UNIVERSITA’ CATTOLICA DEL SACRO CUORE - Milano -

QUADERNI DELL’ISTITUTO DI ECONOMIA E FINANZA

The Intraday price of money: evidence from the e-MID market

Angelo Baglioni Andrea Monticini

n. 63 - luglio 2005

Quaderni dell’Istituto di Economia e Finanza numero 63 luglio 2005

The Intraday price of money: evidence from the e-MID market

Angelo Baglioni (*) Andrea Monticini (^)

(*) Istituto di Economia e Finanza, Università Cattolica del Sacro Cuore, Via Necchi 5 – 20123 Milano, e-mail: angelo.baglioni@unicatt.it (*) Istituto di Economia e Finanza, Università Cattolica del Sacro Cuore, Via Necchi 5 – 20123 Milano, e-mail: andrea.monticini@unicatt.it

Comitato Scientifico Redazione Dino Piero Giarda Istituto di Economia e Finanza Michele Grillo Università Cattolica del S. Cuore Pippo Ranci Via Necchi, 5 Giacomo Vaciago 20123 Milano tel.: 0039.02.7234.2976 fax: 0039.02.7234.2781 e-mail: ist.ef@unicatt.it * La Redazione ottempera agli obblighi previsti dell’art. 1 del D.L.L. 31.8.1945, n. 660 e successive modifiche. * I quaderni sono disponibili on-line all’indirizzo dell’Istituto http://www.unicatt.it/istituti/EconomiaFinanza * I Quaderni dell’Istituto di Economia e Finanza costituiscono un servizio atto a fornire la tempestiva divulgazione di ricerche scientifiche originali, siano esse in forma definitiva o provvisoria. L’accesso alla collana è approvato dal Comitato Scientifico, sentito il parere di un referee.

The intraday price of money:evidence from the e-MID market

Angelo Baglionia - Andrea Monticinia,b

Abstract . We present a simple model, where intraday and overnight interest

rates are linked by a no-arbitrage argument. The hourly interest rate is shown to be

a function of the intraday term structure of the overnight rate. This property holds

under both assumptions, where an explicit intraday market for interbank loans

exists and when it does not. In the first case, such a property is an equilibrium

condition; in the second one it holds by definition, as a synthetic hourly loan is

a portfolio of overnight contracts. We then provide empirical evidence, based on

tick-by-tick data for the e-MID money market (covering the whole 2003). The

overnight rate shows a clear downward pattern throughout the operating day.

A positive hourly interest rate emerges from the intraday term structure of the

overnight rate: we estimate the market price of a one hour interbank loan to be

slightly above a half basis point.

Keywords: intraday interest rate, overnight interbank loans, money mar-

ket.

JEL Codes: G21, E43.

aUniversità Cattolica di MilanobUniversity of Exeter

1 Introduction

Is there a market price for "intraday money"? The answer to this question

is interesting for banks, as it gives some insights for their liquidity manage-

ment and it helps understanding the working of payment systems, and it is

relevant for central banking, in particular for grasping the implications of

different policies in the provision of intraday credit. Actually, an explicit

market for loans with shorter maturities than one day does not (yet) ex-

ist. The shortest maturity for which an interest rate is quoted in financial

markets is everywhere the overnight. The rate prevailing in the overnight

interbank market is also the operational target of monetary policy in several

countries (including USA and the euro area). However, an implicit price for

intraday transactions does exist - despite the fact that such transactions do

not actually take place - whenever the overnight interest rate differs, depend-

ing on the exact time (within the same day) at which the delivery/repayment

of funds takes place. So for example, the difference (if any) between the rate

charged on an overnight loan delivered at 9 a.m. and a loan with the same

maturity delivered at 10 a.m. implicitly defines the price of a one hour loan.

