Sujeeb Money Market Level 3

Contents

Contents

i

▼

Page i

Before you startTime

PacePlace

Discount instruments

Money MarketsInstruments$ $

▼

▼Instrument

Treasury Bill (T-Bill)

Bills of Exchange/Banker’s Acceptance (BA)

Commercial Paper (CP)

page

29

39

47

▼

▼

Code

TBL

BA

CP

DerivativesInstrument

Forward Rate Agreement (FRA)

Interest Rate futures

Interest Rate Swap (IRS)

Options on Interest Rate futures

Options on FRAs – Interest Rate Guarantee (IRGs)

Options on IRSs – Swaptions

page

55

71

93

115

133

147

Code

FRA

FUT

IRS

OPT

IRG

SWP

Coupon bearing instrumentsInstrument

Money Market Deposits

Certificate of Deposit (CD)

Repurchase Agreement (Repo)

page

1

13

23

Code

DEP

CD

REP

53

What’s next?

Contents

Contents

ii

■ Money Markets and Foreign Exchange Instruments

Derivatives

Money Markets






Options on IRS – Swaptions

Foreign Exchange (FX)

Synthetic Agreements for Foreign Exchange (SAFEs)

Currency futures

Currency swap

Currency options – on Cash and on Futures

Level 3 code

MMI:FRA

MMI:FUT

MMI:IRS

MMI:OPT

MMI:IRG

MMI:SWP

FXI:SAF

FXI:FUT

FXI:CSP

FXI:OPT

Instruments

Money Markets





Bill of Exchange/Banker’s Acceptance (BA)


Foreign Exchange (FX)

Spot transactions – Currencies versus USD

Spot transactions – Cross rates

Forward outright transactions

FX Swaps

Level 3 code

MMI:DEP

MMI:CD

MMI:REP

MMI:TBL

MMI:BA

MMI:CP

FXI:SPT

FXI:CRS

FXI:OUT

FXI:SWP

Before you start

Before you start

iii

Time

PacePlace■ Who is this workbook for?

The learning materials for the Know your Markets openlearning package integrate both traditional workbooks withmaterials on the Reuters internal Web site.

The package has a modular structure and is split into threelevels and four market sectors.

This Level 3 workbook is primarily aimed at sales, clienttraining and customer sales staff who need an in-depthunderstanding of markets and related Reuters products.This greater understanding will enable them to discusstheir customers’ problems and needs in the context of the

markets in which they operate.

Both the workbook and Web Level 3 learning materials have beendesigned to answer questions concerning the latter two of the threefundamental areas of information that the Know your Markets packageis intended to address:

❑ Customer information

❑ Market information

❑ Product information

The learning materials for each area of information answer a series ofbasic questions outlined below:

What do I need to knowabout my market so Ican do my job?

Marketinformation

• What instrumentsare used?

• Who uses theinstruments?

• How do theinstruments work– calculations?

▼

▼ Productinformation

• How are theinstruments usedin practice?

• How is theReuters productused?

• Who are thecompetition?

Across the market sectors there are also areas of commoninformation required. For the Know your Markets package these havebeen divided into three workbooks.

❑ Institutions and Regulation❑ Introduction to Derivatives❑ Competition

There are also underlying techniques used in the financial markets,for example, Technical Analysis, which you may also need to knowsomething about. You may find the open learning workbook TechnicalAnalysis: An Introduction useful for the Reuters 3000 products.

Before you start

Before you start

iv

Time

PacePlaceThis workbook is designed to fit into the following series for theMoney Markets and Foreign Exchange.

Level 2 workbooksCustomer information

Money Markets& ForeignExchange

Insitutions &Regulation

Introduction toDerivatives

Competition

Cross market information

Level 3 workbooksMarket and Productinformation Money MarketsInstruments

ForeignExchange

Instruments

From here you can select the Market or Product information for theparticular market sector you want by making the appropriate screenselection.

Market information – What instruments are used?❑ Level 2

• What it is• Who uses it

❑ Level 3• Calculations/charts etc• Reuters products• Endcheck• Customer scenarios

➪ Links to instruments on Web or Study Guides➪ Links to Reuters products

Product information – What do you need to know?❑ What information is needed?❑ How to get information❑ Catalogue of information

➪ Links to Customer profiles/Customer scenarios onWeb or Study Guides

➪ Links to instruments on Web or Study Guides

http://www.trn.uki.ime.reuters.com/markets_matrix

The Web site accompanying the workbooks provides you with a set ofquick reference performance materials which may help you if youneed a quick reminder of any of the three areas of information –Customer, Market or Product. The Web site materials contains someadditional multi-media learning materials such as interviews with andphotographs of market players. These materials are cross-referencedto the workbooks which you should use for more in-depth study.

To access the Web site use the address below for the Markets Matrixpage.

Before you start

Before you start

v

Time

PacePlaceIt is worth noting that although each Level 2 workbook has a sectionon the instruments traded in the particular market, this is a very briefoverview and contains the minimum of information. The first twosections of this Level 3 workbook are suitable for Level 2 use if all thatis required is information concerning the following:

❑ What is the instrument?

❑ Who uses the instrument?

The later sections of the Level 3 workbook deal with calculations andmore complex details about the instrument.

■ What does this workbook contain?

All the workbooks at Level 3 have the same areas of information andanswer the same basic questions. Each area has an icon to identify itwhich is found in the title to the section. The icons and sections areas follows:

What is the instrument?This always has a definition of the instrument and adescription of what the instrument is used for.

Who uses the instrument?This describes the market players and their tradingtechniques.

The instrument in the market placeThis deals with any formulas, calculations and examplesof the way the instrument is used in the markets.

Using Reuters productsThis deals with the relevant Reuters 3000 and RT pages,their contents and how they are used in the markets.The section may also refer to customer scenarios whichmay be relevant.

EndcheckThis section provides an opportunity for you to test yourunderstanding of the formulas, calculations andproducts used.

1 2 3

4 5 6

7 8 9

0

Before you start

Before you start

vi

Time

PacePlace

Before you start using the package you should discusswith your line manager how he/she will help by givingtime for study and giving you feedback and support.Although your learning style is unique to you, you willfind that your learning is much more effective if youallocate reasonable sized periods of time for study. Themost effective learning period is about 30 minutes – souse this as a basis. If you try to fit your learning into oddmoments in a busy schedule you will not get the bestfrom the materials or yourself. You might like to schedulelearning periods into your day just as you would businessmeetings.

Being a successful open learner means more than just reading. Openlearning is interactive – it is designed to enhance your learning bygetting you to be active. There is an old Chinese saying which mayhelp:

The various types of activities and their icons have already beenmentioned – even thinking is an activity.

Try to make sure your study is uninterrupted. This probably meansthat your workplace is not a good environment! You will need to findboth the time and place where you can study – you may have access toa quiet room at work, you may have a room at home, you may need touse a library.

It’s important to remember that learning is not a race – everyonelearns at their own rate. Some people find things easy, some not quiteso easy. So don’t rush your learning – make sure you get the mostfrom the package. You should now have enough information to planthe use of your workbook and the Web materials – remember it’s yourlearning so it’s over to you...

I hear and I forgetI see and I rememberI do and I understand

Throughout the modules you will find that important terms orconcepts are shown in bold, for example, Yield. You will also find thatat certain points learning activities are included which are designedto enhance your learning. The various activities use the followingicons:

This means stop and think about the point being made.You may want to jot a few words in the box provided – itdoesn’t matter if you don’t.

This indicates an activity for you to do. It is usuallysomething written – for example, a calculation.

This indicates a reference to an instrument in this oranother Level 3 workbook. A complete list of theinstruments and their codes is given in the Contents. Across reference to an instrument will appear like this,for example, Certificate of Deposit.

MMI:CD

■ How to use this package

i This indicates an important item of information worthremembering.

This indicates that you should use the appropriateReuters 3000 product or Reuters Terminal (RT) andfollow the instructions. A screen dump of what youshould see is usually included as well. It is important tounderstand that the activities here assume you have abasic knowledge of the Reuters product software. Ifyou do not have this knowledge you may need to startwith this first!

3000

RT

Before you start

Before you start

vii

Time

PacePlace

1

13

23

29

39

47

55

71

93

114

133

147

■ Coupon bearing instruments




■ Discount instruments


Bills of Exchange/Banker’s Acceptance (BA)


■ Derivatives


Interest rate futures


Options on Interest rate futures

Options on FRAs – Interest Rate

Guarantees (IRGs)


Before you start

Before you start

viii

Time

PacePlace

Instruments

Coupon bearing instruments




Discount instruments




Derivatives






Options on IRS – Swaptions

Level 3 code

MMI:DEP

MMI:CD

MMI:REP

MMI:TBL

MMI:BA

MMI:CP

MMI:FRA

MMI:FUT

MMI:IRS

MMI:OPT

MMI:IRG

MMI:SWP

Start date Completion date Comments

You may find the following chart useful for planning your learningand to decide the order in which you would like to study theinstruments


1

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■ What is it?

Within the Money Markets the deposit market is often referred to asthe Interbank deposit market. This is because the market operatesessentially between banks. Deposits are fixed-term, non-negotiableinvestments or loans which yield interest. The interest rates paid areused as a basis for other Money Market and FX instrumentsincluding:

❑ Establishing the price of coupon bearing instruments suchas CDs and Repos, and the price of discount instrumentssuch as CPs and T-Bills

❑ Pricing derivative instruments such as FRAs and shortInterest rate futures

❑ Setting the rates on instruments which have a ‘floating’aspect such as Interest Rate Swaps and Floating Rate Notes

❑ Pricing Forward FX rates

Within the Interbank deposit market there are two basic types – fixedand notice:

A Money Market Deposit is an unsecured, fixed rateinvestment or loan between financial institutions.

Before you have a look at the deposit market in more detail you needto understand some of the terms used for trades in the market place– some of these have already been introduced.

If you are a borrower of funds, you refer to the trade as a taking. Thecounterparty to the same trade refers to the deal as a placement.

The borrower, or taker of the funds pays interest based upon:

❑ An agreed interest rate

❑ A defined amount of loan – the principal

❑ A specified period of the loan – the maturity or tenor

❑ An end date or maturity date on which the taker pays backthe principal and any interest due

A transaction is agreed on its trade date but the start date of the tradefor the purpose of calculating interest is known as the value ordelivery date. This is the date on which the placer delivers theprincipal to the taker. The value date is usually taken as spot which isusually two working days after the trade date. However, as is describedlater, the value date may differ depending on the maturity of thedeposit.

At the end date – the maturity date – of the loan the taker pays backthe principal, plus any owed interest. The lender, or placer of thedeposit, receives the principal and interest from the taker at maturity.

Takers and placers are often referred to as buyers and sellersrespectively, even though the monies are not actually bought or sold.You should note that deposits are generally non-negotiable. Thismeans that the deal remains on the books until the maturity date,even if one of the parties wishes to terminate or ‘break’ the depositprior to the maturity date.

A fixed deposit is one where the rate of interest and thematurity date are agreed at the time of the transaction.

A notice or call deposit is one where the rate of interestmay be changed or the termination of the depositrequested with effect from a specified number of workingdays. A working day means that the Money Marketfinancial centre involved with the trade must be open forbusiness.


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Maturity datesThe maturity or tenor of a loan is important because its duration isused to calculate interest payments. There are three commonmaturities you will encounter:

Short datesMaturities that are up to, but not including one month. The tablebelow indicates the short date name and day count conventions:

Fixed periods Months

Period or tenor 1 2 3 6 12

Fixed datesMaturities that run from one to twelve months out of spot. Fixeddates are often referred to as the periods. The most active periods areindicated in the table below:

Money Markets maturities do not normally extend longer than oneyear. Because of the credit risks recognised by trading institutions fordeals longer than one year in duration, these maturities are not veryliquid.

Broken datesIn this OTC market, irregular or broken dates will be quoted formaturities which do not quite match the short or fixed datesdescribed previously. The rates for broken dates are calculated byinterpolating between the rates for two known dates. For example, a4-month deposit rate can be calculated by interpolating between the3- and 6-month rates.

You must be careful when using the term spot for the value date. Inmost cases for fixed dates spot is two working days but in GBP tradesin London, spot is value today.

The examples below illustrate the events for an overnight and 2-month deposit.

The value date for most Eurocurrency fixed date transactions is spot.Some domestic deposits tarde value date as today.i 10th July

Trade date12th July

Spot12th Sept2 Months

Receiveprincipal+

Interest

Depositprincipal

Investor

10th JulyTrade date

10th JulyToday

11th JulyNext day

Returnprincipal+

Interest

Borrowprincipal

Borrower

2 month:Fixed date

Overnight:Short date

Overnight O/N Deposit today – return tomorrow

Tomorrow/next T/N Deposit tomorrow – return nextbusiness day

Spot/next S/N Deposit on spot date (two days aftertrade date) – return day after

Spot/week S/W Deposit on spot date – return 7calendar days later


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Components of a tradeThe principal particulars of a deposit trade are:

Trade Date

Value Date

MaturityDate

Rate

Basis

Currency

Amount

Taking bank

Placing bank

PaymentInstructions

Method/via

Confirmation

The date on which the trade takes place.

The start date of a deposit. On this date, the lenderdelivers the principal of the trade to the borrower.Interest on the deposit begins to accrue on this date.

The end date of the deposit. On this date, theborrower repays the lender the principal of thetrade, plus all interest due. The last day for interestaccrual on a deposit is the day before the maturitydate.

The agreed upon interest rate expressed as apercentage on a per annum basis. This may also becalled a yield.

The number of days in a year used to calculateinterest. Most of the world uses a 360 day basis,meaning that a year is said to contain 360 days.Countries such as Canada, Ireland, Singapore, HongKong, Belgium and the U.K. use a 365 day basis.

The currency of the deposit.

The amount of the deposit.

The bank that borrows the money. The deposit isrecorded as a liability on this bank’s books.

The bank that lends the money. The deposit isrecorded as an asset on this bank’s books.

Precise instructions advising each bank as to theappropriate details for the delivery of principal onthe value date to the taking bank, and subsequentrepayment of principal plus interest to the placingbank on the maturity date.

The method used to transact the trade. (Direct, via abroker, etc.)

Printed verification of all the terms of the trade.Each counterparty sends the other a confirmation.

As in the FX Markets, the Deposit Markets have a bid side – taker, andan offered side – placer. The table below compares some of theterminology and components of FX and Deposit deals.

Spot FX contract

2

Date on which thecurrencies areexchanged

Not applicable

The agreed uponrate expressed as anamount of the quotecurrency per singleunit of the basecurrency

Expression of anintent to buy thebase currency

Expression of anintent to sell thebase currency

To sell the basecurrency at the bidprice

To buy the basecurrency at theoffered price

MM Deposit contract

1

Date on which theplacer delivers theprincipal to thetaker. This is the startdate of the deposit

Date on which thetaker repays theprincipal plusinterest to the placer.This is the end of thedeposit

The agreed uponrate expressed as apercentage perannum

Expression of anintent to borrow thespecified currency

Expression of anintent to lend thespecified currency

To lend the specifiedcurrency at the bidprice

To borrow thespecified currencyat the offered price

Term or component

No. of currencies

Value date

Maturity date

Price/rate

Bid means

Offer means

Hit the bid means

Take the offer means


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How are interest rates expressed?There are two ways you will see interest rates expressed:

❑ Fractions. Until the early 1990s, interest rates wereexpressed as a combination of a whole number, whenapplicable, and a fraction. Fractions are quoted as adenominator divisible by two or four producing halves,quarters, eighths, sixteenths, thirty-seconds and, rarely,sixty-fourths. Quotes between market-makers generallyhave a spread of or , for example 6 – .

❑ Decimals. Now it is much more common to see decimalsused which allows for narrower spreads. A movement of1/100 of a percent is referred to as a basis point (BP) sofrom 6.03% to 6.04% represents a move of 1 BP. A typicalmarket-maker quote in decimal form usually has a 10 BPspread, for example 6.00 - 6.10%.

1/8 % 1/4 % 6 1/8 %

Before moving on use the RT to have a look at some rates...

To see the rates from a typical bank type in BPNCand BADD and press Enter after each entry.RT

The bid/offer rates from thisbank are quoted in decimals

These arethe maturities

Note: London quotes offer/bid styleOffer = , Bid = .

These arethe maturities

The bid/offer rates from this bankare quoted in fractions

53/4% 51/2%


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■ Who uses Money Market Deposits?

Borrowers/LendersIn the Interbank Deposit markets banks borrow and lendin response to their customers’ requirements. The banksalso accept and relend deposits on their own account in

order to profit from movements in interest rates. If a Money Markettransaction involves different currencies on the two sides of the trade,then the transaction has a FX aspect and gives rise to a deposit swap.

Banks trading on their own account will also be seeking to maximiseprofits from interest arbitrage. This means the banks are constantlylooking for the greatest spread between the rates for accepting andrelending deposits.

A long position means you have bought a currency.A short position means you have sold a currency.i

Offered and Bid ratesThe only official benchmark that exists for interest rates is thatprovided by a Central Bank for overnight funding. The rates for theother maturities are generated by the market. However, nearly everyinstitution has a slightly different opinion of what the rate is for agiven maturity. To cope with this situation the market needs amechanism that provides a semi-official benchmark rate for the fixeddate maturities.

LIBOR London Interbank Offered Rate. This is the rate a bankoffers or charges for lending money.

LIBID London Interbank Bid Rate. This is the rate the bankbids for money or pays for deposited funds.

LIMEAN This is the average of the LIBOR and LIBID rates whichyou may sometimes see used

The banks in London use a system that has been imitated by otherfinancial centres. Each day, at around 11:00 am London time, asurvey of up to 16 British Banking Association (BBA) selected banksis undertaken for their fixed rate maturity lending (offer) rates toeach other for the major Eurocurrencies. A single rate is establishedper currency and maturity which is known as a BBA LIBOR orLIBOR fixing. These LIBOR fixings are used for setting rates onloans, FRNs and interest rate derivatives. It is important to note thefollowing about LIBOR information:

❑ The term LIBOR is always qualified with a currency and amaturity, for example, 3-month Deutschemark LIBOR

❑ LIBOR is a reference rate and a t best can be used to fix ratesfor negotiated deals

❑ Contributing banks cannot be held to LIBOR prices❑ LIBOR refers only to Eurocurrencies – not domestic markets

Other countries have a similar fixing procedure to LIBOR, forexample PIBOR is the Paris Interbank Offered Rate and FIBOR is theFrankfurt Interbank Offered Rate. However, London LIBOR is usedfor most transactions in the Money Markets.

BrokersBrokers are active in the Money Markets where they act asintermediaries between counterparties – they try to match aborrower with a lender. Brokers do not take positions on their ownaccount but receive fees for arranging transactions.

The following criteria must be satisfied before a trade can becompleted:

❑ The two parties must have opposite interests – one mustbe a lender, the other a borrower.

❑ They must agree on currency, rate, tenor (which musthave the same start and maturity dates for the deposit),amount and that enough credit is available between them.It is often the case that the amount is negotiateddownward to reflect the credit availability of one or bothparties.


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6

■ Money Market Deposits in the market place

1 2 3

4 5 6

7 8 9

0

Interest (I) is calculated by taking into account the Principalamount of the deposit (P), the agreed upon interest Rate (R)expressed in its decimal form, the year Basis (B) of thecurrency, either 360 or 365, and the Amount of days (N) thatthe deposit lasts. The formula looks like this:

61/2 %

It is important to recognise that the interest paid at the maturity ofthe deposit is simple interest. Compound interest is interest paid onaccumulated interest which you may encounter in the capitalmarkets.

Suppose now that the deposit had been 10,000,000 GBP. Using thesame tenor and rate the interest due is now:

The Basis for GBP is 365, seen as A/365. Note the difference ininterest amounts due to the different day bases.

Interest due (I) =10,000,000 (P) x 6.5(R) x 92(N)

365 (B) x 100

= 163,835.62 GBP

Example 1The interest due on a three month deposit of 10,000,000 USD at

that has a tenor of 92 days would be calculated as follows:

Interest due (I) =10,000,000 (P) x 6.5 (R) x 92(N)

360 (B) x 100

= 166,111.11 USD

The Basis for USD is 360. The basis is seen as A/360 which meansthe actual number of days (92) over a 360-day year. Actual daysinclude weekends and holidays.

Interest due (I) =Principal (P) x Rate (R) x Amount of days (N)

Basis (B) x 100...Equation 1

Interest on deposits maturing within 12 months is paid at maturityonly.

Coupon bearing instruments have two values:

❑ Present Value (PV) – the fair market value today

❑ Future Value (FV) – the total repayment value, includinginterest, on maturity

...Equation 2Future Value = Principal + Interest due

= P + P x R x N

B x 100

Future Value = P x 1 +

( )][ ( ) R x N

B x 100...Equation 3

Depending on the calculations you need to perform concerninginterest, Present Values and Future Values, a knowledge andunderstanding of Equations 1 – 3 will be useful.

Year day basis conventions

Domestic 360Euro 360

i Except GBP, CAD, BEF, ECU where:



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The difference in Basis can be important if you are comparing theMoney Market Yields, MMY – interest paid – between differentinstruments. To compare rates between instruments you have tocompare like with like. To do this you need to calculate the trueannual yield for both deposits.

Example 2You wish to compare a GBP deposit which uses Actual/365 (A/365) tocalculate interest with a Eurodeposit which uses Actual/360 (A/360)for interest calculations. To compare like with like you need to addinterest for 5 more days for the Eurodeposit. To do this simplymultiply the Rate by 365/360.

For example, a Euromark deposit for DEM 100 million has a quotedrate of 10%. What is the true annual yield for this deposit on a 365day year basis?

= 10 x 365

360

= 10.14%

True annual yield

Similarly if you need to compare an A/360 quoted instrument withone using A/365, the Rate will need to be multiplied by 360/365 –the interest is less because only 360 days are used to calculate the trueannual yield.

This means that you must be careful when comparing the data forinstruments onscreen!

■ Summary


❑ Fixed term, non-negotiable

❑ Domestic and Euro Markets

❑ Maturities or tenors one day to 12 months

• Short dates – up to one month• Fixed dates – 1, 2, 3, 6, and 12 months from spot• Broken dates – dates not matching short or fixed dates

❑ Interbank rates

• Bid/Offer• Offer/Bid – London

❑ Interest rate quoted as a % per annum

❑ Simple interest calculations

• A/360• A/365

❑ LIBOR


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8

Type in MONEY and press Enter to display theSpeed Guide. From this page double-click in<DEPO/1> to display the DEPOSITS Speed Guide.From here double-click in any currency you require

rates for. You may also find it useful to display LIBOR rates forEurocurrencies by typing in ISDA and pressing Enter – forEurodollar LIBOR rates from different banks type in LIBO andpress Enter.

■ Using Reuters products

The following exercises using Reuters products and theRT may help your understanding of Money MarketDeposits and how they are used.

RT


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Coupon bearingExercise 1. Using the MMMW page in Money 3000can be useful as you can display Bid and Ask pricesfor a number of currencies from differentcontributors simultaneously. For example you want

to lend £5 million for 3 months and at the same time you need toborrow 2 million DEM. You use MMMW to display GBP Bid ratesand DEM Ask rates from different contributors to select who youwant to trade with. Assume 3 months is 90 days in both cases.

3000

1) Which GBP contributor would you deposit funds with for the bestrate of return and what interest would you expect to receive?

Answer:

2) Which DEM contributor would you borrow funds from and whatinterest would you pay?

Answer:

You can also use the MMMW page to calculatebroken dates for deposits. But before you look atthe page try the following:

3000

To calculate broken dates carry out the following:

1. Select maturity rates for either side of the broken date.

2. Calculate the rate change for each day between the maturitiesselected.

3. Multiply the result from 2) by the number of days for the brokendate.

4. Add the result from 3) to the rate for the near deposit and this isthe broken date rate.

Exercise 2It is 30th June 1997 and you need the GBP rate for a broken date of15th August 1997 using TTKL Bid prices opposite. Value is 2nd July.The 1 month deposit maturity date is 4th August and the maturitydate for 2 months is 2nd September. There are 29 days from 4thAugust until 2nd September, and 11 days to the broken date.

Calculate the broken date rate for the bid.

Answer:

Before you check your answers on page 12, why not complete the following Endcheck?


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■ End check

1. Which of the following Money Market instruments is notnegotiable?

❑ a) Cash deposit❑ b) Certificate of Deposit❑ c) Eligible Bill❑ d) Commercial Paper

2. Which of the following Eurocurrency deposits is quoted on thebasis of Actual/365 days?

❑ a) Euromarks❑ b) Euroyen❑ c) Eurosterling❑ d) Eurodollars

3. What is the true annual yield of a 12 month Euromark depositquoted at 3.00%?

❑ a) 3.00%❑ b) 3.02%❑ c) 3.04%❑ d) 3.05%

4. A market-maker quotes a 6-month (180 days) Eurodollar rate of . A market-taker takes $20 millions at . Calculate

the interest due for the deposit.

Answer:

53/4 – 515/32% 515/32%

5. You are the Treasurer of a large corporation in London and attimes you need to deposit and borrow dollars. There are fourbanks you could deal with quoting the following Eurodollar ratesfor one month (31 days) on a 360-day year basis.

a) From which bank would you borrow Eurodollars and at whatrate?

b) From your answer in a), if you borrowed $5 million what is thetotal amount payable at maturity?

c) With which bank would you deposit funds and at what rate?

Answer a)

Answer b)

Answer c)

Bank A

611/16 – 69/16

Bank B

63/4 – 65/8

Bank C

67/8 – 611/16

Bank D

613/16 – 63/4

You can now check your answers on page 12.


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Your notes


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12

Exercise 11) The highest Bid rate is from TTKL at 6.84 %. The interest for

90 days is £84328.70.

Use Equation 1.Interest =

2) The lowest Ask rate is from TRDL at 3.10%. The interest duefor 90 days is 15500 DEM.


5,000,000 x 90 x 6.84

365 100

2,000,000 x 90 x 3.10

360 100

Exercise 21) 1 month rate is 6.5938%, 2 month rate is 6.7500%2) Number of days between maturities is 29 days.

Rate change per day is 6.7500 – 6.5938/29 = 0.1562/293) Rate change for broken

date period is 11 x0.1562/29 = 0.0592

4) Broken date rate istherefore 6.5938 +0.0592 = 6.6530

Using the DepositCalculator things are muchsimpler! Make sure youenter the correct data inthe fields and Money 3000performs the calculationfor you. Check your answerhere.

