, EURIBOR refersspeciﬁcally to the interbank offered rate for euros reported as areference rate by the ACI and the EBF. There is therefore both aeuro LIBOR (for euros at 11:00 a.m. in London) and EURIBOR (foreuros at 11:00 a.m. in Europe). STIBOR is the reference rate inStockholm for Swedish kronor, BUBOR for forints in Budapest etc.• Fixed rate or ﬂoating rate Many instruments pay a ﬁxedrate – that is, an interest rate or coupon which is determinedwhen the instrument is issued and remains ﬁxed throughout itslife, regardless of whether the interest is paid only at maturityor on several occasions. Others pay a ﬂoating rate. This meansthat the interest rate is changed in line with market conditions atcertain predetermined times (for example, reﬁxed each 6 monthsto the current LIBOR).• Bid and offer The offered rate, at which a bank wishes to lendfunds to another bank of top credit quality, is higher than the bidrate, at which it wishes to take funds. In most markets, the bid rateis quoted ﬁrst in a two-way price and the offerred rate second – forexample, ‘5.17/5.27%’. In the London market, however, the quoteis traditionally reversed from bid/offer to offer/bid – for example,‘5.27/5.17%’. There is no ambiguity in this, since the lowernumber is always the bid for cash and the higher number isalways the offer for cash, regardless of which comes ﬁrst.• Basis point When discussing interest rates, a basis point isalways 0.01% (which is the same as 0.0001). Note that this is not
Overview of money market instruments
31
necessarily the same as a point in foreign exchange, which canvary according to the size of the exchange rate.
Money market instrumentsFixed deposit/loanA ﬁxed deposit is a deposit placed with a bank for an agreed lengthof time. It is not negotiable, and it is expected therefore to be heldto maturity. It is generally possible for the depositor to break thedeposit – that is, terminate it early – but effectively at a penaltycost. Conceptually, a ﬁxed deposit is exactly the same as a loanor borrowing – the terminology varies only according to circumstanceand whether you are borrowing or lending: a company lending moneyto the bank is making a deposit but a company borrowing moneyfrom the bank is taking a loan. A ﬁxed deposit is also known as aterm deposit, time deposit or clean deposit.
Term:Interest:
Quotation:Currency:Settlement:
Registration:Negotiable:
from 1 day to several years, but usuallyless than 1 yearusually all paid on maturity, but depositsof over a year (and sometimes those ofless than a year) pay interest morefrequently – commonly each year oreach 6 months. A 19-month deposit,for example, would generally payinterest at the end of one year andthen at maturity.as an interest rateany domestic or international currencygenerally same day for a domesticdeposit, 2 working days forEurocurrencythere is no registrationnot negotiable
Certiﬁcate of deposit (CD)A certiﬁcate of deposit is a security issued to a depositor by a bankor building society, to raise money in the same way as a time deposit.A CD is, however, negotiable. This gives the investor ﬂexibility in twoways. Firstly, he can liquidate the CD if he needs the cash backsooner than anticipated. Secondly, it allows him to take a view on
32
Foreign exchange and money markets
how interest rates will move, which is linked to the price at which theCD can be bought and sold. For example, if he buys a 6-month CDat 5% and one week later interest rates have fallen to 4.5%, he canthen sell the CD and make a capital proﬁt. Because of this ﬂexibility,the yield on a CD (which, when it is ﬁrst issued, is the same as thecoupon) should be slightly lower than the yield on a deposit for thesame term with the same bank.Term:
generally up to 1 year, although CDs canbe issued for up to 5 years in theLondon market.usually pays a coupon, althoughoccasionally not. Interest is usually allpaid on maturity, but CDs of over ayear (and sometimes those of less thana year) pay interest morefrequently – commonly each year oreach 6 months. Some CDs pay aﬂoating rate (FRCD), which is paid andreﬁxed at regular intervals.as a yieldany domestic or international currencygenerally same day for a domesticdeposit, 2 working days forEurocurrencyusually in bearer formyes
Interest:
Quotation:Currency:Settlement:
Registration:Negotiable:
Treasury bill (T-bill)Treasury bills are domestic instruments issued by governments toraise short-term ﬁnance. The exact name of the instrument variesfrom country to country.Term:
Interest:Quotation:
generally 13, 26 or 52 weeks; in Francealso 4 to 7 weeks, for example; in theUK generally 13 weeksgenerally non-interest bearing, issued ata discountSterling T-bills in the UK and T-bills inthe USA are quoted as a discount rate.Euro T-bills in the UK and T-bills inother countries are quoted as a yield
Overview of money market instruments
Currency:
Registration:Negotiable:
33
usually the currency of the country;however, the UK government, forexample, also issues T-bills in eurossometimes a bearer security, sometimesregisteredyes
Commercial paper (CP)Commercial paper is an unsecured promissory note. It is issuedusually by a company (although some banks also issue CP) in thesame way that a CD is issued by a bank. CP is, however, usually notinterest-bearing. A company generally needs to have a rating from acredit agency for its CP to be widely acceptable. Details vary betweenmarkets. For example:
Domestic US CPTerm:Interest:Quotation:Currency:Settlement:Registration:Negotiable:
from 1 day to 270 days; usually veryshort termnon-interest bearingas a discount ratedomestic US dollarssame dayin bearer formyes
Eurocommercial paper (ECP)Term:Interest:Quotation:
Currency:Settlement:Registration:Negotiable:
from 1 to 365 days; usually between 30and 180 daysusually non-interest bearingas a yield, calculated on the same yearbasis as other money marketinstruments in that Eurocurrencyany Eurocurrency but largely US dollars2 working daysin bearer formyes
34
Foreign exchange and money markets
Bill of exchangeA bill of exchange is used by a company essentially for trade purposes.It is an unconditional order in writing from one party to another,requiring the second party to pay an amount on a future date. Theparty originating the bill (this is the party to whom the money is owed)is called the drawer of the bill. The party to whom the bill requiresthe money to be paid (usually the same as the drawer) is the payee.The party owing the money is the drawee of the bill. When the draweeaccepts liability to pay the amount, it becomes the acceptor. If a bankstands as guarantor to the drawer, it is also said to accept the bill byendorsing it appropriately. A bill accepted in this way is a bankers’acceptance (BA).A commercial or ﬁnance company can also address a bill directly toa bank, rather than to a trading partner, and discount it immediatelyat the bank, in order to raise funds for general purposes rather thento ﬁnance a speciﬁc sale of goods.In the UK, if the bank accepting a bill is one on a speciﬁc list ofbanks published by the Bank of England, the bill becomes an eligiblebill which means it is eligible for discounting by the Bank of England(i.e. the Bank of England is willing to buy it), and it will thereforecommand a slightly lower yield than an ineligible bill.
Term:Interest:Quotation:Currency:Settlement:Registration:Negotiable:
from 1 week to one year but usually lessthan 6 monthsnon-interest bearingin the USA and UK, quoted as a discountrate, but elsewhere as a yieldmostly domestic, although it is possibleto draw foreign currency billsavailable for discount the same day it isdrawnin bearer formyes, although in practice banks oftentend to hold until maturity the billsthey have discounted
RepoA repo is an arrangement whereby one party sells a security suchas a bond to another party and simultaneously agrees to repurchasethe same security at a subsequent date at an agreed price. This isequivalent to the ﬁrst party borrowing cash from the second party
Overview of money market instruments
35
against collateral, and the interest rate reﬂects this – i.e. it is slightlylower than an unsecured cash borrowing because it is collateralized.The security involved will often be of high credit quality, such as agovernment bond. A reverse repurchase agreement (reverse repo) isthe same arrangement viewed from the other party’s perspective. Thedeal is generally a repo if it is initiated by the party borrowing moneyand lending the security and a reverse repo if it is initiated by theparty borrowing the security and lending the money.A repo is also known as a repurchase agreement, RP, classic repo orUS-style repo. A variation on the structure which achieves essentiallythe same result is a sell/buy-back.As the second leg of a repo reverses the ﬁrst leg, it can be seenas one party lending the security and the other party borrowing thesecurity. Because of this, the borrower in a repo is generally the partyborrowing the security and lending the cash, whereas the lender isthe party lending the security and borrowing the cash.