The reasons behind a positive intraday interest rate essentially rely on the

organization of payment systems and, more generally, on the way in which the

settlement of transactions is handled. When the bulk of payments were set-

tled through netting systems, a sort of "free intraday liquidity" was provided

by the netting mechanism itself: only the multilateral balance of payments

had to be settled at the end of the day. During the nineties, the real time gross

settlement (RTGS) has become widely used, particularly for large value pay-

ments. This method of handling payments is highly demanding: banks have

to maintain sufficient (idle) balances with the central bank, to be able to set-

tle payments one by one in real time; alternatively, they may rely on central

bank intraday credit, which also comes at some cost. The real time settle-

ment has become the common standard also for securities transactions, with

delivery versus payment (DVP). Finally, a payment-versus-payment (PVP)

1

approach has been adopted by CLS (Continuous Linked Settlement), dealing

with foreign exchange transactions.

More recently, the trend towards "hybrid" systems - implementing a sort

of real time net settlement - has somehow reduced the liquidity needed for

settlement purposes. However, these systems also create an incentive for

banks to actively manage their liquidity during the operating day (for exam-

ple in order to optimally allocate the available liquidity to different categories

of payments and to efficiently manage payment queues). A role for an ac-

tive intraday liquidity management is also created by several cut-off times to

be met by bank treasury departments during the day (think for example of

"timed payments" scheduled by CLS).1

On theoretical grounds, the emergence of an intraday interest rate in

the interbank market has been advocated by VanHoose (1991) and Angelini

(1998): they both model bank liquidity management at an intraday level,

distinguishing between a "morning session" and an "afternoon session". De-

spite some differences (the former focusses on trading in the interbank mar-

ket, while the latter focusses on the timing of payment orders processing),

they reach the same basic results: i) a positive value of the intraday inter-

est rate emerges as the equilibrium level in the interbank market; ii) such

a level crucially depends on the price of daylight overdrafts charged by the

central bank; iii) absent an explicit market for intraday transactions, the

intraday interest rate is computed as the difference between the overnight

rate on interbank loans delivered in the morning and the rate on loans deliv-

ered in the afternoon, providing an implicit price for money between the two

periods within the same day. The strategic choice of banks relative to the

timing of payment sending is also the core of the analysis done by Beck and

Garratt (2003), who assume that the interest rate in the (implicit) intraday

money market equals the cost of intraday liquidity supplied by the central

1Examples of hybrid systems are: RTGS-plus, PNS, New BI-Rel in Europe, and CHIPSin USA. For a more detailed analysis of recent changes in payment systems and theirimplications for central banking, see Baglioni (2005).

2

bank: this cost either takes the form of an explicit fee or it is the opportu-

nity cost of pledging collateral. Finally, Zhou (2000) stresses the distinction

between "settlement debt" (intraday) and "consumption/investment debt"

(across days): only the latter affects the intertemporal allocation of resources,

while the former arises for pure settlement purposes; under this approach a

"day" may be defined as any length of time over which there is no point in

optimizing the timing of consumption and production.

The empirical evidence regarding the price of intraday liquidity is still

modest and not conclusive. As far as we know, the only analysis pointing

to the existence of an implicit market for intraday interbank lending has

been done by Furfine (2001): he finds that in the federal funds market an

additional hour is priced 0.9 basis point; this result is attributed to the cost

of borrowing from the central bank through the daylight overdraft facility.2.

Angelini (2000) does not find any clear intraday pattern of the overnight

rate prevailing in the Italian screen-based interbank market (MID, 1993-1996

data): in particular, such rate turns out to be slightly (less than two basis

points) below its midday level both in the early morning and in the early

afternoon.

The aim of this paper is twofold. First, we want to make clear the theo-

retical relationship between intraday and overnight interest rates. As we are

going to see, they are linked by a no-arbitrage argument: the hourly interest

rate is determined by the intraday term structure of the overnight rate, where

the latter is defined by the levels of the overnight rate for different durations

of the contract. This property applies to both cases, where an explicit in-

traday market for interbank loans does exist and when it does not (in the

2The Fed charges an annualized daily rate of 36 basis points; this amounts to a 1.5 b.p.hourly fee. The effective daily rate is 27 b.p. (36 b.p. times 18/24, as Fedwire operatinghours are 18) divided by 360. The daily charge (neglecting the deductible) results fromthe product between such a rate and the average per-minute overdraft incurred by a bankin a day (see McAndrews and Rajan (2000) for more details). Therefore, repaying a 1dollar federal fund loan one hour later enables a bank saving 1.5 basis points (annualized),given that it is running an overdraft at the time of repayment.