Answers to exercises

1. a) ❑

2. c) ❑

3. c) ❑

4. $546,875.00 ❑


✔ or ✖

611/16%

63/4%

][ ( )= 5,000,000 x 1 + 6.6875 x 31 100 x 360

= 5,000,000 x (1.0057586)

5. a) Bank A – This has lowest offer rate of . ❑

b) $5,028,793.00 ❑

Use Equation 3.Total amount

How well did you score? You should have managed to get most ofthese questions correct.

20,000,000 x 180 x 5.46875

360 100

End check answers to questions

c) Bank D – This has the highest bid rate of . ❑


13

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■ What is it?

Certificate of DepositMegaBank

$1,000,000

Maturity 3 monthsInterest 6.75%

In other words it is an IOU with a fixed coupon. Most CDs issued bybanks are negotiable instruments and are bearer certificates whichmeans that ownership belongs to whoever possesses the certificate.

What then is the difference betweenan interbank deposit and a CD? Theproblem with a simple deposit is thatis for a fixed term and is non-negotiable. By buying a negotiableCD for a fixed period, if it becomesnecessary to raise funds before thematurity date, then the buyer can sellthe CD in the secondary market.

The rate of interest paid on a CD depends on factors such as currentmarket conditions, the denomination of the CD and the standing ofthe bank offering the instrument.

The depositor can retain the CD until maturity and receive theguaranteed interest or if funds are required urgently the CD can besold in the money markets. The CD will be sold at the going marketprice which reflects the current interest rates. CDs are issued at alower rate than LIBOR because they may not be held to maturity.

CDs were first issued in the US in 1961, in the Euromarkets in 1966and in London in 1968.

A Certificate of Deposit is a negotiable receipt for fundsdeposited at a bank or other financial institution for aspecified time period and at a specified interest rate.

US Domestic CDsIn order to issue a CD in the US domestic market a bank must have agood or acceptable credit rating in the market place. Most US bankCDs are issued with maturities of 1 to 6 months, in $1 million units –pieces – at face value. The majority of US domestic CDs are payableat maturity in New York.

Many US banks issuing CDs also prefer to place the instrumentsdirectly with their clients. This technique has two advantages:

1. The bank’s borrowing is less visible which influences theircredit rating

2. CDs issued through dealers may reappear in competitionto any new issue the bank may seek to launch

However, US banks do issue CDs on a commission basis through anumber of Securities Houses who make a market in CDs. Thesehouses have distribution networks for the world-wide retail of newissues.

USD denominated CDs issued by Foreign banks in the US are often calledYankee CDsi

This section ofscreen istaken fromMoney 3000page MMBWfor USDDomestic CDs


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14

Euro CDsA Euro CD is a receipt for a Eurocurrency fixed term deposit typicallywith a London-based bank. Euro CDs are mainly USD denominatedbearer instruments issued in $1 million units. It is common to seeearly and late prices quoted for CDs which reflects whether the CDmatures in the first or second half of the month respectively.

The main issuers of Euro CDs are branches of major US banks,British clearing banks, branches of major continental Europe banksand Japanese banks. There is a secondary market in Euro CDsalthough as much as 50% of current issues are lock-ups – the CDs arebought and held to maturity, often in the safe custody of the issuingbank.

In addition to the fixed rate coupon CDs, there are also twovariations which may be encountered:

❑ Discount CDs. In this case a CD offered at £1 million facevalue and a yield of 10% would be bought for, say, £900,000.On maturity the loan would be repaid at £1 million earning£100,000 interest on an investment of £900,000. Thisrepresents a true yield of 11.11%.

❑ Floating Rate CDs. These are based on a benchmark –usually LIBOR and are similar in principal to FloatingRate Notes, FRNs, used in the debt markets. You may findit useful to compare these instruments with FRNs in theDebt Markets section. Although not very common the twotypes which may be encountered are 6-month instrumentswith a 30-day roll and a 1-year paper with a 3-month roll.The buyer of a Floating Rate CD has some protectionagainst rising interest rates but this is offset to some extentbecause this type of CD is less liquid than the normal fixedrate type.

On each roll date accrued interest is paid and a new coupon is set.i

This section ofscreen istaken fromMoney 3000page MMBWfor USDDomesticEuro CDs


15

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■ Who uses CDs?

InvestorsThe advantage of CDs for investors is that the instrumentsare negotiable in the secondary market should they wishto raise cash quickly. However, this means that issuers of

CDs will pay some 10 - 15 basis points below comparable fixed depositrates for such negotiable instruments.

Corporate treasurers are large buyers of CDs but increasingly thebulk of demand has come from specialist money market funds. Thesefunds are required to maintain short average maturity on theirportfolios which makes CDs attractive instruments.

Dealers and brokersAs well as buying and selling CDs to clients, dealers create asecondary market by quoting bid and offer prices to other dealers.The normal settlement date for CDs denominated in a foreigncurrency is 2 business days. Domestic CDs settle the following day –the same for domestic currency deposits.

InterDealer Brokers also operate in the secondary market providinganonymous trading facilities between dealers. Typical brokerage is 1basis point per annum on the amount traded which is paid by theparty initiating the trade.

Brokers typically quote price runs in the 3 to 6-month maturities.However, these quoted prices are more varied than for instrumentssuch as government securities as the credit rating of banks issuingCDs varies which affects the quoted prices.

Brokerage of 1 basis point per annum is sometimes called an 01.i

Your notes


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16

■ CDs in the market place

1 2 3

4 5 6

7 8 9

0

The fair value, or settlement amount, of the CD should be thatamount of money (PV) which when placed on deposit today for thenumber of days left to maturity would result in the same FV if the CDwere left to mature. So the return on the CD should equal the returncurrently available on a deposit for the same maturity.

Example 1Consider the following CD:

CD face value: $1,000,000

Issue date: 1st January 1996

Maturity date: 1st January 1997

Coupon: 8.5% pa

Year basis: 360 days

Interest on short-term CDs is normally payable at maturitywhich in the US is termed a bullet security. For CDs issuedwith maturities of 12 months and greater, interest is typicallypaid semi-annually.

Future Value = Principal + Interest due

A bullet security is one where the principal of a loan is paid in whole onmaturityi

On maturity the bearer of a CD will receive the instrument’sprincipal plus the agreed interest which is due. But supposing thebearer requires cash for a project and decides to sell the CD. What isa fair market value for the CD? What is its Present Value, (PV)?

A dollar received in the future is worth less than a dollar todaybecause there is no opportunity to invest the dollar and earn interest.The Future Value (FV) – the repayment amount – is the amount ofmoney you would have if you invested a sum today, PV, for a period oftime at a given rate of interest.

...Equation 1

Year day basis conventions


i Except GBP, CAD, BEF, ECU etc. where:


The CD has an original maturity of 366 days – a leap year! Theinterest due is simply calculated from the formula:

Interest due (I) =Principal (P) x Rate (R) x Amount of days (N)

Basis (B) x 100

= 1,000,000 x 8.5 x 366

360 x 100

= $86,416.67

So the Future Value of the CD = $1,086,416.67

You now decide that you must sell the CD for settlement on the 1stNovember 1996 when there are only 61 days left to maturity.

Suppose the current 2-month deposit rate is 9.75%. The fair value ofthe CD should be that amount of money, PV, which if placed ondeposit today at 9.75% for 61 days would also result in a FV of$1,086,416.67.

Using Equations 1 and 2:

Future Value = Principal + Interest due

= P + P x R x N

B x 100

Future Value = P x 1 +

( )][ ( ) R x N

B x 100

...Equation 2

...Equation 3


17

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In this case the Principal is the Present Value:

Present value = Future value ÷ Interest due

=

Present Value = $1,068,759.87

So the fair value for this CD, 2-months from maturity, discounted at9.75% is $1,068,759.87.

The general equation for calculating the Present Value for a CDwhich has not reached maturity is given in Equation 4.

You may or may not be offered a fair price if you want to sell your CD.What is required is a measure of how good or bad the price you areoffered is. The important factor for the value of a CD in thesecondary market is its Yield To Maturity, YTM which is also knownas the Money Market Yield, MMY. The YTM is:

The rate of return on a fixed income instrument, such as a CD, ifit is held to maturity.

In order to compare the value of a CD with interest rates on depositsand other instruments, market-makers quote a yield basis rather thancash values.

][ 1086416.67

1 + 9.75 x 61

360 x 100

Present Value = P x 1 + ][ ( ) R x N

B x 100

...Equation 4

1 + ][ ( ) r x n

B x 100

Future Value

Interest due

Where P = Principal or the CD face valueR = Quoted coupon rate for the CDN = Number of days to maturityB = Year basis – 365 or 360r = Current market interest raten = Current number of days to maturity

CDs are quoted on a YTM (MMY) basis rather than in cash terms.i

Although YTM is the rate of return if an instrument is held tomaturity, short-term investors often liquidate their position beforematurity. These investors are therefore concerned with the horizonreturn on the instrument which has two components:

Horizon return = Accrued interest + Capital gains

This means the horizon return is the rate of return achieved on aninvestment, from purchase to sale, expressed as a percentage perannum taking into account both components.

If an investment is held to maturity, then its horizon return equals the YTM.i


$ $

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18

The higher the quoted price, the lower the value of the asset.

If you hold a CD you want broker prices to go down – the lower the price, thegreater the yield.

i

■ Summary


❑ A Certificate of Deposit is an IOU with a fixed couponand which is a negotiable instrument

❑ Many commercial banks issue Domestic CDs which arenormally payable at maturity

❑ A Euro CD is a receipt for a Eurocurrency fixed termdeposit typically with a London-based bank

❑ CDs are often quoted as early or late prices which reflectswhether the instrument matures in the first or second halfof the month

Example 2Using the CD details from Example 1 you are offered $1,065,000.00by a market-maker for its purchase with 61 days left to maturity. WhatYTM does this represent? Should you sell to the market-maker?

Using Equation 3 and rearranging for R, where P is taken as the PV:

At the price offered the CD yields over 2% more than thecomparable deposit rate of 9.75% – this is an excellent deal!

The market-maker is unlikely to quote the price of $1,065,000.00 forthe CD, which is the settlement amount. What the market-maker willquote is a two-way price, for example, 11.92/11.87.

This means that the market-maker will buy a CD from you (bid) for acash amount that produces a yield of 11.92% for him, or that themarket-maker will sell you (offer) a CD for a sum that will yield you11.87%.

It is important to remember that the yields here are Money MarketYields and not true annual yields. Using this method of quotes makesthe true value of CDs very transparent and easy to compare withinterest rates on fixed deposits. When trading CDs the yield price isagreed and then the cash settlement is calculated for the purchase/sale of the CD.

= 360 x 100 x 1086416.67 – 1065000.00

61 1065000.00

= 11.87%

R% = ( ) ( )xB x 100 FV – PV

N PV... Equation 5


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From the MONEY Speed guide double-click in theMoney Market field <MMKT/>. You can display theGBP CD prices from the broker Harlow Butler bydouble-clicking in the field <CD=HBEL>. You may

also find it useful to type in US/MMKT and press Enter. If youdouble-click in the Certificate of Deposits field <USCD1> you willsee a variety of CD prices from different US Commercial Banks.


The following exercises using Reuters products and theRT may help your understanding of CDs and how theyare used.

RT


$ $

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20

Using Money 3000 CD prices can be displayed forany currency of your choice using the MMCB page.In the screen below prices for Domestic CDs fromGarvin Guy Butler are shown. You may find the

Calculator useful if you need to calculate the Horizon return for aCD for a date before maturity. Simply make sure you have thecorrect details for the CD required and change the Horizon Dateand press Enter – the new Horizon Return will be displayed.

3000

Enter the new HorizonDate here and press Enter

The new Horizon Return is calculated and shownhere – it has changed from 5.670% to 5.616% bymoving the date forward to 15th August 1997


21

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■ End check

1. When do Eurodollar CDs issued for 12 months generally payinterest?

❑ a) On the issue date❑ b) At maturity❑ c) Quarterly❑ d) Semi-annually

2. XYZ Bank wishes to invest in a very liquid instrument. Which ofthe following are they most likely to do?

❑ a) Buy a A2/P2 Commercial Paper❑ b) Buy a CD rated AAA❑ c) Buy a CD rated BBB❑ d) Deposit funds in the Money Market

3. What is the main advantage of a CD over other Money Marketinstruments? A CD:

❑ a) Pays a higher rate of interest❑ b) Can be resold in the secondary market❑ c) Is the safest form of investment

4. You have bought a Sterling CD in the secondary market with anominal value of £1,000,000. There are 87 days left to maturityand a yield of 6.5%. The CD was issued for 90 days with a couponof 6.75%. How much do you receive at maturity?

❑ a) £1,015493.10❑ b) £1,015,631.65❑ c) £1,016,643.80❑ d) £1,018,643.60

CD face value: $100,000

Issue date: 20th November

Maturity date: 20th May

Coupon: 9.5% pa


5. On 19th February you buy a 6-month (180 days) Euro CD at8.40% with the following details and which has 90 days tomaturity:

Calculate the following:a) The purchase cost of the CDb) The interest actually paidc) If the CD was sold on 29th February at 8.30% how much profit

is made and what is the Horizon return?

Answer a)

Answer b)

Answer c)


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22

1. b) ❑

2. b) ❑

3. b) ❑

4. c) ❑

Use Equation 3.Sum at maturity

b) Actual interest = $9631.94 ❑

Annually

][ ( )= 100,000 x 1 + 9.50 x 181 100 x 360

5. a) Purchase cost = $102,621.33 ❑

Use Equation 4.Purchase cost

= 1.0477638

1.0210

][ ( )= 1,000,000 x 1 + 6.75 x 90 100 x 365

][ ( ) 1 + 8.40 x 90 100 x 360

= 9.50 x 100,000 x 365

100 x 360

5. c) Profit = $257.51 ❑Horizon rate = 9.159% ❑

Selling cost ][ ( )= 100,000 x 1 + 9.50 x 181 100 x 360

= 1.0477638

1.0184444

= $102,878.84

= Selling – Purchase price

= 102,878.84 – 102,621.33

][ ( ) 1 + 8.30 x 80 100 x 360

Profit

Horizon return = 257.51 x 360 x 100 x 365

102,621.33 10 360

✔ or ✖


✔ or ✖



23

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■ What is it?

Within the Capital Markets, market players need to finance theiractivities using loans. As in most financial loans, lenders requirecollateral – security – for the loan. A Repo is a sale and repurchaseagreement which can use almost any asset as collateral. However,government issued instruments such as T-Bonds and T-Bills are mostoften used because of the credit worthiness of the issues. FRNs, CDsand CPs are also used for Repos.

In a Repo, Dealer A sells instruments to Dealer B with an obligationto repurchase equivalent instruments from B at an agreed futuredate. Dealer B now holds the instruments and can use them forwhatever purpose but has the obligation to deliver equivalentinstruments to A at the agreed future date.

The interest rate implied by the difference between the sale andpurchase price is known as the repo rate.

If Dealer A uses a Repo as a means to raise capital, the repo rate is ineffect the cost of the loan.

A Repurchase Agreement (Repo) is an agreement for thesale of an instrument with the simultaneous agreement bythe seller to repurchase the instrument at an agreedfuture date and agreed price.

A Reverse Repurchase Agreement – Reverse Repo – is anagreement for the purchase of an instrument with thesimultaneous agreement by the seller to resell theinstrument at an agreed future date and agreed price.

��

Dealer A sells instrumentsworth $1 million

▼

Dealer B pays A $1 million

Dealer A(Seller)

Dealer B(Buyer)

▼

The following diagrams illustrate the process of using a Repo.

Dealer A now has $1 million for delivering the instruments worth $1million to Dealer B.

First leg – the sale

Dealer B has earned 6.5% interest on the Repo.

In a Reverse Repo Dealer A agrees to buy the instruments and re-sellthem back to Dealer B at an agreed price at an agreed future date.

��

Dealer A pays $1 millionplus a repo rate of 6.5%

▼

Dealer B sells instrumentsworth $1 million

Dealer A(Seller)

Dealer B(Buyer)

▼

Second leg – the repurchase


$ $

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24

■ Who uses Repos?

Central BanksRepo transactions are often used by Central Banks as ameans of monetary control. For example, in the US thelargest Repo market involves trading T-Bills overnight

which spans the closing and opening times of the Money Markets.When the Fed uses a Repo it is initially buying T-Bills to temporarilyadd cash to the Money Markets. A Reverse Repo is where the Fed sellsT-Bills to the Money Markets to drain money from the system. Youmay think that these explanations are the wrong way round but if youconsider the Fed as Dealer B in the previous diagrams, then all iswell.

In the UK the Gilt Repo market is relatively new and the globalMaster Repurchase Agreement (GMRA) establishes what type ofinterest bearing instrument can be used for Repos and allows dealersto substitute eligible instruments.

CorporationsRepos may be used by corporations who are trying to match fundswith their available cash which is needed at a future date. In effectthey buy cash instruments – usually T-Bills – to hedge a futureposition. Using a Repo means the T-Bills are immediately sold buttheir repurchase is agreed for a future date.

DealersDealers now run books in Repos and Reverse Repos hoping to matchcounterparties and make a profitable spread in the middle. In effectthis means the dealer is acting in a similar way to a bank – lendingmoney for instruments on one side and taking deposits on the otherside.

Counterparties to Repos are typically:

❑ Central Banks

❑ Pension funds

❑ Insurance funds

❑ Large corporations

In many cases government bonds are used for Repos and RepoDealers often use Currency Swaps to eliminate FX exposure whichmay arise on interest rate differentials between bonds denominatedin different currencies.


25

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■ Repos in the market place

1 2 3

4 5 6

7 8 9

0

The Repo market formalises to some extent the use ofinterest bearing instruments – particularly Governmentbonds – as collateral for loans. In some cases dealers use thecash raised on existing bonds to buy more bonds. In othercases dealers may have sold bonds they do not actually

possess and use the Repo markets to borrow the bonds they requirefor cash. Repos can resemble futures contracts in that dealers canopen and close large financial positions without involving too muchof their capital. Within the Repo markets it is useful to understandthe following terms:

Description

Where the Repo transaction is covered by a bilateralmargining agreement between counterparties, a thirdparty such as a Custodian Bank or Clearing House isused to revalue the collateral and manage the transferof cash and instruments involved.

This is the margin a Repo dealer puts up and is theamount by which the value of the instruments involvedexceeds the cash invested in the Repo transaction.

A simultaneous spot purchase and forward sale ofinstruments with the agreed repo rate being used toderive the forward purchase price. The buyer receivesthe accrued interest and any coupon payments duringthe Repo period. This type of Repo requires nocollateral monitoring or margining provisions.

Term

Margin(cont.)

Haircut

Buy/sellbackRepo

Description

The interest rate at which a dealer will pay for a Repo toobtain cash.

The interest rate at which a dealer will pay for a Repo toobtain instruments.

Cash provider. The buyer provides cash through thetemporary purchase of instruments.

Cash taker or instrument lender. The seller provides theinstruments in the Repo transaction.

Annual interest rate.

This refers to the revaluation of the collateral that hasbeen provided by the instrument lender. If the price ofthe collateral moves in the markets then this will giverise to a change in value.

Any deficits or surpluses will need to be adjustedbetween the counterparties. Revaluation is usuallycarried out daily.

Term

Ask

Bid

Buyer

Seller

Repo rate

Margin


$ $

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26

■ Summary


❑ A Repo is an agreement for the sale of an instrument withthe simultaneous agreement by the seller to repurchasethe instrument at an agreed future date and agreed price

❑ A Reverse Repo is an agreement for the purchase of aninstrument with the simultaneous agreement by the sellerto resell the instrument at an agreed future date andagreed price

❑ A repo rate is the interest rate implied by the differencebetween the sale and purchase prices

❑ The Repo markets for government treasury instrumentsare important as the bills and bonds involved areconsidered to be the most creditworthy collateral

Your notes


27

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To see Reuters Repurchase Agreement Rates type inREPO and press Enter. This screen displays theOvernight to 3-month rates for US Treasury Repos.

You will see a screen similar to that shown here.


The following exercises using Reuters products and theRT may help your understanding of Repos and how theyare used.

RT


$ $

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28

US Treasury repo rates from Garvin Guy Butler canbe displayed from the MMDI page for USD.


3000


29

$ $

Discount

■ What is it?

T-Bills are short-term government instruments issued in both the USand UK. Normally T-Bill prices are quoted at a discount whichreflects the prevailing short-term interest rate. If you buy T-Bills youare effectively lending money to the government and as such there islittle risk attached. However, the main purpose of T-Bills is not tofinance government spending but to help control monetary policy.

Yields on T-Bills are therefore lower than other short-term moneymarket instruments because the loan is guaranteed by thegovernment – less risk, less reward. As a result of their reliability theseinstruments are used as benchmarks for other investments to becompared with.

In the US and UK T-Bills are recorded centrally so there are nophysical certificates of ownership.

US T-BillsIn the US the Fed typically auctions 13- and 26-week T-Bills on behalfof the government every Monday for delivery on Thursday. It alsoauctions 52-week bills every month. Bids can either be competitive ornon-competitive. Competitive bids state the actual price the investoris willing to pay whereas for non-competitive bids the investor iswilling to pay the average of all bids accepted.

A Treasury Bill is a short-term negotiable Bill ofExchange issued by a government to help financenational debt.

13 week 26 week

Applications $55,735,696 $48,878,949Accepted bills $13,073,966 $13,080,408Accepted non-compet. $1.118,192 $861,519Average price rate 99.227 98.352

3.06% 3.26%

Yield

The results of the auction are published in The Wall Street Journal andlook something like this:

UK T-BillsOn the last business day of each week the Bank of England issues 91-day bills usually for amounts £5000 – 250,000. Tenders are invitedeach Friday with bills being issued the following week.

The results of the tenders are published in the Financial Times andthey look something like this:

BANK OF ENGLAND TREASURY BILL TENDER

Friday 2 Friday 1

Bills on offer £700m £700mTotal of applications £2900m £2246mTotal allocated £700m £700mMinimum accepted bid £98.475 £98.495Allotment at minimum level 59% 83%


$ $

Discount

30

■ Who uses T-Bills?

US T-Bill investorsIn the primary market, market-players such as primarydealers, large institutional investors, money-centre banksand non-professional investors buy T-Bills in competitive

bids on a discounted basis. For example, a bill with a face value of$100,000 may be bought for $97,000. The discount is $3000 whichrepresents the interest on the loan to the government if the bill isheld to maturity. The professional market-players bid for the bills ina competitive auction whereas non-professional investors can makenon-competitive bids with no price. If successful the professionalmarket-players pay their bid price; non-competitive bids are priced asan average of the professional market-players bid prices.

Between the auction and settlement of new issues, primary dealersmake a market in when issued (W/I) bills. This is attractive fordealers who want to run positions as there is no immediate deliveryor costs involved.

The US T-Bill secondary market is the most active US Money Market.The Fed will only deal with primary dealers who must have adequate:

• Capital• Market turnover• Experience and knowledge of government markets

Virtually all secondary T-Bill trading in the US is carried out usingInterDealer Brokers (IDBs). The 40 or so primary dealers use theIDBs on a no-names basis. This means trades are settled with an IDBdirectly rather than between counterparties which makes it difficultto assess who is in the market and the size of their position.

Because T-Bills carry virtually no risk of default, brokers quote priceruns for different maturities. This is possible because all billsmaturing on the same date should have the same price, irrespectiveof their issue date.

In contrast to the primary market, settlement in the secondarymarket takes place on the following business day at the latest – T+1or Trade + 1.

Bills are traded traditionally by large investors in minimum lots of $5million. The US T-Bill is a very liquid market and with the easyavailability of Repurchase Agreements (Repos) dealers build upsubstantial long or short T-Bill positions running into many $100millions.

UK T-Bill investorsThe main holders of UK T-Bills are the Discount Houses whodominate the secondary market and act as intermediaries betweenthe Bank of England and investors. The Bank of England can alsoinvite Discount Houses and Clearing banks to absorb surplus MoneyMarket supplies on a particular day and issue T-Bills by allotment.

Market pricesT-Bills are guaranteed instruments carrying no risk and as such theyield is lower than on Money Market deposits and CDs. T-Bills arequoted on a discount to par basis not on a yield basis. The practice ofdiscounting to par dates back to the issue of Bills of Exchange fromMerchant Banks.

In the secondary market traders deal with each other using quotedbid and offer discount rates. A broker’s price run might look likethis:

US T-Bill

13 week 6.50 – 49 2 x 5

26 week 6.70 – 69+ 10 x 12

52 week 6.96 – 95 1 x 10

But what do these quotes mean?


31

$ $

Discount

Take the rates for 26 weeks:

The bid discount rateis the rate you pay tobuy the bill from thebroker – 6.70%.

The offer discount rate isthe rate you receive if yousell the bill to the broker–6.695%. The 69+ means 69.5basis points.

This means there are10 million Bid lotsand 12 million Offerlots available

The Big Figure of 6% is alsoknown as the handle and is rarelyreferred to in conversations. Thisquote would be 70 – 69+

6.70 – 69+ 10 x 12Bid Offer

As for CDs once a rate has been agreed the settlement amounts arecalculated.

■ T-Bills in the market place

1 2 3

4 5 6

7 8 9

0

The relationship between discount rate and yield isimportant, particularly if you need to compare instrumentswhich are quoted in different ways. To illustrate therelationship consider the following simple case. Suppose anexporter sells a $100 instrument which is discounted by 10%

so receiving $90. What is the equivalent interest rate for this loan? Itis not 10%. If the exporter placed the $90 on deposit for a year at arate of 10%, then the interest would be $9. The most the exportercould receive in interest and from the sale of the instrument is $99,not $100. So the effective rate of interest to the exporter for issuingthe instrument is greater than 10%

The settlement amount payable on a discount instrument iscalculated using Equation 1.

Within the discount markets, instruments have two values which youneed to understand:

❑ Present value (PV) – the settlement amount payabletoday

❑ Future value (FV) – the redemption amountpayable on maturity

Settlement amount , S = P x 1 – ][ ( ) R x N


Where P = Redemption value, FVR = Discount rate as a decimalN = Number of days to maturityB = Year basis – 365 or 360

The discount rate quoted is always less than the true yield to maturity on aninstrument or the effective rate of interest paid.i


$ $

Discount

32

T-Bill face value: £100,000

Settlement date: 9th May

Maturity date: 8th August

Settlement value: £98,485


Example 2 – A UK T-BillCalculate the discount rate for the following UK T-Bill which has 91days to maturity.