Term:Interest:Quotation:Currency:Settlement:Registration:Negotiable:
usually very short term, although inprinciple a repo can be for any termimplied in the difference between thepurchase and repurchase pricesas a yieldany currencygenerally cash against delivery of thesecurity (DVP)N/Ano
4
Deposits andcoupon-bearinginstrumentsFixed depositsAs discussed in Chapter 2, interest on a ﬁxed deposit is normallypaid in one single amount at maturity:
Interest earned = principal × interest rate ×
daysyear
The total repayment at maturity, including principal and interest, isthen given by either:
Maturity proceeds = principal amountdays+ principal amount × interest rate ×year
or:Maturity proceeds = principal amountdays× 1 + interest rate ×year
Deposits and coupon-bearing instruments
37
Throughout the book, ‘days’ means the number of days in theperiod, including the ﬁrst date but not the last date; in the moneymarkets, this generally means the number of actual calendar days inthe normal way. ‘Year’ means the number of days in a conventionalyear, which in the money markets is generally 360 or 365.
Example 1A dealer takes a ﬁxed deposit of EUR 5 million from a customerfor 73 days at 4.63%. At maturity, he repays EUR 5,046,943.06:73EUR 5,000,000 + EUR 5,000,000 × 0.0463 ×360= EUR 5,046,943.06or:
73EUR 5,000,000 × 1 + 0.0463 ×= EUR 5,046,943.06360
Quoting for ﬁxed deposits with delayed interestsettlementA ﬁxed deposit for longer than 1 year conventionally pays interest atthe end of each year and then at maturity. Sometimes a customerasks for all the interest to be paid at maturity instead but for theinterest rate to be quoted on a simple basis. Effectively in this case,the bank is keeping the interim interest payments, reinvesting themuntil maturity, and then giving them to the customer. In quoting tothe customer in such a case, account must therefore be taken ofthe rate at which it is possible to reinvest the interim cashﬂows. Thecalculation for the interest rate to be quoted to the customer in thiscase is considered in Chapter 6.
Taking a positionA company borrows money because it needs to ﬁnance its operations.An investor deposits money in a bank because he wishes to earninterest on it. To some extent, a bank will also have similar underlyingrequirements – funding its operations and investing surpluses. To alarge extent, however, a money market trader borrows and lends
38
Foreign exchange and money markets
money as an activity in itself, in order to make a proﬁt from doing so.This can be through ﬁxed deposits and repos, or through negotiablesecurities.To earn proﬁt from dealing, the dealer’s objective is to borrow (i.e.take in deposits, issue securities or sell securities) at a lower interestrate and lend (i.e. make deposits, lend money or buy securities) at ahigher interest rate.A dealer who has been borrowing and lending in one particularmaturity needs to know his net position, average interest rate andproﬁt or loss in that maturity.Example 2You borrow USD 5 million for 1 month (31 days) at 4.75%,you lend USD 4 million for 1 month at 4.77%, you borrowUSD 8 million for 1 month at 4.72% and you lend USD 6 millionfor 1 month at 4.79%. The current 1-month rate is 4.71/4.82%.What is your net position, your average rate and your proﬁt orloss?+5,000,000 ×0.0475 = +237,500−4,000,000 ×0.0477 = −190,800+8,000,000 ×0.0472 = +377,600−6,000,000 ×0.0479 = −287,400+3,000,000
+136,900
136,900= 0.04563 = 4.563%3,000,000The net position is therefore long of USD 3 million at an averagerate of 4.563%. The dealer can compare this average rate withthe current market rate to determine whether he is running aproﬁt or a loss; in this example, he is running a proﬁt.To calculate the proﬁt, assume that he closes out his positionby lending USD 3 million at the current rate of 4.71% (the bidside because he will be hitting someone else’s bid rate). Thiswould give a proﬁt of 0.147% (=4.71% − 4.563%) for 31 days onUSD 3 million:USD 3,000,000 × 0.00147 ×
31= USD 380360
Typically, the present value of this amount would then be calculated (see Chapter 2) to give the dealer’s proﬁt:
Deposits and coupon-bearing instruments
39
USD 380 = USD 378311 + 0.0471 ×360The exact average rate and proﬁt or loss will depend on whetherthe transactions are all for exactly the same maturity. It may bethat the dealer has grouped together on his book various dealswhich have slightly different maturities, but are all within 1 month.