3

latter case, synthetic intraday loans are created through overnight contracts

delivered at different times during the day). Second, we provide some em-

pirical evidence, based on tick-by-tick data for the e-MID euro-area money

market, showing that a positive hourly interest rate (implicitly) emerges in

the overnight market: we estimate the market price of a one hour interbank

loan to be slightly above a half basis point.

2 An arbitrage model for the intraday inter-

est rate

In this section we lay out a simple model, where intraday and overnight

interest rates are linked by a no-arbitrage argument. We focus on a single

day, and denote by t = 0, 1, ..., 24 the hours during the day: t = 0 denotes

the opening time of the interbank market (say 9 a.m.), t = 1 one hour later

and so forth until t = 24 (9 a.m. of the next day). The interbank market

closing time is T : in principle, it might be T = 24; in practice, it is T < 24; in

the following, we will consider different cases about the value of T . Assume

that all overnight interbank loans have to be repaid at t = 24.We call r0 the

interest rate on an overnight interbank loan delivered at t = 0; r1 is the rate

on a loan delivered at t = 1, and so forth until rT . So the list [r0, r1, ..., rT ]

describes the "intraday term structure" as the levels of the overnight rate for

different durations: 24 hours, 23 hours, ..., 24− T hours respectively.

2.1 An explicit market for hourly interbank loans

Assume that in the interbank market it is possible to trade on an hourly basis:

for example, a bank may borrow funds from t = 2 to t = 3. This assumption

is not realistic, and we are going to drop it in the next subsection, but it

is useful to begin our analysis; on theoretical grounds, it is equivalent to

assuming that there is no transaction cost. Assume further, for simplicity,

4

that the hourly interest rate is constant throughout a single day, and it is

denoted by r ≥ 0 (we have discussed in the Introduction the reasons why r

might be strictly positive).

It is easy to see that the following no-arbitrage condition must hold in

equilibrium:

(1 + r)t(1 + rt) = 1 + r0 for t = 1, ..., T (1)

In words, a roll-over strategy of investing in hourly contracts for t hours

(starting at t = 0) and in an overnight contract for the remaining 24 − t

hours must provide the same return as a 24-hour length overnight contract.

Otherwise, arbitrage opportunities would arise. Condition (1) holds for both

r > 0 and r = 0. In the latter case the intraday term structure is flat (rt = r0

for t = 1, ..., T ), while in the former case a decreasing intraday term structure

emerges (r0 > r1 > ... > rT ).

By taking the log of condition (1), we can easily derive the following:

r =r0 − rt

tfor t = 1, ..., T (2)

where the equilibrium (arbitrage free) hourly interest rate is a function

of the intraday term structure of the overnight rate.

From (2) it is evident that a specific level of the overnight rate is com-

patible with any level of the hourly rate: the latter depends only on the

difference between overnight rates with different durations, so the level of r0is irrelevant for determining r.

This property fails to hold when T ≥ 23 (this is not a realistic case,

and we consider it only for completeness). It is intuitive to set r23 = r and

r24 = 0. Then for t = 23, 24 conditions (1) and (2) respectively become:

(1 + r)24 = 1 + r0 and r =r024

(3)

implying that the level of the 24-hour overnight rate uniquely determines

5

the level of the hourly rate: in fact, the latter is simply a fraction of the

former. This simple relation would hold if it were possible to replicate an

overnight contract with 24 hourly contracts. This is not true in practice.

2.2 An implicit market for hourly interbank loans

We come now to the more realistic assumption that transaction costs prevent

an explicit market for hourly interbank loans to arise. However, synthetic

hourly contracts may be created by making use of overnight loans with dif-

ferent delivery times. Then the hourly interest rate turns out to be implicitly

defined by the intraday term structure of the overnight rate. Take for exam-

ple the following position in the overnight market: lend at t = 0 and borrow

at t = 1; this is equivalent to lending for one hour and it gives a return equal

to r0− r1. More generally, a synthetic long position in the interbank market

for t hours may be created by lending overnight at t = 0 and borrowing the

same amount at t (with 1 ≤ t ≤ T ); the hourly return on such a position is

defined as in equation (2).3

Therefore, when the hourly interest rate is implicitly defined by the intra-

day term structure of the overnight rate - as it is the case when no explicit

hourly market exists - the no-arbitrage condition (1) is trivially satisfied.

