S
155
All major ®nancial institutions maintain, as we said, a treasurydepartment, effectively engaged in the central management of fundingneeds. Traders in need of liquidity can always turn to this internalsource to obtain funding.7 Naturally transactions have to be executedat market rates, but there is no credit spread, which means that tradersessentially get liquidity, when needed, at interbank rates. Obviously ifthe credit rating of the institution as a whole is poor, prices quoted bythe treasury manager already re¯ect the spread resulting from thisrating. However, we have restricted our universe to large and adequately capitalized ®nancial institutions, which means that credit rating is probably not an issue.8What applies to cash transactions also applies to money marketderivatives such as swaps. Again major banks and money marketparticipants maintain a swap-trading desk, and traders throughoutthe institution are usually required to get their quotes from this desk.As a result, the rates quoted are also usually free of any credit riskpremium.It is necessary to emphasize again that such an environment isextremely favorable in terms of funding cost because of the backingof a strong balance sheet. All the formal developments we will carryout in this chapter are still valid in any other environment, but actualprices can be signi®cantly higher.
OVERNIGHTOut of the typical money market transactions, overnight loans have aparticular importance because all ®nancial institutions are required tocover their treasury needs on a daily basis. Cash de®cits have to becovered with a borrowing, whereas excesses have to be lent away. Thereason the overnight market is particularly active is related to theunpredictability of ¯ows: Banks, for example, cannot generally determine accurately their customers' ¯ows long in advance. In order toavoid borrowing or lending too much, at the risk of an opposite transaction the next day, the treasurer covers their exact needs, as long asthey can actually estimate them. The calculation of interest is very7
In fact, they have no other choice. The purpose of the central treasury management isto aggregate ¯ows and liquidity needs; therefore, every money market transaction foran internal client has to go through it.8In the case of hedge funds engaged in various arbitrage activities, this statement isobviously inaccurate and credit risk reappears.
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straightforward: The money is made available today and returnedtomorrow with the interest.In the United States the overnight market is traded in conjunctionwith the fed funds market. All depository institutions are required byfederal law to maintain a certain amount of reserves at a federal bank,9dependent upon the type of deposits held, notably in terms of liquidityand duration. The reserves must be cash held in a vault or non-interestbearing deposits at a federal bank, which essentially represents a netcost to the institution. Broadly speaking, reserves requirements rangefrom 0 to 14 percent depending on the speci®cs of the liabilities held,with an average value around 10 percent.Fed fund rates are the rates charged on money lent by banks withexcess reserves at a federal reserve bank to banks with a reserve deficit.10 Typically these transactions serve as a reference for the broaderovernight market, which includes not only reserve requirements butalso all sorts of transactions, for example, stock loans. The fed fundsrate is quoted in real time by major data providers, and the FederalReserve also publishes a daily weighted average of all reserve-relatedtransactions effected on that day, called the effective rate (see Figure 4-1).The fundamental mechanism of the overnight market is similar inmany countries. Banks need to maintain reserves with the centralmonetary institution and at the same time trade frequently with eachother to cover their needs. In Europe, for example, the EuropeanBanking Federation computes a rate called eonia (euro overnightindex average), as the weighted average of all overnight unsecuredlending transactions entered by its members.11 Figures 4-2 through9
Depository institutions include commercial banks, savings banks, savings and loans,credit unions, U.S. agencies and branches of foreign banks, and Edge Act and agreement corporations, regardless of their membership in the Federal Reserve System. Atthe end of 1993, 4,148 member banks, 6,042 nonmember banks, 495 branches andagencies of foreign banks, 61 Edge Act and agreement corporations, and 3,238 thriftinstitutions were subject to reserve requirements. [Source: The Federal Reserve System,Purposes & Functions, (Washington D.C., 1994). Board of Governors of the FederalReserve System.]10The operating procedure for reserves is worth mentioning. To provide banks with¯exibility, the requirement sets a target on average over a maintenance period of twoweeks, instead of on a daily balance. A bank may have an excess or de®cit for severaldays in a row as long as it maintains the minimum reserve balance on average overthe maintenance period. This calculation method has been proposed as an explanation for the high volatility of fed fund rates every other week. Cf. footnote 13.11Note that this ®gure is inclusive of all transactions, whereas the ®gure reported by theFederal Reserve aggregates reserve requirements only. Unsecured transactions areloans with no collateral; thus stock loans are excluded.
