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1 Journal of Banking & Finance 34 (2010) Contents lists available at ScienceDirect Journal of Banking & Finance journal homepage: Covered interest arbitrage profits: The role of liquidity and credit risk Wai-Ming Fong a, Giorgio Valente b, *, Joseph K.W. Fung c a The Chinese University of Hong Kong, Shatin, N.T., Hong Kong b University of Leicester, University Road, Leicester LE1 7RH, United Kingdom c Hong Kong Baptist University, Kowloon Tong, Kowloon, Hong Kong article info abstract Article history: Received 20 July 2009 Accepted 6 November 2009 Available online 11 November 2009 JEL classification: F31 F41 G14 G15 We study the profitability of Covered Interest Parity (CIP) arbitrage violations and their relationship with market liquidity and credit risk using a novel and unique dataset of tick-by-tick firm quotes for all financial instruments involved in the arbitrage strategy. The empirical analysis shows that positive CIP arbitrage deviations include a compensation for liquidity and credit risk. Once these risk premia are taken into account, small arbitrage profits only accrue to traders who are able to negotiate low trading costs. The results are robust to stale pricing and the nonsynchronous trading occurring in the markets involved in the arbitrage strategy. Ó 2009 Elsevier B.V. All rights reserved. Keywords: Exchange rates Arbitrage Covered interest rate parity Foreign exchange microstructure 1. Introduction The Covered Interest Parity (henceforth CIP) theorem states that the covered interest rate differential between two identical riskfree securities denominated in two different currencies should be equal to zero. Since Keynes (1923) and Einzig (1937) a vast body of empirical and theoretical literature investigated the joint behavior of foreign exchange (henceforth FX) and money markets and the occurrence of arbitrage opportunities. The general consensus is that CIP is a reasonably mild assumption, given the extensive empirical evidence suggesting that CIP holds (Sarno, 2005, p. 675) especially when transaction costs are taken into account. 1 However, some studies pointed out that currency markets were and still are characterized by a substantial number of instances in which CIP deviations exceed the transaction cost band, implying profitable arbitrage opportunities (see, inter alia, Balke and Wohar, 1998; Peel and Taylor, 2002; Akram et al., 2008, 2009; Marshall et al., 2008; Mancini Griffoli and Ranaldo, 2009 and the references * Corresponding author. Tel.: ; fax: addresses: wmfong@cuhk.edu.hk (W.-M. Fong), giorgio.valente@le.ac.uk (G. Valente), jfung@hkbu.edu.hk (J.K.W. Fung). 1 A selective list of early studies investigating the validity of CIP include, among others, Frenkel and Levich (1975, 1977), Deardorff (1979), Taylor (1987, 1989), Rhee and Chang (1992) and the references therein. therein). Although these findings could be explained by means of slow and infrequent communications between London and New York banks in the early 1920s (Einzig, 1937, p. 57; Peel and Taylor, 2002), it is more difficult to rationalize them in presence of modern FX dealing rooms, where prices can be obtained within seconds and orders can be carried out in an automated and synchronized fashion. CIP arbitrage profits are generally assumed to be riskless 2 and attainable without capital outlay. However, real-world arbitrage activities are subject to impediments which prevent arbitrageurs to fully exploit arbitrage opportunities and move asset prices to their equilibrium no-arbitrage values (see, inter alia, Shleifer and Vishny, 1997 and the references therein). Two of these impediments are par- 2 In the spirit of Deardorff (1979), a different test of CIP may arise from considering one-way arbitrage opportunities in the form of owner s arbitrage (OA) and borrower s arbitrage (BA). However, it is important to point out that round-trip and one-way arbitrage conditions differ in that violations of the latter do not necessarily prove the existence of riskless profits. This is due to the fact that one-way arbitrage opportunities require an excess supply or demand of funds, while round-trip arbitrage does not require funds to be lent or borrowed. They only indicate the presence of price differentials that are due to different pricing practices, market segmentation and/or different demand/supply conditions in all of the markets involved in the CIP arbitrage. For these reasons we consider CIP (or round-trip) arbitrage as the relevant arbitrage condition throughout the paper. See also Akram et al. (2009) /$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi: /j.jbankfin

2 W.-M. Fong et al. / Journal of Banking & Finance 34 (2010) ticularly important in the context of CIP arbitrage: market liquidity and credit risk. It is well known that the Law of One Price (LOP) holds when markets have few frictions associated with transacting, especially illiquidity indicators such as the spread. In these cases, few arbitrage opportunities arise in real time and the violations of LOP are generally not profitable if all transaction costs are taken into account. However, LOP does not hold when markets are illiquid. Several studies have documented that aspects of the market microstructure may cause the temporary deviation of prices from their no-arbitrage values (Stoll, 1978; O Hara and Oldfield, 1986; Gârleanu and Pedersen, 2009) and financial market liquidity plays a key role in moving prices to eliminate arbitrage opportunities (Kumar and Seppi, 1994; Roll et al., 2007 and the references