This is not surprising, as r is defined as an implicit price in the overnight

market, rather than being the equilibrium price of an explicit hourly market4.

Absent an explicit hourly market, the hourly interest rate r is not ob-

servable. However, equation (2) provides a way to estimate such rate by

exploiting the intraday term structure in the overnight market. Let us write

that equation as:

3Of course, a short position for t hours and its hourly cost are defined in a similar way.4Another way to look at this point is by considering a roll-over strategy of investing

in a synthetic long position for t hours (starting at t = 0) and lending overnight for theremaining 24−t hours: this boils down to lending overnight with a 24-hour length contract,giving a return equal to r0; again, condition 1 is trivially met.

6

rt = r0 − r · t (4)

where the overnight rate linearly depends on the time of delivery. The

estimated coefficient of this regression line provides an empirical measure of

the hourly interest rate. This task is taken up in the next section.

3 Empirical analysis

An empirical analysis was performed using data from the e-MID money mar-

ket to investigate the existence of an implicit intraday market for bank liq-

uidity. E-MID is a screen-based market located in Milan and it is currently

the most liquid market in the euro zone for the exchange of interbank de-

posits. This market has expanded considerably in recent years and it is now

fully used by major European banks: indeed, non Italian banks account for

about 40% of daily trades (as of March 2005).

Dealings in e-MID start at 8 a.m. and end up at 6 p.m. One important

aspect of the market microstructure concerns the overnight contract: this has

a fixed maturity time. In particular, dealings between Italian banks matures

at 9 a.m. of the day following the one in which the contract was made: at this

time previous day trades are settled in real time, as the borrowing bank has

to repay the amount due through a Target payment. Dealings involving - at

least - a foreign bank matures by noon (next day). This feature enables us to

apply the framework introduced in the previous section, where the starting

time of a contract unambiguously determines the length of such a contract,

and this is known by both participants in the deal.

For the purposes of our analysis we consider trades (tick-by-tick data)

that occurred in the e-MID market from 2003:01:02 to 2003:12:29, for a total

of 125,536 observations5. In order to measure changes in the overnight rate

as a function of different times of the day, we divided the day into 9 hourly

5We thank e-MID s.p.a. for providing this data set to us.

7

time bands from 9 a.m. to 6 p.m., denoted by t = 0, ..., 8. The period between

8.00 a.m. and 9.00 a.m. was not considered because trading in this period is

extremely volatile. For each working day the average daily overnight rate, the

average overnight rate for each hourly time band and the differences between

the latter and the former were calculated: these differences will be denoted by

rt in the following. By making use of interest rate differentials from the daily

average, instead of relying on their levels, we are able to insulate intraday

patterns - which are our focus - from day-to-day changes in money market

rates. Monthly aggregates were then computed: the regression below was

then run on 108 observations (9 times bands times 12 months).

It is then possible to see whether intraday changes in overnight rates are

linked to the different hourly time bands. Before coming to the econometric

analysis, a quick look at the data is quite suggestive: see Figure 1, where

the differentials between the overnight rates in each time band and the daily

average are plotted (data are aggregated over the whole year 2003). The

intraday pattern of the overnight rate is clearly shown in the picture, with a

steady decline over the whole day - taking a break during lunch time. The

overall decrease amounts to 4.5 basis points.