CHAPTER 4 MONEY MARKETS
157
Figure 4-1 Fed Fund Effective Rates(Source: Compiled by author from Datastream data.)
4-5 show for example domestic overnight rates over recent years inTokyo, London, Frankfurt, and Paris. Clearly the overnight marketsthroughout the world have very different behaviors, and we need tokeep this particular point in mind when examining ®nancing-intensiveactivities such as index arbitrage.The overnight rate is not the only very short term rate in the market:To cover a shortage of funds predictable one day in advance, treasurymanagers can trade the tom-next rate, from tomorrow to the next day.The overnight (O/N) and tom-next (T/N) are usually equal except inparticular situationsÐfor example, if tomorrow is the end of a corporate®scal year. Most corporations and ®nancial institutions end their ®scalyear on December 31, and at that time they settle many ¯ows and covertheir treasury needs very precisely.12 The accumulation of these events
12
Research suggests that end-of-year adjustments also include window dressing on thepart of banks in advance of required ®nancial disclosure. See, for example, LindaAllen and Anthony Saunders, ``Bank Window Dressing: Theory and Evidence,''Journal of Banking and Finance, 16, 1992, pp. 585±623. For a more general examinationof the end-of-year effect, see Craig H. Fur®ne, The Price of Risk at Year-End: Evidencefrom Interbank Lending, Working Paper No. 76, October 1999, Bank of InternationalSettlements.
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Figure 4-2 Overnight JPY(Source: Compiled by author from Datastream data. From January 1, 1999, the data forthe DEM and FRF rates are eonia rates computed by the Central European Bank.)
Figure 4-3 Overnight GBP(Source: Compiled by author from Datastream data. From January 1, 1999, the data forthe DEM and FRF rates are eonia rates computed by the Central European Bank.)
CHAPTER 4 MONEY MARKETS
159
Frankfurt Inter-Bank Overnight DEM Rate, 1997-99
Figure 4-4 Overnight DEM(Source: Compiled by author from Datastream data. From January 1, 1999, the data forthe DEM and FRF rates are eonia rates computed by the Central European Bank.)
Figure 4-5 Overnight FRF(Source: Compiled by author from Datastream data. From January 1, 1999, the data forthe DEM and FRF rates are eonia rates computed by the Central European Bank.)
160
THEORY and TOOLS
creates a high demand for funds over a single day. The overnight rateusually shoots up, and the tom-next does the same one day before. Forsimilar reasons, a spike in the overnight is common at the end of theinterim period on the last open day of June, and to a lesser extent at theend of each calendar month.13 This effect is not equal in magnitudeeverywhere; it is, for example, particularly visible in the DEM overnightchart in Figure 4-4, and nonexistent in the case of FRF rates.
TREASURY MANAGEMENT VERSUS INTERESTRATE EXPOSUREIf overnight is a fundamental requirement to square the books everyday, leaving little liberty for planning, short-term money market transactionsÐsay, between a few days and several monthsÐgenerally offermuch more latitude in their execution and usually result from cashmanagement decisions. In other words, beyond the immediate needfor cash, treasurers are responsible for optimizing all short-term ¯ows,trying to take advantage of opportunities or reduce risk.Even if the vast majority of cash ¯ows are necessarily uncertain, askilled treasury manager has a fairly good idea about the aggregatecommitments resulting from day-to-day operations. In addition, undera time horizon of one year the macroeconomic environment is relatively well known, and interest rates tend to be predictable.Naturally, there may be a Federal Open Market CommitteeÐor itsequivalent in a foreign marketÐhere and there, and the threat of anadverse move. But overall it is possible to build a reliable intuitionabout the market, and optimizing ¯ows based on that intuition helpsmanage the need for cash in a cost-ef®cient manner.Longer term, the situation changes signi®cantly.14 Cash is not themain concern anymore because it does not make sense to start plan13
Indeed the dynamics of the overnight market in the United States have been studiedextensively. The rates exhibit strong temporal variation, even day-of-the-week effects.Proposed explanations include regulatory and accounting conventionsÐsee, forexample, ``The Micromechanics of the Federal Funds Market: Implications for Dayof-the-Week Effects in Funds Rates Variability,'' Journal of Financial and QuantitativeAnalysis, 23, 1988Ðand bank payment activityÐsee, for example, Craig H. Fur®ne,``Interbank Payments and the Daily Federal Funds Rate,'' Federal Reserve Board ofGovernors Finance and Economics Discussion Series No. 1998-31.14The widespread market convention is to introduce swap rates in the yield curve formaturities over one year. Therefore, our interpretation of ``long-term'' will typicallybe ``over one year.''