Using Equation 2:

...Equation 2

By rearranging Equation 1 the Discount rate can be calculated usingEquation 2.

R% = x( ) P – S

P ( ) B x 100

N

T-Bill face value: $100,000


Maturity date: 28th June

Discount rate: 8.12%


][ ( ) 8.12 x 50

360 x 100

Example 1 – A US T-BillCalculate the settlement amount for the following US T-Bill whichhas 50 days to maturity.

Using Equation 1:

S = 100,000 x 1 –

Therefore the settlement value = $98,872.22. This is also written as98.87% of face value.

If the discount rate remains constant, then as the instrumentapproaches maturity N becomes smaller and the settlement price forthe T-Bill rises to converge with its face value.

= 100,000 – 98,485 x 365 x 100

100,000 91

= 6.0766%

Discount rate


33

$ $

Discount

...Equation 4

As in the case of other Money Market instruments, quoting a ratemay not be that useful if you need to compare rates of return fromdifferent instruments. Rates of return for instruments held tomaturity are compared by calculating the Money Market Yield, MMYfor each instrument.

The MMY for an instrument can be calculated as follows:

1. Calculate the profit to maturity on the instrument.This is equal to (P – S).

2. Express 1. as a proportion of the amount invested.This is equal to (P – S) ÷ S

3. Express 2. on a percentage annual basis

Therefore:

...Equation 3MMY = x( ) P – S

S ( ) B x 100

N

Equation 3 is very similar to Equation 2 which can be used to expressMMY in terms of the Discount rate as in Equation 4.

MMY =

][ ( ) R x N

B x 1001 –

R/100

Using Equation 4:

MMY =

][1 –

8.12/100

( ) 8.12 x 50

360 x 100

Therefore the MMY = 8.21%

To convert this yield into a true annual yield you would need tomultiply MMY by 365/360.

T-Bill face value: $100,000


Maturity date: 28th June



Example 3 – A US T-BillUsing the same information from Example 1 calculate the MMY forthe US T-Bill which has 50 days to maturity.

= 8.21 x 365

360

= 8.32%

True annual yield


$ $

Discount

34

Although the MMY is useful for comparing short-term Money Marketinstruments a different yield basis is used for comparisons withcoupon bearing instruments which are nearing maturity.

The Bond Equivalent Yield, BEY allows such a comparison to bemade and is particularly useful for comparing T-Bills with TreasuryBonds and Notes with only a short time to maturity.

BEY takes into account compounding of interest for couponpayments and adjusts for a coupon period of 365 days. A complicatedformula is used for calculations which will not be discussed here.However, a good approximation for US T-Bills with a maturity of 6months or less is given by the following equation:

... Equation 5= MMY x 365

360BEY

In the case of UK T-Bills, as both bills and Gilts are priced on a 365basis using Equation 5 means that MMY equals BEY.

■ Summary


❑ Treasury Bills are short-term, negotiable, governmentinstruments which are issued at a discount. In the US theyare known as T-Bills and in the UK they are commonlycalled Gilts.

❑ T-Bills are used as benchmarks for other instruments to becompared with

❑ US T-Bills are auctioned and investors buy eithercompetitively or non-competitively on a discount basis

❑ UK Gilts are allocated by invitation to tender from theBank of England, mainly to Discount Houses andClearing banks. The Discount Houses dominate thesecondary market by acting as intermediaries between theBank of England and investors.


35

$ $

Discount

For US T-Bills type in US/GOVT1 and press Enterto display the US Government Debt Speed Guide.To see the end of the day prices for T-Bills fromGOVPX double-click in the < 0#USBILLS3PM>

field – the weekly issues for each month are listed here. You canalso obtain chains of GOVPX prices from the GPXINDEX page.

You will see screens similar to those shown here.


The following exercises using Reuters products and theRT may help your understanding of T-Bills and how theyare used.

RT

This chain has been accessed fromthe GPXINDEX page


$ $

Discount

36

For UK T-Bills you can display the latest T-Billtender results by typing in BOE/MONEYOPS5 andpressing Enter. To see the UK Government DebtSpeed Guide type in GB/GOVT1 and press Enter.

To display OTC prices for Treasury Bills double click in the <GB/TBIL> field. Then double-click in the fields for prices – inthis case <BASD> and <3CLIVE> for Barclays Bank PLC andClive Discount Co Ltd respectively.

RT

Compare T-Bill prices


37

$ $

Discount

611/16%

■ End check

1. You want to buy a UK T-Bill with a face value of £100,000 maturingin 3-months (91 days). Barclays Bank is quoting whilst CliveDiscount House is quoting .

a) Which Bank would you buy the T-Bill from?

b) What is the settlement rate for the bill?

c) What is the Money Market Yield for the bill?

65/8%2. You check on the RT and find the latest price for a US T-Bill with

a face value of $100,000 with a 3-month maturity (90 days) is5.05%.

a) What is the settlement rate for the bill?

b) What is the Money Market Yield for the bill?

c) What is the true annual yield for the bill?


$ $

Discount

38


2. a) $98,735.50 ❑

Use Equation 1.Settlement

b) 5.115% ❑

Use Equation 4.MMY

✔ or ✖

][ ( )= 100,000 x 1 – 5.05 x 90 100 x 360

= 100,000 x [(1 – (0.012625)]

= 5.05/100

[(1 – (0.012625)]

c) 5.186% ❑

True annual yield = 5.115 x 365

360

1. a) Barclays Bank – the lowest discount rate ❑

b) £98,348.29 ❑


c) 6.74% ❑

Use Equation 4.MMY

][ ( )= 100,000 x 1 – 6.625 x 91 100 x 365

= 100,000 x [(1 – (0.0165171)]

= 6.625/100

[(1 – (0.0165171)]

= 0.06625

0.98348

✔ or ✖



39

$ $

Discount

■ What is it?

These instruments have been used in financing international tradefor hundreds of years. A Bill of Exchange in the UK is essentially thesame as a BA in the US. These discount instruments are basicallyshort-term IOUs issued to support a commercial transaction.

Originally a Bill of Exchange was where an importer agreed to pay anexporter a specific sum of money at a definite future date for goodsor services. The exporter – the drawer – draws a Bill of Exchange onthe importer – the drawee. The bill can be drawn as a Sight draftwhich means that it must be paid immediately on presentation or itcan be a Time draft which means payment is due a number of daysafter it has been presented.

Once the importer acknowledges his obligation to honour the bill hewrites ACCEPTED across the bill which now becomes an acceptance.

If the acceptance is between the importer and exporter directly it isknown as a Trade Bill. If the bill is accepted by the drawer’s/drawee’sbank then it is known as a Bank Bill. Once a bill has been acceptedthen it must be paid at maturity.

In many cases a Time draft is drawn by an exporter under a Letter ofCredit, L/C from the importer’s bank. The L/C is a non-negotiableorder from a bank which is required by the exporter who wishes tohave proof that he or she will be paid. Once the exporter provides

the bank issuing the L/C with the necessary documentation such asBill of Lading, invoices, warehouse receipts etc the bank accepts thedraft and stamps it ACCEPTED. The resulting Banker’s Acceptancemeans the importer’s bank will pay the full amount at the due date.The actual instrument issued is simply a note specifying:

❑ The name of the accepting bank

❑ A brief description of the underlying transaction

The exporter can now keep the BA until maturity or if necessary sellit in the secondary market to raise cash. The BA is now a negotiableinstrument which carries the bank’s obligation to pay.

If the exporter does sell the BA in the secondary market, then thebuyer pays less than the face value of the bill. In other words the billtrades at a discount which has a value determined by the differencebetween purchase and face values. The buyer of the BA is effectivelylending money to the original holder and the discount is the interest.

On maturity, the importer has to pay the accepting bank the facevalue of the bill. If the importer fails to pay, then the accepting bankstill has the obligation to pay the bearer. In consequence acceptingbanks need to be assured of the credit worthiness of the importer.

Typically the exporter sells the BA to his own bank. The bank caneither hold the BA to maturity or re-discount it in the secondarymarket.

Most BAs are now issued to support international trade and arebearer instruments drawn on banks having the best credit ratings.BAs are drawn for various maturities and face value amounts reflectsthe nature of the business transaction. BAs are usually created andtraded in lots of USD 1 million or equivalent in other currencies,although some accepting banks issue smaller lots to attract smallerinvestors.

A commercial Bill of Exchange, or Trade Bill, is an orderto pay a specified amount of money to the holder eitherat a specified future date – Time draft – or onpresentation – Sight draft. It is a short-term IOU insupport of a commercial transaction.

A Banker’s Acceptance, or Banker’s Bill, is a Bill ofExchange drawn or accepted by a commercial bank.Once accepted the instrument becomes negotiable.


$ $

Discount

40

ImporterDrawee

ExporterDrawer

Accepted/Trade Bill

Sight or Time draft

Accepting Bank

L/C

Bill of Lading

Accepted/Bank Bill

BA soldat

discount

Secondary marketInvestors

BA re-discounted

The following diagram summarises the processes described in issuingand trading a typical BA.

■ Who uses BAs?

BanksIn London Bills of Exchange and Banker’s Acceptanceshave been issued by Merchant Banks or Accepting Housefor centuries. In taking on the credit risk for the original

drawee, the bank charges a fee to guarantee payment of the bill’s facevalue at maturity. The more credit worthy the accepting bank, theeasier it is to sell the bills in the secondary market.

The accepting bank’s fee is derived from the difference between thediscount rate the bank buys the original bill from its customer andthe lower re-discount rate at which it sells the accepted bill in thesecondary market.

The majority of BAs in the US are created by internationalsubsidiaries of money-centre banks. Originally the US marketdeveloped to finance US import and export markets – in much thesame way as Bills of Exchange had developed in the UK. However,many BAs now issued in the US finance trade in which neitherimporter nor exporter are US organisations.

Eligible BAsThe type of BA described so far is one created for a commercialtransaction involving the supply of goods or services and which isusually supported by a Letter of Credit. However, BAs are also issuedon the basis of less formal contractual agreements as a means ofsatisfying credit demand which avoids Central Bank rules andpenalties.

During the 1960s and 1970s Central Banks in both the US and theUK attempted to control the growth of money supply through bankcredit rationing rather than by raising interest rates. If banksexceeded their domestic lending targets, then they were penalised bytheir Central Bank.

▼

▼

▲

▼

▼▼

▲

On this Bill of Exchange of 1898 youcan see that it has been Accepted

This photograph is reproduced by kind permissionof the Archives Department, Midland Bank plc


41

$ $

Discount

To overcome these difficulties banks developed the following tactics:

❑ Lending was channelled through the Eurocurrency marketswhich were not subject to the same Central Bank rules andregulations

❑ Working Capital BAs or Finance Bills were created whichwere then sold in the secondary markets. Finance Bills are amajor source of working capital for organisations whichlack the credit rating to issue a Commercial Paper.

The result was that both the Bank of England and the Fed madethese bills ineligible for re-discount at the Central Bank and theymade the sale of such bills subject to reserve requirements.

What then is an eligible bill?

An eligible bill is a BA which a Central Bank is prepared to buy andsell which does not incur a reserve requirement.

In broad terms an eligible bill is an acceptance which has beencreated to fund specific types of short-term – usually up to 6 months –commercial transactions.

Eligible BAs issued in the US tend to track T-Bill rates quite closely.The distinction between eligible and ineligible BAs is thereforeimportant and it is normal to see quotes only for eligible BAs.

■ BAs in the market place

1 2 3

4 5 6

7 8 9

0

Within the discount markets, instruments have two valueswhich you need to understand:




Settlement amount = P x 1 – ][ ( ) R x N




$ $

Discount

42

Settlement value: £500,000

Issue date: 5th January

Maturity date: 5th July

Rate: 615/16% pa


][ ( ) 6.9375 x 180

365 x 100

Example 1You are a Corporate Treasurer who needs to borrow £500,000 for thenext 182 days. Your bank offers you the following BA. If you took thisBA what would be the redemption value or cost of the instrument atmaturity?

Using Equation 1:

500,000 = P x 1 –

Therefore the redemption or face value, P

][ ( ) 6.9375 x 180

365 x 100

P = 500,000

1 –

= 500,000

(1 – 0.03421)

= £517,705.52

The cost of using the BA is therefore £17,705.52

Example 2What would be the settlement amount for the following BA issued byBarclays Bank Plc.

Underlying trade: Beet export

Face value: £200,000

Days to maturity: 142

Quoted rate: 6.5% pa


][ ( ) 6.5 x 142

365 x 100

Using Equation 1:

Settlement amount = 200,000 x 1 –

Settlement amount = 200,000 x (1 – .02529)

= £194,942. 46

In this case you would expect to pay £194,942.46 if you purchased thisBA with 142 days remaining to maturity. At maturity you wouldreceive £200,000. The difference between the two values is thediscount – the amount you receive to lend your money.


43

$ $

Discount

■ Summary


❑ A Bill of Exchange is an IOU in support of a commercialtransaction which is issued at a discount. Once a Bill ofExchange is accepted there is an obligation by theaccepting party to honour the instrument.

❑ A Banker’s Acceptance or Banker’s Bill is a Bill ofExchange drawn or accepted by a commercial bank whichis a negotiable instrument

❑ An Eligible Bill is a BA which a Central Bank is preparedto buy and sell which does not incur a reserverequirement

Your notes


$ $

Discount

44

For UK Eligible Bills type in GB/GOVT1 and pressEnter. If you double-click in the <GB/TBIL> fieldyou will see OTC Prices from contributors for T-Billsand Eligible Bills. Double-click in the fields for

prices – in this case <ALEX> and <GNDB> for AlexandersDiscount PLC and Gerrard and King Ltd respectively.


The following exercises using Reuters products and theRT may help your understanding of BAs and how they areused.

RT

Compare T-Bill prices


45

$ $

DiscountUS Domestic BA rates from Garvin Guy Butler canbe displayed from the MMDI page for USD.


3000


$ $

Discount

46

Your notes

For US BAs type in US/MMKT and press Enter. Ifyou double-click in the <NYAS> field you will seeReuters prices for BAs from primary dealers.

RT


47

$ $

Discount

■ What is it?

A CP is an unsecured bearer form, fixed maturity, promissory noteissued on a discount basis by large corporations with good creditratings.

They are used as an alternative to bank loans where the issuerpromises to pay the buyer a fixed sum at a future date but withoutbeing backed by assets. Large corporations often borrow large sumsfor capital investment using debt instruments and then ‘park’ themoney temporarily in the CP market.

Maturities range from a few days to 270 days – the usual period is 30days. The rates offered are typically higher than for T-Bills of thesame maturity.

A CP is a bearer instrument and because it is unsecured only thecredit rating of the borrower is available as security. A CP does notpay interest and is issued on a discount basis.

A Commercial Paper is a short-term unsecured,promissory note issued for a specified amount andmaturing on a specified date. It is a negotiableinstrument typically issued in bearer form.

■ Who uses CPs?

Corporations and banksThe Commercial Paper originated in the US in thenineteenth century as a way of allowing largecorporations to access capital across the country. At this

time most US commercial banks were restricted to lendingoperations in the State in which they were located. Banks sponsoringCP issues could thus earn issue fees from corporations without havingto lend funds.

CPs do not pay interest but are discount instruments issued to raiseworking capital. The CP to a corporation is what a Certificate ofDeposit (CD) is to a bank. Although many large corporations issueCPs, many banks now use short-term CPs to raise money which isused to swap USD into a LIBOR funding basis in other currencies.Most CPs issued by banks have maturities of 30 days or less so thatthey do not compete with the CD market.

Issuers of CPs tend to ‘roll-over’ the paper on maturity. This meansthey sell a new CP to obtain funds to redeem the maturing paper.However, there is a risk that the new CP issue will not take place onthe required day. To avoid this risk most CP issues are backed by aline of credit from a bank.

InvestorsIn general the CP market is a wholesale market for large institutionalinvestors although some large US issuers make some provision forsmaller investors.

A secondary market exists in CPs but most are sold to investors whohold them to maturity. Dealers will buy back CPs they handle but onlyafter adding a wide spread to ensure a profit. CPs are not therefore asliquid as T-Bills and CDs.


$ $

Discount

48

...Equation 2

The yield differential between A1/P1 and A2/P2 rated CPs can be ashigh as 200 points and as low as 15 points depending on the name ofthe issuer and the availability of credit.

Yields on CPs are usually slightly higher than those on T-Bills whichreflects the increased credit risk and reduced liquidity of theinstrument.

Euro Commercial Paper, Euro CP or ECPAlcoa, the US corporation, issued the first Euro CP in 1970 at a timewhen US corporations were seeking USD funding outside the US.

A Euro CP is a commercial paper issued on a Eurocurrency basis.This means the regulatory conditions which apply to normal CPsin their country of issue do not apply to ECPs which are issuedoutside the country in which the corporation or bank is located.

Euro CPs are similar in most respect to CPs in that they are usuallyissued in bearer form with maturities ranging from 30-270 days.However, the main difference between the instruments is as follows:

❑ CPs are quoted on a discount to par or face value basis

❑ Euro CPs are quoted on a discount to yield basis. Thismeans that the quoted rate is the same as the MoneyMarket Yield, MMY

Euro CPs face stiff competition from CPs and the Eurocurrencydeposit and lending markets which tend to be used for short-termcorporate financing.

■ CPs in the market place

1 2 3

4 5 6

7 8 9

0

Within the discount markets, instruments have two valueswhich you need to understand:




Settlement amount , S = P x 1 – ][ ( ) R x N



By rearranging Equation 1 the Discount rate can be calculated usingEquation 2.

R% = x( ) P – S

P ( ) B x 100

N


49

$ $

Discount

...Equation 4

As in the case of other Money Market instruments, quoting a ratemay not be that useful if you need to compare rates of return fromdifferent instruments. Rates of return for instruments held tomaturity are compared by calculating the Money Market Yield, MMYfor each instrument.

The MMY for an instrument can be calculated as follows:

1. Calculate the profit to maturity on the instrument.This is equal to (P – S).

2. Express 1. as a proportion of the amount invested.This is equal to (P – S) ÷ S

3. Express 2. on a percentage annual basis

Therefore:

...Equation 3MMY = x( ) P – S

S ( ) B x 100

N

Equation 3 is very similar to Equation 2 which can be used to expressMMY in terms of the Discount rate as in Equation 4.

MMY =

][ ( ) R x N

B x 1001 –

R/100

CP face value: $100,000

Settlement date: 1st April

Maturity date: 1st May



][ ( ) 8.83 x 30

360 x 100

Example 1 – A US CPCalculate the settlement amount and the MMY for the following USCP issued by Motorola Finance. The quoted rate is on a discount topar basis for a normal CP.

Using Equation 1:

S = 100,000 x 1 –

Therefore the settlement value = $99,264.17

MMY =

][1 –

8.83/100

( ) 8.83 x 30

360 x 100

Using Equation 4:

Therefore the MMY = 8.8955%


$ $

Discount

50

Example 2 – A Euro CPCalculate the settlement amount and the MMY for the following EuroCP issued by Eurotunnel. The quoted rate is on a discount to yieldbasis for a Euro CP. In this case the settlement value is calculatedusing an equation similar to that used for CDs.

CP face value: $100,000

Settlement date: 1st December

Maturity date: 1st January



Settlement value, S = P x 1 + ][ ( ) R x N

B x 100

1 + ][ ( ) r x n

B x 100

Where P = Redemption valueR = Quoted coupon rate which is zero for a CPN = Number of days to maturityB = Year basis – 365 or 360r = Current discount raten = Current number of days to maturity

So for a Euro CP where R = 0, Equation 1 reduces to:

...Equation 5

Settlement value, S = P

1 + ][ ( ) r x n

B x 100

...Equation 6

Using Equation 6:

Therefore the settlement value = $99,390.63

In the case of a Euro CP the MMY is the same as the Discount rate sono calculation is involved!

][ ( )Settlement value, S =

1 +

100,000

7.12 x 31

360 x 100


51

$ $

Discount

■ Summary


❑ A Commercial Paper is an unsecured, negotiable,promissory note issued at a discount by organisations withgood credit ratings

❑ A Euro CP is a commercial paper issued on aEurocurrency basis which avoids normal regulatoryconditions which may apply to Domestic CPs

❑ A Domestic CP is quoted on a discount basis whereas aEuro CP is quoted on a Money Market Yield basis

Your notes


$ $

Discount

52

To see prices for US CPs use the MMDI page forUSD. Select COMM PAPER to view prices fromGarvin Guy Butler. You can also select the rating ofthe CP you require by selecting A1P1, A1P2 or

A2P2. Why not select all three and compare the rates?


The following exercises using Reuters products and theRT may help your understanding of CPs and how they areused.

3000

ExerciseYou are considering buying an A1P1 US CP and you view the GGBprices on Money 3000. You are considering a CP with a 60 daymaturity period and face value of $1,000,000. The prices on screenare as follows:

a) If you bought the 60 day CP as quoted, what would the settlementrate or price be?

b) Calculate the Money Market Yield and the true annual yield forthe CP.Remember these

are discountprices not theyields


53

$ $

DiscountTo see prices for US CPs for the primary markettype in US/MMKT and then double-click in thefield < CPAPERA>. This page displays BAs for largeUS organisations for 5 – 240 days. You can also

double-click in the <RMFA> field to see a Reuters overview of USCP, CD and BA rates.

In the UK the Bank of England publishes Euro CP rates it willobserve – type in BOE/ECP and press Enter.

RT


$ $

Discount

54


a) $990,650.00 or price 99.065 ❑


b) Money Market Yield = 5.6629% ❑True annual yield = 5.7416% ❑

Use Equation 4.MMY

= 100,000 x [(1 – (0.0093500)]

= 5.61/100

[(1 – (0.009350)]

True annual yield = 5.6629 x 365

360

Need you have calculated these values? The answer, as you mightexpect is no – Money 3000 displays all these values in theInstrument details fields.

MMY

True annual yieldPrice/settlement valuedepending on face value

Your notes

✔ or ✖

Answers to exercise

][ ( ) 5.61 x 60

360 x 100 = 100,000 x 1 –


55

$ $

Derivative

■ What is it?

A FRA is a derivative instrument in that its market price is calculatedfrom Money Market deposit rates. The instrument is similar to anInterest Rate futures contract but involves no margin payments. FRAshave developed since 1983 and are the most widely used of the OTCMoney Market derivatives. They are used by market players to lock inshort-term borrowing and lending rates.

ExampleA Corporate Treasurer has a forward borrowing requirement in 3months time for a 3-month loan, but he believes that interest rateswill have risen by the time he requires the loan. To hedge thepossibility of future borrowing costs the Treasurer buys a FRA for theforward period. At the start of the FRA, interest rates have risen andthe Treasurer has to borrow in the cash markets at a higher rate.However, the Treasurer receives cash compensation from thesettlement of the FRA for the difference between LIBOR and theFRA agreed rate. The Treasurer has in effect locked-in the cost of theforward borrowing at the FRA rate.

The buyer of a FRA will be paid in cash by the seller for any rise inthe reference interest rate, over and above the agreed contract rate.Borrowers wishing to hedge against rises in future borrowing coststherefore buy FRAs.

A Forward Rate Agreement is a contract between twoparties which fixes the rate of interest that will apply to anotional future loan or deposit for which the followinghave been agreed:

❑ The amount and its currency❑ A future date for the loan/deposit to be drawn/

placed❑ The term

ExampleIf a FRA is bought at an agreed rate of 5.00%, but at the start of theagreement LIBOR has been fixed at 6.00%, then cash must beborrowed at the higher rate of 6.00%. The buyer receives a cashsettlement of 1.00% on the notional principal amount to compensatefor the increased borrowing costs.

The seller of a FRA will be paid in cash by the buyer for any fall inthe reference interest rate, below the agreed contract rate. Depositorswishing to hedge against any future falls in interest rates thereforesell FRAs

ExampleIf a FRA is sold at an agreed rate of 10.00%, but at the start of theagreement LIBOR has been fixed at only 8.00%, then cash isdeposited at the lower rate of 8.00%. The seller receives a cashsettlement of 2.00% on the notional principal amount to compensatefor the reduced income.

��

If interest rates rise

Buyer Seller

▼

▼

If interest rates fall

It is important to remember that a FRA is an agreement to fix aforward rate – there is no obligation to borrow or lend the notionalprincipal amount involved.


$ $

Derivative

56

Key features of a FRAFRAs have a number of features which market players need to assessbefore they decide on using the instrument. These features includethe following:

❑ Cash settlement. As the loan/deposit is for notional fundsthere is no exchange of principal. Cash compensation ispaid at the beginning of the notional loan/deposit period.

❑ Flexibility. As the loan/deposit is for notional funds there isno obligation by buyers/sellers in the markets to actuallylend or deposit their funds. Market players can use otherinstruments which offer the best returns for their specificneeds.

❑ Lock-in rate. Like Forward FX contracts, if future interestrates fall the buyer will have to compensate the seller andforego any benefit from lower interest rates. Equally, ifinterest rates rise the seller has to compensate the buyer.FRAs effectively lock-in future interest rates for marketplayers.

❑ Low credit risk. As there is no exchange of principal a FRAis an off-balance sheet instrument. The credit risk is lowbecause the main risk is concerned with finding areplacement counterparty should the original party default.The risk involved is therefore on the settlement amountrather than the notional amount.

❑ Cancellation and assignment. A FRA is a binding contractand cannot be cancelled or assigned to a third partywithout the agreement of both counterparties. As withother instruments with binding contracts, FRA positionscan be closed using off-setting contracts.

Terms usedThere are a number of terms you need to know if you are tounderstand how FRAs work and are used. The table below indicatesthe terms and their meanings.

Term

Contract currency and amount

Trade date

Fixing date

Settlement date

Maturity date

Contract period

Contract rate

Which means...

The currency and amount of thenotional loan/deposit

The date the deal is actuallymade

This is two business days beforethe start of the FRA. It is the datewhen the LIBOR, or other,reference rate is fixed. Thesettlement amount is calculatedusing this rate.

For domestic currency FRAs thefixing date is usually the same asthe settlement date.