8

Figure 1 - The intraday pattern of interest rates

-3

-2,5

-2

-1,5

-1

-0,5

0

0,5

1

1,5

2

2,5

9.00 AM 10.00 AM 11.00 AM 12.00 PM 1.00 PM 2.00 PM 3.00 PM 4.00 PM 5.00 PM

Time

Ove

rnig

ht ra

te: s

prea

d ov

er d

aily

ave

rage

(bas

is p

oint

s)

The impression given by the picture is fully confirmed by the econometric

analysis conducted on the sample data: we estimate the parameters of equa-

tion (5). This assumes that the overnight interest rate is a linear function of

the time when a trade takes place:

rt = c+8X

i=1

βi · xi + εt (5)

where c is the constant and εt is the usual white noise. The xi are dummy

variables - where i stands for the hourly time bands following the first one

- taking value 1 when t = i and zero otherwise. The regression results are

given in Table 1. The intercept provides an estimate for the deviation of

the overnight rate in the first hourly band considered (9-10 a.m.) from the

daily average. The value of each βi provides an estimate of the change of the

overnight rate between the beginning of the day and the hourly band t = i.

As p-values show, all coefficients are significant at 5% level (with the only

9

exception of β1).

Table 1 - Estimated regressionCoefficient Value p-value βi − βi−1

c 2, 002 0

β1 −0, 378 0, 207 −0, 378β2 −0, 744 0, 012 −0, 366β3 −1, 567 0 −0, 823β4 −2, 206 0 −0, 639β5 −2, 129 0 0, 077

β6 −2, 659 0 −0, 53β7 −3, 818 0 −1, 159β8 −4, 518 0 −0, 7R2 0, 8 Sum = −4, 518

F − stat 49, 78 Mean = −0, 565D.W. 1, 962

It can be seen from the table that the overnight rate in the first hourly

band is two basis points higher than the daily average. As the beta values

show, the overnight rate gradually declines during the day; in the last oper-

ating hour, its level is 4.5 basis points below the initial level. The last column

(βi − βi−1) shows that the change of the overnight rate with respect to the

previous hour is negative in all time bands, with only one exception (namely

between the 1-2 p.m. and the 2-3 p.m. bands).

The above evidence seems to confirm the hypothesis that an implicit

intraday money market exists: the price of an overnight interbank loan does

depend on the length of the contract; in other words, the intraday term

structure of the overnight interest rate defines a strictly positive hourly rate

in the money market.

Equation (5), used for regression purposes, is an extension of equation

(4): the latter relies on the simplifying assumption that the hourly interest

10

rate is constant throughout the operating day. A synthetic measure of the

hourly interest rate charged in the money market is obtained by restating

our results as in equation (6) below, by making use of the beta estimated

values. This provides an empirical evaluation of equation (4) above, and it

shows that the hourly price of money is estimated to be more than half a

basis point on average.

rt = 2.002− 0.565t (6)

4 Summary and conclusions

We have presented a simple model, where intraday and overnight interest

rates are linked by a no-arbitrage argument: even when it is not possible

to replicate an overnight contract with intraday contracts, a relationship

between hourly and overnight interest rates must hold to avoid arbitrage

opportunities. Such a relationship makes the hourly rate be a function of the

intraday term structure of the overnight rate. This property holds under both

assumptions, where an explicit intraday market for interbank loans exists

and when it does not. In the first case, such a property is an equilibrium

condition; in the second one it holds by definition, as a synthetic hourly loan

is a portfolio of overnight contracts.

We then provide empirical evidence, based on tick-by-tick data for the

e-MID money market (covering the whole 2003). The overnight rate shows a

clear downward pattern throughout the operating day. Therefore, a positive

hourly interest rate emerges from the intraday term structure of the overnight

rate: we estimate the market price of a one hour interbank loan to be slightly

above a half basis point.

Compared with previous results relative to the MID market (Angelini

2000), our estimates point to an evolution of the interbank market: a price

for intraday loans did not emerge during the mid nineties, while it does a few

11

years later. This pattern confirms what we presumed in our Introduction,

namely that the recent evolution of settlement procedures calls for a more

active intraday management of bank liquidity.

On the other hand, our estimate for a one hour interest rate is lower than

that (0.9 basis point) obtained by Furfine (2001) for the federal funds market.

The reason may be found in the absence of an explicit fee for the intraday

liquidity provided by the ECB, contrary to what happens in US. In the euro

area, the cost of the central bank intraday credit is only an implicit one,

namely the opportunity cost of pledging collateral. Actually, our estimate

for the intraday interbank interest rate might be interpreted as a market

price of collateral.