CHAPTER 4 MONEY MARKETS
161
ning ¯ows two years ahead. The general level of interest rates is muchmore important because under that time horizon it cannot be considered stable anymore. Furthermore, the fundamental question of solvency takes a whole new dimension, again because of theuncertainties related to the ®nancial strengths of participants over along period.Whereas cash transactions rule the short-term money marketworld, swaps dominate unchallenged the longer-term money marketworld because they offer a remedy to this situation by considerablylowering the amount of credit risk. The need here is to manage anexposure to interest rates rather than a stream of cash ¯ows. Swapsare particularly well suited for this task because they are relativelysimple instruments offering a lot of ¯exibility in decoupling the two.The distinction between cash management and interest rate riskmanagement is indeed capital. It is already apparent from the abovediscussion that the yield curve can be segmented on the basis of thismetric and that the instruments involved have fundamentally differentproperties. One is no substitute for the other, meaning it is possible tolose money every day from inadequate overnight management whileprotected from an overall move in interest rates. In addition, it is extremely important to dissociate the two in the risk management analysis.Index arbitrage will provide a good example of such dichotomy.
LONDON INTER-BANK OFFERED RATEThe theory of market ef®ciency, and by extension modern ®nancialtheory, relies heavily on information availability. In that respect,London played a major role over the centuries, until it lost its positionas the world banking center to New York in the aftermath of WorldWar II. It is still today a major ®nancial center in the sense that transactions may not originate there, but prices of international commoditiesare for the most part available and quoted there. Gold markets, forexample, are located in London, which made the British capital afocus point for 40 years after the Bretton Woods agreement on theGold Standard.For all these reasons, London still plays a privileged role in conveying market information, and that is particularly true on the moneymarket. The British Bankers Association (BBA) publishes everyday aset of interest rates known as the London Inter-Bank Offered Rate(LIBOR). As their names indicate, these rates represent a market indication of the rates at which it is possible for ®nancial institutions to pro-
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THEORY and TOOLS
cure a particular currency over a given period. They are collected everyday from a list of 16 ®nancial institutions, chosen according to certaincriteriaÐfor example, their main place of business or the main place ofbusiness of their parent company. For instance, on the dollar, U.S. organizations are naturally considered, as well as non-U.S. institutions atleast in equal number, to offer a rate as indicative as possible of a broadmarket. Thirteen rates are collected in totalÐ1 week, 1 and 1 to 12months. The higher and lower four indications are removed for eachmaturity, and the remaining eight numbers are averaged to obtain the®nal ®gure. This whole process is repeated every day for a number ofcurrencies, at 11:00 a.m., London time. Results are available usuallyaround 12:00 p.m. from data providers. Table 4-1 shows, for example,the LIBOR rates as of September 13, 1999.Why are these rates so important? The main reason is that they arewidely accepted as being a fair indication of the interbank market, andthey have become highly visible over the years, even if many individual countries have come up with daily rates as well on their owncurrency. Paris, for example, publishes a PIBOR, Frankfurt a FIBOR,Tokyo a TIBOR, Hong-Kong a HIBOR, and so on. In the vast majorityof cases, indications from London are in perfect coherence with local®gures. If differences appear, they are an indication of possible inef®ciencies in the ¯ows of money. Not surprisingly, during the Japanpremium crisis, TIBOR rates re¯ected domestic market conditionsTABLE 4-1Maturitya
USD
GBP
JPY
EUR
1WK1MO2MO3MO4MO5MO6MO7MO8MO9MO10MO11MO12MO
5.356255.380005.440005.510005.963755.950005.941255.946255.951255.957505.985006.015006.04750
5.000005.240005.369225.479385.819695.875005.941566.000006.060946.116256.179066.250006.30688
0.061250.072500.080000.087500.022000.217500.217500.223750.225000.226250.228750.233750.23625
2.548132.581252.642502.689383.080003.096883.112503.137503.168133.200003.235883.275253.31563
a
The end of the year falls somewhere between 3 and 4 months. Note the ``jump'' between the ratesfor these two dates: 0.45375 percent for USD, for example, when at the same time the ampitude ofthe change from 4 to 12 months is only 0.10 percent.(Source:
Compiled by author from Bloomberg data.)