For someone trading in repos rather than deposits, the calculationis the same since repos can be seen as secured deposits.As discussed below, when a dealer is trading in negotiable securities, a change in interest rates appears as a change in the value ofthe security. When interest rates rise, the value of a security falls andvice versa. Therefore a dealer hoping that interest rates will rise is thesame as a dealer hoping that prices will fall.Suppose that a dealer effectively borrows by selling security A at alower interest rate and effectively lends by buying security B (with thesame term and coupon as security A) at a higher interest rate. Thismeans that when he sells security A, he receives a higher price for itthan he pays when he buys security B. His proﬁt therefore appearsas a capital gain.
The price of a CDWhen a CD is issued, the original purchaser in the primary marketpays the face value for it. In this way, if the original purchaser holdsit until maturity, it is the same as a ﬁxed deposit – he pays theprincipal amount at the start and receives back the principal amountplus coupon at the end.If the CD is sold again to someone else during its life, however, theamount paid will depend on its value at that time. For an instrumentsuch as a CD which pays a coupon, that value in the market dependson both the coupon rate, because the coupon rate affects the size ofthe cashﬂow received at maturity, and the current yield which variesfrom time to time.For any security, the price an investor is prepared to pay is essentiallythe present value of the future cashﬂow which he will receive at maturity because he owns it. This is the same as the cash investment needednow, at the current market yield, to achieve this amount at maturity.This present value depends, as explained in Chapter 2, on the yield heexpects to earn, the time to the cashﬂow and the size of the cashﬂow.
40
Foreign exchange and money markets
Price = present valueThe coupon paid at maturity of a CD is calculated at the couponrate, for the term of the CD, based on the CD’s face value:Coupon amount = face value× coupon rate ×
days from issue to maturityyear
The total maturity proceeds of a CD are the face value plus thecoupon:Maturity proceeds = face valuedays from issue to maturity+ face value × coupon rate ×yearExactly as with the maturity proceeds of a ﬁxed deposit, this can berewritten slightly more neatly as follows:Maturity proceeds = face valuedays from issue to maturity× 1 + coupon rate ×yearThe value of this CD now – the amount which must be paid to buyit – is the present value now of the maturity proceeds:Amount paid
days from issue to maturityface value × 1 + coupon rate ×year=days from settlement to maturity1 + yield ×year
The price is normally quoted based on a face value amount of 100.For a CDMaturity proceeds = face valuedays from issue to maturity× 1 + coupon rate ×yearAmount paid
⎛
⎛
⎞⎞days from issueto maturity ⎟⎟⎜⎜face value × ⎝1 + ⎝coupon rate ×⎠⎠year
=
days from settlement to maturity1 + yield ×year
Deposits and coupon-bearing instruments
41
Example 3A CD is issued with face value USD 3 million, a coupon of 5.25%and a term of 91 days. A dealer buys this CD in the secondarymarket, when it has only 30 days left to maturity and the yieldis quoted as 5.17/5.27%. How much does he pay for it?On the two-sided quote he receives, he will have the worseside because he is the price-taker. As the purchaser of the CD,he would prefer to invest at 5.27%, so in fact he can only deal at5.17%.91USD 3,000,000 × 1 + 0.0525 ×360= USD 3,026,772.16301 + 0.0517 ×360
Note that because the price of a CD is the present value of itscashﬂow at maturity, the price goes up as the yield down and viceversa. The holder of a CD therefore wants interest rates to fall, sothat he can sell the CD at a proﬁt. This is in fact true of any security,including those which do not pay a coupon:At any given time:A higher yield means a lower priceA lower yield means a higher price