This is the date when thecontract period starts and cashcompensation is paid

The date the contract ends

This is the term of the notionalloan/deposit – the period fromsettlement to maturity in days

The agreed forward interest ratefor the contract period – theprice of the FRA in % per annum


57

$ $

Derivative

The events of the following 3 month FRA are summarised here:

Contractstarts

Contractagreed

Contractends

Contract period – 92 days

3 month FRA

▼

The British Bankers Association (BBA) publishes a set of recommendedcontract terms and conditions – referred to as FRABBA terms. Thismeans that most banks deal automatically on FRABBA terms unlessotherwise stated. FRA fixing rates are based on LIBOR which areavailable daily to the markets. The fixings are made at 11.00 amLondon time and are calculated as an average of 16 banks quotingLIBOR in the London market.

Use the Benchmark Watch page, MMBW for GBPand select BBALIBOR from the drop down menu.You can also use page FRASETT on the RT to see alist of all the fixings.

You should see pages similar to those shown here.

3000

10th AprilTrade

12th JuneFixing

15th SeptMaturity

16th JuneSettlement

LIBORrate fixed

Rules1. The start and end dates are calculated from spot dates.2. The fixing date is 2 days before the start date.

For the above FRA:

• The trade is agreed on 10th April 1997• Spot is therefore two business days later – 14th April• The start date of the FRA is two business days from the forward

date – 16th June• The fixing date is two business days before the start date – 12th

June• The maturity date is 3 months from 16th June – 15th

September

Before moving on use Money 3000 to have a look at BBALIBOR ...


$ $

Derivative

58

Market pricing of FRAsThe FRA is quoted as a two-way price with bid/offer prices in thesame way as for Money Market deposit rates. FRA market-makers takeon large trades because the credit risk is low as there is no notionalexchange of principal. This means that the bid/offer spreadsavailable are tighter compared with cash deposit rates – typically 3 – 5basis points for Eurodollar FRAs. These tighter spreads are availableonly for standard minimum deal sizes of USD 5 million or equivalent.

Prices quoted are for standard or fixed dates. The table below givesexamples of the conventions for 3- and 6-month series of FRAs:

1 x 4

2 x 5

3 x 6

6 x 9

Startsforward

1 month

2 months

3 months

6 months

Endsforward

4 months

5 months

6months

9 months

3-month series

1 x 7

2 x 8

3 x 9

6 x 12

Startsforward

1 month

2 months

3 months

6 months

Endsforward

7 months

8 months

9 months

12 months

6-month series

The most liquid FRAs are those for 3 x 6, 3 x 9, 6 x 9 and 6 x 12agreements. Broken dates are available but the dealing spread may bewider. Some FRA market-makers are prepared to quote shorter datesthan 1 month.

In most financial centres market-makers quote the bid price firstwhereas in London it is the offered rate which is quoted first – therate at which they sell. Either way the market-taker always pays thehigher rate!

New York

Bid/Offer

London

Offer/Bid

Under the FRABBA system Eurocurrency FRAs involving currenciesnot linked to LIBOR cannot be traded. However, provided there areunderlying cash Money Market prices, ‘exotic’ FRAs can be pricedand settled against mutually pre-determined reference rates.

Contractagreed

Endforward

Contract period– 3 months

1 x 4 FRA

▼

Trade 1 month 4 months

Startforward


59

$ $

Derivative

How are FRA prices determined?In most cases today, FRA prices are derived from short-term InterestRate futures contracts for the same currency. For example,Deutschemark FRAs are typically priced off the EuroDeutschemarkfuture contracts traded on LIFFE or MATIF. It is for this reason theFRA market has been referred to as the new Interbank FutureInterest Rate market. Because of the close relationship between FRAsand the futures market, FRAs are often quoted for the same periodsas are traded on Futures Exchanges.

There are a number of ways FRA prices can be calculated includingthose derived from:

❑ Cash depositsFor example, to price a 3 x 6 FRA the 3-month and 6-monthdeposit rates are used.

❑ Interest Rate futures contracts

❑ Zero coupon yield curve

The FRA is a Money Market instrument involving maturities up to 12months. However, longer date FRAs are available, for example, 18 x24. Typically these instruments are priced using the Zero couponyield curve.

Instruments such as bonds and Interest Rate Swaps typically paycoupons regularly to maturity. Therefore their actual yields dependon the reinvestment rates that can be achieved on the earnedinterest. A Zero coupon instrument is one that pays no coupon but isissued at a deep discount. The difference between the issue andredemption prices compensates for any such reinvestment ofpotential interest payments.

The Zero coupon yield curve, also known as the Spot curve, is agraphical representation of the theoretical Yield To Maturity (YTM)estimate of the yield which should be paid on non-coupon bearinginstruments of different maturities, given the yields currentlyavailable for coupon bearing instruments.

Contractagreed

6 monthdeposit

FRA rate?

▼

Trade 3 m rate 6 m rate

3-monthdeposit

Use the Analysis page, FRA for GBP and selectDeposits-MID, Futures curve and Zero curve fromthe drop down menus for the same FRAs in the TVfields. You can now compare the rates derived fromthe different methods.

3000

Before moving on use Money 3000 to have a FRA analysis page...


$ $

Derivative

60

Comparing FRAs with Interest Rate futures contractsAs Interest Rate futures contracts could easily be used in place ofFRAs, it is useful to compare the following aspects of the instruments:

Forward Rate Agreement...

It is an OTC contract between counterparties. In somecases the deal may be made via a broker.

Amount, period and settlement procedures arenegotiated between the counterparties.

There are no obligations placed on the counterpartiesto divulge the terms of the contract. Different market-makers may well quote different bid/offer prices.

No margin payments are required. Usuallycompensation payments are made on the settlementdate.

Each side is taking a risk on the counterparty, so eachside accepts a small credit risk.

A FRA contract is binding and cannot be cancelled orassigned to a third party without the agreement of bothsides.

Interest Rate futures contract...

Contracts are traded in pits or electronically on anExchange.

Amounts, expiry dates and settlement periods are fixedand standardised by the Exchange.

Deals are transacted open out cry or using electronicsystems. Orders and trades are immediately visible andtransparent to all market players. On an exchange thereis only one market price at any one time.

Initial margin is paid as a % of the trade amount –marked-to-market. The margin payments are held bythe Clearing House. Variation margin is also paid to theClearing House on a daily basis depending on themarket price movement.

After a trade is made on the Exchange, the ClearingHouse stands as the counterparty, acting as seller toevery buyer and vice versa. The Clearing Houseguarantees the performance of contracts and so there isno credit risk to the contract parties.

Futures contracts can be off-set.

Trading

Contract terms

Confidentiality

Margin payments

Credit risk

Right of offset


61

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Derivative

■ Who uses FRAs?

BanksWithin banks, Money Market desks are regular users ofFRAs. The larger US, UK, European and Australian banksare active market-makers and use FRAs for a number of

reasons including the following:

❑ Balancing the bank’s books

❑ Matching client FRA positions

❑ Arbitrage opportunities against futures contracts

❑ Hedging future loan/deposit positions

❑ Hedging mismatches in interest rate sensitive instruments– forward gaps

Banks make a profit from the bid/offer FRA price spread.

Corporations and non-bank financial institutionsThese organisations also use FRAs to manage interest rate risk. Thecredit risk to the market-maker is small as it only involves risk to thepotential settlement involved. No premium is paid by clients for FRAs– the only costs they incur are those for any compensation payments.

Organisations can also use FRAs to speculate on future interest ratemovements. As FRAs are binding contracts, if a FRA needs to beclosed out for any reason, this is done by arranging a new FRA whichis opposite to the original instrument.

Futures

Interestrate rises

Interestrate falls

FRAs

Interestrate rises

Interestrate falls

To hedge fall in interestrates

Buy contract

Loss

Profit

Sell FRA

Loss

Profit

To hedge rise in interestrates

Sell contract

Profit

Loss

Buy FRA

Profit

Loss

The ways FRAs and futures contracts can be used to hedge a rise/fallin interest rates is summarised in the chart below:


$ $

Derivative

62

Risks involvedThere are two types of risk to be considered when using FRAs:

❑ Basis risk. This arises if the instrument being hedged is notlinked to LIBOR, for example, a US CP. In this case the riskexists because the rate setting process for the underlyinginstrument is independent of the rate setting for the FRA.

❑ Funding risk. This is related to the creditworthiness of theparties involved. Can both sides meet any compensationpayments due on the settlement date?

There are also risks involved from both the bank’s and the client’spoints of view. If a bank sells a FRA and interest rates risesubsequently, then the bank will suffer a loss and have to pay theclient compensation. The risk clients take is that the FRA locks-in afuture interest rate. If interest rates move in favour of the clients thenthey cannot benefit, if they move against them then they compensatethe bank.

■ FRAs in the market place

1 2 3

4 5 6

7 8 9

0

FRA settlement paymentsThe settlement rate is usually determined two business daysbefore the period of the notional loan/deposit for thespecified reference rate, LIBOR. It is important to note thatthe settlement payment is made at the beginning of the loan

period rather than at maturity – the usual procedure for MoneyMarket deposits. Therefore the settlement payment has to bediscounted to its present value at the current market interest rate.

You will need to know two equations in order to calculate settlementpayments – both equations are very similar. One caters for thesituation where the settlement rate is greater than the contract rate sothe FRA seller compensates the buyer. The other equation is for theopposite situation where the settlement rate is less than the contractrate so the FRA buyer compensates the seller.

(L – R) x D x A

(B x 100) + (L x D)Settlement payment =

Settlement rate greater than contract rate

...Equation 1a

(R – L) x D x A

(B x 100) + (L x D)Settlement payment =

Settlement rate less than contract rate

...Equation 1b

L = Settlement rate as a number not %R = Contract rate as a number not %B = Day basis – 360 or 365D = Contract period in daysA = Contract amount


63

$ $

Derivative

Example 1It is the 10th April 1997 and the XYZ Corporate Treasurer foresees aforward funding requirement for 3 months (92 days) from 16th Juneto 15th September 1997. The Treasurer thinks that there is a possiblerise in interest rates and therefore wants to hedge against any interestrate rise. The Treasurer buys a 2 x 5 FRA on the 10th April fromOkiBank with the following terms:

What is the settlement due if the BBALIBOR 3-month fixing rate is7.25% the 10th June fixing date, and who receives payment?

Even though XYZ have bought a FRA contract they still have to raisethe funds they require for 16th June to 15th September in the MoneyMarkets at the increased rate of 7.25%. However, as the interest rateshave risen, OkiBank have to compensate XYZ a cash sum. Thesettlement amount is therefore calculated using Equation 1a.

(7.25 – 6.75) x 92 x 10,000,000

(360 x 100) + (7.25 x 92)Settlement payment =

460,000,000

36667=

$12,545.34=

At this point the FRA contract ceases to exist and the XYZ CorporateTreasurer can now either reinvest the FRA settlement payment in theMoney Markets or arrange a loan for $10,000,000 – 12,545.34.

In either case the XYZ loan will be based on the current LIBOR. TheFRA payment acts as a subsidy bringing down the net cost ofborrowing.

But what would have happened if the Treasurer’s fears of an interestrate rise were unfounded and on fixing LIBOR was 6.50%? This timeXYZ have to compensate OkiBank. The settlement amount can becalculated using Equation 1b.

(6.75 – 6.50) x 92 x 10,000,000

(360 x 100) + (6.50 x 92)Settlement payment =

230,000,000

36598=

$6,284.50=

FRA contract amt. $10,000,000

Fixing date: 12th June 1997

Settlement date: 16th June 1997

Maturity date: 15th Sept. 1997

Contract rate: 6.75% pa



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Derivative

64

Forward/forward ratesIt is possible to calculate forward/forward rates from deposit ratesusing the following equation:

RL = Rate from spot to the far date – long periodRS = Rate from spot to the near date – short periodDL = Number of days from spot to far dateDS = Number of days from spot to near dateB = Day basis

RFWD = (RL x DL) – (RS x DS)

(DL – DS) x 1 + RS x DS

B x 100 ][ ( )

...Equation 2

Forward/forward bid rateIf a dealer wants to sell a 3 x 6 FRA, then he thinks that interest rateswill fall in the period from 3 to 6 months forward. The 3 x 6 FRA canbe considered to be the result of borrowing for 3 months and lendingfor 6 as shown in the diagram below.

This means that the Forward/forward Bid rate is calculated inEquation 2 using:

RL = Far deposit BidRS = Near deposit Ask

6 months▼Spot ▼

Borrow Fwd/fwd BID3 months

▼

Lend

Forward/forward ask rateIf a dealer wants to buy a 3 x 6 FRA, then he thinks that interest rateswill rise in the period from 3 to 6 months forward. The 3 x 6 FRA canbe considered to be the result of lending for 3 months and borrowingfor 6 as shown in the diagram below.

This means that the Forward/forward Ask rate is calculated inEquation 2 using:

RL = Far deposit AskRS = Near deposit Bid

6 months▼Spot ▼

Lend Fwd/fwd ASK3 months

▼

Borrow


65

$ $

Derivative

Interest due fortime period, N

Interest due fortime period, n

Interest due fortime period, N – n( ) ( )x=

x= 1 + ][ ( ) r x n

B x 1001 + ][ ( ) R

N - n x N – n

B x 100

RN x N

B x 1001 + ][ ( )

Therefore:

...Equation 3

RN x N

B x 1001 + ][ ( )1 + ][ ( ) r x n

B x 100

– 1 x 360 x 100

N R

N - n =

If you need to calculate the effective annual interest rate for a strip ofFRAs the following equation can be used which is based on Equation 3.

L0 x 3

= Current LIBOR or reference rate

F3 x 6

, F6 x 9

, F9 x 12

= FRA rates for periods 3 x 6, 6 x 9

and 9 x 12 respectively

Effective annual rate, R =

]1 +[ ( ) L0 x 3

4 ]1 +[ ( ) F3 x 6

4 ]1 +[ ( ) F6 x 9

4 ]1 +[ ( ) F9 x 12

4x x x[ ]– 1

...Equation 4

In many cases FRA strips of contracts are used to hedge againstlonger term interest rate rises. A strip is simply a number ofconsecutive contracts. For example, a strip of four FRA contracts,1 x 3, 3 x 6, 6 x 9, 9 x 12 could be used to hedge for a 12 monthperiod. However, if a strip of FRAs are used what is the effective rateover the whole period as different contract rates are used for eachFRA?

Suppose the following strip of two FRAs spans the two period 0 to nand 0 to N. The rate of return for the time period n to N can becalculated using an equation based on the interest rates due for thetime periods.

Rate =R

N

▼

Timeperiod

0

FRA2FRA1

Timeperiod

n

Timeperiod

N

Rate =R

N - n

Rate =r

▼

Example 2XYZ Corporation now needs to protect interest rates for a six monthperiod beginning in 6 months time – a 6 x 12 forward position. TheXYZ Corporate Treasurer could use a 6 x 12 FRA. However, a strip oftwo 3-month FRAs, 6 x 9 and 9 x 12, offers the Treasurer theflexibility of reversing the hedge at the 9 month period if necessary.The strip also provides a market limit for a 6 x 12 FRA quote.

XYZ need to borrow $5,000,000 in 6 months time for a loan period of6 months, but the Treasurer thinks interest rates will rise in this time.The Treasurer investigates quotes from a number of banks offeringFRAs indexed on a 3-month LIBOR basis.

FRA Bank A Bank B

6 x 9 (91d) 6.21 – 6.15 6.23 – 6.18

9 x 12 (92d) 6.28 – 6.22 6.30 – 6.25


$ $

Derivative

66

The Treasurer accepts the bid FRA prices from Bank A as thecheaper and buys a strip of two FRAs – 6 x 9 plus 9 x 12. Thiseffectively locks in the interest rates for the 6-month borrowingperiod.

Rate =?

Timeperiod6 mths

FRA 9 x 12FRA 6 x 9

Timeperiod9 mths

Timeperiod

12 mths

Buy @6.28%

Buy @6.21%

6 x 12 month exposure of $5,000,000

▼

What is the effective FRA rate?

▼

The effective FRA rate for the strip is calculated using Equation 3.

][ ( ][ ( ) 6.28 x 92

360 x 100x= 1 + ) 6.21 x 91

360 x 1001 +

= 1.0157 x 1.01605

= 1.03200

Therefore R6 x 12 = (1.03200 – 1) x 360 x 100

183

= 6.2955 or 6.30% rounded up

■ Summary


❑ FRAs are OTC contracts used to hedge interest rate riskbased on a notional future loan or deposit

❑ Settlement payments are made at the beginning of thenotional loan or deposit period

❑ Rises and falls in future Money Market interest rates arecompensated by payments/receipts at the settlement date

❑ FRA contracts are firmly binding

❑ FRA contracts involve no transfer of principal. The onlycash payments made are those associated with settlementpayments

❑ Most FRA contracts use LIBOR as the reference rate

❑ FRA contracts are indicated using the convention of(Start month forward) x (End month forward). Forexample, 6 x 12 means the contract starts in 6 monthstime and ends in 12 months, therefore lasting 12 months

R9 x 12 x N – n

B x 100x= 1 + ][ ( ) R6 x 9 x n

B x 1001 + ][ ( ) R6 x 12 x N

B x 1001 + ][ ( )


67

$ $

Derivative

To see the Forward Rate Agreement Speed Guidetype in FRA/1 and press Enter. To display the MajorCurrency FRAs double-click in the <TOPFRA>field.


The following exercises using Reuters products and theRT may help your understanding of FRAs and how theyare used.

RT


$ $

Derivative

68

Exercise. Using the FRMW page in Money 3000 canbe useful as you can display Bid and Ask prices for anumber of currencies from different contributorssimultaneously. For example, you decide to look at

3 x 6 rates for DEM FRAs from 3 different contributors in orderto select the best rates for you for buying and selling. You look atthe rates and decide that those from HBEL are best. You nowdecide to check these rates and calculate the forward/forwardbid and ask prices from deposit rates you display in the MMMWpage.

3000From the 3-month and 6-month Bid and Ask deposit rates shownopposite calculate the forward/forward Bid and Ask rates. Assume 3-months is 90 days and 6-months is 180 days.

a) Forward/forward Bid rate

b) Forward/forward Ask rate


69

$ $

Derivative

■ End check

1. If you as a customer buy a FRA you are:

❑ a) Protecting against a rise in interest rates❑ b) Protecting against a fall in interest rates❑ c) Taking a cash delivery of principal from the counterparty❑ d) Making a cash delivery of principal to the counterparty

2. Today is the fixing date for a 1x4 FRA which you sold for 5.67%.LIBOR has been fixed at 6.00%. Which of the followingstatements is true?

❑ a) You pay the counterparty❑ b) The counterparty pays you❑ c) No payment takes place until later

3. Which of the following statements best describes why corporationsmay prefer to use FRAs rather than Interest Rate futures contractsto hedge?

❑ a) FRAs are more liquid❑ b) FRA prices are less volatile❑ c) FRAs are priced more competitively❑ d) FRAs are OTC and can be tailored

4. A Forward/forward rate is the direct result of:

❑ a) Market expectations of future interest rates❑ b) Prices quoted for exchange traded Interest Rate futures❑ c) Values derived from existing deposit rates❑ d) None of the above

5. Bank A sells Bank B a 3 x 6 USD FRA at a contract rate of 5.86%.On the settlement the LIBOR 3-month fixing rate is 5.75%. TheFRA contract details are as follows:

a) What is the cash settlement amount involved?b) Who receives payment?

Answer a)

Answer b)

FRA contract amt.: $50,000,000

Contract period: 90 days

Contract rate: 5.86% pa



$ $

Derivative

70

Bid = 2.9762

Answers to exercises

✔ or ✖


= (3.0625 x 180) – (3.125 x 90)

(180 – 90) x 1 + 3.125 x 90 ][ ( )360 x 100=

270.00

90.703125

Exercisea) Forward/forward bid rate = 2.976%

Use Equation 2 – for Bid use Far depo Bid and Near depo Ask

Interest

b) Forward/forward bid rate = 3.349%Use Equation 2 – for Ask use Far depo Ask and Near depo Bid

Interest=

(3.1875 x 180) – (3.00 x 90)

(180 – 90) x 1 + 3.00 x 90 ][ ( )360 x 100=

303.75

90.6750By inputting the correct details in the FRA you require you cancheck your calculations using the Model FRM page.

Ask = 3.3493

1. a) ❑

2. a) ❑

3. d) ❑

4. c)

5. a) $13,555.14 ❑

Use Equation 1b.Settlement =

=

b) Bank B pays Bank A ❑

(5.86 – 5.75) x 90 x 50,000,000

(360 x 100) + (5.75 x 90)

0.11 x 90 x 50,000,000

36000 + (517.5)



71

$ $

Derivative

■ What are they?

If you need an overview of futures derivatives or you needto remind yourself about derivatives in general, then youmay find it useful to refer to the Introduction to Derivativesworkbook, Section 2 at this stage.

Interest Rate futures are some of the most common futures contractstraded on exchanges. Their growth stems from the mid 1970s afterthe breakdown of the Bretton Woods Agreement in 1973. Theresulting floating exchange rates in currencies created much morevolatility in interest rates and the subsequent need to hedgeinvestments.

The Chicago Board of Trade (CBOT) introduced the first futurescontracts to hedge interest rate exposure in 1975 when it introducedcontracts on the US Government National Mortgage Associationcertificates – known as Ginnie Maes. These contracts are no longertraded but by 1977 CBOT has added contracts on T-Bonds and in1982 LIFFE started trading futures contracts on 3 month Sterlingtime deposits.

Interest Rate futures are essentially forward contracts in underlyingfixed coupon instruments such as bank deposits and governmentbonds, notes and bills. Short-term Interest Rate futures based onEurocurrencies are cash settled based on interest rates for the

Interest Rate futures are forward transactions withstandard contract sizes and maturity dates which aretraded on a formal exchange.

Short-term Interest Rate futures contracts are almostexclusively based on Eurocurrency deposits and are cashsettled based on an Exchange Delivery Settlement Price(EDSP) or the last price traded.

Long-term Interest Rate futures contracts are settledbased on government bonds or notes with a coupon andmaturity period specified by the exchange.

DerivativesSection 2

particular currency deposited outside the country of origin. Forexample, a 3-month Eurodollar Interest Rate future is settled basedon US Dollars deposited outside the US.

An exchange traded futures contract has the following characteristics:

❑ A standardised specification in terms of unit of trading,trading cycle of contract months, delivery days, quotation,minimum price movement etc

❑ The opportunity to trade the instrument and offset theoriginal contract with an equal and opposite trade. Very fewcontracts, less than 2%, reach maturity

❑ A public market in that prices for contracts are freelyavailable. Trading takes place open outcry on an exchangefloor and prices are published on exchange indicatorboards, in the financial press and by providers such asReuters.

❑ Once a trade has been made a Clearing house acts as thecounterparty to both sides of the trade. The contract is notdirectly between buyer and seller. The Clearing house takeson the credit risk should a counterparty default. This isimportant because it means anyone can have access to themarkets provided they have the required creditworthinessby the Clearing house – in this way large organisations haveno advantage over smaller organisations or investors.

��

▼

▼

Buyer Seller

▼

▼

Clearing house


$ $

Derivative

72

CBOT

Exchange contractsShort and long-term Interest Rate futures contracts are traded onexchanges worldwide. Some of the more important contracts aresummarised in the charts below.

Short-term Cash settled based on LIBOR

Three month Sterling (Short Sterling)Three month Eurodeutschemark (Euromark)Three month EuroliraThree month Euroswiss Franc (Euroswiss)Three month ECUThree month Eurodollar

Unit of trading

GBP 500,000DEM 1,000,000

ITL 1,000,000,000CHF 1,000,000ECU 1,000,000USD 1,000,000

Long-termGovernment Bonds

Long Gilt (UK)German – BundJapanese – JGBItalian – BTP

Nominal value

GBP 50,000DEM 250,000

JPY 100,000,000ITL 200,000,000

Maturity range years

10 - 158.5 - 107 - 11

8 - 10.5

Notionalcoupon, %

966

12

LIFFE

Short-term Cash settled based on interbank rates

Three month EurodollarOne month LIBOROne year T-BillsThree month EuromarkThree month Euroyen13-week US T-Bills(This contract is for physical delivery)

Unit of trading

USD 1,000,000USD 3,000,000USD 500,000

DEM 1,000,000JPY 100,000,000USD 1,000,000


US T-Bonds10 year US T-Notes

Nominal value

USD 100,000USD 100,000


At least 156.5 - 10

Notionalcoupon, %

88

CME


73

$ $

Derivative

Typical contract specificationsShort-termFutures contracts specifications vary from type to type and fromexchange to exchange. Have a look at the following 3-month LIFFE‘Short sterling’ contract details below.

LIFFE 3-month SterlingInterest Rate Future

£500,000

Mar, JunSept, Dec

First business dayafter the lasttrading day

11.00Third Wednesdayof delivery month

100 minus rate ofinterest

0.01

(£12.50)

07.15 – 16.02London time

16.27 – 17.57

Unit ofTrading

DeliveryMonths

Delivery Day

Last TradingDay

Quotation

Minimumpricemovement(Tick sizeand value)

Tradinghours

APT Tradinghours

This is the trading cycle ofcontract months

This is the standardcontract size

This is the day contract issettled

This is the last day andtime on which trading cantake place

The futures price is quotedaccording to the type offuture

This is the smallest amounta contract can changevalue and the ‘tick’ size

Exchange trading hours –open outcry

Computer-based tradingsystem hours

But what does it all mean?

This Interest Rate futures contract is for a notional amount of£500,000 – unit of trading – which is placed on a 3-month depositcommencing on the delivery day (maturity) of the contract, at aninterest rate which is implied in the futures price agreed at the timeof the trade.

Typically for financial futures there are 4 delivery months per year –March, June, September and December. It is also possible to havematurity dates out to several years but ‘far month’ contracts are muchless liquid than the ‘near months’. This means that it is not alwayspossible to get prices for ‘far months’.

Short-term futures are not quoted as an interest rate percentage.Instead they are quoted as:

100 minus the implied forward interest rate

ExampleA forward implied interest rate for a $1 million deposit is 5.55%.

The futures contract price would therefore be 100 – 5.55 = 94.45.

This convention for pricing short-term futures is based on the way T-Bills are quoted – at a discount from the face value of the bill.

The price movement of a futures contract is measured in ticks. Theminimum price movement for a contract is determined by theexchange. Depending on the contract, its value is expressed in termsof basis points – a basis point is one hundredth of one percent,0.01%. So one tick equals one basis point.


