4.40% p.a. in two months ’ time.

What would be the effect if in two months ’ time LIBOR were: (a) to increase to 6.5% p.a.;

(b) to fall to 3% p.a.?

In this example note that three months = 92 days.

INTEREST-RATE FUTURES 6 . 2

We now look at an alternative method to FRAs of locking in future interest rates – interest rate futures. As we do so, we find out about futures trading more generally and the next few pages should be seen as pertinent to Unit 8 as well as this one. Many aspects of futures are the same regardless of whether you are dealing in contracts for bonds, gold, wheat or Florida orange juice.

BOX 6.1

THE BIRTH OF FUTURES

The first important contracts for exchange traded futures were developed in Chicago in the middle of the nineteenth century. Osaka might dispute this, since merchants there had a form of rice futures contract more than 250 years ago, but Chicago is normally regarded as the birthplace of modern futures. In the 1840s Chicago became the market centre for grain from the farmlands of Illinois, Michigan, Indiana and Wisconsin. After the harvest, large quantities of grain came to the city in loaded carts, resulting in queues stretching a number of miles.

Unfortunately, there

were

no

adequate

storage

facilities

in

the

city

and, furthermore, the merchants did not have the capital required to buy all the grain that was needed. The result was that only a





LIFFE is the London International Financial Futures Exchange. In 2002, the company was acquired by pan European exchange, Euronext, and now it is a subsidiary of this company.

proportion of the grain could be bought and, often, the farmers who could not sell their product found it more economical to dump it rather than cart it all the way home. In the Autumn there was plenty of bread, but grain ran out in the winter and the price of bread often trebled as new grain had to be carted in. In 1848, the

grain merchants formed the Board of Trade of the City of Chicago and addressed this problem by creating an organised market and, by the early 1870s, the elements of a futures market were in place. This incorporated a totally new method of trading, futures, which we shall describe shortly.

The introduction of futures contracts on financial instruments is much more recent: in 1971, foreign currency futures were introduced; in 1975, interest rate futures were started; in 1982, stock index futures were launched. Chicago played a key role in all these areas because of its long experience in commodity futures and it is still the world ’s major market centre for futures. There are now, however, a number of major exchanges engaged in futures trading, in financial centres such as London, Frankfurt, Singapore and Tokyo. Indeed, the competition between rival exchanges is fierce and drives continuous development of both products and systems, which is to the benefit of customers.

Futures trading developed from an older practice, that of forward trading. A forward trade is a contract between two parties, for one to deliver to the other a specified quantity of goods of a specified

quality at a specified date in the future and at an agreed price.

Futures: standardised contracts

With futures contracts, the deals are standardised in terms of the size of the contract and the future settlement dates. For example, the standardised size of one contract for short term UK interest rate futures is £500,000 on the LIFFE/Euronext and there are four settlement dates a year – the third Wednesday in March, June, September and December. It is not possible to trade in fractions

of contracts.

Futures

contracts

are

not

made

directly

with

a

counterparty, but through a clearing house. This eliminates the need to worry about the potential for default by the counterparty as this risk is borne by the clearing house.

BOX 6.2

THE USEFULNESS OF CLEARING HOUSES

The danger of default in forward and futures contracts can be very real: there have been a number of major cases reported and here

we describe briefly one of them. The International Tin Council (ITC) was an organisation set up by twenty two countries to smooth





the fluctuations in the price of tin. In 1985 the price of tin was dropping and the Council tried to support the price by buying forward on the London Metal Exchange, which at the time did not operate a clearing house. The price of tin continued to fall and eventually the support operation collapsed. The sellers of the

forward contracts claimed that the Council owed them £513m and when the case was tried, the view of the English court was that ITC sovereign countries could not be obliged in law to pay. Eventually, after five years and several tens of millions of pounds in legal fees, the case was settled out of court with the ITC paying only £182.5m . This kind of risk can be avoided if there is a clearing house, which was one of the innovations of the Chicago futures market and is now almost universal in futures markets. We describe the activities of clearing houses in Box 6.3 below.