CHAPTER 4 MONEY MARKETS
163
and were signi®cantly higher than LIBOR.15 At that point, anybodywould have picked up an inconsistency just by looking at a ®nancialpaper.Recently, the emergence of the Euro zone in Europe has reducedthe need for independent calculations, and the European BankingAssociation (EBA) has undertaken a campaign to promote the euroas a reference currency in international money markets. In particular,the EBA publishes now a set of rates termed EURIBOR computed in amanner similar to the LIBOR.16 The rates are published every day at11:00 a.m. Brussels time, and the sample of banks include 47 banks ofthe European Union from countries participating in the euro from theoutset, four banks from EU countries not participating in the euro, andsix non-EU banks with important Euro zone operations. The results aretrimmed to remove highest and lowest rates, and the average is published. From the beginning of 1999, the EURIBOR has replaced thehistorical rates published as PIBOR and FIBOR. Table 4-2 shows eurorates from EURIBOR and LIBOR on September 13, 1999.The table shows clearly that while being very close, both sets arenot identical. The choice of contributing institutions is the mainsource of differences, and it can be argued that because theEURIBOR has a larger base, it is somewhat closer to being a broadmarket indication. On the other hand, LIBOR has been in existencefor much longer and has an established ``mind share.'' Above all theBBA has the indisputable advantage of consisting of a large panel ofcurrencies, which provides worldwide money managers with a onestop reference.
DOMESTIC VERSUS INTERNATIONAL RATESThe market for a particular currency is by nature a worldwide market,but it is not necessarily homogeneous. There sometimes exists signi®cant differences between the availability of funds within the domesticeconomy and the international markets. A simple example will illustrate this situation: Japan levies a withholding tax on foreign borrow15
The Japan premium refers to the premium charged to Japanese borrowers due toworries about the developing bad-loan problem in Japan. Cf. next section``Domestic versus International Rates.''16Naturally, because the United Kingdom is not in the European Monetary Union,the BBA has maintained its LIBOR calculations. Considering, however, the ®nancial weight of the Euro zone and of its banking association, it remains to be seen ifLIBOR rates will keep their predominant role as reference ®gures.
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THEORY and TOOLS
TABLE 4-2
(Source:
Maturity
Euro LIBOR
EURIBOR
1WK1MO2MO3MO4MO5MO6MO7MO8MO9MO10MO11MO12MO
2.548132.581252.642502.689383.080003.096883.112503.137503.168133.200003.235883.275253.31563
2.5472.5842.6442.6933.0813.0963.1143.1393.1673.2023.2373.2773.314
Compiled by author from Bloomberg data.)
ings, and an international corporation or institution lending yens to adomestic counterpart is taxed on the interest. For this reason, international participants will try to structure their transactions to avoid thattax, for example, in trading with an offshore subsidiary of the borrower. In any case, this situation tends to constrain the money ¯owsin and out of Japan from offshore entities.Beyond ®scal disadvantages, international and domestic marketsmay differ for other reasons, and Japan will give again a good illustration with the apparition of the ``Japan premium'' in 1995 and again in1998. After the collapse of the stock and real estate market at the end ofthe 1980s, the Japanese banking system was left with an extraordinaryamount of under-performing debt. As a result, the rate of default in theeconomy increased sharply, causing seven mortgage companiesÐknown as jusen corporationsÐto fail at the same time. A wave of panicspread around the world, and Japan's solvency became the concern ofthe day. All major creditors worldwide put Japan on the red list ofunwelcome borrowers. The resulting credit crunch forced the Bank ofJapan to massively inject liquidity into the ®nancial system, creatingvirtually a dual money market. Domestically, institutions and corporations had access to funds at normal interest ratesÐthat is, rates thatwere more or less in line with what they were before the crisis.Internationally, however, all credit lines were dramatically reduced toJapanese borrowers, which had to pay huge premiums to ®nance theiroperations and eventually were unable to borrow as existing credit lineswere rapidly exhausted. The lack of free ¯ows between the domestic
CHAPTER 4 MONEY MARKETS
165
and international yen markets also meant that international yen lenders,with no access to domestic borrowers, and unwilling to extend morecredit to Japanese institutions offshore, were ready to accept low ratesfrom offshore counterparts. Therefore, whereas the domestic threemonth rate was still around 0.50 percent, the same maturity was tradingat 0.15 percent to about 0.20 percent internationally between counterparts with the adequate ratingsÐthat is, not Japanese. The same difference prevailed across the whole term structure and remained inexistence for several months, as shown in Figure 4-6.17The Three-Month LIBOR/TIBOR Spead40
5-Dec-97
Through the early 1990s 3-month LIBOR/TIBORconfined itself to a narrow trading range around zero.