therein). The other important aspect that has been surprisingly neglected in the literature on CIP is the fact that CIP arbitrage opportunities are generally computed using interbank deposit rates which are not risk-free since they are subject to different levels of credit risk. Arbitrage activities can eliminate the market risk associated with the movements of exchange rates and interest rates, but they cannot eliminate the credit risk associated with the interbank deposits and the counterparty risk in the forward contracts. Furthermore, when interbank markets are highly concentrated, the banks that have an extensive retail deposit-taking network have also a high degree of market power that is exercised by means of a very selective assessment of counterparty credit-worthiness and the imposition of tight credit limits (i.e. trading volumes). All of these arguments suggest that some of the arbitrage profits recorded in recent studies may reflect premia demanded by market participants as compensation for the liquidity and credit risk faced during arbitrage transactions. 3 In this paper we test this conjecture by investigating CIP arbitrage profits for a single currency market (i.e. Hong Kong dollar, henceforth HKD) which is among the 10 largest currency markets in terms of daily average turnover (Bank for International Settlement, BIS 2007) but its overall liquidity is poorer than in major currency markets and its banking market is highly concentrated. Using a novel and unique dataset of tick-bytick tradable (firm) spot and forward quotes for HK dollar vis-àvis US dollar (USD), as well as tradable HKD- and USD-denominated deposit rates over different short-term maturity tenors, we carry out an extensive analysis of CIP deviations and their relationship with market liquidity and credit risk. Our main findings are as follows. First, we find that HKD/USD FX market is characterized by a large number of CIP deviations and most of these deviations exceed the transaction cost band implied by the spreads of the individual financial instruments. Second, positive CIP deviations are clustered at the side of the market and their economic value is sizable across the maturity spectrum. Third, positive CIP deviations are associated with market illiquidity at very short maturities and with differences in credit risk between the Hong Kong and US financial institutions across the full maturity spectrum. Fourth, small residual arbitrage profits are still present even after taking into account liquidity and credit risk. However, since additional trading costs (i.e. brokerage fees and settlement costs) are generally not included in quoted prices, their explicit consideration is likely to offset any profits that arise from arbitrage activities. Given the existence of heterogeneous additional trading costs (Mavrides, 1992), only the traders who are able to negotiate low trading costs will be able to reap genuine arbitrage profits as compensation for their activity (Deardorff, 1979; Grossman and Stiglitz, 1980). This study differs and improves upon previous contributions in several respects. The dataset employed in this study, to the best of our knowledge, is the first to record tradable quotes at tick-by-tick frequency for all financial instruments involved in the CIP arbitrage over a period of eight months. Taylor (1987), a landmark study in the literature on CIP arbitrage, employed interest rates and exchange rates data that are recorded by phoning several London brokers at 10 min frequency during the most active hours (9:00 16:30 GMT) over three days in Other studies re-examining Taylor s results, employ datasets which exhibit various limitations. One of the most relevant limitations is that all or some of the prices used to compute arbitrage deviations are purely indicative, hence evidence of arbitrage opportunities recorded using these datasets may not necessarily imply glaring profitable opportunities. The dataset employed in this paper is therefore unique and allows us to carry out a thorough economic assessment of CIP arbitrage since contemporaneous tradable quotes of domestic and foreign deposit rates and spot and forward exchange rates are crucial to establish whether an apparent deviation from the no-arbitrage conditions in the FX market represents a genuine profitable arbitrage opportunity. Our work builds on Cheung and Chan (1994) and Akram et al. (2008, 2009) who investigate CIP arbitrage violations in both round-trip and one-way arbitrage in the Hong Kong market and for the major currencies respectively. Our work differs from theirs in several important ways. First, Cheung and Chan (1994) employ daily indicative quotes over a shorter period of time (3 months) recorded over an interval of 30 min (between 10:45 am and 11:15 am Hong Kong time) while Akram et al. (2008, 2009) employ a tick-by-tick dataset comprising tradable quotes for spot FX rates and indicative quotes of FX swaps and currency deposit rates. Second, Cheung and Chan (1994) data are collected from only two commercial banks (i.e. Tokyo Forex and Tullett and Hua Chiao Commercial Bank Limited), while our tradable quotes are provided by ICAP, the world s largest voice and electronic interdealer broker which exhibits a substantial market share of the spot and forward FX trading in Hong Kong (ICAP, 2007). 