Whether you buy a forward or a futures contract you do not have to hold your contract until the settlement (or expiry) date. If you have bought futures contracts you can close your position at any time by selling the same number. Conversely, if you have sold futures contracts you can close your position by buying an equivalent number. However, you may lose money if the prices of the futures contracts have changed between you buying or selling futures contracts initially and then closing the position. In fact, very few contracts actually reach delivery. Most contracts are closed before settlement.

Standardisation makes a liquid market in which people and organisations can easily buy and sell contracts, their reasons for trading ranging from a business need to hedge exposures to the desire for a speculative bet. Futures have the great advantage of liquidity: the investor can buy or sell them whenever the futures market is open. Another related advantage is that an active and liquid futures market provides complete transparency about fair market prices to all participants.

BOX 6.3

THE CLEARING HOUSE AND THE MARGIN CALLS

As mentioned earlier in this section, the other characteristic that differentiates futures contracts from forward contracts, such as FRAs, is that, with futures contracts, settlement is guaranteed by a clearing house. With large sums of money at stake, forward contracts may well suffer from the danger of default, either through dishonesty or from the straight financial failure of the loser.

When you buy or sell futures contracts you do so with the futures exchange and settlement is via the exchange ’s clearing house. Unlike an FRA, you do not deal and settle with a counterparty. Note, though, that a futures exchange will only allow its member







EXAMPLE 6.3

On 1 March a corporate borrower has a £1m three month loan from the money market which costs 7% p.a. and will be rolled over (i.e. renewed) on 1 June. The borrower wants protection against a rise in interest rates and considers using two three month interestrate futures contracts, each of £500,000 face value, to hedge the £1m loan.

The borrower arranges to sell two June futures contracts (remember a June futures contract is based on a notional threemonth deposit beginning in June). The futures contracts are priced by subtracting the implied annualised LIBOR interest rate from 100. Market expectations are such that the implied rate on June futures contracts when sold on 1 March is equal to the present spot rate: that is, 7% p.a. The price of the futures contracts will therefore be 93.00. The market thus expects no change in interest rates between 1 March and the beginning of June.

Now let us assume that when the loan is rolled over on 1 June interest rates have, contrary to the market ’s expectation three months earlier, actually risen to 8.5% p.a. and implied rates in the futures market have moved similarly. The price of a June futures contract has fallen to 91.50, that is 100 – 8.50. The borrower buys an offsetting contract at the lower price.

Note that the borrower has to reverse the hedge by buying back two June contracts. If an FRA had been used, it could probably have been arranged to mature on 1 June, the required date. Futures were used because they were cheaper overall.

Since each futures contract has a £500,000 face value, the 1.5% increase in interest rates (150 basis points) results in a gain from selling and then buying back of

Two contracts 6 1.5% increase 6 £500,000 6 1=4 of the year = £3,750

or

Two contracts 6 150 basis points (ticks) 6 £12.50 = £3,750

When the loan is ‘rolled over ’ (renewed) on 1 June, the borrower has to pay 8.5% p.a. in the cash market, costing

£1,000,000 6 0.085 6 1=4 = £21,250

for the three month loan; but she has gained £3,750 from the futures hedge, so her net interest cost is £17,500. This equates to a net rate of 7% p.a. – the rate at which the borrower hedged their company in March.





As we saw in Box 6.3, the actual cash flows that take place when you buy or sell futures contracts include the payment of margins. Whether you buy or sell futures contracts, there is an initial margin on opening the position, followed by a daily variation margin as the position is marked to market. You close your position by buying back a contract you have previously sold, or by selling a

contract you have previously bought. In terms of cash flows, your account will be up to date as far as profits or losses are concerned and once the position is closed there will be no more margin flows.

EXERCISE 6.2

In a number of futures markets the maximum movement up and down for each type of contract in a day is prescribed. When the limit is reached the contract is closed for the day,

so that

no

more

trading

takes

place.

What,

in

your

view,

are

the advantages and disadvantages of the setting of such limits?

BOX 6.4

TO BUY OR TO SELL FUTURES?

