Does liquidity in the FX market depend on volatility?

Abstract

We re-examine the relationship between exchange rates and order flow as proposed by Evans and Lyons (2002). Compared to their linear specification, we find that the response of exchange rates to order flow may depend on market historical volatility. If market historical volatility is high, a given order seems to have a lower price impact than in calmer periods. Overall, our simple threshold mechanism has the power to produce higher correlation coefficients.

Full text

Does liquidity in the FX market depend on volatility?
Frank Westerhoff Sebastiano Manzan
University of Osnabrueck, Department of Economics University of Amsterdam, CeNDEF, Department of
Quantitative Economics
Abstract
We re−examine the relationship between exchange rates and order flow as proposed by
Evans and Lyons (2002). Compared to their linear specification, we find that the response of
exchange rates to order flow may depend on market historical volatility. If market historical
volatility is high, a given order seems to have a lower price impact than in calmer periods.
Overall, our simple threshold mechanism has the power to produce higher correlation
coefficients.
We gratefully acknowledge the helpful comments of an anonymous referee and of Robert Dekle.
Citation: Westerhoff, Frank and Sebastiano Manzan, (2004) "Does liquidity in the FX market depend on volatility?."
Economics Bulletin, Vol. 6, No. 10 pp. 1−8
Submitted: March 19, 2004. Accepted: August 25, 2004.
URL: http://www.economicsbulletin.com/2004/volume6/EB−04F30001A.pdf

1
1. Introduction
Empirical macro models have difficulties in predicting exchange rates. Meese and Rogoff
(1983) find that structural models are not able to outperform a random walk in an out-of-
sample forecast. Their conclusions are still valid when a longer time span of data is used
(Cheung et al. 2002). A more promising approach to capture the behavior of the exchange
rate may be to focus on the microstructure of foreign exchange markets, e.g. Lyons (2001),
Evans (2002) and Evans and Lyons (2003). As reported by Evans and Lyons (2002), order
flow, i.e. the difference between buyer- and seller-initiated trades, explains a large fraction
of the variability of nominal exchange rate changes at short horizons. While structural
models may be useful in explaining the long-term dynamics of the exchange rate, order
flow seems to be a more appropriate variable in the short run.
In this note, we explore the link between order flow and exchange rates in a novel
way. Note that there is now widespread evidence of nonlinear effects in exchange rate
dynamics. Hence, we study whether the relationship between order flow and exchange rates
may be characterized by a simple piece-wise linear model. As it turns out, the already
remarkable fit of Evans and Lyons (2002) may be improved if one incorporates threshold
effects: R
2
statistics increase by about 5 to 8 percent. From an economic point of view, the
response of exchange rates to order flow seems to respond asymmetrically to the market
historical volatility. If market historical volatility is high, an order has a lower price impact
than in calmer periods.
The remainder of this note is organized as follow: Section (2) describes the model,
Section (3) presents the estimation results and Section (4) concludes.

2
2. The Setup
Evans and Lyons (2002) propose a microstructural model that leads to the following linear
relationship
ttt
ηxαs +∆=∆ , (1)
where
t
s∆ is the change of the log nominal exchange rate at time t,
t
x∆ is the order flow, α
is a coefficient and
t
η
is an i.i.d. disturbance term. Estimation results based on daily
observations show that the order flow variable significantly and positively causes
t
s∆ .
Overall,
t
x∆ explains about 64 percent of the variability of USD/DM exchange rates, which
stands in sharp contrast to the typically low R
2
achieved by traditional exchange rate
models. Although Evans and Lyons (2002) detect weak evidence of nonlinearities, they
conclude that a linear specification is appropriate.
Notwithstanding, we explore whether the price impact of order flow may depend on
market historical volatility and inspect the following threshold relationship
1
ï
ï
î
ï
ï
í
ì
+∆
>∆=+∆
=∆
å
=
−
otherwiseεxβ
csyforεxβ
s
tt
ktttt
t
2
K
1k
K
1
1
. (2)
Market historical volatility is measured as the average absolute price change in the last K
lag periods. The coefficients
1
β and
2
β are estimated by OLS while the threshold constant c
is selected by a grid search on the values of the 80% interval of
t
y .
t
ε is a noise term.
Summing up, (2) is a piece-wise linear model with coefficients equal to
1
β if market
historical volatility is larger than c and
2
β otherwise.
1
According to Easley and O´Hara (1992), such a relationship may result from event uncertainty, the basic
idea being that trades are more informative when trading intensity is high. To be precise, their model predicts
that the informational content of order flow is positively correlated with volume and volatility.

