Abstract

This paper finds some evidence of market inefficiency by examining the existence of exploitable

arbitrage opportunities across banks in foreign exchange markets. It further extends the

analysis by providing controls for non-synchronicity of the quotes, which is likely to be the

main source of the measurement error, and shows that the arbitrage opportunity is more likely

to occur when deviating from the strict assumptions underlying the efficient and frictionless

market. Past arbitrage opportunities in a market is likely to yield arbitrage returns in the same

opportunities, but larger magnitude of positive arbitrage returns. The results hold for the time

series dimension of the data as well as across market within the same time frame.

1. Introduction

Theory often assumes that markets are efficient, meaning that prices fully reflect

their fundamental values. It is also widely believed that the foreign exchange market is

one of the most efficient markets. In reality, however, there exist frictions, information

asymmetry, and non-synchronous trading that cause market inefficiency. The extent of

this market inefficiency is still under debate as almost any pricing anomaly can be

interpreted in a rational way. However, the least disputed evidence against market

inefficiency may be the existence of arbitrage.

This paper focuses on exchange rate arbitrage across banks using bid-ask exchange

rates of three banks. The objectives of this paper are to investigate whether profitable

arbitrage opportunities in foreign exchange rate markets exist, and whether the

existence of arbitrage is caused by violations of the assumption underlying the notion of

market efficiency. The latter is examined by studying the persistency of the profitable

arbitrage opportunities over time in a market as well as their consistency across

markets with different liquidity.

Frankel and Levich (1975, 1977) examine the deviations from the interest rate

parity, and show the neutral band around the interest rate parity with transactions

costs.1 Using high frequency data, Rhee and Chang (1992) find profit opportunities from

the one-way arbitrage as well as the covered interest arbitrage. However, no study has

investigated the arbitrage opportunities across banks in the foreign exchange rate

markets in the long term or the existence of unexploited arbitrage profitability.

This paper uses the daily bid-ask exchange rates of three international banks for

nine currencies of developed countries for the period from October 9th, 1986 to

from one bank at its low rate and simultaneously selling to another bank at its high rate.

Secondly, there indeed exist arbitrage opportunities in the foreign exchange markets.

The probability of making arbitrage profits ranges between 14 and 70 percent for the

sample period across currencies and across maturities.2 Thirdly, the magnitude of

arbitrage profits is small but may be economically meaningful since transactions are

usually sizable. The average arbitrage return ranges from 0.02 percent to 0.12 percent.

It represents on average about 10 percent to 128 percent of the bid-ask spread.

Moreover, the 90th percentile of arbitrage returns ranges from 0.04 to 0.31 percent,

meaning that every 1 out of 10 transaction would give on average between 4 and 31

cents of arbitrage profits for every 100 dollar transaction volume. Profits from arbitrage

operations are necessarily small in competitive and well-informed markets. However,

absolute profits from successful arbitrage may be large since transactions are usually

sizeable.

The large number of arbitrage opportunities leads us to the question, whether these

arbitrage opportunities are in fact a reflection of measurement error in the data. The

measurement error may arise due to coding error or — more likely — due to non-

synchronicity of data collection. This particular source of measurement error arises as

the data is not collected at exactly the same time from all banks. A one minute difference

in the quote time may lead to a gap that is due to a change in the underlying price

rather than a true arbitrage opportunity. Thus, even in this carefully crafted database,

measurement error is still an important concern. To further take into account a

potential measurement error, we employ the two ways of econometric methods:

controlling and instrumenting. Non-synchronicity of data collection would be likely to

occur when the market is volatile. As a control variable, we incorporate the volatility of

the exchange rate in the estimation regression. As the main instrument, we use past

markets, where investors do not take advantage of arbitrage opportunities

instantaneously.

Moreover, persistency indicates that arbitrage transactions are indeed

implementable, and that arbitrage opportunities are not likely to disappear before

execution takes place. Parameter estimates of past arbitrage returns can measure

persistency of profitable arbitrage. That is, if making profits from arbitrage is persistent,

then it can be exploitable even though the arbitrage return is small. We find that there

is persistency in arbitrage return. Depending on currencies and maturities, the

parameter estimates of past excess returns range from 0.02 for the 3 month UK Pound

forward to 0.83 for the 1 year French Franc forward. Excess arbitrage returns in a

given market at any point in time may provide some information for forecasting the

future, i.e. excess arbitrage returns may be partly predictable in a market.

Making arbitrage profits is possible when the market is deviating from the no-

arbitrage conditions underlying interest rate parity theory. Markets are not efficient

due to the illiquidity in the market, non-synchronicity among the market players

resulting from high uncertainty for example, and constrained market information. If a

market is not efficient, then this gives rise to unexploited arbitrage profitability. Banks

that are facing markets with potentially large arbitrage returns due to market illiquidity

may choose to widen their bid-ask spread, which in turn reduces the number of

arbitrage opportunities. Thus, while illiquid markets may exhibit larger arbitrage, the

chance of arbitrage is lower than in liquid markets. Thus, the overall effect on the

arbitrage profit is ambiguous. Indeed, we find that the bid-ask spread is negatively

related to the likelihood of arbitrage opportunities, and at the same time the wider the

spread, the higher the arbitrage return. Using all the observations, we find mixed signs

comparison of returns across different markets at the same point in time. It allows us to

investigate whether markets with lower liquidity, as well as other characteristics, are

more likely to exhibit higher arbitrage situations than others. This analysis, which is

based on the standard Fama-MacBeth regression,3 controls for the time-series variation

in the data. Using information orthogonal to the time series variation, this analysis finds

that lagged profitable arbitrage opportunities, volatility and bid-ask spreads are also

useful in explaining cross sectional differences in arbitrage opportunities, thereby

confirming the results in the time series analysis.

Arbitrage opportunities show some persistency, which means arbitrage

opportunities are partly predictable, and implementable. The magnitude of exploitable

arbitrage, however, decreases significantly fast, which implies that arbitrage

opportunities may not be as they appeared at first glance.

Finally, this paper finds that exploitable arbitrage opportunities exist and are partly

persistent. If the market is efficient, the return should be random. However, the finding

of persistent arbitrage opportunities does not necessarily imply that the banks provide

arbitrage opportunities on two consecutive days. In fact, a transaction position that

generates profitable arbitrage today is unlikely to offer profitable arbitrage opportunity

on the next day. Indeed, we find that replicating the transaction position the next day