If you want to hedge, should you buy or sell futures contracts? The answer depends on your underlying exposure. If you are worried that interest rates will go up and you want to borrow at some time in the future, you need to take out a futures contract that will make money and compensate you in the event that interest rates do rise. We have already noted that there is an inverse relationship between the prices of financial asset, including futures prices, and interest rates. If interest rates go up, futures prices will therefore fall. How can you make money from a fall in futures prices? The answer is to sell the futures contract now and buy it back later when the price has fallen. You will close the position and at the same time make money, as did the borrower in Example 6.3. By contrast if you want to protect yourself against the risk of lower rates – e.g. if you were an investor – you would do the reverse and buy futures. If rates did fall the price of futures would rise, thereby making you money.





So if a five year semi annual swap is quoted as

4.75% p.a. – 4.70% p.a.

it means that the bank quoting is prepared to: l pay 4.70% p.a. against receiving six month LIBOR (the floating

rate) every six months for the next five years; l receive 4.75% p.a. against paying six month LIBOR (the floating

rate) every six months for the next five years.

BOX 7.1

NETTING

Note that these fixed rate and floating rate payments can be offset and, in practice, usually only a net difference will be paid from one party to the other on swap payment dates – these usually match

the dates for setting the LIBOR rates on the swap. If the fixed rate is, say, 5% p.a. and the LIBOR fixing is 4.5% p.a. the fixed rate payer pays the net 0.5% p.a. to the floating rate payer. If the LIBOR fixing was 5.5%, the net difference of 0.5% p.a. would be paid by the floating rate payer to the fixed rate payer.

Unlike FRAs, this ‘difference ’ payment is normally made at the end of the LIBOR period and not at the start. Consequently the payment, again unlike those arising from FRAs, is not discounted.

In some jurisdictions ‘netting ’ of payments does not occur and swap counterparties therefore have to make payments to each

other on

a

‘

gross’

basis

From the point of view of the market-making bank

The differential between the two rates quoted by the bank (the ‘ bid to offer’ spread) is one way the bank tries to make money out of the transaction. You will note that the bank will always try to receive a higher fixed rate than it pays on the swaps it transacts. Operationally, this means that when the bank enters into a new swap it will often immediately try to cover (‘ hedge ’ ) its new position by transacting the reverse swap with another party. The bank will not always achieve its objective to make a profit (or ‘ turn ’ ) between the two deals, however, because market rates are not stable. Swap rates can often move quickly: for example, immediately after the publication of surprising economic data.

The other way banks may try to make money out of swap transactions is to use them to establish trading positions where it bets on the future movement of swap rates. In these circumstances the bank would not, immediately at least, try to ‘ hedge ’ the

position resulting from the swap deal.




7 INTEREST-RATE RISK MANAGEMENT INSTRUMENTS: SWAPS

HOW CAN SWAPS SAVE MONEY? 7 . 2

We have seen how swaps enable borrowers to manage interest rate risk in a convenient way by changing the terms on which they are borrowing into those which fit their risk profiles and risk appetites. Additionally, swaps can offer, on occasion, a means of lowering the

cost of their funds. How can borrowers do this simply by swapping interest obligations? Does this imply that debt markets are not efficient? Actually, it does reflect some market inefficiency; debt is traded in separate and independent investor markets. This situation enables the buyer to shop around for the best deal available, across all markets.

Saving on interest payments for borrowers can arise for three reasons.

1 Name recognition A particular borrower may be better known in some markets than in others. This borrower is likely

to achieve better rates (relatively) from investors to whom it is familiar. Let us assume a company is well known to fixed rate investors, but is largely unknown to the floating rate market. If the company wanted to borrow on a floating rate basis it might achieve a better overall rate if it used the fixed rate market and then entered into an interest rate swap to convert the proceeds to the desired floating rate form.

2 Differential risk spreads Investors in fixed rate bonds tend to demand a greater increase in credit risk premiums as quality falls than investors in the floating rate market. In other words, floating rate lenders might accept an increase in ‘ spread ’ from, say, 0.05% p.a. to 0.1% p.a. as sufficient inducement to accept an ‘ A ’ quality borrower rather than an ‘ AA ’ one, but fixed rate investors could well demand a differential of 0.1% p.a. to 0.15% p.a. between ‘ A ’ and ‘ AA ’ borrowers. The explanation is that investing in a long term fixed rate security involves more market risk for an investor than does an equivalent floating rate deal. This is because fixed rate bonds normally have a much longer duration than floating rate bonds and (as we know) are, therefore, more exposed to movements in interest rates. So some borrowers may, in these circumstances, find that the

cheaper way

to

raise

fixed

rate

debt

is

to

issue

floating

rate

debt and then swap the bond to a fixed rate.

