Arbitrage in the foreign exchange market: Turning on the microscope

Farooq Akram, Dagfinn Rime, Lucio Sarno, 25 October 2008

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Textbook finance theory is based on the law of one price, which postulates that in efficient financial markets two assets with identical cash flows must trade at the same price. In international financial markets, it says that the domestic interest rates should equal the foreign lending rate for similar assets (of equal maturity, liquidity, and default risk), after hedging for exchange rate risks. Violations of the law of one price are referred to as one-way arbitrage opportunities.

Another common assumption in the finance literature is that it is not possible to obtain net gains from borrowing in one currency to lend in another currency while covering the exchange rate risk. This is the covered interest rate parity condition, which states that net returns on an investment that borrows at home and lends abroad (or vice versa) in similar interest-bearing assets will be zero when exchange rate risk is hedged through forward or swap contracts. Covered interest rate parity is the cornerstone riskless no-arbitrage condition in the foreign exchange market. Since such round-trip arbitrage requires no own funds or borrowing needs, it is a pure arbitrage opportunity.

Deviations from the law of one price for lending services should interest sovereign wealth funds, as the possibility of earning risk-free net returns by lending borrowed funds makes it possible to exploit possible market inefficiencies irrespective of borrowing needs and capital endowments.

Are there arbitrage opportunities in international finance?

Financial markets are commonly assumed to be efficient where potential lenders and borrowers almost continuously possess relevant information to rule out exploitable arbitrage opportunities. This assumption has been supported by numerous empirical studies that have been unable to detect short-term arbitrage opportunities in a variety of financial markets including the international foreign exchange and capital markets (Taylor, 1987). In periods of market volatility, however, some earlier studies have suggested that arbitrage opportunities may arise.1

However, the absence of arbitrage opportunities gives rise to the so-called ‘arbitrage paradox’, first pointed out by Grossman and Stiglitz (1976, 1980). That is, if arbitrage is never observed, market participants may not have sufficient incentives to watch the market, in which case arbitrage opportunities could arise. A possible resolution of this paradox is for very short-term arbitrage opportunities to arise, inviting traders to exploit them, and hence be quickly eliminated.

Real-time trading data

We have empirically investigated the existence of both one-way and round-trip arbitrage opportunities and their properties.2 In contrast with existing studies, we have employed contemporaneously sampled real-time quotes of comparable domestic and foreign interest rates and spot and forward exchange rates. Such data are required to establish whether apparent deviations from no-arbitrage conditions actually represented profitable opportunities to agents at a given time.

Our data set includes contemporaneous tick quotes of exchange rates and interest rates that pertain to the most liquid segments of the foreign exchange and capital markets. The sample includes ask and bid quotes for three major US dollar spot exchange rates: euro, UK sterling, and Japanese yen. It also includes ask and bid quotes for exchange rate swaps and for interest rates on deposits with four different maturities. The tick quotes cover a period of more than seven months spanning from February 13 to September 30, 2004, and is the longest and highest-frequency data set ever used for examining foreign exchange arbitrage.

In contrast with many existing studies, we also account quite precisely for transaction costs as well as pricing and trading conventions when calculating net gains from possible arbitrage opportunities.

How frequently do markets deviate?

We find that trading aimed at exploiting one-way and round-trip no-arbitrage conditions is, on average, not profit-making. However, we document numerous short-lived profitable deviations from the law of one price for borrowing and lending services and from covered interest rate parity. The shares of deviations from the law of one price constituting profitable one-way arbitrage opportunities range from about 10% to 50%.

In contrast, the number of profitable round-trip arbitrage opportunities given the total number of deviations from covered interest rate parity is minuscule. The shares range from 0% to 2.5%. Yet, given the markets’ pace and the almost continuous arrival of new quotes, several covered interest rate parity arbitrage opportunities arrive every hour.

Sizeable opportunities

The size of the profitable deviations can be economically significant and is comparable across different maturities of the interest rates examined. When examining the annualised mean return from profitable one-way and round trip arbitrage deviations, we find that these returns range from a minimum of 2 pips to a maximum of 15 pips. These are relatively large returns when compared with the typical size of spreads in the major dealer markets, which are usually around 2 pips.3 However, the size of the returns may seem small relative to the returns targeted by major players in the FX market, such as hedge funds, but it is not small if we bear in mind that round-trip arbitrage opportunities are riskless and require no capital.

The average number of orders available for trade (so-called limit orders) at the best quotes varies from about 3 to 7. This suggests that occasionally there can be a relatively large number of limit orders at the best quotes. Moreover, since the size of profitable deviations may amount to several pips in some cases, the spot quotes can deviate from the best quotes without necessarily eliminating the arbitrage opportunities. The number of limit orders available when profitable arbitrage opportunities occur may therefore be higher than those available at the best quotes. Given the frequency and size of profitable covered interest rate parity deviations and the depth of the market, even relatively small profits of a few pips per arbitrage trade can accumulate to yield sizable profits over time.