$ $

Derivative

74

This means that a tick has a specific value determined using thefollowing equation:

Tick = Unit oftrading

x xBasis points

100

Proportion of year overwhich contract runs

ExampleThe tick value for the 3-month LIFFE Short sterling contract is:

= £500,000 x 0.01

100x 1

4

= £12.50

On the last day of trading, if a futures position is still open, mostshort-term Interest Rate futures are cash settled against the EDSP.The exception is the 13-week US T-Bills contract which involvesphysical delivery of the instruments.

The EDSP depends on the exchange but typically involves acalculation of interest rates for the Eurocurrency deposit in question.For example, LIFFE use the British Banking Association InterestSettlement Rate (BBAISR) and the CME uses an average of a surveyof rates of the London interbank rates for Eurodollars, LIBOR andEuromark.

On the last day of trading the futures contract ceases to exist and theunderlying cash market instrument and futures prices are the same.It is the difference in contract and settlement prices that is paid incash – as the principal of these contracts is notional no delivery cantake place on expiry .

Long-termThe contract specifications for these Interest Rate futures are verysimilar to those for short-term instruments. The major difference isthat settlement is by physical delivery of bonds or notes with couponrates and maturity dates stipulated by the exchange.

Although some long-term futures for bonds have prices andminimum price movements quoted as hundredths of a basis point,UK Gilts and US T-Bonds are quoted as thirty-seconds of a percentagepoint.

ExampleA UK Long Gilt futures quoted at 111-23 means a price of 111 23/32.However there are indications that the market convention for UKGilts and US T-Bonds may be changed in the near future to that ofusing basis points.

Tick values are easy to calculate for long-term futures:

Tick = Unit of trading x minimum price movement

The contract details for CBOT T-Bonds are shown opposite.


75

$ $

Derivative

T-Bond with facevalue $100,000

Mar, JunSept, Dec

Last business dayof delivery month

7th business daypreceding lastbusiness day of month

Points and 32ndsof point

1/32 of a point

($31.25)

07.20 – 14.00Chicago time

14.30 – 16.6022.30 – 06.00

Chicago Board of TradeUS Treasury Bond futures

Unit ofTrading

DeliveryMonths

Delivery Day

Last TradingDay

Quotation

Minimumpricemovement(Tick sizeand value)

Tradinghours

Project ATrading hours

This is the trading cycle ofcontract months

This is the standardcontract size

This is the day contract issettled

This is the last day andtime on which trading cantake place

The futures price is quotedaccording to the type offuture

This is the smallest amounta contract can changevalue and the ‘tick’ size

Exchange trading hours –open outcry

Computer-based tradingsystem hours

Profit and loss on a futures contractThis is easy to calculate using the following method:

1. Determine the number of ticks the price has moved up or down.The number of ticks is the number of one-hundredths of thequotation price.

2. Multiply the number of ticks by the tick value and the number ofcontracts.

Profit/ loss = Number of ticks x Tick value x Number of contracts

ExampleTwo 3-month Short-sterling LIFFE contracts are bought when theinterest rate is 6.25%. The contracts are therefore priced at 100 –6.25 = 93.75.

At the delivery date the 3-month LIBOR stands at 6.10% whichrepresents a price of 100 – 6.10 = 93.90.

The contract has therefore gained in value and the number of ticksequals 93.90 – 93.75 = 15.

The profit on the contract = 15 x £12.50 x 2= £375.00


$ $

Derivative

76

Typical contract quotationsInterest rate futures quotations are available from the financial presssuch as the Financial Times and The Wall Street Journal and fromproducts such as Reuters 3000. The information appears in formatssimilar to those following.

LIFFE 3 month Sterling Futures £500,000 points of 100%

Open High Low SettleMar 93.74 93.76 93.74 93.75Jun 93.55 93.57 93.55 93.56Sep 93.35 93.37 93.33 93.35Dec 93.20 93.21 93.17 93.18

Reuters 3000 – LIFFE Short and Long-term Interest Rate futures

Financial press – Short-term Interest Rate futures

CBOT Treasury Bonds $100,000 points 32nds of 100%

Open High Low SettleMar 112-19 112-24 110-25 110-28Jun 112-03 112-13 110-09 110-13Sep 111-24 111-24 109-29 109-31Dec 110-16 110-16 109-17 109-17

Reuters 3000 – CBOT Short and Long-term Interest Rate futures

Financial press – Long-term Interest Rate futures


77

$ $

Derivative

■ Who uses Interest Rate futures?

Hedgers and speculatorsOriginally futures contracts were devised so that holdersof an asset could hedge or insure its price today forsometime in the future. Hedgers seek to transfer the risk

of future price fluctuations by selling future contracts whichguarantee them a future price for their asset. If the future cash priceof their asset falls then they have protected themselves. However, ifthe future cash price rises then they have lost the opportunity toprofit. Hedging offers some degree of certainty for future prices andtherefore allows market players to fix prices, interest rate payments orreceipts etc.

Hedgers are typically banks, multinational organisations,governments, bond dealers and fund managers.

Speculators are market players who take on the risk of a futurescontract for an appropriate price and the potential rewards.

The transfer of risk sought by hedgers is possible in the marketsbecause different market players have different strategies andinclude:

❑ Hedgers with opposite risks

❑ Hedgers already holding positions who need to offset theirpositions

❑ Speculators with market views on likely price changes whoprovide the futures markets with extra liquidity

As in any futures market place for commodities, hedgers can holdlong or short positions and in order to hedge their positions marketplayers need to take an opposite position to the ones they hold.

It is important to understand that the principle of hedging is tomaintain a neutral position. As prices in the cash market for the assetmove one way, the move is compensated by an equal and oppositemove in the futures’ price. You can imagine the situation similar tothe movement of the pans on a pair of scales.

Cash Futures

Going short futuresIf a market player holds, or intends to hold, an asset in the cashmarket, then he has a long position. The opposite position in thefutures markets means he must go short or sell futures.

A borrower, who intends to hold cash, needs to protect against thepossibility that spot prices fall with a corresponding rise in interestrates. A short hedge will therefore lock in a selling price.

Going long futuresIf a market player is short, or intends to go short, in the cash market,then the opposite position in the futures markets means he must golong or buy futures.

A lender, who intends to deposit cash, needs to protect against thepossibility that spot prices rise with a corresponding fall in interestrates. A long hedge will therefore lock in a selling price.


$ $

Derivative

78

Another way of considering market players using Interest Rate futurescontracts is to look at whether they are buyers or sellers of thecontracts.

Buyers of Interest Rate futures

❑ Agree to take delivery of the underlying instrument andtherefore go long.

❑ Are lenders and are hedging against any fall in interestrates. If interest rates do fall, then any losses in buying theunderlying in the future are offset by gains from the futurescontracts on delivery.

The diagrams below show how the losses in the underlyinginstrument are offset by gains in the futures market.

+

–

Prof

itL

oss

falling rising

Cash price

Underlying market

Net cash loss

Prof

itL

oss

falling rising

Futures price

Futures market

Net futures gain

As interest rates

Rise

Fall

So futures prices

Fall

Rise

Sellers of Interest Rate futures

❑ Agree to deliver the underlying instrument andtherefore go short.

❑ Are borrowers and are hedging against any rise in interestrates. If interest rates do rise, then any losses in selling theunderlying in the future are offset by gains from the futurescontracts on delivery.

The diagrams below show how the losses in the underlyinginstrument are offset by gains in the futures market.

In summary:

+

–

Prof

itL

oss

falling rising

Cash price

Underlying market

Net cash loss

Prof

itL

oss

fallingrising

Futures price

Futures market

Net futures gain

Short hedge

• Sell futures

• Protects against risein interest rates

• Locks in selling price

• Used by borrowers

Long hedge

• Buy futures

• Protects against fallin interest rates

• Locks in buying price

• Used by lenders


79

$ $

Derivative

Hedging and hedge ratioIn order to hedge a position it is necessary to match the futurescontracts as closely as possible with that for the underlyinginstrument in terms of maturity dates, amounts involved etc. Inpractice it is difficult to obtain the conditions for a perfect hedge!

The number of futures contracts required – the hedge ratio – issimply calculated from the equation:

Number of contracts required =

Sum to be hedged

Unit of trading

Number of futures

contracts per year

Actual number of days

Day basis x No. contracts/year

Number of

contracts required

Sum to be hedged

Unit of trading

xx

For most short-term Interest Rate futures this equation reduces to:

=

In the examples that follow the sums to be hedged have beenselected to match unit of trading amounts to simplify thecalculations.

ExampleIt is 12th June and a Corporate Treasurer has just borrowed £1million for a 3-month period at an interest rate of 6.0%. In 3-monthstime the loan will roll-over and the Treasurer is worried that interestrates will rise by then. The treasurer decides to hedge his position byselling 3-month LIFFE Short sterling futures at 93.50. But howmany?

Money markets

12th JuneFears of interest rate will rise from6%

30th AprilRoll over loan at 6.75%%

Extra cost0.75% on £1m for 3 months = £1875

Futures market

Sell 2 x Sept contracts at 93.50(implied interest rate of 6.5%)

Buy 2 x Sept contracts for 92.75(implied interest rate of 7.25%) to close position

Gain75 ticks x £12.50 x 2 = £1875

Short hedge – selling futuresA short hedge can be used by an investor needing to hedge againstprice falls resulting from rising interest rates. This type of hedge canalso be used to hedge a future loan to prevent higher borrowingcosts.

Number of

contracts required

£1,000,000

£500,000= = 2

It is 11th September and the loan is rolled over and interest rateshave risen to 6.75%. What is the result of the Treasurer’s hedge?

This perfect hedge is unlikely in practice. For example, the futuresgain is not paid as a single instalment but as daily margin paymentswhich are described later. Also the extra roll over loan interest wouldnot be payable until the maturity of the loan in 3 months time.


$ $

Derivative

80

50,000,000 31

5,000,000 30 x 12x 12 = 10.33x

So by selling the futures contracts the Corporate Treasurer hashedged the expected rise in interest rates. He has to borrow at amore expensive rate in the Money Markets but this is compensated bythe gain in buying the futures cheaper than they were sold originally.

The hedge would also have worked if rates had fallen. The CorporateTreasurer would have borrowed at a lower rate in the Money Marketsthus making a gain which would have been offset by a loss on thefutures because they would have risen in price from the original saleprice.

Long hedge – buying futuresA long hedge is typically used by lenders of cash market funds whoneed to fix an interest rate for a future date and are worried thatinterest rates might fall.

ExampleIt is 12th June and a Corporate Treasurer has USD funds to lend inJuly. The Treasurer is worried that rates may fall during June thusaffecting the interest he is likely to receive.

The Corporate Treasurer will have $50 million to lend and decides tohedge his position using CBOT 30-Day Fed Funds futures. The unitof trading is $5 million and the tick size is $41.67 per basis point.

Money markets

1st JulyDeposits $50 million at 4.80%

31st JulyReceive back $50 million plusinterest at 4.80% for 1 month.Interest = $206,666.66

Futures market

Buy 10 futures at 94.56

Sell 10 futures at 95.16

Gain on long position =60 ticks x $41.67 x 10 =$25,002.00

The perfect hedge requires a 5.44% return, but as only 10 contractscould be bought, this compares well with a cash market return onunhedged funds at 4.80%.

Number of contracts required =

This means that the Treasurer has to buy 10 contracts – a perfecthedge is not possible – and hold the futures until maturity or closeout prior to expiration.

Suppose the following:

30-Day Fed Funds futures price

Implied 30-Day interest rate

1st July

94.56

5.44%

31st July

95.16

4.84%

On 1st July the rates have fallen, as expected by the Treasurer to4.80%. What is the result of the Treasurer’s hedge?

Net gain on position = 206,666.66 + 25,002.00 = $231,668.66

Net % return = 231,668.66 x 360

50,000,000 31

= 0.0538

= 5.38%


81

$ $

Derivative

SpeculationSpeculators attempt to exploit price movements in the markets andthus provide additional liquidity for hedging activities. Speculators donot necessarily have a position and use their market knowledge toprofit.

ExampleA trader is expecting that the June balance of trade figures will bebetter than expected causing short-term interest rates to fall andtherefore futures prices to rise. Based on this view the trader buys one3-month June LIFFE Short sterling contract at 93.55. This implies a 3-month GBP interest rate of 6.45%.

The next day the trader is viewing the news on his RT and is provencorrect – interest rates have fallen by 0.5%. The trader therefore sellshis contract at the new market price of 94.05 and gains 50 ticks.

His profit is 50 x £12.50 x 1 = £625.00.

Suppose, however, that the trade figures had been worse thanexpected and interest rates had risen by 0.5%? The trader would haveclosed out the contract at 93.05 and made a loss of 50 ticks which is£625.00.

Relationship with OTC forward contractsAn interest rate future contract is in effect an exchangetraded 3-month Forward Rate Agreement (FRA). It is theequivalent of a FRA with margins.

FRAInterest

Ratefutures

+ margins

▼

The two instruments are compared in the table below.

Interest rate future

• Standard contractterms

• Exchange traded

• Margin required

• No credit risk asclearing house standsas counterparty

FRA

• Flexible

• OTC market

• No margin required

• Credit risk betweencounterparties

• No right of offset

• Terms of contract areconfidential

MMI:FRA

Futures

FRAs

Fall

Buy

Sell

To hedge aninterest rate ..

Rise

Sell

Buy

The chart below compares the relative ways in which the twoinstruments are used to hedge interest rate price movements.


$ $

Derivative

82

■ Interest Rate futures in the market place

1 2 3

4 5 6

7 8 9

0

This section deals with a number of important mattersconcerning Interest Rate futures which you will need tounderstand.

How an Interest Rate futures contract worksWhen a futures contract is agreed no payment is made. Instead bothparties are required to deposit a margin with the Clearing housewhich acts as the counterparty to both sides. The initial margin is onlya small percentage of the contract price and it is used to cover dailyprice movements of the futures’ price in relation to the agreed price.Each day the futures’ position is marked-to-market which means it isrevalued at the current market price. Any profits and losses are paidover daily. By marking-to-market and settling all positions daily theClearing house effectively rewrites all futures contracts at theprevailing market price.

If the initial margin is depleted then extra margin – variation margin– is required. If a profit is made the account will receive it and it maybe withdrawn. The system of maintaining the correct margin ensuresthat the loser can bear any losses and the winner is credited withgains.

Dealing on margin is an example of gearing or leverage. Gearingallows investors to make a larger investment than could otherwise beafforded. Small investments are used to generate large profits,however, losses can be correspondingly large! For example, a £1000investment in a futures contract is equivalent to buying a basicinvestment of £10,000 – 20,000.

As the expiry date of the contract approaches the futures price willequal the current instrument price and so the differential is not verylarge. This is why the vast majority, over 98%, of futures contracts areclosed out before the contract reaches the agreed expiry date.

The process is illustrated as follows:

��

▼

Buyer Seller

▼

Clearing house

On the contract dateThe Seller sells a contract to the Buyer and both deposit initialmargin with the Clearing house.

During the contractThe Seller’s and the Buyer’s profit and loss accounts are adjusteddaily.

initial marginpayment

initial marginpayment

��

▼

▼

Buyer Seller

▼

▼

Clearing house

variationmarginpayment



83

$ $

Derivative

On the delivery date or contract closureThe Seller’s and the Buyer’s profit and loss accounts are settled forthe last time.

��

▼

▼

Buyer Seller

▼

▼

Clearing house



Advantages and disadvantages of Interest Rate futuresThe following chart summarises the advantages and disadvantages ofInterest Rate futures:

Advantages

• Markets in the majorcontracts for Eurodollars,

US T-Bonds and UK Gilts arelarge and very liquid

• The use of margin paymentsallows highly leveragedpositions

• Contracts can be bought andsold without having to ownthe underlying

• Most contracts are offset andonly a very small percentageexpire resulting in delivery

Disadvantages

• Only a limited number ofcontracts available

• It can be difficult to hedgepositions exactly – matchingexact amounts and requireddates is not always easy

• When hedging long-termfutures, the price/yieldrelationship variescontinuously with time andtherefore the hedge ratiovaries continuously

• The mark-to-marketsettlement system can leadto large cash outflows foradverse price movements

• Trading is usuallyconcentrated in near monthcontracts

• Liquidity can be limited forfar month contracts


$ $

Derivative

84

Trading strategies for Interest Rate futuresThere are a number of strategies that traders adopt in order to hedgepositions which do not have ‘perfect’ matches in the futures markets.The simplest strategies used are:

❑ Futures strips

❑ Stacking futures

❑ Spread trading

Futures stripsThese are used to hedge interest rate exposures which span severalfutures expiry dates, or span dates which do not exactly matchfutures expiry dates.

The buyer of a September LIFFE Short sterling futures at 94.29effectively commits him or herself to lending a notional £500,000 for3 months commencing on the contract expiry rate of 5.71%. Theseller of the same contract commits him or herself to borrowing thenotional amount.

ExampleIt is early June and a Corporate Treasurer calls a bank to ask for theprice of a one year deposit loan for £5 million starting in September– a 3 x 15 forward price. The Treasurer is worried that rates will risein the next three months and wishes to hedge the current loaninterest rates. The period required for the hedge spans fourconsecutive, futures expiry dates and the Treasurer can sell a strip offour futures. The number of contracts required to sell ( borroweffectively) is 10 per contract – the unit of trading for the contract is£500,000.

Have a look at the prevailing futures prices that the Treasurer sellsthe contracts:

Sell 10 Sept contracts at 94.29 Implied rate 5.71%Sell 10 Dec contracts at 94.27 Implied rate 5.73%Sell 10 Mar contracts at 93.95 Implied rate 6.05%Sell 10 Jun contracts at 93.56 Implied rate 6.44%

Using a strip of futures has effectively locked in the interest rate forthe forward 12 month period but what is the rate. The average of thefour interest rates is 5.98% but unfortunately the calculation is notthat simple!

The general equation to calculate a forward-forward rate is givenbelow:

Sept SeptDec Mar June

Sell 10 Sell 10 Sell 10 Sell 10

Exposure

Futures strip

F a x b

(La x da) (Lb x db)

(Lb x db )

360 or 365

1

(db – da)x

1 + ][ ( )x

=

= Forward starting in a days and ending in b days

= Long period interest rate as a decimal

= Short period interest rate as a decimal

= Long period in days

= Short period in days

F a x b

La

Lb

da

db


85

$ $

Derivative

The rate is in fact a compound of the notional quarterly interest ratepayments given by the following equation:

Stacking futuresSuppose in the previous example that the September futures contractwas the only one available. There is still a risk that interest rate willrise over the next year but the Treasurer has only one contractavailable.

In such a situation a stack of futures are used. In this case 40contracts are used – 4 x 10 contracts for the four periods. Using thesame futures prices for selling and buying 40 September futures witha gain of 74 ticks results in a profit of 74 x £12.50 x 40 = £37,000.

F = Forward compound rateRn = Rate for period nn = Number of contracts in strip

][( ) R1

41 +1 – x( ) R2

41 + ( ) Rn

41 +x . . .F =

In this example the rate is 6.12%.

Suppose in September, the one year LIBOR is 6.75%. If the Treasurerhad accepted a quote of 6.12% then the loss covering the cash loanwould have been 5,000,000 x 0.0063 = £31,500.

However, if the Treasurer closes out 10 contracts for each period bybuying, then the gains are as follows. For each contract subtract thebuy from the previous sell price and to calculate the profit multiplythe number of ticks by £12.50 and by 10 for the number of contracts.

Buy 10 Sept contracts at 93.55 +74 ticks profit = £9,250Buy 10 Dec contracts at 93.45 +82 ticks profit = £10,250Buy 10 Mar contracts at 93.35 +60 ticks profit = £7,500Buy 10 June contracts at 93.26 +30 ticks profit = £3,750

Total gains = £30,750

The net loss to the Treasurer is therefore 31,500 – 30,750 = £750.

The hedge is not perfect but a large loss which could have resultedfrom not hedging the deposit has been averted.

The use of strips is restricted to prices for the far months required,but what happens if this is not the case?

Sept SeptDec Mar June

Sell 10

Exposure

Futures stack

Sell 10

Sell 10

Sell 10

The effectiveness of using a stack of futures depends on the yieldcurve of interest rates. If the yield curve retains its shape then thehedge using a stack is as effective as using a strip of futures. If theyield curve is positive and steepens, then the stack produces poorerresults. However, even though the stack may not be as effective asdesired it produces better results than no hedge at all!


$ $

Derivative

86

Spread tradingA spread trade is also known as a straddle. This method of tradinginvolves buying/selling futures contracts for one delivery month andsimultaneously selling/buying the same number of contracts for adifferent month.

If interest rates move, then one position hedges the other. The resultis a less risky position than an outright long or short position.

Basis and Basis riskCash futures basis is a reflection of the net cost of carry for a cashposition to expiry date of the futures contract. The relationships areshown here:

Futures price = Cash price + Net cost of carry

Basis = Cash price – Futures price

For futures contracts basis is also a term used to describe thedifference between the forward price of a gap in the underlying cashmarkets, for example, 3 x 15, and the implied forward price in therelevant futures contract. Basis risk describes how these prices vary orthe extent to which risk changes. The extent of this basis riskdetermines the effectiveness of the hedge.

When dates of the underlying gap matches dates implied in relevantfutures contracts, basis risk can be small.

Where strips are used, mismatches in dates or underlying assets arenot directly priced against Money Markets, then basis risk can beconsiderable.

Market players need to monitor basis and basis risk to hedge futuresto maximise profitability. It is also important to remember thatfutures are marked-to-market daily which means that the underlyingMoney Market exposure being hedged must be revalued daily.


87

$ $

Derivative

■ Summary


❑ An Interest Rate future is an exchange traded forwardtransaction with a standard contract size and maturitydates

❑ Short-term futures are mostly based on Eurocurrenciesand are cash settled against an Exchange DeliverySettlement Price

❑ Long-term futures are settled by physical delivery of theunderlying government bonds or notes

❑ Hedgers who are lenders, buy futures or go long, toprotect against any fall in interest rates

❑ Hedgers who are borrowers, sell futures or go short, toprotect against any rise in interest rates

❑ A Clearing house acts as counterparty to both buyers andsellers of a futures contract which is marked-to-marketdaily

Your notes


$ $

Derivative

88

To view the Speed Guide for Global Futures andOptions Exchanges type in FUTURES and pressEnter. Select the field for the country you areinterested in – in this case double-click in the

<GB/FUTEX1> field. From the list of exchanges select theexchange of interest – double-click in the <LIF/FUTEX1> field.From this page you can now select a chain of prices for aparticular contract and the contract specification if you requirethis. The screens below show information for the LIFFE 3-monthShort Sterling contract.


The following exercises using Reuters products and theRT may help your understanding of Interest Rate futuresand how they are used.

RT


89

$ $

DerivativeYou may also find the Exchange Traded InterestRate Futures Speed Guide useful. These pages listall the contracts and easy access to chains of prices.Type in FUT/IR1 and press Enter. Use the F12 and

F11 keys to page up and down respectively.

RT The Futures folder, IR Watch page, IFW, is usefulfor any particular currency to compare short andlong-term futures contracts. In the Contract 1 and 2fields enter the details you require. In the example

here LIFFE Short sterling and Long Gilt information is displayed.

3000


$ $

Derivative

90

The IFW page can also be used to display one of themost important futures contracts – the IMM 3-month Eurodollar contract. The example hereshows details for the IMM 3-month Eurodollar

contracts and the long-term CBOT US T-Bonds contracts.

3000 Finally the IFW page can be used to display detailsof similar futures contracts offered by differentexchanges. In the example here you can compareprices of Euroyen contracts from LIFFE and SIMEX.

3000


91

$ $

Derivative

■ End check

1. Which of the following interest rates is implied for a LIFFE 3-month Short sterling futures contract with a price of 93.18?

❑ a) 5.82%❑ b) 6.72%❑ c) 6.82%❑ d) 7.82%

2. If you place an order for a futures contract, when will you berequired to pay initial margin?

❑ a) At expiry of the contract❑ b) Only if you buy a contract❑ c) At the time of trading the contract❑ d) Only if you sell a contract

3. When trading in futures, credit risk lies with which of thefollowing?

❑ a) The exchange Clearing house❑ b) The broker who takes your order❑ c) The counterparty with whom the trade is made❑ d) The pit trader placing your order

4. Consider the following CME Eurodollar futures prices.Mar 9378 Jun 9374 Sep 9370 Dec 9366

Which one of the following statements is true?

❑ a) The USD yield curve is inverted❑ b) The USD yield curve is positive❑ c) A weak USD on foreign exchanges is expected❑ d) None of the above

5. A trader at XYZ Bank thinks that trade figures will be better thanexpected resulting in a short-term interest rate fall. He buys 5June LIFFE 3-month Short sterling contracts at 93.72. Thecontract’s minimum price movement is 0.01 and the tick value is£12.50.

a) What is the implied interest rate for the contract?b) If the trader is correct and interest rates fall and he sells the

contract at 93.17, how much profit does the dealer make?c) If the trader is wrong and he has to close the contract at 94.03,

what is his loss?

Answer a)

Answer b)

Answer c)


$ $

Derivative

92

Your notes

1. c) ❑

2. c) ❑

3. a) ❑

4. b) ❑

5. a) 6.28% ❑Implied interest rate = 100 – 93.72

= 6.28

b) £3437.50 ❑Contract moves 93.72 – 93.17 = 0.55 = 55 ticksTherefore profit = 55 x £12.50 x 5 = £3437.50

c) £1937.50 ❑Contract moves 94.03 – 93.72 = 0.55 = 31 ticksTherefore profit = 31 x £12.50 x 5 = £1937.50


✔ or ✖



93

$ $

Derivative

■ What is it?

If you need an overview of swap derivatives or you need toremind yourself about derivatives in general, then youmay find it useful to refer to the Introduction to Derivativesworkbook, Section 4 at this stage.

IRSs are the most important of the OTC swap derivatives currentlytraded in the global markets. An IRS is in effect an agreement whichallows both parties access to better interest rates than they wouldnormally receive in the markets.

In other words Party A and Party B both borrow the same amount, atthe best interest rates they can and then swap the interest ratepayments to the benefit of both parties. The cost of borrowing forboth parties is reduced without altering the underlying principalloans. The interest rates bases for the loans are therefore separatedfrom the underlying instruments.