Example 4In Example 3, if the yield at which the dealer purchased the CDwere 5.08% instead of 5.17%, the amount he would pay for itwould be more:91USD 3,000,000 × 1 + 0.0525 ×360= USD 3,026,998.21301 + 0.0508 ×360
The time left to maturity also affects the value of CD. As the time tomaturity shortens, the value increases. Therefore if the time to maturity shortens (so that the value rises) and at the same time the yield
42
Foreign exchange and money markets
rises (so that the value falls), there is no obvious answer – withoutcalculating using the formula – to the question: ‘‘Has the value risenor fallen?’’ However, if the time to maturity shortens and the yieldfalls, the value of the CD will always rise because both effects are inthe same direction.In Chapter 2 we saw that the yield earned on any investment canbe calculated as:yearcashﬂow at the end−1 ×Yield =cashﬂow at the startdaysSuppose that I buy a CD and then sell it again later. The yield thatI have earned over this period of holding the CD can be calculated inthis way. The cashﬂow at the start is the amount I pay for the CDwhen I buy it. The cashﬂow at the end is the amount I receive for theCD when I sell it.It is in fact possible to combine this formula with the one givenearlier for the price of a CD, to give the following:
For a CDYield over holding period⎛⎛⎛
⎞⎞⎞days from purchaseto maturity⎜⎟⎟⎜⎜⎟⎠⎠⎜ ⎝1 + ⎝purchase yield ×⎟year⎜⎟⎜⎟⎟=⎜−1⎜⎟⎜ 1 + sale yield × days from sale to maturity⎟⎜⎟year⎝⎠
×
yeardays held
Example 5The dealer in Example 3, having purchased the CD as describedin that example, then sells it again a week later, when it has only23 days left to maturity, when yields are quoted as 5.07/5.17%.This time, assuming that he is again the price-taker, he willdeal on the other side of the price at 5.17% (the same rate atwhich he purchased the CD originally) – as a price-taker, hedeals at the higher yield, which implies the lower price.
Deposits and coupon-bearing instruments
43
The amount he receives on the sale is:91USD 3,000,000 × 1 + 0.0525 ×360= USD 3,029,804.88231 + 0.0517 ×360The return he has made on his investment over the 7 days is asfollows:yearYield over thecashﬂow at the end−1 ×=cashﬂow at the startdays heldholding period3603,029,804.88−1 ×=3,026,772.167= 0.0515 = 5.15%Alternatively, using the formula given above:⎡⎤301 + 0.0517 ×⎢⎥ 360360 − 1⎥yield on holding a CD = ⎢⎣⎦× 7231 + 0.0517 ×360= 0.0515 = 5.15%
Note that in Example 5, the dealer purchased the CD at a yield of5.17% and sold it again later at the same yield of 5.17%, but that theyield he has earned by doing so is less than 5.17%. This will alwaysbe the case if he buys and sells at the same yield.
Money market yield of a bondin its last coupon periodThe same idea we have used to value a CD can be used to value anysecurity where there is only one cashﬂow left. Suppose, for example,that a dealer wishes to invest for 5 months in a security issued byBank A. This could be because he considers that Bank A representsboth a good yield and an acceptable credit risk.Suppose that the dealer is able to choose between a CD previouslyissued by that bank which now has 5 months left to maturity and abond issued by that bank several years ago, but which also now has
44
Foreign exchange and money markets
5 months left to maturity. From the investor’s point of view, assumingthat the two securities are equally liquid, he might be indifferent towhether he buys the ﬁrst or the second. They both represent a singlecashﬂow in 5 months’ time. Therefore in valuing the bond, he couldvalue it in exactly the same way as the CD, on the basis of a moneymarket yield. There is more than one way of doing this. Our approachhere is to calculate a money market yield which is exactly comparablewith the yield on a money market instrument.The bond market is outside the scope of this book. It is worthnoting, however, that the normal convention for expressing the yieldof a bond is slightly different from this. A bond price is also normallyquoted excluding accrued coupon (a clean price), unlike a CD pricewhich includes everything (a dirty price).