Is arbitrage feasible?

The duration of arbitrage opportunities is, on average, high enough to allow agents to exploit these opportunities, but low enough to explain why such opportunities can be difficult to detect using low-frequency data. We measure duration of profitable arbitrage opportunities by the duration of profitable clusters of consecutive arbitrage opportunities.

Most clusters of profitable deviations do not seem to last beyond a few minutes. Moreover, in most of the cases, average duration falls in the range from 30 seconds to less than about 4 minutes. We found that durations of clusters tend to decline, albeit non-monotonically, with the maturity of contracts. This seems to be consistent with the relatively high market pace (low inter-quote time) at higher maturities. Notably, we find that the duration of profitable arbitrage opportunities increases with market volatility.

We may envision that a dealer observing an arbitrage opportunity would, given the non-negligible duration of profitable arbitrage opportunities, consider it worthwhile to inquire from her trading partners (including the electronic broker for currency trading) about the relevant quotes that she would face, conditional on her (institution's) credit rating and desired trade size.

To exploit arbitrage opportunities, a dealer would have to undertake several deals virtually simultaneously. This is feasible on the Reuters electronic trading system, which provides easy access to money and currency markets from one platform. Alternatively, virtually simultaneous trading in the money markets and the swap markets can be accomplished through tight cooperation between money market dealers and swap market dealers that seems to exist in a typical dealing room.

Conclusions

We find that trading aimed at exploiting one-way and round-trip no-arbitrage conditions is, on average, not profit-making. Arbitrage-free prices are restored rapidly, generally consistent with the notion of market efficiency. Finance theory, however, postulates that in well-functioning markets no-arbitrage conditions hold continuously, not just on average. We provide evidence that short-lived economically significant arbitrage opportunities arise in the major foreign exchange and capital markets in the form of violations of covered interest rate parity and the law of one price.

The results suggest that it may be worthwhile to look for round-trip arbitrage opportunities. It is possible to reduce borrowing costs (net of transaction costs) or earn higher returns on given funds by borrowing or investing abroad while covering the exchange rate risk through a forward contract.

We find it comforting that the observed short-lived arbitrage opportunities provide evidence in support of the resolution proposed for the Grossman-Stiglitz `arbitrage paradox'. That is, very short-term arbitrage opportunities invite traders to exploit them and are quickly eliminated. If arbitrage were never observed, market participants would not have sufficient incentives to watch the market, in which case persistent arbitrage opportunities could arise. These results, coupled with the unpredictability of the arbitrage opportunities, imply that a typical researcher in international macro-finance can safely assume arbitrage-free prices in the foreign exchange market when working with daily or lower frequency data.

References

Akram, Q.F., Rime, D. and Sarno, L. (2008a), "Does the law of one price hold in international financial markets? Evidence from tick data", Journal of Banking and Finance, forthcoming.

Akram, Q.F., Rime, D. and Sarno, L. (2008b), "Arbitrage in the Foreign Exchange Market: Turning on the Microscope," Journal of International Economics, In press.

Frenkel, J.A. and Levich, R.M. (1975), "Covered Interest Arbitrage: Unexploited Profits," Journal of Political Economy, 83, 325--338.

Frenkel, J.A. and Levich, R.M. (1977), "Transaction Costs and Interest Arbitrage: Tranquil Versus Turbulent Periods," Journal of Political Economy, 85, 1209--1226.

Grossman, S.J. and Stiglitz, J.E. (1976), "Information and Competitive Price Systems," American Economic Review, 66, 246--252.

Grossman, S.J. and Stiglitz, J.E. (1980), "On the Impossibility of Informationally Efficient Markets," American Economic Review, 70, 393--407.

Taylor, M.P. (1987), "Covered Interest Parity: A High--Frequency, High--Quality Data Study," Economica, 54, 429--438.

Footnotes

1 See e.g. Frenkel and Levich (1975) and (1977).

2 See Akram, Rime and Sarno (2008a) and (2008b) which focus on the law of one price and covered interest rate parity, respectively.

3 A pip is the smallest price movement of a traded currency. For most currencies a pip is 0.0001 or 1/100 of a cent. For currencies in relation to Japanese yen a pip is 0.01 or 1 cent.

Topics: International finance
Tags: arbitrage, interest rate parity, law of one price

Head of Research, Banking and Finance Group at the Research Department of Norges Bank

Senior Researcher, Norges Bank

Lucio Sarno

Professor, Associate Dean and Head, Finance Faculty, Cass Business School, London

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