References

[1] Angelini P. (1998): An analysis of competitive externalities in gross set-

tlement systems, Journal of Banking and Finance, 22, 1-18.

[2] – (2000): Are banks risk averse? Intraday timing of operations in

the interbank market, Journal of Money, Credit, and Banking, 32, 54-73.

[3] Baglioni A. (2005): The organization of interbank settlement systems:

current trends and implications for central banking, in Institutional

change in the payment system and its impact on monetary policy, edited

by S. Schmitz and G. Wood, Routledge, London, forthcoming.

[4] Bech M. and Garratt R. (2003): The intraday liquidity management

game, Journal of Economic Theory, 109, 198-219.

[5] Furfine C. (2001): Banks as monitors of other banks: evidence from the

overnight federal funds market, Journal of Business, 74, 33-57.

12

[6] McAndrews J. and Rajan S. (2000): The timing and funding of Fedwire

funds transfers, FRBNY Economic Policy Review, July, 17-28.

[7] VanHoose D. (1991): Bank behavior, interest rate determination, and

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market, Journal of Banking and Finance, 15, 343-365.

[8] Zhou R. (2000): Understanding intraday credit in large-value payment

systems, Economic Perspectives, Federal Reserve Bank of Chicago, 3,

29-44.

13

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43. P. Giarda, Fiscal federalism in the Italian Constitution: the aftermath of the October 7th referendum, novembre 2001.

44. M. Bordignon, F. Cerniglia, F. Revelli, In Search for Yardstick Competition: Property Tax Rates and Electoral Behavior in Italian Cities, marzo 2002.

45. F. Etro, International Policy Coordination with Economic Unions, marzo 2002.

46. Z. Rotondi, G. Vaciago, A Puzzle Solved: the Euro is the D.Mark, settembre 2002.

47. A. Baglioni, Bank Capital Regulation and Monetary Policy Transmission: an heterogeneous agents approach, ottobre 2002.

48. A. Baglioni, The New Basle Accord: Which Implications for Monetary Policy Transmission?, ottobre 2002.

49. F. Etro, P. Giarda, Redistribution, Decentralization and Constitutional Rules, ottobre 2002.

50. L. Colombo, G. Turati, La Dimensione Territoriale nei Processi di Concentrazione dell’Industria Bancaria Italiana, novembre 2002.

51. Z. Rotondi, G. Vaciago, The Reputation of a newborn Central Bank, marzo 2003.

52. M. Bordignon, L. Colombo, U. Galmarini, Fiscal Federalism and Endogenous Lobbies’ Formation, ottobre 2003.

53. Z. Rotondi, G. Vaciago, The Reaction of central banks to Stock Markets, novembre 2003.

54. A. Boitani, C. Cambini, Le gare per i servizi di trasporto locale in Europa e in Italia: molto rumore per nulla?, febbraio 2004.

55. V. Oppedisano, I buoni scuola: un’analisi teorica e un esperimento empirico sulla realtà lombarda, aprile 2004.

56. M. F. Ambrosanio, Il ruolo degli enti locali per lo sviluppo sostenibile: prime valutazioni, luglio 2004.

57. M. F. Ambrosanio, M. S. Caroppo, The Response of Tax Havens to Initiatives Against Harmful Tax Competition: Formal Statements and Concrete Policies, ottobre 2004.

58. A. Monticini, G. Vaciago, Are Europe’s Interest Rates led by FED Announcements?, dicembre 2004.

59. A. Prandini, P. Ranci, The Privatisation Process, dicembre 2004.

60. G. Mastromatteo, L. Ventura, Fundamentals, beliefs, and the origin of money: a search theoretic perspective, dicembre 2004.

61. A. Baglioni, L. Colombo, Managers’ Compensation and Misreporting. A Costly State Verification Approach, dicembre 2004.

62. P. Giarda, Decentralization and intergovernmental fiscal relations in Italy: a review of past and recent trends, gennaio 2005.

63. A. Baglioni, A. Monticini, The Intraday price of money: evidence from the e-MID market, luglio 2005.