3
3. Evidence
Our analysis is based on the dataset of Evans and Lyons (2002). The time series consist of
USD/DM and USD/JY rates and order flow observations at daily frequency from May 1 to
August 31, 1996.
2
Further details are available in their article. The estimation results of the
linear regression are reproduced in Table (1).
Tables (2) displays the findings for the threshold model. Due to the rather short
sample, we consider only up to K=5 lags. In the USD/DM case, both
1
β
and
2
β
are always
statistically significant and different from each other. Moreover, for all lags, the R
2
statistic
improves. This is also confirmed by the Akaike Information Criteria that is larger for all
values of K considered. All in all, there exists clear support for the threshold mechanism.
For K=4, for instance, the threshold regression is able to explain about 69.3 percent of
the variability of the changes in the exchange rates, compared to the 63.6 percent explained
by the linear regression.
3
The interpretation is quite simple. When the 4-day moving
average of absolute exchange rate changes is higher than 0.00191, the coefficient of the
order flow is close to 1.7, otherwise it is around to 2.9. Hence, when market historical
volatility is high, the order flow causes a smaller change of the USD/DM rate compared to
the case when it is low. In the misspecified linear model, the price adjustment is about 2.2.
Similar results are obtained for the USD/JY market. The threshold variable with the
highest R
2
statistic is the one-period lagged absolute price change, i.e.
1−
∆=
tt
sy . The
coefficients in the regression are significantly different from each other but the coefficient
2
We thank the authors for making available their data.
3
The grid search procedure indicates that the optimal value of the threshold is quite close to its median value.

4
in the regime for
cy
t
> is not significantly different from zero. The fraction of variability
of the exchange rate explained by the regression increases from 0.392 (for the linear case)
to 0.478. Again, the response of exchange rate changes to order flow is asymmetric: The
coefficient is equal to 3.075 if the last absolute change in the exchange rate is below 0.45
percent, but it is statistically insignificant otherwise. Put differently, if volatility is low,
order flow has a stronger effect on exchange rates than predicted by the linear model.
4. Conclusion
We investigate whether there exist nonlinearities in the relation between order flow and
changes in exchange rates. In fact, estimation of a piece-wise linear model reveals clear
evidence for asymmetric effects in the data: In one regime, characterized by high exchange
rate volatility, the impact of order flow on exchange rate changes is rather modest while in
the other regime it is large (and larger than predicted by the linear model).
Although this is an empirical note, the question arises what is driving our finding. As
pointed out by the referee, high volatility periods may be followed by periods more heavily
weighted toward (uninformative) inventory adjustment trading, which translates into high
liquidity, due to the increased share of uninformed trades in the order flow mix.
To sum up, the linear specification proposed in the seminal work of Evans and Lyons
(2002) may be improved by considering piece-wise linear models. Given such a strong
relationship, the question of the determinants of order flow becomes even more
challenging.

5
References
Cheung Y.-W., M.D. Chinn and A. Garcia Pascual (2002). Empirical Exchange Rate
Models of the Nineties: Are Any Fit to Survive?, NBER Working Paper Series, No.
9393.
Easley, D. and M. O'Hara (1992): Time and the Process of Security Price Adjustment.
Journal of Finance, 47, 577-605.
Evans (2002), FX Trading and Exchange Rate Dynamics. Journal of Finance, 57(6), 2405-
2447.
Evans M. and R. Lyons (2002). Order Flow and Exchange Rate Dynamics. Journal of
Political Economy, 110, 170-180.
Evans, M. and Lyons, R. (2003). How is Macro News Transmitted to Exchange Rates?,
NBER Working Paper Series, No. 9433.
Lyons, R. (2001). The Microstructure Approach to Exchange Rates. MIT Press:
Cambridge.
Meese R.A. and K. Rogoff (1983). Empirical Exchange Rate Models of the Seventies: Do
They Fit Out of Sample?, Journal of International Economics, 14, 3-24.

6
Table 1: Linear Model
USD/DM USD/JY
α
2
R
AIC
α
2
R
AIC
2.156
(11.7)
0.636 -2.818
2.538
(7.13)
0.392 -4.273
Estimation of Equation (1). The t-values are given in parentheses.
Table 2: Threshold Model
USD/DM USD/JY
K
1
β
2
β
c
2
R
AIC
1
β
2
β
c
2
R
AIC
1
1.558
(5.78)
2.666
(11.3)
0.00210 0.681 -2.594
0.500
(0.64)
3.075
(8.32)
0.00450 0.478 -3.951
2
1.769
(8.29)
3.037
(9.88)
0.00160 0.688 -2.589
1.939
(3.54)
3.060
(6.74)
0.00310 0.436 -4.174
3
1.789
(8.02)
2.889
(9.72)
0.00200 0.682 -2.593
0.067
(0.49)
2.763
(7.55)
0.0055 0.436 -4.174
4
1.677
(7.22)
2.893
(10.6)
0.00191 0.693 -2.572
2.054
(5.15)
4.147
(6.22)
0.0019 0.472 -3.960
5
1.809
(6.75)
2.538
(9.80)
0.00225 0.663 -2.633
2.268
(5.80)
4.082
(4.82)
0.0019 0.441 -4.123
Estimation of Equation (2). The t-values are given in parentheses.