Example 6An investor purchases a bond, face value EUR 10 million, whichpays an annual coupon of 7%. The price he pays, includingaccrued coupon, is 104.98326 per 100 face value. There are158 days left until maturity of the bond.Almost all ﬁxed-rate bonds pay a coupon which is calculated asa round amount, rather than on the basis of the exact numberof calendar days in the coupon period. Therefore the couponpaid by the issuer of this bond at maturity will be exactlyEUR 700,000 (=EUR 10 million × 7%), regardless of exactly howmany days there have been since the last coupon was paid, orthe effect of any non-business days at either end of the couponperiod.The cashﬂow which the investor is purchasing – face valueplus coupon – is therefore EUR 10,700,000 in 158 days’ time.The amount he is paying is EUR 10,498,326. Therefore themoney market yield is:year10,700,000360cashﬂow at the end−1 ×=−1 ×cashﬂow at the startdays10,498,326158= 0.04377 = 4.377%
Breaking a ﬁxed depositA ﬁxed deposit is expected to be held to maturity. It is generally possible, however, for the depositor to break the deposit – that
Deposits and coupon-bearing instruments
45
is, terminate it early – although the bank will usually charge thecustomer a penalty for this.The bank wishes to make sure that it is not losing by repaying thedeposit early. This can be achieved as follows:• First, calculate the amount (principal plus interest) which it wouldhave expected to repay on the normal maturity date of the deposit.• Second, calculate how much the bank will need to borrow atcurrent market rates, from now until that original maturity date,in order to repay that same amount as originally expected.If the bank repays this amount to the depositor, it will be neitherlosing nor gaining. This amount is in fact the present value of theoriginal maturing principal and interest. The rate of discount to beused is the rate at which the bank believes it could borrow new money,taking into account any spread over LIBOR which it typically pays.
Example 7A customer places a deposit of GBP 1 million with you at5.12% for 183 days. After 30 days, the customer asks to breakthe deposit. The interest rate at that time is 5.92/6.04% for153 days. Your bank normally funds itself at around LIBORplus 10 basis points. If you agree to break the deposit, howmuch cash might you agree to return to your customer?The maturing proceeds of the deposit, if it is not broken, wouldbe:183= GBP 1,025,670.14GBP 1,000,000 × 1 + 0.0512 ×365If you repay the cash early, you would need to reﬁnanceat around 6.14% (=6.04% + 0.10%). The present value of thematuring deposit at this rate of discount is:GBP 1,025,670.14 = GBP 999,934.301531 + 0.0614 ×365You would therefore repay a total (including interest) of GBP999,934.30 because, if you borrow this amount from a differentsource now at current rates, you will need to repay GBP1,025,670.14 – i.e. the same amount that you originally expectedto repay. You are therefore left in the same position as if thedeposit had not been broken.
46
Foreign exchange and money markets
In practice, you might wish to protect yourself by taking a morepessimistic view on the rate at which you can refund yourself inthe market, and therefore use an interest rate higher than 6.14% todiscount to a present value.The customer in this example receives back a total of less thanhe deposited. If interest rates had fallen rather than risen since thedeposit had been made, the repayment amount calculated in thisway would be rather higher, to the customer’s advantage. However,in order to discourage customers from breaking deposits, the bankmight agree to do so only on condition that the interest rate used forthe calculation is unrealistically high.The calculation used here is in fact the same as calculating theprice of a CD – it is the present value of the maturing amount.
To calculate the total amount repayable whena ﬁxed deposit is brokenFirst, calculate the principal plus interest due on the normalmaturity date.Second, calculate the present value of this, using the bank’sfunding rate.
CDs paying more than onecouponMost CDs are short-term instruments paying interest only at maturity. Some CDs, however, are issued with a maturity of several years.In this case, interest is paid periodically – generally every 6 monthsor every year. The price for a CD paying more than one couponwill therefore depend on all the intervening coupons before maturity,valued at the current yield.Suppose that a CD has several more coupons yet to be paid, thelast of which will be paid on maturity together with the face value ofthe CD.The pricing method is ﬁrst to discount the ﬁnal cashﬂow – the ﬁnalcoupon payment plus the face value of the CD – back to the previouscoupon payment date, using the current yield as the rate of discount.The result is then added to the coupon payment actually made onthat date and the