Liquidity In Forex Markets.pdf

Journal of Empirical Finance 8 2001 157–170

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Liquidity in the forward exchange market

Michael J. Moore a,) , Maurice J. Roche b

School of Management and Economics, The Queen’s Uni Õ ersity of Belfast, Belfast BT7 1NN,

Northern Ireland, UK

Department of Economics, National Uni Õ ersity of Ireland, Maynooth, Co. Kildare, Ireland

Received 22 May 1997; accepted 2 February 2001

Abstract

The forward foreign exchange market is modelled within the framework of a limited

participation two-country model and then simulated using the artificial economy methodol-

ogy. The new model improves on the standard two-country cash-in-advance model in a

number of ways. It gets closer to the observed lack of autocorrelation in spot returns and it

helps to explain the persistence in the forward discount. However, it cannot account for the

relative volatilities of spot returns and the forward discount. Finally, the model goes some

distance in explaining the forward discount bias puzzle but falls short of resolving it.

JEL classification: F31; F41; G12

Keywords: Artificial economy; Forward foreign exchange; Cash in advance; Liquidity

1. Introduction

advance CIA model. Our focus is to explain the behaviour of the forward

exchange rate. However, the framework is a general equilibrium one so it has

some useful insights into other variables, particularly the spot exchange rate.

Specifically, we construct a limited participation household model along the lines

) Corresponding author. Tel.: q44-28-9027-3208; fax: q44-28-9033-5156.

Ž .

In this paper, we present an improvement on the standard two-country cash-in-

E-mail address: m.moore@qub.ac.uk M.J. Moore .

PII: S 0927-5398 01 00019-6

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of Lucas 1990 and Grilli and Roubini 1992 . An explicit forward market that

throws light on the importance of liquidity effects in this market is added. We also

allow for endowment as well as monetary shocks.

One of the striking, but little, noted features of the standard CIA model is that it

predicts that spot returns are autocorrelated if the underlying international money

growth differential is itself autocorrelated. Indeed, if the international money

growth differential is a long memory process, the CIA model even predicts that

this property transfers onto spot returns. This is clearly unsatisfactory because spot

returns are close to white noise while the money growth differential is certainly

not. Our model succeeds in seriously weakening this implausible relationship.

A number of writers, including Macklem 1991 , Backus et al. 1993 and

Bekaert 1994, 1996 have tried to explain the

puzzle

that forward exchange rate

premia are persistent and may even be fractionally integrated e.g., Baillie and

Bollerslev, 1994; Masih and Masih, 1998 . One of the contributions of the paper is

that we succeed in making clear how this can arise from within the standard CIA

model, if the international money growth differential is persistent.

It is often argued e.g., Flood and Rose, 1998 that standard CIA models simply

cannot explain the extent of volatility of spot returns. This is undoubtedly true and

we will reinforce this point. However, the model we have constructed is capable of

mimicking observed volatilities under certain circumstances.

According to the standard CIA model, the forward discount is an unbiased

predictor of realised future spot returns. It is well known that this is not the case

Engel, 1996; Sibert, 1996; Bekaert, 1996 . Our model brings the theory closer to

the data but it still falls far short. One advantage of our analysis is that it clarifies

what is required of a satisfactory theory. The structure of the paper is as follows.

Section 2 provides a critical background to the standard CIA theory. In Section 3,

our model is introduced. Section 4 reports the result of simulating an artificial

economy. Section 5 gives directions for future research.

2. Background

2.1. General formulation

Hodrick 1987 provides an excellent summary. There are two features of the

standard model that are important for this paper. The first is that though goods are

paid for in cash, the model is quite silent on the means of payment for the

purchase of assets. The second is that assets are priced and traded in each time

period after real and monetary shocks are made known. The standard model can

be crystallised in the following four ‘efficiency’ conditions.

The assumptions of the standard two-country CIA model are well known and

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Firstly, the spot exchange rate is provided by a purchasing power parity

condition. This is derived from the notion that the bilateral real exchange rate

equals the marginal rate of substitution between home and foreign goods.

U r P 2

2 t

S s

Ž.

U r P

1 t t

where S is the spot exchange rate, measured as the home price of foreign

currency; U and U are the period t marginal utilities of the home and the

1 t 2 t

foreign goods, respectively; P 1

and P 2

are the period t nominal prices of home

and foreign goods, respectively.

The second and third efficiency conditions are the familiar home and foreign

nominal bond-pricing formulae. These are, of course, not peculiar to just cash-in-

advance models but are shared by many monetary models.

r P

q sb E

it q1

t q1

i s1,2

Ž.

U r P

subjective rate of discount and E is the expectations operator conditional on time

are the home and foreign nominal prices of one-period bonds, b is the

t .

The final efficiency condition is the no-arbitrage identity of covered interest

parity that is a feature of all models.

Ž.

S t t

where F is the one period ahead forward foreign exchange rate expressed as the

home price of foreign currency.

The four efficiency conditions provide us with home and foreign nominal bond

prices along with spot and forward exchange rates. In this discussion, we are only

concerned with the behaviour of the exchange rates. The importance of the two

bond prices lies in the fact that they enable us to derive the forward exchange rate

through covered interest parity.