13-Nov-98
3-Month TIBOR minus 3-Month LIBOR (Basis Pt)
In mid-September 1995 it broke out of this range.Since then it has mirrored market sentiment
30
regarding the creditworthiness of Japanese banksrelative to European and US banks.
20
27-Oct-95
10
8-Sept-95
3-Apr-96
031-Oct-97
2-Apr-99
Data Source: Bloomberg
24-Sep-99
15-Jan-99
21-May-99
11-Sep-98
2-Jan-98
8-May-98
25-Apr-97
29-Aug-97
20-Dec-96
16-Aug-96
8-Dec-95
12-Apr-96
4-Aug-95
31-Mar-95
22-Jul-94
25-Nov-94
18-Mar-94
9-Jul-93
12-Nov-93
5-Mar-93
30-Oct-92
1026-Jun-92
_
Average Spread for Week Ending...
Figure 4-6 LIBOR/TIBOR(Source: Fred Sturm, ``Opportunities in the Euroyen LIBOR/TIBOR Spread,'' CarrFutures, www.carrfut.com. Reprinted with permission.)17
The premium was naturally visible in other markets as well, notably in the dollar-yenswap rates and corporate bond yields. See, for example, Tetsuro Hanajiri, Three JapanPremiums in Autumn 1997 and Autumn 1998: Why Did Premiums Differ BetweenMarkets? Financial Markets Department Working Paper Series 99-E-1, Bank ofJapan, August 1999, and Akira Leda and Toshikazu, Recent Trends in the Spreadover LIBOR on the Domestic Straight Bond Trading Market in Japan, Monetary andEconomic Studies, Bank of Japan, December 1998. Both papers are available onlinefrom www.boj.co.jp.
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THEORY and TOOLS
Even if this situation resulted from a crisis and is indeed anextreme example, in general interest rates are not the same betweendomestic and international players. As an additional illustration, consider the differences between the three-month domestic rates fromGermany and FranceÐrespectively, the Frankfurt Interbank OfferedRate (FIBOR) and the Paris Interbank Offered Rate (PIBOR)Ðand thesame rates quoted in London (LIBOR), as shown in Figures 4-7 and 4-8.Broadly speaking, the differencesÐgenerally small but frequentÐre¯ect numerous factors, notably comparative advantages of participants in their respective marketplaces. For example, French or Germaninstitutions may have more visibility when dealing with Europeancounterparts, even for dollar-denominated operations, than theywould with Japanese entities. In the case of LIBOR versus domesticrates, other reasons may include time differences,18 or the non-homogeneity of the sample banks used to compute the averages.An interesting question naturally arises as to whether these differences can be captured for a pro®t, and clearly the answer was positivein the case of Japan. An international organization with a subsidiary
Figure 4-7 LIBOR/PIBOR(Source: Compiled by author from Datastream data. From January 1, 1999, all rates areeuribor rates for the euro.)
18
The FIBOR and PIBOR are computed at 11:00 a.m. in France and Germany, whereasthe LIBOR is computed at 11:00 a.m. London timeÐthat is, one hour earlier.