An Interest Rate Swap is an agreement betweencounterparties in which each party agrees to make aseries of payments to the other on agreed future datesuntil maturity of the agreement. Each party’s interestpayments are calculated using different formulas byapplying the agreement terms to the notional principalamount of the swap.

Fixed rate interest payments

��

▼

▼

Party A Party B

Floating rate interest payments


The growth of IRSs can be traced to the early 1980s. But why havethese long term OTC derivatives become so important? IRSs arecharacterised by the following:

❑ The interest amounts for both sides of the agreement arecalculated from the same notional principal amount. Thismeans that there is no physical exchange of the principal.Therefore the risk involved in the swap is reduced to that ofassessing the credit risk that the other side may default ontheir interest rate payments.

❑ The two rates of interest are calculated for the samecurrency.

❑ The interest payments between both parties are usuallynetted so it is only the difference in payments which is paidto one side or the other. It is for this reason that IRSs aresometimes known as contracts for difference.

The OTC nature of IRSs means that their terms and conditions canbe very flexible. However, in practice, most agreements are for plainvanilla – fixed-for-floating – swaps. One side pays a fixed rate whilstthe other pays a floating rate – the situation illustrated in the originaldiagram opposite.

Floating-for-floating swaps are available but terms and conditionsinvolved with these can be quite complex.


$ $

Derivative

94

Although OTC agreements are customised for individual customerrequirements, both the British Bankers Association (BBA) and theInternational Swaps and Derivatives Association (ISDA) issuestandard terms and conditions relating to a range of swap derivatives.Once an agreement is made, most confirmation notes include therelevant information. For example, a plain vanilla IRS confirmationnote typically includes:

❑ Effective dateThis is the date of the swap when interest on both sidesstarts to accrue. For plain vanilla swaps this dateis taken as spot and LIBOR is fixed on the tradedate. These are the same conventions as usedfor Money Market deposits.

❑ Termination dateThis is the end date of the contract – the date of the finaldifference in interest payments.

❑ Notional amountThis is the amount used for interest rate calculations onboth sides.

❑ Fixed rate payor/receiverAs it could be misleading to refer to buying or selling swaps,it is usual to refer to the party who pays or receives the fixedrate.

❑ Floating rate payor/receiverIf the fixed rate receiver has been specified, then byimplication this side must be also the floating rate payerand vice versa. In many cases swap traders only specify whatis happening on the fixed side.

❑ Interest rate calculationsThis includes all the necessary details relating to:• Reference interest rate, for example, LIBOR• Payment periods and dates• Day count conventions

❑ Arrangement fees

MMI:DEP

Confirmation

Date: July 1, 1997To: OkiBankAttention: Swaps Group LeaderFrom: MegaBank

We are pleased to confirm our mutually binding agreement to enter into a Rate Swap Transaction with you in accordance with our telephone conversation with Mr. Deal on July 1, 1997, pursuant to the Master Interest Rate Exchange Agreement between us dated as of July 1, 1997.

OkiBank Rate Swap Transaction Reference Number 00000

Effective Date: July 1, 1997Termination Date: July 1, 2002

Notional Amount $50,000,000

Fixed Rate Payor: OkiBankFloating Rate Payor: MegaBank

MegaBank Calculation Periods for Payments:First period: Effective Date to but excluding January 5, 1998.Last period and End Dates: Each July 1 and January 1 after the first Period End Date,

subject to the Modified Following Banking Day convention, and finally the Termination Date.

OkiBank Calculation Periods for Payments:First period: Effective Date to but excluding July 1, 1998.Last period and End Dates: Each July 1 after the first Period End Date, subject to the

Modified Following Banking Day convention, and finally the Termination Date.

Payment Dates: Each party date on its own Period End DatesFixed Rate: x percent per annum

Fixed Rate Day Count Fraction: 30/360

Floating Rate Option: LIBORDesignated maturity: six monthsFloating Rate Day Count Fraction: Actual/360Reset Dates: First day of each MegaBank Calculation Period

Office or branch through which we are acting: Principal Office in New YorkOffice or branch through which you are acting: Principal Office in New York

Arrangement Fee: None

Documentation: The Master Interest Rate Exchange dated as a July 1, 1997 between OkiBank and MegaBank as modified by this confirmation.

Please confirm to us that the terms set forth herein accurately reflect our Rate Swap Transaction with you by signing a copy of this Confirmation and sending it back promptly by hand or by facsimile transmission. Please notify us immediately if you believe there is an error in this Confirmation.

Confirmed:

MegaBank OkiBank

By By

Title: Title:

An example of a typical Fixed/Floating Swap Confirmation note based onSajitas Das, Swaps, IFR 1987


95

$ $

Derivative

IRSs are the most important of the swap derivatives both in terms ofthe face value of OTC contracts not yet settled – the notionaloutstanding values, and in terms of the average daily turnover. Thefollowing statistics are taken from the BIS Report 1995: Central BankSurvey of Foreign Exchange and Derivatives Market Activity.

Outstanding notionalUSD billions

18,283

1,957

Average daily turnoverUSD billions

62

7

Derivative

Interest Rate Swap

Currency swap

The latest data from the ISDA Summary of Market Survey Statistics: 1995Year End confirm the dominance of the IRS markets as the chartbelow shows.

The ISDA data also shows that IRSs involving the USD dominate themarkets. The chart below indicates the top five currencies bypercentage market share based on the USD equivalent of notionalprincipal outstanding.

Currency

USDJPY

DEMFRFGBP

Other

Total

% Market

34.1222.6111.239.526.6715.85

100.00

USD billionequivalent

4,371.72,895.91,438.91,219.9 854.02030.6

12,811.0

USD

JPY

DEMFRF

GBP

Other

Source: ISDA

Source: ISDA

InterestRate Swaps

Interestrate options

Currencyswaps

12,811

3,704

1,197

15

12

9

6

3

0

USD

Equ

ival

ent,

Bill

ion

s

Notional principal outstandings


$ $

Derivative

96

■ Who uses IRSs?

Banks and corporationsThe ISDA data below shows that the market players usingIRSs the most are banks and multinational corporations.

Market player

CorporationsBanksInstitutional investorsGovernmentOther

Total

% of users based onyear end outstandings

2453797

100

IRSs are used increasingly by these market players for two mainreasons:

❑ To hedge exposure on interest rates

❑ To speculate in the swaps markets in order to make a profitfrom offsetting fixed/floating rate transactions

IRSs also offer the following benefits to corporations and banks:

❑ Counterparties are able to convert underlying interest ratesfrom fixed to floating and vice versa over a long termperiod

❑ Usually there are cost savings to both sides

❑ IRSs provide access to markets not normally available to themarket players, for example, for reasons relating to creditrating

It is this access to different markets which in effect provides creditarbitrage in the markets. The difference in organisations‘ creditratings can result in considerable differences in yield gaps on fixedrate debt such as bonds and floating rates paid on loans. Many bondissues are swap driven because issuers can take advantageof IRSs to swap the interest payments on the funds raisedinto a different rate basis. Often these transactions alsoinvolve a Currency swap which effectively converts adomestic loan into one for a foreign currency.

Organisations with good credit ratings usually find it easier to borrowat fixed rates, whilst those with lower ratings tend to get their bestterms on a floating rate basis.

Have a look at the following example to see how a plain vanilla IRSworks between the XYZ and AYZ Corporations. The original lendersof the loans on both sides need not even know that thecounterparties have entered into a swap agreement.

Example – a plain vanilla IRSConsider the following situation:

XYZ is a multinational corporation with a creditrating of AAA. XYZ needs to borrow $50 millionsfor 5 years. XYZ can borrow at a low fixed rate butwould prefer to take advantage of a floating rate

basis loan. XYZ would like to take advantage of floating rates in orderto maximise any interest rate gaps.

AYZ is a corporation with a lower credit rating ofBBB who also need to raise $50 millions for 5years. Because of AYZ‘s lower credit ratingborrowing on a floating rate basis or issuing a

bond with a high value coupon is easier than obtaining a fixed rateloan. AYZ would prefer a fixed rate loan in order to predict futureinterest rate payments.

FXI:CSP


97

$ $

DerivativeXYZ can borrow

10.00%

LIBOR

Fixed

AYZ can borrow

12.00%

LIBOR + 1%

Floating

Rates

Fixed @

Floating @

Required basis

In order to obtain the type of loan both corporations require theyenter into a swap agreement. Both corporations need to assess therisks involved if the other side defaults on payments – if this doeshappen then the party who does not receive an interest payment stillhas to pay the interest due on the underlying loan.

This is how the IRS works...

❶ XYZ borrows at a fixed rate of 10%

❷ AYZ borrows at a floating rate of LIBOR + 1%

❸ XYZ and AYZ enter into an IRS agreement for a notionalprincipal amount of $50 millions with interest payments tobe exchanged for a 5 year period where:

• XYZ make floating rate payments of LIBOR + 1% to AYZ• AYZ make fixed rate payments of 11.75% to XYZAYZ pays this higher fixed rate to XYZ to compensate thiscorporation as it has the higher credit rating

The chart below summarises both corporation’s position.

XYZ AYZ

11.75%

LIBOR + 1%

Pays fixed rate of10% to lender

Pays floating rate of LIBOR + 1% tolender

The chart below shows how both sides benefit from the swap.

XYZ

LIBOR + 1% + 10%

11.75%

LIBOR + 0.75%

LIBOR

0.75%

AYZ

11.75% + LIBOR + 1%

LIBOR + 1%

11.75%

12.00%

0.25%

Pays out

Receives in

Payments =

Without swap

Savings


$ $

Derivative

98

Another way of considering the swap is as follows:

❑ Without the swap both XYZ and AYZ pay a total of12.00% + LIBOR in interest rate charges

❑ With the swap both parties pay a total of 11.00% + LIBOR(10.00% + LIBOR + 1%) in charges

Thus using the swap there is a net saving of 1.00% which in this caseis split 0.75%/0.25% in favour of XYZ which is the organisation withthe better credit rating.

Originally swaps were arranged directly between counterparties withbanks merely acting as agents for both sides. Now many banks act asintermediaries and make a two-way market in swaps by taking oneside of the transaction.

Market-makersMost IRS agreements now involve a market-maker and two separateclients who wish to enter a swap, but not necessarily with each other.For example, it may be that the perceived credit risks involved in adirect swap agreement are not acceptable to one or both parties. Byacting as a two-way market-maker a bank acts as an intermediarycreating a double swap in which both parties are effectivelyguaranteed interest payments will take place.

Fixed rate

��

▼

▼Party A Party B

Floating rate

Fixed rate

▼

▼

Floating rate

Market-maker

Of course, the market-maker does not enter into these swaps for noreward. The intermediary is paid a fee which is either based on theprincipal notional amount involved, a spread between the two-wayprices quoted for swap repayments – the swap rate, or both.

In the US and to a lesser extent in the UK, swap rates are quoted overthe yield on a Treasury note with comparable maturity.

For example, a market-maker may quote ‘70/75 over’ for a swapbased on a 5-year T-Bond which has a yield of 8.00%. This means themarket-maker pays at a rate of 8.70% and receives at a rate of 8.75%.

Have a look at the following example to see how a double swapworks...


99

$ $

Derivative

Example – a double swapConsider the following situation:

A US swap market-maker, BigBank, are quoting afixed rate of 70/75 over for a 5-year period againsta floating rate of LIBOR flat.

XYZ is a Money Markets fund which has invested infloating rate assets which are yielding, on average,LIBOR + 0.2%. XYZ believe that LIBOR will fall sothey would prefer fixed rate interest payments.XYZ enter into a swap with BigBank to receive a

fixed rate of 8.70% against paying a floating rate of LIBOR.

AYZ is a corporation that can either borrow at afixed rate of 10% or issue a Floating Rate Note(FRN) with a floating rate repayment of LIBOR +1%. AYZ would also prefer fixed rate interestpayments for their loan. AYZ also enter into an IRS

with BigBank but AYZ pay 8.75% against receiving LIBOR.

XYZ AYZBigBank

LIBOR

8.70%

LIBOR

8.75%

8.70/8.75

LIBOR + 0.2%

Floating

LIBOR + 1%

Floating

The chart below shows how both XYZ and AYZ effectively turn theirinterest rate payments/receipts into fixed rates and the savings AYZmakes.

XYZ

LIBOR

LIBOR + 0.2% + 8.70%

8.90%

–

–

Fixed

AYZ

LIBOR + 1% + 8.75%

LIBOR

9.75%

10.00%

0.25%

Fixed

Pays out

Receives in

Payments =

Without swap

Savings

Loan basis


$ $

Derivative

100

The convention of quoting a swap rate as described separates thecredit risk element from the general interest rate in the market.However not all currencies have well developed government Treasuryinstruments across a range of maturity dates. In these cases swapdealers will quote all-in prices as a total rate.

Are IRSs as simple as has been described. Well, in principle theanswer is yes, but in practice there are a number of issues to bereconciled if you are trying to compare swap rates. In other words areyou comparing like-with-like?

Differences between swap rates can arise based on the following:

❑ Quotation terms for fixed and floating rates

❑ The underlying instruments used to calculate swap rates

❑ The frequency of interest rate payments

❑ Day count bases used to calculate interest rate payments

These issues are all discussed in the next section.

If you were asked to explain the mechanics of anIRS to a colleague would be able to do it?

Your notes


101

$ $

Derivative

■ IRSs in the market place

1 2 3

4 5 6

7 8 9

0

This section deals with a number of important mattersconcerning IRSs which you will need to understand:

❑ Swap differences

❑ Swap spreads

❑ Swap valuations

❑ Swap structures

Swap differencesThe four main types of difference were mentioned at the end of thelast section.

Quotation termsWithin the US markets in particular there are a number of differentways interest payments can be calculated for fixed and floating ratestogether with a number of different ways payment schedules can bestipulated. Different swaps may use a combination of any of thefollowing terms

Fixed rate

• Absolute level• Spread over

Treasury instrument

• Quarterly• Semi-annually• Annually

• Eurobond• T-Bond• Money Market

Instrument

Floating rate

• Any LIBOR• Prime rate• CD, CP or T-Bill

• Periodic• Irregular

• Bond• Money Market

Instrument

Terms

Rate quotation

Paymentschedule

Basis

Underlying instrumentsThe instruments used to calculate swap rates for different currenciesvary. For example, USD swaps are usually quoted as a spread over theappropriate Treasury instrument which have semi-annual coupons;DEM swaps are quoted on an annual Eurobond basis.

The chart below indicates the various instruments used for the majorcurrencies together with the Day count method used for the interestpayment calculations.

Quoted as...

Spread over T-BondFixed EurobondFixed EurobondFixed EurobondSpread over GiltFixed Government Bond

Currency

USDDEMCHFFRFGBPJPY

Coupon

Semi-annualAnnualAnnualAnnualSemi-annualSemi-annual

Day count

Actl/Actl30/36030/36030/360

Actl/365Actl/365

Frequency of interest paymentsIn order to compare swap rates fairly you may need to convert annualpayments into semi-annual or vice versa.

The chart below indicates the equations to use to convert yields orswap rates as appropriate.

From ➟

Semi-annual

Annual

To ➟

Annual

Semi-annual

Use ➟

RS = ][])[( RS

2RA = 1 + – 1

2

RA = Annual rate % ÷ 100RS = Semi-annual rate % ÷ 100

2 x (1 + RA ) – 1


$ $

Derivative

102

Day count basesYou may also need to convert swap rates depending on the day countbasis used to calculate interest payments in order to compare like-with-like or value swaps.

The chart below gives the various methods of converting differentday counts.

From ➟

30/360 orActual/365

Actual/360

Actual/365

30/360

To ➟

Actual/360

30/360 orActual/365

30/360

Actual/365

Use ➟

No adjustment

No adjustment

Yield x 360

365

Yield x 365

360

Swap spreadsInterest rate trends cause variations in swap spreads over the yieldcurves for Government benchmark instruments.

When interest rates are expected to fall there are many fixed rateissuers wanting to swap into paying floating and receiving fixed, sospreads narrow.

When interest rates are expected to rise there are plenty ofborrowers wanting to swap into fixed but not many willing to receiveit, so spreads widen.

Another factor affecting swap spreads is credit risk. In a swap themarket player and the market-maker take on each other’s risk. Ifeither party fail to honour payment commitments, then the otherparty has an unwanted interest rate exposure.

For IRSs the net difference in fixed/floating payments is made, sothe risk of loss is based to some extent on an estimate of thevolatility of the future floating rate basis, for example, LIBOR.


103

$ $

Derivative

Swap valuationConsider a plain vanilla IRS in which XYZ Corporation borrow $100millions for 5 years at a floating rate but enter into an IRS agreementwith AYZ Bank to make fixed rate payments at 9.00% every 6 months.In return the swap dealer, AYZ, will pay a floating rate of LIBOR every6 months.

XYZ AYZ

9.00% Fixed

LIBOR Floating

Both payments aremade every 6 months

The spot rate for the transaction is 1st June so the first payment isdue on 1st December. The amount of interest due on the 1stDecember is already known on the 1st June. How can this be thecase? The answer is that LIBOR for the first payment is fixed on the1st June as the floating rate to be paid in 6 months time. In a similarmanner the 1st December LIBOR fixing determines the rate to bepaid for the second payment on the following 1st June and so onuntil the final payment in 5 years.

Spot Payment 1

1st June

LIBORfixed

Use LIBORfrom

1st June

LIBORfixed

1st June 1st Dec.

Netpayment

made

➝

➝

Payment 2

Use LIBORfrom

1st Dec.

LIBORfixed

1st June

Netpayment

made

➝

➝

The interest payments are netted between XYZ and AYZ based on thefollowing calculation:

LIBOR – 9 x $100 millions x No. of days in 6 month period

360 x 100

Depending on the value, either XYZ or AYZ receive the net payment.

At the start of the plain vanilla swap the derivative has no value toeither party. The interest rates that have been agreed for both sidesare determined so that the present value – the value the swap willhave at a future date – of the fixed side equals the present value ofthe floating side taking into account the conditions of the agreement.

If the terms of the agreement remain constant then neither side gainor lose at the expense of the other.

However, suppose interest rates rise and LIBOR increases. In this caseXYZ will gain at the expense of AYZ because XYZ pays a fixed rateand receives a floating rate which has just increased. So the swap nowhas a positive value to XYZ which can be considered to be an asset.The actual value of the asset can be calculated from the difference inpresent values. Unfortunately in the case of AYZ the swap has anegative value and is considered to be a liability.

There are two basic ways that swaps can be valued:

❑ Pricing from swap curve

❑ Pricing from the spot curve

Using the spot curve method produces a more accurate figure thanthe swap curve method, but the calculations involved can be quitecomplex. Both methods of pricing involve calculations for bondswhich are dealt with in more detail in the Debt Instruments workbook.Why Debt Market instruments? Read on...


$ $

Derivative

104

Pricing from the swap curveYield curves are an essential part of valuing future cash flows andcalculating forward interest rates. Plain vanilla swap rates are pricedfrom benchmark bond yield prices as has already been mentioned.The benchmark Yield To Maturity (YTM) curves are used for pricingover a range of maturities.

In terms of valuing a fixed-for-floating swap the transaction can bethought of as a series of coupon payments from an imaginary straightbond on the fixed side netted against a series of payments from animaginary or synthetic Floating Rate Note (FRN) on the floating side.

Can you see how this works?

This is taken from page SMWMfor a DEM swap

9.30%

LIBOR?

9.30%

LIBOR?

Fixed

Floating

Example – Fixed side – Straight bond: Floating side – FRNSuppose a plain vanilla swap has been arranged between XYZCorporation and AYZ Bank for a $100 millions notional principalamount for a 3 year period. On the fixed side the payments are9.30% on an annual basis; on the floating side the payments are 12months LIBOR.

The cash flows over the 3 year period would look something likethose shown in the chart below.

Payment 1

9.30%

LIBOR?

Payments equivalent to coupons from a straight bond

Payment 1 Payment 3Payment 2

Payments equivalent to those from a Floating Rate Note

A plain vanilla swap can therefore be valued as follows:

Notional straight bond – Notional floating instrument present value present value


105

$ $

Derivative

XYZ and AYZ enter into the swap on the stated conditions. On thespot date LIBOR is fixed at 7.50% for the first payment. As has beenmentioned the swap has no value at the start of the agreement. Onthe first payment date the 3 year swap rate is now quoted at 9.00% onthe fixed side and 12 months LIBOR is fixed at 7.79%. What is thevalue of the swap now? Is the swap an asset or a liability to the receiverof the fixed side?

What is the value now of the swap that matures in the future? Thepresent value of the fixed side can be calculated using the generalstraight bond valuation equation. For a bond with an annual couponthis is Equation 1.

Present Value (PV) =C

1 + R 2

C

(1 + R)+ + ...+

(C + 100)

(1 + R)n

Where: C = Coupon rateR = Discount or swap rate as a decimaln = Number of years to maturity

...Equation 1

In this example then: C = 9.30%; R = 0.090; n = 3

PV =

= $100.7594 million

+ +9.30

1.09

9.30

(1.09)

109.30

(1.09)32

The present value for the floating side can be calculated using themore direct relationship between the present and future value of aninstrument, Equation 2.

PV =

...Equation 2

PV =

Principal + Interest due

(1 + R)

Future Value

(1 + R)

=

Where: R = Discount or LIBOR rateas a decimal

In this example then: Principal = 100 millions; Interest = 7.50;R = 0.0779. Because the floating rate is based on Actual/360 thevalues used need to be adjusted to a 365 day year.

1 + )(0.0779 x 365

360

])[ (7.50 x 365

360100 +

= $99.7257 millions

The net value of the swap is therefore $1.03 millions in favour of thefixed side. This is because the swap rate quoted by the bank at theend of the first payment is less than the coupon rate of 9.30% on theposition. The floating side has lost value because LIBOR hasincreased.


$ $

Derivative

106

Treating the value of a swap as the difference between a straight bondand a floating rate instrument gives rise to market-makers hedging orwarehousing a swap position by temporarily buying or selling theunderlying bond.

The payer of the fixed side buys the underlying which can then besold to offset the position if the swap rates fall.

The receiver of the fixed side sells the underlying to offset any lossesif swap rates rise.

The calculations here are quite complicated and time consuming toperform. In practice, traders will often use a graphical representationto assess the relationship of the swap with a benchmark instrument ofthe same maturity. The graphical representation used is the spotcurve or Zero Coupon yield curve.

Pricing from the spot curveThe Yield To Maturity (YTM) curve is simply a graph of YTM valuesof bonds against maturity period. Unfortunately this is a simplisticview of yields and it is better to use a graph of spot rate againstmaturity period. The spot rate is a measure of the YTM on aninstrument at any moment in time which takes into account a varietyof market factors. A graph of spot rate against maturity is known as aspot curve. It is also known as a Zero Coupon yield curve because thespot rate for an instrument is equivalent to the yield on aninstrument which has no coupon repayment – zero coupon. Thismeans that spot rates for a series of instruments with zero couponsfor a range of maturity periods can be compared directly.

The curves represent the perceived relationship between the returnon an instrument and its maturity – usually measured in years.Depending on the shape of the curve it is described as either:

❑ Positive

❑ Negative or inverse

Positive yield curveIn this case the shorter term interest rates are lower than the longerterm rates. This is usually the case – the longer the period of theinvestment the higher the yield paid. If an interest rate rise isexpected, then investors will move their assets into long terminstruments which produces a fall in short term rates and an increasein long term rates.

Negative or inverse curveWhen short term rates fall investors move their investments intolonger term instruments to lock in a higher rate of return. Thisincrease in supply of long term funds causes the long term rates tofall.


107

$ $

Derivative

The shapes of ‘theoretical’ yield curves are shown below – in practicethey may not appear so clear!

Yield curves are used to identify anomalies between instruments ofsimilar credit standing, for example, an IRS and a T-Bond of similarmaturity.

The following chart may help in assessing the value of an instrumentwhen compared to its spot curve.

Instrument curve

Above spot

Below spot

Instrument value

Cheap

Expensive

Maturity

Yiel

d

Positive yield curve

Maturity

Yiel

d

Negative or inverse yield curve

How does the spot curve help in pricing a swap? A more accurate wayof considering an IRS is to consider the instrument as a series of fixedcash flows on one side combined with a series of notionalfloating cash flows on the other which are considered as astrip of FRAs or futures contracts.

In other words the spot curve rates are used to calculate,in advance, the net settlement amount of each futureinterest payment date.

The swap rate is effectively an average rate for a strip ofFRAs or futures contracts.

The calculations are quite complex and in the previous example ifthe swap were valued using this more accurate method, then the netvalue in favour of the fixed side is $1.043 millions.

MMI:FRA

MMI:FUT


$ $

Derivative

108

Swap structuresPlain vanilla swaps usually have very narrow spreads – typically only 5to 10 basis points. This means that the profit margins for dealers aresmall. In order to widen their profit margins and to cater for morecomplicated client requirements, dealers can structure morecomplex IRSs based on the following basic types:

❑ Plain vanilla swap

❑ Forward start swapThis is a fixed-for-floating IRS in which the accrual date ofthe swap for the first interest period starts sometime afterthe spot date. This type of swap can still be considered as astrip of FRAs on the floating side except the near FRAs havebeen removed. Forward start swaps are often used to hedgeagainst forward interest rate movements.

❑ SwaptionThis is similar to a forward start swap to which has beenadded the option whether or not to start the swap on theaccrual date. Hence the name is derived from the fact it isan option on a swap. One counterparty buys the option,whilst the other writes or sells the option.

If you need to know more about the basics ofoptions then you may need to refer to theIntroduction to Derivatives workbook Section 3.Swaptions are also dealt with in more detail inthis workbook – Options on IRSs - Swaptions.


There are many types of structured swaps available now – some of themore common types are briefly discussed next.

Accreters, Amortisers and RollercoastersThese are all IRSs which involve variable notional principal amountsin the agreement.

Accreting and amortising swaps consist of strips of swaps withdifferent start or end dates.

❑ Accreting swaps have notional amounts that increase insteps over the life of the swap

❑ Amortising swaps have notional amounts that decrease insteps over the life of the swap

These types of swaps are used in real estate markets where developersseek to lock in the interest cost of future floating rate borrowingswhich either diminish or expand over time. The following chartsillustrate these swaps.

Not

iona

l am

ount

Maturity

Accreting swaps

Not

iona

l am

ount

Maturity

Amortising swaps

MMI:SWP


109

$ $

Derivative

A rollercoaster swap is simply a combination of one or moreaccreting and amortising swaps and is illustrated in the chart below.