3 Independent markets The various markets for fixed and floating rates are separate and individual, and the interest rates in each are defined independently by supply and demand in each. Different conditions, tax regimes or regulations can affect the different market rates as can changes in the appetite of investors for the bonds issued by particular companies. Interest rate swaps therefore enable a company to look at all the markets to see where the best value could be obtained. With so many independent markets available, all governed by their own economic situations, it is not unusual to find that one market has – at least temporarily – moved out of line to others, providing an opportunity to raise funds at lower than normal rate.





A B

Investors receive LIBOR + 0.35%Investors receive 7.75%

Figure 7.3 Borrowings actually undertaken

7.55% p.a. It is market practice in floating/fixed swaps normally to pay LIBOR flat, adjusting the fixed rate to change the price of the swap.

A

7.55%

Bank

LIBOR

Investors receive 7.75%

Figure 7.4 The result for Company A

Figure 7.4 shows the result for Company A. Having issued fixed rate debt, it is liable to pay investors 7.75% p.a. for five years, but each year it will receive 7.55% p.a. from the bank, reducing the net cost to 0.20% or 20 bps p.a. It will, however, have to pay LIBOR to the bank each year. Overall, thereafter, it will pay 20 bps p.a. and LIBOR, giving it an overall interest cost of LIBOR + 20 bps p.a. Company A has issued fixed rate debt, but has ended up with a floating rate

liability, costing it LIBOR +20 bps p.a. rather than LIBOR + 25 bps p.a. if it had raised floating rate debt initially. Company A is thus 5 bps p.a. better off, equivalent to $40,000 each year for five years.

Company B, having issued floating rate debt at LIBOR + 35 bps p.a., negotiates to pay the bank a fixed rate of 7.57% p.a. and the bank pays Company B a floating rate of LIBOR, as in Figure 7.5.

Bank

7.57%

B

LIBOR

Investors receiveLIBOR+0.35%

Figure 7.5 The result for B

Figure 7.5 shows the result for Company B. Having issued floatingrate debt, it is liable to pay investors LIBOR + 35 bps p.a. for five years, but each year it will receive LIBOR from the bank, which will cancel out the LIBOR payment to investors, making a net liability of 35 bps p.a. However, Company B is required to pay the

Bank 7.57% p.a. interest each year for five years. Overall, therefore, it will pay out 35 bps and 7.57% p.a. giving it a total fixed interest cost of 7.92% p.a. Company B has therefore issued a floating rate





ACTIVITY 7.1

Table 7.2 shows that Company A gained more thanCompany B from the swaps arrangement: 5 bps versus 3 bps.Can you think of any reasons why this might be the case?

Is the bank ’ s return of 2 bps p.a. risk free?

The most likely reason is that Company A is the stronger credit and would reasonably expect to extract greater value from the arrangement than the weaker credit, Company B. Alternatively, it could be that the swap dealers at Company A are cleverer than those at Company B!

The bank ’ s return is not risk free. It is taking credit risks in respect of both Company A and Company B. If one of the companies defaults on its swap transaction the bank still has to honour its contract with the other. This may result in

the bank

incurring

financial

losses

since

it

no

longer

has

one swap offsetting the other.

EXERCISE 7.1

Trends plc is a manufacturing company based in the United Kingdom. Part of the finance for its operations is provided by a £250m fixed-rate bond with a remaining maturity of three years that carries an annual coupon of 6% p.a. and has a prevailing market price of 100.

The view held in Trends ’ Treasury Department is that interest rates will fall in the next few months to levels lower than those forecast by the financial markets.

In the current three-year interest-rate swap market, Trends could receive 4.8% p.a. annually versus paying three-month LIBOR.

In the light of this information how could Trends use the swap market to take advantage of its forecast of falling interest

rates? If it does so, what is the resultant effective cost of funds on the bond-plus-swap arrangement? How will Trends be able to determine whether entering into the swap transaction is a good decision?