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Figure 4-8 LIBOR/FIBOR(Source: Compiled by author from Datastream data. From January 1, 1999, all rates areEURIBOR rates for the euro.)
and treasury management in Japan could borrow at 0.15 to 20 percenton one hand and lend away at 0.50 percent on the other. Even assuming taxes, the operation turned out to be quite pro®table, under theÐreasonableÐassumption that the Japan premium was grossly mispriced and that Japan was in no danger of default as a country.Individual institutions, however, were, and some of them did defaultover the years, so this arbitrage was not exactly risk free. Still over athree-month period it can be argued that credit visibility is high, and inany case the Ministry of Finance would never have let a major institution go bust at that particular moment. Ironically the credit of largeJapanese banks may not have been better than during this crisisbecause they probably enjoyed aÐdiscrete but realÐde facto guarantee from the government. As far as Europe is concerned, however, it ismuch less clear that what we see between PIBOR, FIBOR, and LIBORcan be translated into pro®table arbitrage.In the near future, closer integration of world capital markets willprobably reduce the discrepancies between the diverse sets of ratesapplicable to a particular currency. Note, for example, in Figures 4-7and 4-8 that the divergence between the LIBOR and EURIBOR rates isconsiderably smaller after January 1, 1999, showing indeed that the
168
THEORY and TOOLS
implementation of a single currency helped integrate markets in continental Europe.
CONVENTIONSBefore any further discussion about interest rates, it is necessary todiscuss market conventions because interest rate calculations varywildly from one country to another. The important notions we needto consider are time basis, accrual convention, and holidays, but before wedo so we will introduce several fundamental concepts.
Introduction: Accrual and Compounding
Intuitively it is very clear that the borrower of a certain amount ofmoney should pay interest on the period over which he or she enjoysthat money. This fundamental concept is very simple, yet accountingfor it may be tricky. Consider, for example, a loan of $100 at 6 percentfor six months. Should the borrower pay $6 or $3 of interest at the endof six months? The answer naturally depends on the terms of the loan,but each amount is theoretically acceptable. If 6 percent is the appropriate six-month rate, $6 is the correct amount of interest due. On theother hand, if 6 percent is an annual rate, the borrower is liable for $3because the period is half a year.More generally, an interest rate is useless in and of itself if itsunderlying de®nition is not speci®ed or implicit. Speci®cally, theoperative information is the period on which it is accruing, as opposedto the period over which it is applied. For example, a six-month rate of 6percent yields close to 12 percent in return over one year because it isaccruing over six monthsÐthat is, twice in a year. A 6 percent annualrate, on the other hand, yields a return of 6 percent over a year becauseit is accruing only once.To complicate things further, consider now the notion of compounding. Compounding describes an investment that is automaticallyreinvested periodically. For example, a six-month loan at a six-monthrate of 6 percent compounded every three months yields: (1 + 6 percent/2)2 1  6:09 percent. At the end of three months, the principalÐ$100Ðand interestÐ$100  6 percent/2Ðare reinvested at the samerate. At the end of six months, the ®nal ¯ow is $100  1  6 percent/2)2 from which we deduct the above yield.19 The square is therefore a19
Speci®cally, we receive $100  (1 + 6 percent/2)2 for an initial investment of $100.Therefore, the yield is [$100  (1 + 6 percent/2)2 $100]/$100  6:09 percent.
CHAPTER 4 MONEY MARKETS
169
result of the compounding period of three months, whereas the 1/2factor is a result of the fact that the rate is a six-month rate, and weneed to divide by 2 to get a three-month equivalent. If we had taken anannual rate of 6 percent and had kept the same period and compounding, the yield would have been: (1 + 6 percent/4)2 1  3:02 percent.The square is still necessary to account for the compounding, but therelevant three-month rate is now 6 percent/4.Thus there is a need for a rigorous nomenclature: We de®ne theaccrual period as the fundamental period over which the rate is accrued.An annual rate, for example, has an accrual period of one year. Thematurity is the period over which the investment or transaction istraded. The compounding factor is the number of times reinvestment ismade during this period.Unless speci®ed otherwise, all rates from now on will be annualrates.
Time Basis
With a better understanding of the accrual concept, consider now thetime basis, which refers to the way days are accumulated in the interestcalculations. There are four major basis used:. Actual/360:
The time fraction between two dates is the actualnumber of days divided by 360. For example, between February10, 1999, and February 15, 1999, the number of days is 5, whichwould give a fraction of 5/360 in the interest calculation.Under this system one year is more than 1 in the interest formula.. Actual/365: The fraction is computed the same way, but the totalnumber of days in a year