Basis swapsWhereas most IRS are plain vanilla swaps, basis swaps cater forfloating interest payments on both sides. The interest rates for bothfloating sides are calculated on different bases. Typical basis swapsinclude the following:

❑ USD prime rate against LIBOR

❑ 12 month LIBOR against 6 month LIBOR

❑ LIBOR against US Commercial Paper (CP) rates

In all other respects basis swaps are used, priced etc in the same wayas described previously.

One important variation is the cross-currency basis swap in whichfloating rates in different currencies are exchanged, for example,USD LIBOR against DEM LIBOR.

Why is this type of basis swap important? If a plain vanilla swapis arranged in one currency and combined with a cross-currency basis swap, then the result is a Currency swap.

This is how it works...A market-maker enters into a plain vanilla DEM swap for fixed DEMand floating DEM LIBOR. This swap is then combined with a cross-currency basis swap for USD LIBOR and DEM LIBOR. In effect theDEM LIBOR payments cancel out leaving a swap of fixed DEM forfloating USD LIBOR – a Currency swap.

Market-makerDEM LIBOR

USD LIBOR

DEM LIBOR

DEM

Not

iona

l am

ount

Maturity

Rollercoaster swaps

FXI:CSP


$ $

Derivative

110

■ Summary Your notes


❑ An IRS is an exchange or swap of interest rate paymentscalculated according to different formulas on the samenotional principal amount

❑ No exchange of principal occurs during a swap – no fundsare lent or borrowed between the counterparties as part ofthe swap

❑ Interest rate payments are usually netted and only thedifference is paid to one party or the other

❑ Any underlying loan or deposit is not affected by the swap– the swap is a separate transaction


111

$ $

Derivative

To see the Speed Guide for Currency and InterestRate Swaps type in SWAP/1 and press Enter.Double-click in the <TOPIRS> field to see theInterest Rate Swap rates for the major currencies.

The fixed/floating basis for each currency is indicated. If youneed to find out more about a particular price, double-click on itand the latest prices from different contributors will be displayed.


The following exercises using Reuters products and theRT may help your understanding of IRSs and how theyare used.

RT

Double-clicking on thisprice displays this screen

Fixed/floating basis forswap


$ $

Derivative

112

Use the Multiple Watch page, SWMW, in the Swapsfolder to view up to three different contributorquotes for the same currency. Different contributorsmay use different swap terms so you may need to

check this in the Basis fields. You can also compare up to threedifferent currency swap rates in this page.

You may also find it useful to use the Model page, SWM. Enterthe details of the swap you are interested in and the fixed/floating payments are calculated and displayed in the Cash FlowAnalysis fields.

3000

Fixed/floating terms

Enter details in these fields

Fixed/floatingcash flows


113

$ $

Derivative

■ End check

1. In an IRS, the principal amounts involved are usually:

❑ a) Exchanged at the end date❑ b) Exchanged at the start date❑ c) Not exchanged❑ d) Exchanged at an interim date

2. In an IRS, interest payments are exchanged:

❑ a) On a net basis at the end of each interest period❑ b) On a gross basis at the end of each interest period❑ c) At the start of each interest period, as with a FRA❑ d) On a cumulative basis at maturity

3. A client asks you to quote for a 2 year GBP IRS. You quote7.43 – 7.39. The client deals at 7.39. What have you done?

❑ a) Agreed to receive fixed/pay floating❑ b) Transacted a basis swap❑ c) Agreed to pay fixed/receive floating❑ d) Transacted a fixed/fixed swap

4. A borrower pays LIBOR + for floating USD. He decides to fixhis interest repayments using an IRS. He receives a quote of6.75 – 80 using the same interest basis and decides to fix. Whatwill be the net cost of his borrowing?

❑ a) 6.750%❑ b) 6.800%❑ c) 7.375%❑ d) 7.425%

5/8%

Your notes


$ $

Derivative

114

1. c) ❑

2. a) ❑

3. c) ❑

4. d) ❑


Your notes

✔ or ✖



115

$ $

Derivative

■ What is it?

If you need an overview of options or you need to remindyourself about derivatives in general, then you may find ituseful to refer to the Introduction to Derivatives workbook,Section 3 at this stage.


The relationship between the rights and obligations for the differenttypes of options is summarised in the following diagram – you mayfind it useful to refer to when considering some of the exampleswhich follow.

An Interest Rate option is an agreement by which thebuyer of the option pays the seller a premium for theright, but not the obligation –

to buy a call option

or sell a put option

a specific quantity contract amount

of a specific instrument the underlying instrumentis a short or long-termInterest Rate futures contract

on or by a set date the expiry date depends onthe style of the option –American or European

at an agreed price Strike price for theinterest rate

Buyer/holderLong Call

Right but notobligation to:• Buy underlying

instrument• At the strike

price• If the call is

exercised

Call

Seller/writerShort Call

Obligation to:

• Sell underlyinginstrument

• At the strikeprice

• If the holderdecides to buy

Buyer/holderLong Put

Right but notobligation to:• Sell underlying

instrument• At the strike

price• If the put is

exercised

Put

Seller/writerShort Put

Obligation to:

• Buy underlyinginstrument

• At the strikeprice

• If the holderdecides to sell

Options


$ $

Derivative

116

Interest Rate options are financial derivatives first introduced in the1980s to hedge interest rate exposure.

If the option is Exchange traded, then it is settled using the sameconditions as for the underlying futures contracts. There are twotypes of Exchange traded options on futures contracts:

❑ Options on short-term Interest Rate futures contracts whichare cash settled if the option expires

❑ Options on long-term Interest Rate futures contracts whichare settled on Government bonds if the option expires

OTC Interest Rate options are used to control maximumand minimum levels of borrowing and lending moneyand are in effect options on Forward Rate Agreements(FRAs). These options are described in greater detail inthe section Options on FRAs – Interest Rate Guarantees.

The diagram below indicates the availability of Interest Rate options.

Exchange traded Interest Rate optionsThe underlying instrument for Interest Rate options on an exchangecan either be for cash or for Government bonds. Exchange tradedoptions are standardised in terms of :

❑ Underlying instrument and its trading amount

❑ Strike prices – in general exchanges try to have a range ofIn-The-Money, At-The-Money and Out-of-The-Money strikeprices

❑ Expiry dates

❑ Style – most exchange options are American

❑ Premium quotations – these are percentage rates expressedin decimal points for short-term contracts and as fractionsfor long-term contracts

❑ Margin payments are required to be paid to the Clearinghouse

In effect Interest Rate options on futures give the buyer or the sellerof the instrument the right to lend or borrow money. The followingchart indicates these rights from the buyer’s perspective – sellerswould have the opposite views.

Interest Rate options

Exchange tradedOTC

Short-term

Settled forcash

Long-term

Settled forGovernment

bonds

IRGs

CapsFloors

Buyer

Gives right to lendmoney at a

predetermined rate

Gives right to borrowmoney at a

predetermined rate

Used to hedge

Falling interest rates

Rising interest rates

Option

Call

Put

MMI:IRG


117

$ $

Derivative

Exchange contractsOptions on both short-term and long-term Interest Rates areavailable on a number of exchanges worldwide. The charts belowindicate a selection of the Interest Rate options on futures available.

CBOT

Short-term Cash settled based on LIBOR

Three month Sterling (Short Sterling)

Three month Eurodeutschemark (Euromark)

Three month Eurolira

Three month Euroswiss Franc (Euroswiss)

Unit of trading

GBP 500,000

DEM 1,000,000

ITL 1,000,000,000

CHF 1,000,000


Long Gilt (UK)

German – Bund

Italian – BTP

Nominal value

GBP 50,000

DEM 250,000

ITL 200,000,000


10 - 15

8.5 - 10

8 - 10.5

Notionalcoupon, %

9

6

12

LIFFE

Short-term Cash settled based on interbank rates

Three month Eurodollar

One month LIBOR

One year T-Bills

Three month Euromark

13-week US T-Bills

Unit of trading

USD 1,000,000

USD 3,000,000

USD 500,000

DEM 1,000,000

USD 1,000,000


US T-Bonds

10 year US T-Notes

Nominal value

USD 100,000

USD 100,000


At least 15

6.5 - 10

Notionalcoupon, %

8

8

CME


$ $

Derivative

118

Underlying contract

Premium quotations

Minimum PriceFluctuation (Tick)

Contract expiry

Exercise procedure

Typical contract specificationsOptions contracts details vary from type to type and from exchangeto exchange but the following examples taken from a LIFFE contractand a CBOT contract are typical specifications.

Option contracts are referred toby the trading cycle of the futurescontract months.

This is the standard contract size.

Quotes as either decimals orfractions of rate

This means that contract can beexercised on or before expirydate – American

This is the smallest amount acontract can change value andthe ‘tick’ size.

Option on 3 month Sterling Interest Rate future

One 3-month Sterling futurescontract – GBP 500,000

Multiples of 0.01 ( 0.01%)

0.01(£12.50)

March, June, September,December

American

Underlying contract

Premium quotations

Minimum PriceFluctuation (Tick)

Contract expiry

Exercise procedure

Options on US Treasury Bond futures

One US Treasury Bondfutures contract – $100,000

Multiples of 1/64th of a point

1/64( $15.625)

March, June, September,December

American


119

$ $

Derivative

■ Who uses Options on Interest Rate futures?

Buyers/sellersInterest Rate options are used to hedge interest rateexposure. The chart below indicates the buyers andsellers of options and the rights to the respective

underlying instruments if the options are exercised.

Buyer/holder hasright to:

Buy a futures contract–

Go long

Sell a futures contract–

Go short

On exercise Seller/writer has obligation to:

Sell a futures contract–

Go short

Buy a futures contract–

Go long

Option on futurescontract

Call

Put

ExampleA Corporate Treasurer has a loan of $1 million with an interest rateof LIBOR, reset every 3 months. The current interest rate is 6.25%but she feels that interest rates may rise. If she buys an Interest Ratefutures contract she effectively locks in her borrowing at the futurescontract rate and cannot take advantage of any interest rate falls.Using the futures contract limits her losses but does not give her theopportunity to profit. The solution is to use an option contract. Inthis case she buys an interest rate call option with a strike price of93.75 (6.25%) and a maturity to suit the roll-over date of the loan.

On maturity:

If LIBOR is 6.25% or less

The treasurer pays the interestand allows the option toexpire.

If LIBOR is greater than 6.25%

The treasurer exercises herright to buy the option and paysthe strike price of 93.75.

If the treasurer had been in the position of a lender of funds andwanted to guarantee a minimum rate of interest on a deposit thenshe would have used a put option.

Originally these types of option were written on real loans/deposits.Now they are settled on a cash compensation basis where the writeror the holder, pays or receives the difference between the interestrate on the underlying loan or deposit and the strike price of theoption. This means that options are traded independently andseparately from the actual instruments.

Another way of looking at the use of Interest Rate options on futuresis summarised in the chart below:

who is a ...

buyer of a Call

seller of a Put

wants to...

guarantee minimumdeposit rates on future

deposits – a floor

guarantee maximumborrowing rates onfuture loans – a cap

Market player

Money Marketfund manager

CorporateTreasurer


$ $

Derivative

120

■ Options on Interest Rate futures in the market place

1 2 3

4 5 6

7 8 9

0

This section deals with typical contract quotations and howoptions are traded and premiums are calculated for InterestRate options which are derived from exchange traded futurescontracts based on:

❑ Short-term interest rate instruments

❑ Long-term interest rate instruments

Typical exchange contract quotationsInterest Rate option quotations are available from the financial presssuch as the Financial Times and The Wall Street Journal and fromproducts such as Reuters Money 3000. The information appears in asimilar style to those in the following examples.

Financial press – Option on short-term Interest Rate futures contract

The information in the chart allows you to calculate the premiumcost of any option which is quoted.

ExampleSuppose you need to hedge a 6.25% interest rate on a 3-monthEurodollar investment starting at the end of September. To hedgethe return on this investment you decide to use an option. You willneed to buy a Sep Call option but what strike price should you use?

The strike price for 6.25% is simply determined by subtracting 6.25from 100. So the strike price is 100 – 6.25 = 93.75. Buying a Sep Calloption gives you the right, but not obligation, to buy a 3-monthEurodollars futures contract on or before the September expiry dateat an interest rate of 6.25%. But how much will you have to pay theseller for this right?

Contract premium priceThis is calculated using the following simple equation:

Premium cost = Number of ticks x Tick size

From the chart opposite the premium for a Sep9375 Call is 0.11. Sothe premium cost is therefore:

= 0.11 (quote) x $25 (tick size)

0.01 (tick size)

= 11 x $25 = $275.00

3-month Eurodollarcontract

Eurodollar (CME) $ million; pts of 100%

Strike Calls Putsprice Mar Jun Sep Mar Jun Sep

9325 0.50 0.30 0.29 0.00 0.15 0.429350 0.26 0.16 0.18 0.01 0.26 0.559375 0.05 0.07 0.11 0.05 0.42 0.73

Expirydates offuturescontracts

The rates of interest implied in the strikeprices are calculated by deducting thequoted strike price from 100.

A March 9350 strike represents a forwardrate interest of 100 – 93.50 = 6.50%

Minimum price movement= 0.01: Tick price = $25


121

$ $

Derivative

Reuters Money 3000 – Options on short-term Interest Rate futuresOptions on short-term Interest Rate futures can be found using theIR Options folder, Futures Option Watch page IFOW for anyparticular currency. The following is a section of a screen dumpshowing Bid/Ask prices for the IMM 3-month Eurodollars futuresCall and Put options on the Index and Option Market (IOM) of theCME.

Financial press – Option on long-term Interest Rate futures contract

US Treasury Bond future

T-Bonds (CBOT) $ 100,000; 64ths of 100%

Strike Calls Putsprice Apr Jun Sep Apr Jun Sep

110 1-23 2-15 2-61 0-61 1-53 2-63111 0-55 - - 1-29 - -112 0-32 1-21 2-04 2-06 2-58 4-03

Expirydates offuturescontracts

This is the strike price for the underlyingfutures contract. This means that theunderlying T-Bond futures contract has amarket value of $112,000

Minimum price movement= 1/64: Tick price = $15.625

This representsa premium of43/64%

Contract premium priceThis is calculated as before. The premium cost for a Sep110 Putwhich gives you the right to sell US Treasury Bond futures at thestrike price at any time to expiry is quoted at in the chartabove. So the premium cost is therefore:

= Number of ticks x $15.625

= x $15.625

= 191 x $15.625 = $2984.38

263/64%

263/64

1/64


$ $

Derivative

122

Reuters Money 3000 – Options on futures contractsOptions on long-term Interest Rate futures can be found also usingthe IFOW page for any particular currency. The following is a sectionof a screen dump showing Bid/Ask prices for US T-Bond futures Calland Put options on CBOT.

How an Exchange traded Interest Rate option contract worksExchange traded Interest Rate options on futures are traded in asimilar way to exchange traded futures contracts in that marginpayments are required by the Clearing house. Initial margin ispayable by the appropriate party at the time of the trade.

The price of an option is marked-to-market every day that the optionis open and the resulting profits/losses are credited/debited to bothcounterparty margin accounts.

��

▼

▼

Buyer Seller

▼

▼

Clearing house

Profits andlosses

Profits andlosses

If an Interest Rate option on a short-term futures contract is allowedto expire, then expiry takes place on the same date as the underlyingfutures contract. Also, as for the underlying futures contract, theoption is cash settled.

The settlement price is calculated simply from the differencebetween the Exchange Delivery Settlement Price (EDSP) and thestrike price using the following equation:

Settlement price = (EDSP – Strike price) x Tick price


123

$ $

Derivative

ExampleA buyer of a LIFFE Short sterling Jun9300 Call allows the option toexpire. This gives the buyer the right to receive interest at a rate of7.00% on the underlying futures contract. At the time of expiry theEDSP is 9375 – an interest rate of 6.25%. Therefore the buyerreceives a cash settlement:

= (9375 – 9300) x £12.50

= 75 x £12.50 = £937.50

The option premium was 0.30. This means that the premium costwas:

= 30 x £12.50 = £375.00

The net profit on the option is therefore £937.50 – 375.00 = £562.50.

A simpler way of calculating the option profit is to use the followingequation:

Profit = (EDSP – Strike price – Premium in ticks) x Tick value

So in this case the profit is calculated as:

= (9375 – 9300 – 30) x £12.50

= 45 x £12.50 = £562.50

Trading strategies for optionsThere are many strategies available in the options markets – some arequite complex and have colourful names.

The various strategies are usually represented diagrammatically asbreak-even graphs which show the potential for making a profit. Thediagrams use the break-even point as the basis for the diagram where

Break-even point = Strike price ± premium

The most basic buy /sell strategies for puts and calls areillustrated using profit/loss charts in the followingexamples. You may find it useful to refer to optionstrategies in general by referring to the Introduction toderivatives workbook.

Depending on whether the market player is a buyer or seller of a callor put, gains or losses either have ceiling values or are limitless.



$ $

Derivative

124

Buying a Call option – Long CallA fund manager has investments that mature in the future which hewill need to re-invest. The manager believes that interest rates will belower in the future and needs to protect his position. He buys Calloptions on futures contracts that correspond to the fundinvestments. In other words he buys the right, but not obligation tomake a future Money Market loan at a pre-determined interest rate.

If interest rates decline, then gains made on the options should helpoffset the lower interest rate return. However, if interest rates rise,then the fund manager can still take advantage of the higher ratesand not exercise the options.

The fund manager decides to protect his investment by buying Calloptions on a LIFFE 3-month Short sterling futures contract having astrike price corresponding to an interest rate of 7.00%. He buys9300Sept Calls with a premium of 0.04.

Remember that short-term futures contracts have strike pricesdetermined from 100 – interest rate. So as strike price increase, theinterest rate falls.

At expiry the profit/loss chart for the Long Call looks like this:

Outcome

Profit increases as futures prices rise(interest rates fall) and are unlimited

Break-even point

Loss which decreases as futures pricefalls ( interest rates rise)

Loss is limited to a maximum of thepremium price

Market price

> 9304

9304

9304 – 9300

< 9300

Break-even point= 93.00 + 0.04 = 93.04

Profit

Loss

Strike price = 93.00

9325

Maximum loss = premium price= 0.04

9225 93009250 9275Futuresprice


125

$ $

Derivative

Buying a Put option – Long PutThe Treasurer of XYZ Corporation may or may not need to borrowfunds at a specified time in the future depending on the outcome ofa tender bid but he is worried that interest rates will rise. By buyingPut options the Treasurer can lock in the maximum interest cost inthe event he needs to borrow. In other words the Treasurer buys theright to sell the underlying futures contract and therefore he isentitled to borrow money at a future date at a fixed interest rate.This protects him against a future rise in interest rates.

If interest rates rise, then the option can be exercised at a profit tooffset the increased borrowing costs. If interest rates fall, then theTreasurer can take advantage of lower interest rates and not exercisethe option. If the tender is unsuccessful and no borrowing isrequired, then the Treasurer can exercise or sell the option forwhatever value it has but his loss is limited to the option premiumcost.

The Treasurer decides to buy Put options on a LIFFE 3-month Shortsterling futures contract having a strike price corresponding to aninterest rate of 7.00%. He buys 9300Sept Puts with a premium of0.21.

At expiry the profit/loss chart for the Long Put looks like this:

Break-even point= 93.00 – 0.21 = 92.79

Profit

Loss

Strike price = 93.00

9375

Maximum loss = premium price= 0.21


Outcome

Maximum loss is equal to the premium

Loss decreases as future prices fall(interest rates rise)

Break-even point

Profit increases as future prices fall(interest rates rise) and is unlimited

Market price

> 9300

9300 – 9279

9279

< 9279


$ $

Derivative

126

Selling a Call option – Short CallA fund manager expects interest rates to remain relatively steady forthe next few months or possibly fall slightly. The manager would liketo earn extra income on his portfolio and decides to sell Calloptions on long-term futures contracts.

If interest rates remain steady and the options are not exercised,then they expire worthless and the fund manager has earned extraincome equal to the value of the premium received.

The risk the fund manager takes is that prices on the underlyingbond contracts rise. If the options are exercised then he has theobligation to deliver the bonds.

Writing At-The-Money Calls produces more premium and may beappropriate if the Treasurer firmly believes the underlying bondprices are unlikely to rise. By writing Out-of-The-Money Calls, lesspremium is received but the options are less likely to be exercised.

Selling a Put option – Short PutThis is more or less the same scenario as for a Short Call except thatthis time the fund manager believes that interest rates will remainsteady or rise slightly.

At expiry the profit/loss chart for the Short Call looks like this:

If bond prices increasethen the option may beexercised

Profit

Loss

114

Maximum profit = premium received


At expiry the profit/loss chart for the Short Call looks like this:

If bond prices decreasethen the option may beexercised

Profit

Loss

114

Maximum profit = premium received



127

$ $

Derivative

■ Summary


❑ Exchange traded Interest Rate options are available onshort and long-term futures contracts. On expiry optionson short-term futures are cash settled, options on long-term futures are settled by physical delivery of the bonds.

❑ The buyer or holder of a Call/Put has the right to buy/sell the underlying futures contract if the option isexercised

❑ The seller or writer of a Call/Put has the obligation tosell/buy the underlying futures contract if the option isexercised

❑ Most options traded on exchanges are American style

❑ Premium quotations are as decimal percentage points forshort-term underlying futures and fractional percentagevalues for long-term underlying contracts

Your notes


$ $

Derivative

128

To view the Exchange Traded Interest Rate OptionsSpeed Guide type in OPS/IR1 and press Enter.From this page there are a limited number ofcontracts to view – mainly those from CBOE and

EOE. Double-click in a field of interest – the screen here showsthe CBOE 10 Year Treasury Yield Calls and Puts for a number ofstrike prices for different months.


The following exercises using Reuters products and theRT may help your understanding of options on InterestRate futures and how they are used.

RT


129

$ $

DerivativeTo see premium prices for Interest Rate optionsselect the FuOpt Watch page, IFOW, for IR Optionsfor any particular currency you need. In the screensshown here LIFFE 3-month Short sterling and IOM

3-month Eurodollar Call and Put premiums are displayed forvarious strike prices for the underlying September and Decemberfutures contracts respectively. If it is more convenient, you canview the information by name rather than the contract RIC.

3000


$ $

Derivative

130

You may also find it useful to use the Interest RateHistory page, IOIR, and FuOpt Model, IFOM page.The IOIR page displays the deposit rates you selectfor up to three currencies simultaneously – you can

choose any combination of currencies and deposit periods asrequired from the drop down menus. The IFOM page can beuseful if you need to know the option delta values and whetheran option premium is In-The-Money, At-The-Money or Out-of-The-Money.

3000

Interest rate history for GBP using the IOIR pageUsing this IFOM page you can see that the Call for this 9275 strikefor the September contract which has an underlying value of 92.85has a delta value of 0.6281 which means it is ITM

Using this IFOM page you can see that the Call for this 9300 strikefor the September contract which has an underlying value of 92.85has a delta value of 0.2965 which means it is OTM


131

$ $

Derivative

■ End check

Using the chart of premium prices for options on Eurodollars answerthe following:

1. Why are the Calls with higher strikes cheaper than those withlower strikes, and why are the Puts with higher strikes moreexpensive than those with lower strikes?

Answer:

2. At what price would the buyer of a 9325Jun Put break even atexpiry?

Answer:

3. What is the maximum interest rate that the buyer of a 9375SeptPut is guaranteed on a future loan?

Answer:

4. What is the premium cost for a 9350Jun Call?

Answer:

5. You buy an option on LIFFE which can exercised at any time.Which of the following describes this type of option?

❑ a) European❑ b) American❑ c) Asian❑ d) Average

Eurodollar (CME) $ million; pts of 100%

Strike Calls Putsprice Mar Jun Sep Mar Jun Sep

9325 0.50 0.30 0.29 0.00 0.15 0.429350 0.26 0.16 0.18 0.01 0.26 0.559375 0.05 0.07 0.11 0.05 0.42 0.73

Tick size for this contract is 0.01 and the tick value is $25


$ $

Derivative

132

1. The higher the strike the lower the Call prices ❑because they are further Out-of-The -Money.The higher the Put prices because they are furtherIn-The-Money.

2. Put break even = Strike – Premium ❑= 93.25 – 0.15= 93.10

3. Maximum interest rate locked in by the potential ❑ borrower is given by 100 – (Strike – Premium)

= 100 – (93.75 – 0.73)= 100 – 93.02= 6.98%

4. Premium is 0.16, the tick size for this contract is ❑0.01 and the tick value is $25

Premium cost = 0.16/0.01 x $25= 16 x 25= $400

5. b) ❑


Your notes

✔ or ✖


Options on FRAs – Interest Rate Guarantees (IRGs)

133

$ $

Derivative

■ What is it?

If you need an overview of options or you need to remindyourself about derivatives in general, then you may find ituseful to refer to the Introduction to Derivatives workbook,Section 3 at this stage.

Caps and floors are OTC options which in effect ‘guarantee’ buyers ahedge on rising and falling interest rates respectively. Hence theseoptions are also known as Interest Rate Guarantees (IRGs).

Caps and floors are based on a floating rate such as LIBOR, Primerates and CPs and are sold for a one-off premium. The mostcommonly quoted caps and floors use 3-month or 6-month LIBOR.

Exercise for both caps and floors occurs automatically on set datesduring the maturity period of the option if this is to the holder’sadvantage.


An Interest Rate Guarantee is a financial derivative whichcan be considered to be an option on a series of ForwardRate Agreements (FRAs).

An Interest Rate Cap is an agreement betweencounterparties in which one party agrees to makepayments to the other if floating rates exceed an agreedstrike rate.

An Interest Rate Floor is an agreement betweencounterparties in which one party agrees to makepayments to the other if floating rates fall below anagreed strike rate.

Interest Rate caps and floors thus provide insurance against interestrate movements over a consecutive number of roll-over loan dateswhich are subject to floating rate payments. They can be used byborrowers and lenders for the protection they need.

Caps and floors are a series of OTC options which coincide with theroll-over dates on floating rate loans which can be considered to be aseries of Forward Rate Agreements (FRAs) with the same strike pricesfor the loan maturity period.

FRA ▼ IRGsseries of

options

An OTC call is an option to buy a FRA and is known as a borrower’soption.