SUMMARY AND CONCLUSIONS

By now you should, therefore, be able to: l understand the general implications of risk for an organisation

and how types of financial risk fit into the overall risk situation; l categorise the forms of risk to which an organisation is

exposed; l

make use of the results of a risk mapping exercise; l understand the concept of interest rate risk; l calculate ‘ duration ’ and understand how it quantifies for

interest rate risk; l understand how gap analysis and value at risk (VaR) can

provide aggregate measures of interest rate exposure; l understand the usage of financial instruments, such as forward

rate agreements (FRAs), futures and interest rate swaps to manage interest rate risk.

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �





ANSWERS TO EXERCISES

EXERCISE 3.1

With a coupon rate of 5% and a face value of £100, the coupon will pay £5 interest for each of the next two years. The full £100 will be repaid after the two years.

(a)

Year 0 Year 1 Year 2

Cash flow (£) – 5 105

Present value at 5% (£) – 4.76 95.24

Price of bond = £4.76 + £95.24 = £100. The price of the bond is the same as its face value, as the yield to maturity is the same as the coupon rate being paid.

(b)


Cash flow (£) – 5 105

Present value at 3% (£) – 4.86 99.02

Price of bond = £4.86 + £99.02 = £103.88

The bond is trading above its face value, as the coupon rate of 5% is higher than the yield to maturity of the bond.

(c)


Cash flow (£) – 5 105

Present value at 8% (£) – 4.63 89.99

Price of bond = £4.63 + £89.99 = £94.62

The bond is trading below its face value, as the coupon rate of 5% is lower than the yield to maturity of the bond.

The yield to maturity of the bond is the rate of return on the bond required by investors at a particular point in time. As interest rates rise and fall, so does the required yield to maturity.




ANSWERS TO EXERCISES

EXERCISE 4.1

(a)

Time (year)

CF £

Discount factor (10%)

Present value (CF) £

t 6 PV (CF)

1 – 0.909 – –

2 – 0.826 – –

3 – 0.751 – –

4 100 0.683 68.30 273.20

68.30 273.20

Duration = 273 20 68 30

. .

= 4 years

For a zero-coupon bond the duration is the same as the maturity.

(b)

Time (year)

CF £

DF (10%)

PV (CF) £

t 6 PV (CF)

1 5 0.909 4.55 4.55

2 5 0.826 4.13 8.26

3 5 0.751 3.76 11.27

4 105 0.683 71.72 286.88

84.16 310.96

Duration = 310 96 84 16

. .

= 3.69 years

For a 5% bond the duration is less than the maturity of the bond.

(c)

Time (year)

CF £

DF (10%)

PV (CF) £

t 6 PV (CF)

1 20 0.909 18.18 18.18

2 20 0.826 16.52 33.04

3 20 0.751 15.02 45.06

4 120 0.683 81.96 327.84

131.68 424.12





424 17 Duration = .

= 3.22 years 131 68 .

For a 20% bond the duration is much less than the maturity of the bond.

EXERCISE 4.2

ΔP 1= −D × × Δr ×100 P 1 + r

1= − × 3 × −( .0 01 ) ×100 + .1 0 06

= 3 1 06 / .= 2 83. %

The price would therefore rise from £100 to £102.83

EXERCISE 6.1

(a) The

contract

would

be

settled

at

( . − . ) ×92/365 ×£ , ,0 065 0 044 1 000 000 £ , .= 5 207 83

1 + ( . ×92/0 065 365)

The bank would pay Wembley Wheels £5,207.83 to compensate for the extra borrowing costs of 2.1%.

(b) The contract would be settled at

( . − . ) ×92/365 × £ , ,0 03 0 044 1 000 000 £ , .= − 3 502 28

1 + ( . ×92/0 03 365)

Wembley Wheels would pay the bank £3,502.28 to compensate for the fall in rates of 1.4%.

EXERCISE 6.2

An important advantage of such a procedure is that initial margins can be set in line with these limits. Participants in the market can therefore be sure that all losses are covered by the

margin money that has already been paid into the clearing





Trends

receives4.8% p.a.

Bank (market maker)

Pays 3-monthLIBOR

Pays 6% p.a.