2.2. Some re Õ ealing approximations

The theory outlined in Section 2.1 is too general to identify the predicted

stochastic properties of spot and forward exchange rates. To progress further, we

need to make concrete assumptions about the functional form for utility as well as

the sources of uncertainty. Assume that utility is intertemporally separable with an

iso-elastic equal shares instantaneous utility function. Next, assume that home and

foreign consumption growth follow mean-stationary stochastic processes with

normally distributed i.i.d. innovations, which have the same variance for both

countries. The assumption that the innovation variance is the same in both

where q i

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countries affects nothing of substance and simply eases exposition. Assume that

the money growth processes are defined analogously. In this case, it is helpful to

develop some explicit notation. Let u i

t q1

, i s1,2 be a normally distributed i.i.d.

innovation with the same variance s 2

for both countries and p i , i s1,2 be the

conditional expectation of country i ’s money growth at time t .

The following assumption is significant. Like a number of previous writers,

most notably Engel 1992, 1996 , we point out that the observed covariances of

real and nominal shock innovations are typically zero. This is an empirical

regularity in the asset pricing literature generally but we have replicated this yet

again on a G7 data set, which we report in Section 4 of the paper. The

combination of this stylised fact and iso-elastic time inseparable utility makes the

standard CIA model a very weak basis for explaining time-varying risk premia.

We also assume that cross-country real and nominal covariances are also zero.

This involves very little loss of generality but evidence is provided for it in

Section 4 anyway.

We are now in a position to examine the predicted stochastic properties of the

spot and forward exchange rates in the standard CIA model. Using the cash-in-ad-

Ž.

vance-for-goods constraint, Eq. 1 enables us to write the spot return as:

log

S t q1

s p yp q u

y u

Ž.

S t

t q1

properties of the money growth differential whatever they are are mapped

directly onto spot returns. There is abundant evidence that the money shocks are,

in fact, persistent. Moreover, we explore the suggestion in Section 5 that money

shocks may even follow long memory processes. If the money growth differential

also has a long memory, it is alarming that the standard CIA model predicts that

this property would also be held by spot returns.

The properties of the forward rate are obtained indirectly through bond prices.

Ž. Ž.

Using Eqs. 2 and 3 and the properties of the lognormal distribution, we obtain

the following expression for the forward discount 1

log

F t

sp yp

Ž.

S t

1 The standard CIA model with homoscedastic forcing processes can generate a constant risk

premium as well as a constant non-convexity term. They are both zero because of our assumptions on

the variance–covariance matrix of the innovations to exogenous shocks.

Hence, spot rate returns are equal to the money growth differential. The only way

in which the standard CIA model will successfully predict that spot returns are

non-autocorrelated, as they typically are, is if the underlying money growth

differential is white noise. Indeed, the standard model predicts that the stochastic

M.J. Moore, M.J. Roche r Journal of Empirical Finance 8 2001 157–170

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161

which is the difference between conditionally expected home and foreign money

growth. Hence, the forward discount will have a persistent autocorrelation function

if the money growth differentials are persistent.

Ž. Ž.

Moore, 1994 for testing for unbiasedness, namely regressing spot returns,

log S r S , on the forward discount. The standard CIA theory clearly implies

t q1 t

that the forward discount should be an unbiased predictor of spot returns.

The standard CIA theory also implies that speculative profits and the forward

discount should be orthogonal, irrespecti Õ e of the nature of the forcing processes

for money . Backus et al. 1993 suggest that a useful summary statistic for the

extent of the forward market bias is provided by the estimated variance of the

fitted values from the regression of log S

t q1

r F , on the forward discount.

3. The model

tion model in a two-country world along the lines of Lucas 1990 , Fuerst 1992 ,

Grilli and Roubini 1992 and Christiano et al. 1997 . Limited participation

models differ from the standard CIA two-country models as follows. Asset

portfolios cannot be adjusted costlessly. This idea is implemented by specifying

that all portfolio decisions are made before the realisation of money shocks, both

foreign and domestic. This is significant because assets, as well as goods, must be

purchased with cash that must be accumulated in advance.

The specific contribution made in this paper is to extend this class of models to

allow for forward foreign exchange contracts. The sluggish portfolio adjustment

behaviour, which we have modelled for all other assets including spot exchange

rates, does not affect forward contracts. Since there are no margin requirements,

the model drives an additional liquidity ‘ wedge’ between spot returns and the

forward discount. The formal specification of the model is derived in the Ap-

pendix. We again crystallise its main features into four ‘efficiency’ conditions.

These should be compared directly with the analogous conditions for the standard

CIA model Eqs. 1 – 3 .

Firstly, purchasing power parity no longer holds in any conventional form.

Ž.

Ž . Ž ..

Instead of Eq. 1 , the spot exchange rate is determined as follows:

2 t q1

r P 2

t q1

q 1

Ž.

S s

EU r P

1 t q1

t q1

In contrast to Eq. 1 , the price-weighted marginal utilities are expected values.

This reflects the fact that all decisions are made before shocks are known. The

Ž.

appearance of the bond price ratio in Eq. 6 is its most important feature. It

A comparison of Eqs. 4 and 5 reminds us of the traditional vehicle e.g.,

To address the challenges posed in Section 2, we develop a limited participa-

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