ExampleA borrower has a loan which has floating rate LIBOR interest ratepayments. The borrower fears that interest rates could rise. Theborrower could buy a FRA which would fix payments but whathappens if interest rates fall? The borrower would not be able to takeadvantage of the fall. If the borrower buys an OTC call option onLIBOR to match the roll-over dates of the loan, then the borrowerhas the right to buy a FRA at each roll-over date.

If floating rates rise, then the option is exercised and the borrowerreceives a cash settlement. If floating rates fall, then the option is notexercised but the borrower can take advantage of lower cash marketrates. The borrower pays a premium for this insurance protection tothe option writer or seller.


$ $

Derivative

134

CapsA cap is a series of options that gives the buyer the right to pay thelower of the market rate or strike rate.

A cap offers the buyer the protection against rising interest rates bysetting a maximum limit for payments whilst the buyer retains theright to benefit from falling prices. The use of Interest Rate Swaps orInterest Rate futures locks in borrowing rates to a fixed rate for thewhole transaction.

The cost to the buyer is limited to the premium which is paid to theseller – the buyer has no further obligations.

Most caps are based on LIBOR and the following example illustrateshow a cap works.

ExampleA Corporate Treasurer has borrowed $10 million on a floating ratebasis for 15 months using 3-month LIBOR roll-over dates. TheTreasurer believes that interest rates will rise and wants to cap theloan at 6.00%. The Treasurer buys a cap option and pays a premiumto the seller.

The Treasurer’s loan can therefore be considered to be a series ofFRAs starting in 3 months from the first loan period – 3 x 6, 6 x 9, 9 x12, 12 x 15.

If on any roll over date LIBOR exceeds the cap rate agreed, the sellerof the option has to pay the Treasurer the difference between LIBORand the cap rate as a cash settlement.

The chart opposite indicates the LIBOR fluctuations over 15 monthsand the various payments made to the buyer of the cap.

An OTC put is an option to sell a FRA and is known as a lender’soption.

ExampleAn investor is due to receive floating rate LIBOR payments 3 monthlyfor the next 15 months. The investor fears that interest rates will falland in this case buys an OTC put option on LIBOR to match the roll-over dates of the payments. The investor now has the right to sell aFRA at each roll-over date.

If interest rates fall, then the option is exercised and the investorreceives a cash settlement from the option seller. If floating rates rise,then the option is not exercised but the investor can take advantageof the higher cash market rates.

Some of the advantages offered by these OTC options include:

❑ Flexibility covering a wide range of maturity periods,amounts and strike prices

❑ The one-off cost of the option premium is known at thebeginning of the transaction

❑ A single agreement may cover a maturity period of severalyears and is therefore less costly in fees


135

$ $

Derivative

FloorsThese are the opposite type of options to caps in as much as theyprovide the buyer with a guaranteed minimum interest rate. They canbe considered to be a series of put options on FRAs all with the samestrike price.

A floor offers the buyer protection against falling interest rates bysetting a minimum limit for the rate of return whilst the buyer retainsthe right to benefit from rising rates.

ExampleA Corporate Treasurer has invested $10 million in FRNs with aninterest rate linked to 3-month LIBOR. The Treasurer is concernedthat interest rates might fall and needs to protect against interestrates below 6.00%. The Treasurer buys a 6.00% floor for 15 monthsbased on 3-month LIBOR and pays a premium to the seller.

The chart below indicates the LIBOR fluctuations over 15 monthsand the various payments made to the buyer of the floor.If LIBOR is above the cap rate then the Corporate Treasurer can take

out a loan at LIBOR knowing that the extra cost above the agreed caprate is guaranteed by the option. In other words the CorporateTreasurer’s interest payments have been limited to the cap level set.

If LIBOR is below the cap rate, then the seller makes no payments tothe buyer. However, the Corporate Treasurer now pays interest at alower rate than the cap level which is within the interest ratemaximum set.

The overall effect is that the Corporate Treasurer protects his interestrate payments from rises above a cap level whilst simultaneouslytaking advantage of any falls in interest rates.

Cap rate

LIB

OR

Maturity

3 x 6FRA

6 x 9FRA

9 x 12FRA

12 x 15FRA

Difference between LIBOR andcap rate is paid to the buyer

No payment No payment

Floor rate

LIB

OR

Maturity

3 x 6FRA

6 x 9FRA

9 x 12FRA

12 x 15FRA

Seller has to pay the buyer thedifference between LIBOR andfloor rate

No payment No payment


$ $

Derivative

136

If the interest rate falls below the floor rate agreed, then the buyerreceives the difference between LIBOR and the floor rate as a cashpayment.

If the interest rate is above the floor level, then the buyer receives nopayment. The option is not exercised and the Treasurer receives ahigher rate of return from the underlying.

The overall effect is that the Corporate Treasurer protects the rate ofreturn on the investment from falls below a floor level whilstsimultaneously taking advantage of any rises in interest rates.

CollarsThe collar is the natural combination of a cap and a floor where amarket player wants to restrict interest rates between guaranteedmaximum and minimum limits and reduce overall premium costs.

This can be achieved by buying a cap to place a maximum interestrate limit whilst simultaneously selling a floor to earn premiumincome or vice versa.

Caps

• Protect buyers from risinginterest rates above anagreed level whilstallowing the opportunityto benefit from any fall inrates

• Establish a maximumborrowing cost for buyersover the maturity periodof the option

• Do not affect theunderlying loan

• Provide a flexiblealternative to fixed rateborrowing

• Are a series of call optionson FRAs all with the samestrike price

Floors

• Protect buyers from fallinginterest rates below anagreed level whilstallowing the opportunityto benefit from any rise inrates

• Establish a minimum rateof return for buyers overthe maturity period of theoption

• Do not affect theunderlying deposit orinvestment

• Provide a flexiblealternative to fixed ratelending

• Are a series of put optionson FRAs all with the samestrike price

Summary


137

$ $

Derivative

■ Who uses IRGs?

Buyers/sellers of caps and floorsThe various buyers and sellers of caps and floors aresummarised in the charts below:

Buyers

• Organisations with afloating rate debt whoanticipate rising interestrates

• Investors with fixed rateassets who want to protectthe net interest marginson their investments

• Organisations wanting tohedge the risk of risinginterest rates whilst at thesame time takingadvantage of any falls ininterest rates. The cost ofthe option is limited tothe premium payment.

Sellers

• Organisations with afixed rate debt whoanticipate interest rateswill fall or remain stable

• Financial institutions whohave issued cappedfloating rate liabilities sella cap to hedge the valueof the liability

• Organisations who takethe risk that interest rateswill rise and have to makea payment to the buyer.This risk is taken inreturn for a premiumpayment.

Caps

Buyers

• Organisations with afloating rate debt whoanticipate falling interestrates

• Investors wishing to set aminimum return forinterest rates on theirinvestments

• Organisations wanting tohedge the risk of fallinginterest rates whilst at thesame time takingadvantage of rises ininterest rates. The cost ofthe option is limited tothe premium payment.

Sellers

• Organisations with afloating rate debt whotake the view that interestrates will not fall below aminimum value

• Organisations who takethe risk that interest rateswill fall and have to makea payment to the buyer.This risk is taken inreturn for a premiumpayment.

Floors


$ $

Derivative

138

Collar – Buyer of a cap/seller of a floorIn this case a market player has the view that market rates will rise soa cap is required. However buying a cap requires a premiumpayment. By selling a floor, premium is received which the marketplayer uses to offset the cap premium. The market player’s view isthat interest rates will not fall and therefore the floor will not beexercised – this is a risk.

ExampleA Corporate Treasurer borrowing money decides to limit borrowingcosts to 6.0% because the current interest rates are only slightlyhigher than this. This is therefore the Treasurer’s cap. At the sametime the Treasurer sells a floor at 4.0% thus placing a collar oninterest rate payments and earns premium income. The collar isindicated in the chart below.

The option guarantees that if LIBOR rises above 6.0%, then theTreasurer receives payment from the seller. If LIBOR falls below4.0%, then the Treasurer will have to make a payment to the floorbuyer.

Collar – Buyer of a floor/seller of a capExampleIn a similar way to the previous example a Corporate Treasurerwishes to hedge an investment by setting the minimum rate of returnhe expects. This is therefore the Treasurer’s floor. At the same timethe Treasurer sells a cap which will earn premium income. If thefloor is bought at 5.0% and the cap sold at 7.0%, then the collar isindicated in the chart below.

If LIBOR falls below 5.0%, then the Treasurer receives a paymentfrom the floor option. If LIBOR rises above 7.0% then the Treasurerwill have to make a payment to the cap buyer. However, theTreasurer’s view is that interest rates will not rise and that the capoption will not be exercised.

For collars in general, because the option involves a simultaneouspurchase and sale, the premium charges involved are partially or fullyeliminated. One premium is received whilst the other is paid.

Cap rate 7.0%

LIB

OR

Maturity

Buyer of floor receives thedifference between LIBOR andfloor rate

Seller of cap pays the buyer thedifference between LIBOR andcap rate

Collar – margin 2.0%

Floor rate 5.0%Cap rate 6.0%

LIB

OR

Maturity

Buyer of cap receives thedifference between LIBOR andcap rate

Floor rate 4.0%Seller of floor pays the buyerthe difference betweenLIBOR and floor rate

Collar – margin 2.0%


139

$ $

Derivative

■ IRGs in the market place

1 2 3

4 5 6

7 8 9

0

This section deals with premiums and OTC caps and floorsquotations with particular reference to the importance ofimplied volatilities in pricing these options.

Premium payments and settlementsThe purchase of caps and floors involve the payments of premiums.Usually market-players requiring quotations from banks for IRGs arequoted premiums in terms of basis points.

The value of the premium is then calculated by multiplying the basispoints by the notional principal amount of the loan.

ExampleA Corporate Treasurer wishes to buy a 3 year 6.5% USD 3-monthLIBOR cap for a $20 million notional principal amount. Thepremium is quoted at 115 basis points – one basis point is onehundredth of a percentage point.

The cash premium required to be paid by the Treasurer to the capseller is:

20,000,000 x 0.0115 = $230,000

Any cash settlements due on the roll-over LIBOR dates are calculatedusing the simple equation:

(LIBOR% – cap/floor rate %)

100

Notionalx principal x

amount

Actual no. of days

360

ExampleFor the cap bought by the Treasurer in the previous example, on thefirst LIBOR roll-over date, the floating rate is 7.00%.

The Treasurer therefore receives a cash payment which equals:

7.00 – 6.50

100

x 20,000,000 x 90

360

= $25,000

Typical OTC contract quotationsInterbank quotations for IRGs are not made using basis points.Instead professional options market-makers use complex analyticalmodels to calculate option prices based on the following factors.

1. Strike price

2. Time to expiry

3. Interest rates

4. Volatility

Of the factors, volatility is the only one for which the market-makerdoes not have a precise value. But what is this volatility? In the case ofInterest Rate options, the volatility is a measure of the rate offluctuation in interest rates. How is a volatility value derived?

The volatility implied in an option price is calculated using statisticalstandard deviations of historic underlying price movements over agiven period, expressed as a percentage per annum.


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140

The implied volatilities are therefore forecasts of the proportionalpercentage range, up or down, within which the underlying interestrate is expected to finish at the expiry date of the option.

The confidence level of thevolatility forecast beingcorrect for one standarddeviation either side of themean in a statistical normaldistribution is 68%. For twostandard deviations theconfidence level offorecasting the correctvolatility range is 95%.

ExampleDEM one year forward interest rates are 4.00% and the one yearvolatility is forecast at 10%. So the standard deviation is ±0.04 and twostandard deviations is ±0.08.

The price ranges for the two confidence levels are shown in the tablebelow:

Confidence level

68%

95%

USD/DEM price range

3.96 to 4.04 (4.00 ± 0.04)

3.92 to 4.08 (4.00 ± 0.08)

Probability

It is important to recognise that the implied volatility percentages arenot the implied forward interest rates.

Cap and floor volatilities are available from individual market-makerson the RT.

Type in IRGS/1 and press Enter. From the list ofvarious currency Caps and Floors double-click in afield of interest, for example, <GBPCAP=ICAP>.You will now see the cap Bid and Ask volatility prices

as percentages from International Brokers Ltd. If you need to seemore information about the contributor just double-click on thefigure to display a page of information. Why not try? You shouldsee screens similar to those shown here.

RT

68%

95%

+ Market price– Market price


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$ $

Derivative

ExampleA market-maker might quote 11.50 – 13.50 % volatility for a 3 monthLIBOR GBP At-The-Money Cap.

This two-way Bid/Ask price quotation means:

On Bid side The market-maker will buy Puts or Calls at 11.50%per annum

On Ask side The market-maker will sell Puts or Calls at 13.50%per annum

This Bid/Ask spread in volatility translates into a correspondingspread in the option premium.

The prices are for At-The-Money options – the strike price is at thecurrent underlying forward rate.

Once the counterparties want to trade, all the factors, including thevolatilities, are entered into each side’s pricing models to calculatethe premium to be paid. If both sides agree then the transactionproceeds.

Eachcounterparty

▼

Premium

Pricing model

▼

Strike price

▼

Expiry date

▼

Interest rate

▼

Volatility

The following chart is a summary of the movement in premium levelsfor options based on the movement of four of the pricing factors. Youmay find it useful in looking at historic option prices.

Why not test the summary above by using the RT?

Strike price

➞

➞

Underlying forward price

Expiry date ➞

Volatility ➞

➞

➞➞

➞

Price of Call Price of PutIncrease in...


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Derivative

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■ Summary Your notes


❑ An OTC financial derivative which can be considered tobe an option on a series of Forward Rate Agreements(FRAs)

❑ OTC contracts for caps which place a maximum oninterest rate payments and floors which fix a minimumrate of return

❑ The combination of a cap and floor is a collar whichconfines interest rate commitments betweenpredetermined maximum and minimum limits

❑ Interbank premium quotations are quoted in terms ofimplied volatilities for caps and floors


143

$ $

Derivative

As interbank OTC caps and floors are quoted asimplied volatilities type in VOL/1 and press Enterto see the Implied Volatilities Speed Guide. In theInterest Rate Volatilities field double-click in the

<IRGS/1> field. Now double-click in the field for the cap or floorfor the currency you require, from the contributor you require.Try double-clicking in <GBPCAP=ICAP> to see the At-The-Moneyvolatilities for GBP from Intercapital Brokers Ltd.


The following exercises using Reuters products and theRT may help your understanding of IRGs and how theyare used.

RT

To see moreinformation from thecontributor, double-click on the quote


$ $

Derivative

144

To see a different way of presenting contributorinformation use F12 to page forward from IRGS/1.Double-click in the <USDIRG=TKFX> field. Youshould now see IRG caps and floors volatility quotes

together with other options and swaps quotes from Tokyo Forex.

RT

Your notes


145

$ $

Derivative

■ End check

1. Your company obtained a 3-year rollover credit for $10 million onthe basis of 6-month LIBOR from XYZ Bank one year ago. AsTreasurer you are of the opinion that interest rates are likely torise in the future. Therefore you want to hedge against an interestrise of 0.25% above the prevailing interest level of 5.00%.

a) Do you buy a Cap or Floor?Answer:

b) Note the terms of the contract here:

c) If the premium costs 120 basis points, how much does theoption cost you?Answer:

d) At the first settlement date 6-month LIBOR is at 6.00%. Do youexercise the option? Calculate any settlement amount involved.Answer:

e) At the third settlement date the rate is 5.00%. Do youexercise this option?Answer:

Underlying index

Term

Reset period

Strike

Notional amount

2. Your organisation wishes to speculate by placing $10 million inFRNs for 2 years based on 6-month LIBOR. Although you areconvinced that interest rates will rise from their current rate of5.00% and you would like to benefit from any rise, you would stilllike to protect yourself against an adverse movement of 1% ininterest rates.

a) Do you buy a Cap or Floor?Answer:

b) Note the terms of the contract here:

c) If the premium costs 50 basis points, how much does theoption cost you?Answer:

d) At the first settlement date 6-month LIBOR is at 3.50%. Do youexercise the option? Calculate any settlement amount involved.Answer:

e) At the third settlement date the rate is 6.00%. Do youexercise this option?Answer:

Underlying index

Term

Reset period

Strike

Notional amount


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Derivative

146

✔ or ✖

1. a) Buy a Cap

b)

c) 1.20% of $10,000,000 = $120,000

d) You exercise the option because you have toborrow at 6.00%.You receive compensation

= 10,000,000 x 0.75 x 180 100 x 360

= $37,500

e) You do not exercise the option because you canborrow in the market at 5.00%

❑

❑

❑

❑

❑

❑

Underlying index 6 month LIBOR

Term 2 years

Reset period Every 6 months

Strike 5.00 + 0.25 = 5.25

Notional amount $10,000,000

✔ or ✖



2. a) Buy a Floor

b)

c) 0.50% of $10,000,000 = $50,000

d) You exercise the option because you have tolend at 3.50%.You receive compensation

= 10,000,000 x 0.50 x 180 100 x 360

= $25,000

e) You do not exercise the option because you canlend in the market at 6.00%

❑

❑

❑

❑

❑

❑

Underlying index 6 month LIBOR

Term 2 years

Reset period Every 6 months

Strike 5.00 – 1.00 = 4.00

Notional amount $10,000,000


147

$ $

Derivative

■ What is it?

If you need an overview of options and swaps derivativesor you need to remind yourself about the types ofderivatives available, then you may find it useful to referto the Introduction to Derivatives workbook, Sections 3 & 4 atthis stage.

Swaptions are OTC contracts used by market players who seek theadvantages of an IRS but who also would like to benefit from anyfavourable interest rate movements.

Swaptions, in common with other options, use the terms Call andPut. However, their meanings are not quite as obvious as before. Themeanings and uses of Swaptions Calls and Puts are described in thechart below.

DerivativesSection 3/4

A Swaption is a financial derivative which grants theright, but not the obligation, to buy or sell an InterestRate Swap (IRS) on agreed terms of interest rate,maturity, fixed or floating rate payer, on or by an agreeddate. In return for this right the buyer of a swaption paysthe seller a premium.

Call Swaption

• Also called a Payer orRight-to-pay Swaption

• The buyer has the right topay the fixed side to andreceive the floating sidefrom the holder of theunderlying IRS

• The buyer is hedgingagainst falling interestrates

Put Swaption

• Also called a Receiver orRight-to-receive Swaption

• The buyer has the right toreceive the fixed sidefrom and pay the floatingside to the holder of theunderlying IRS

• The buyer is hedgingagainst rising interestrates

■ Who uses Swaptions?

Banks and corporationsSwaptions are used by the same market players who useIRSs – banks and multinational corporations.

Swaptions are used increasingly by these market players for two mainreasons:

❑ To hedge exposure on interest rates

❑ To speculate in the swaps markets in order to make a profitfrom offsetting fixed/floating rate transactions

Swaptions offer similar benefits to corporations and banks as IRSs:

❑ Counterparties are able to convert underlying interest ratesfrom fixed to floating and vice versa over a long termperiod

❑ Usually there are cost savings to both sides

❑ IRSs provide access to markets not normally available to themarket players, for example, for reasons relating to creditrating


$ $

Derivative

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■ Swaptions in the market place

1 2 3

4 5 6

7 8 9

0

This section deals with examples of how Call and PutSwaptions work in the market place.

Call SwaptionsExampleXYZ Corporation decides to hedge against falling interest rates usinga 1 plus 4 Call Swaption. This means they buy an instrument whichgrants the right to exercise the option in one year for an underlying 4year Fixed pay/Floating receive (Current interest rate/LIBOR) IRSfor a Swaption rate of Fixed pay/Floating receive, 6.5%/LIBOR.

This means that if XYZ, the Swaption holder, exercises their right in ayear, they will pay the IRS holder a fixed rate and receive LIBOR, andat the same time receive 6.5% fixed interest from the option sellerand pay LIBOR.

To justify exercising the swaption, the interest rates of the underlyinginstrument must be less than the Swaption rates.

At expiration the current rate for a 4 year Fixed pay/Floating receiveIRS is 6.0%/LIBOR. XYZ exercise their right on the Swaption andmake a net gain of 0.5% in interest rate payments, so hedging againstfalling interest rates.

The process is illustrated in the chart opposite.

XYZ receive

6.50%

LIBOR

Payments

Fixed

Floating

LIBOR

6.50%

��

Swaptionseller

Swaptionbuyer

UnderlyingIRS

LIBOR

6.00%

XYZ pay

6.00%

LIBOR

Net % position

+ 0.50

Cancel out


149

$ $

Derivative

Put SwaptionsExampleXYZ Corporation needs to hedge against rising interest rates using a1 plus 4 Put Swaption. This means they buy an instrument whichgrants the right to exercise the option in one year for an underlying 4year Fixed receive/Floating pay (Current interest rate/LIBOR) IRSfor a Swaption rate of Fixed receive/Floating pay, 6.5%/LIBOR.

This means that if XYZ, the Swaption holder, exercises their right in ayear, they will pay the IRS holder LIBOR and receive a fixed rate, andat the same time receive LIBOR from the option seller and pay afixed rate of 6.5%.

To justify exercising the swaption, the interest rates of the underlyinginstrument must be greater than the Swaption rates.

At expiration the current rate for a 4 year Fixed receive/Floating payIRS is 7.0%/LIBOR. XYZ exercise their right on the Swaption andmake a net gain of 0.5% in interest rate payments, so hedging againstrising interest rates.

The process is illustrated in the chart opposite.

XYZ receive

7.00%

LIBOR

Payments

Fixed

Floating

LIBOR

6.50%

��

Swaptionseller

Swaptionbuyer

UnderlyingIRS

LIBOR

6.00%

XYZ pay

6.00%

LIBOR

Net % position

+ 0.50

Cancel out


$ $

Derivative

150

■ Summary


❑ A Swaption is an OTC derivative which grants the right,but not obligation, to buy or sell an Interest Rate Swap atagreed terms on or by an agreed date

❑ A Call Swaption – also known as a Payer or Right-to-payswaption – gives the buyer the right to pay the fixed side/receive the floating side from the holder of theunderlying IRS

❑ A Put Swaption – also known as a Receiver or Right-to-receive swaption – gives the buyer the right to receive thefixed side/pay the floating side from the holder of theunderlying IRS

Your notes


151

$ $

Derivative

To view the Speed Guide for Swaptions type inSWAPTION/1 and press Enter. As with other OTCoption prices the Bid and Ask quotes from thevarious contributors are as volatilities. If you double-

click in the <USDSTN=TXFX> field you will see Swaptionvolatilities for the USD from the Tokyo Forex Co Ltd. If youdouble-click in the <DEMSWPTNS=TTKL> field you will see thevolatilities from Tullets on DEM – these are mid-quotes.


The following exercises using Reuters products and theRT may help your understanding of Swaptions and howthey are used.

RT


$ $

Derivative

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Your notes

What’s next?

What’s next?

153

■ Do you need to study further?

You have now completed this Level 3 workbook which hasbeen designed to give you a better understanding of themarket and product information you may need for yourjob.

You may have all the knowledge and understanding yourequire or you may still need to study further workbooksand /or Web materials in the Know your Markets series.

In particular you may need to study the Level 3 workbook:Foreign Exchange Instruments – the companion workbook tothis one.

The remaining workbooks in the Know your Markets package cover thefollowing markets at both Level 2 and Level 3:

❑ Debt

❑ Equities

❑ Commodities, Energy and Shipping

You may also find the Further resources useful for further reference.The order of the materials/information has no significance andcovers many of the sources used in the preparation of this workbook.If you have access to the Internet, then you may find the Webaddresses listed useful.

The decision to study further workbooks or use the Web site is yours –Good luck!

Further resources

BooksThe Penguin International Dictionary of FinanceGraham Bannock & William Manser, Penguin, 2nd Edition 1995ISBN 0 14 051279 9

InvestmentsWilliam F. Sharpe, Gordon J. Alexander & Jeffrey V. Bailey, PrenticeHall, 5th Edition 1995ISBN 0 13 18 3344 8

A–Z of International FinanceStephen Mahony, FT/Pitman Publishing, 1997ISBN 0 273 62552 7

Financial DerivativesDavid Winstone, Chapman & Hall, 1st Edition 1995ISBN 0 412 62770 1

BookletsChicago Mercantile Exchange• An Introduction to Futures and Options: Interest Rates

Swiss Bank Corporation• Financial Futures and Options• Options: The fundamentals

ISBN 0 9641112 0 9

Chicago Board of Trade• Financial Instruments Guide• An Introduction to Options on Financial Futures• Trading in Futures

London International Financial Futures and Options Exchange• An Introduction• Options: a guide to trading strategies

What’s next?

What’s next?

154

Further resources

Reuters Money 3000 – Training Programme1. Foreign Exchange & Money Markets2. Futures & Forward Rate Agreements3. Bonds & Swaps4. Options

Intuition Plus: CATCall & Fixed Deposits - Fundamentals• Item code: UKCA0290

Fixed Deposits - Dealing• Item code: UKCA0320

Treasury Bills - Fundamentals• Item code: UKCA0291

Treasury Bills - Dealing• Item code: UKCA0323

Certificates of Deposit - Fundamentals• Item code: UKCA0292

Certificates of Deposit - Dealing• Item code: UKCA0322

Bills of Exchange - Fundamentals• Item code: UKCA0293

Commercial Paper - Fundamentals• Item code: UKCA0294

Futures - Fundamentals• Item code: UKCA0301

Futures - Hedging with Long-term Interest Rate Futures• Item code: UKCA0348

Futures - Hedging with Long-term Interest Rate Futures• Item code: UKCA0348

Futures - Hedging with Short-term Interest Rate Futures• Item code: UKCA0349

FRAs - Fundamentals• Item code: UKCA0306

FRAs - Applications• Item code: UKCA0364

Swaps - Interest Rate Swaps - Fundamentals• Item code: UKCA0385

Swaps - Interest Rate Swaps - Applications• Item code: UKCA0386

Options - Fundamentals• Item code: UKCA0308

Options - Transactions• Item code: UKCA0309

Options - OTC Options - Fundamentals• Item code: UKCA0403

Repurchase Agreements - Fundamentals• Item code: UKCA0314

Internet Web sitesApplied Derivatives Trading• http://www.adtrading.com/Have a look at the ADT Guide

Derivatives Research Unincorporated• http://fbox.vt.edu:10021/business/finance/dmc/DRU/contents.htmlA good collection of well explained articles

AIB: Derivatives in plain English• http://cgi-bin.iol.ie/aib/derivs-pe/

Sujeeb Money Market Level 3

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