Figure EA.1 Bond plus swap package

Whether this is a good move will depend on whether over the three-year residual term three-month LIBOR + 1.2% produces a lower average cost of funds than the fixed coupon of 6% p.a.

EXERCISE 7.2

The impact of the swap is shown in the additional line, labelled ‘ swap ’ , in Table EA.1. The swap gives the organisation a synthetic five-year fixed-rate liability of £250m (costing 5% p.a.) against, on the other side of the swap, a synthetic five-year floating-rate asset, but with the asset refixing its rate every three months. At the start of each three-month period, LIBOR is fixed and at the end the difference between 5% p.a. and the floating rate is paid or received depending on where the floating rate fixes. At the end of the first period the organisation will pay (5% - 3%) 6 1/4 6 £250m = £1.25m to the swap counterparty. Clearly, if floating rates rise above 5% the organisation will receive payments under the swap arrangement.

The representation of this in the gap chart is to place the £250m floating-rate synthetic asset in the 0 – 6 month time period less the known payment of £1.25m that will occur after three months on the first leg of the swap. A £250m liability is placed in the 54 – 60-month time period to reflect the five-year fixed-rate synthetic liability. No other flows are added

to the table in this example since we do not know what the future net swap interest flows will amount to until each fixing of the floating rate takes place.

Note that although the notional principal size of the swap (£250m) is not an actual cash flow, it has to be entered on the gap chart to ‘ convert ’ the interest rate exposure of the actual cash flows it is set against.





T a b l e E A

. 1

F o r w a r d

p e r i o d

T o t a l

£ m

0

– 6 m t h

6

– 1 2 m t h

1 2

– 1 8 m t h

1 8

– 2 4 m t h

2 4

– 3 0 m t h

3 0

– 3 6 m t h

3 6

– 4 2 m t h

4 2

– 4 8 m t h

4 8

– 5 4

m t h

5 4

– 6 0 m t h

M i d - p o i n t

3 m t h

9 m t h

1 5 m t h

2 1 m t h

2 7 m t h

3 3 m t h

3 9 m t h

4 5 m t h

5 1 m

t h

5 7 m t h


p . a . )

3 . 0 0 %

3 . 2 5 %

3 . 5 0 %

3 . 7 5 %

4 . 0 0 %

4 . 2 5 %

4 . 5 0 %

4 . 7 5 %

5 . 0 0 %

5 . 2 5 %


1

0 . 9 9 2

0 . 9 7 6

0 . 9 5 8

0 . 9 3 8

0 . 9 1 6

0 . 8 9 2

0 . 8 6 7

0 . 8 4 1

0 . 8 1 3

0 . 7 8 5


r a t e ( %

p . a . )

6 . 0 0 %

6 . 1 5 %

6 . 3 0 %

6 . 4 5 %

6 . 6 0 %

6 . 7 5 %

6 . 9 0 %

7 . 0 5 %

7 . 2 0 %

7 . 3 5 %


2

0 . 9 8 5

0 . 9 5 6

0 . 9 2 7

0 . 8 9 7

0 . 8 6 6

0 . 8 3 6

0 . 8 0 5

0 . 7 7 5

0 . 7 4 5

0 . 7 1 5

D F

2 -

D F

1

- 0 . 0 0 7

- 0 . 0 2 0

- 0 . 0 3 1

- 0 . 0 4 1

- 0 . 0 5 0

- 0 . 0 5 6

- 0 . 0 6 2

- 0 . 0 6 6

- 0 . 0 6 8

- 0 . 0 7 0

G a p ( £ m )

-

1 9

9 3

1 6

1 7 1

1 3

8

3

8

1 3

2 0 8

S w a p

2 4 8 . 7 5

- 2 5 0

R e v i s e d g a p

2 2 9 . 7 5

9 3

1 6

1 7 1

1 3

8

3

8

1 3

- 4 2

R e v i s e d N P V o f ‘ s h o c k ’ ( £ m )

- 1 0 . 8

- 1 . 6

- 1 . 9

- 0 . 5

- 7 . 0

- 0 . 7

- 0 . 4

- 0 . 2

- 0 . 5

- 0 . 9

2 . 9


b821 block4unit7 risk assessment and interest rate risk

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