4 Third, both Cheung and Chan (1994) and Akram et al. (2008, 2009), along the lines of earlier studies, do not consider the role of market liquidity and credit risk in affecting CIP arbitrage profits, which is the main goal of our paper. Other related papers are Baba and Packer (2009), Genberg et al. (2009), Mancini Griffoli and Ranaldo (2009) and McAndrews and Sarkar (2009) who investigate the spillover effects of the money market turbulence in on short-term CIP deviations between the US dollar and the major currencies and the effects of the Federal Reserve s responses to the crisis on credit and liquidity risk. Our work differs from theirs in that we do not focus on the behavior of the FX and money markets during turbulent periods, such as the recent financial crisis, but we try to understand the role of market liquidity and credit risk on arbitrage activities under normal market conditions. Furthermore, we assess the impact of market liquidity and credit risk on CIP arbitrage profits computed by taking into account features which reflect very closely realistic conditions faced by arbitrageurs, while most of the other studies look at CIP deviations computed without taking into account transaction costs or use interest rate spreads. 5 3 Another way of rationalizing the effect of liquidity on arbitrage profits relates to the intimate relationship between market liquidity and funding liquidity. If market liquidity is correlated with funding liquidity (as in models with liquidity spirals such as Brunnermeier and Pedersen, 2009) the effect we document in this paper may not be necessarily interpreted as a liquidity risk, but as a higher cost of arbitrage capital. See also Mancini Griffoli and Ranaldo (2009). 4 Further details on the market coverage of our dataset are discussed in Section Mancini Griffoli and Ranaldo (2009) also investigate deviations from CIP for the major currencies incorporating realistic features of the FX market. However, our work differs from theirs since we use tick-by-tick firm (transactable) quotes provided by the world s largest electronic and voice interdealer broker (ICAP) while Mancini Griffoli and Ranaldo (2009) use indicative quotes provided by one single intermediary (Tullet Prebon) recorded four times per day.

3 1100 W.-M. Fong et al. / Journal of Banking & Finance 34 (2010) The remainder of this paper is organized as follows. In Section 2 we discuss the theoretical underpinnings, our dataset and the main institutional features of the HKD FX market. Section 3 reports preliminary summary statistics and in Section 4 the results of empirical analysis are discussed. Section 5 contains some robustness checks and a final section concludes. 2. Computations, data and institutional issues 2.1. CIP deviations Deviations from CIP are routinely expressed as ð1 þ i d;k Þ F k ð1þ ð1 þ i f ;k Þ S where i d and i f are the domestic and foreign interest rates on similar assets of a certain maturity tenor k, S is the prevailing spot exchange rate and F k is the forward exchange rate with maturity tenor k. Any deviations from Eq. (1) would represent a risk-free arbitrage opportunity in a frictionless world. If we introduce and prices to Eq. (1), any deviations from CIP are profitable if either of the following inequalities hold 6 : F b k S a ð1 þ i d;k Þ ð1 þ i b f ;k Þ > 0 S b F a k ð1 þ ia f ;k Þ ð1 þ i b d;k Þ > 0 a where superscript a and b denote the and prices, respectively. Since the quotes in the deposit markets are reported as annualized rates and HKD deposits and USD deposits have a different day count convention, throughout the paper we compute CIP deviations as follows: 2 3 CIP ðþ : Fb k S a ð1 þ i a d;k Þ 365 D 4 5 ð1 þ i b f ;k Þ > 0 or D 360 CIP ðþ : Sb F a k 2 4 ð1 þ ia f ;k Þ D 360 ð1 þ i b d;k Þ D 365 ð2þ 3 5 > 0 ð3þ where D is the number of days to maturity of the forward and deposit contracts over the maturity tenor k, 7 and superscripts a and b denote the and prices respectively. Eq. (3) indicate that only positive deviations are profitable Data The empirical analysis performed in the paper employs data for the HKD FX market. The BIS triennial survey on FX market activity shows that, in April 2007, the HKD market is the 10th-largest currency market in terms of percentage share of the daily world average turnover, together with the Swedish krona (SEK) and just above the Norwegian krone (NOK), two currencies that have been investigated in recent empirical studies (Bjønees and Rime, 2005). 6 We assume that CIP arbitrage is conducted by trading four instruments: spot and forward exchange rates and domestic and foreign deposit rates. An alternative characterization of the arbitrage strategy would imply trading swap points rather than spot and outright forward rates (Cheung and Chan, 1994; Akram et al., 2008, 2009 and the references therein). Although we do not consider this alternative characterization of the CIP strategy in this paper, we note that the use of swaps may affect the number of arbitrage opportunities which could be somewhat different than the ones we report in Section 4. 7 In Eq. (3) the days to maturity D are computed as the actual number of business days between the spot date (or value date) and the maturity date after taking into account bank holidays in Hong Kong (see Akram et al., 2008, Appendix A). Our dataset is a collection of tick-by-tick data obtained from ICAP for the sample period ranging between May 17th, 2005 and December 31st, ICAP is the world s largest voice and electronic interdealer broker; in 2006 it covered 65% of the worldwide FX spot voice market and 35% of the FX voice forward market. Although recent market trends have exhibited a furious shift from voice broking to electronic broking, the voice-broking FX market is still very active and in certain geographical areas it is the dominant trading venue. In fact, in 2006, FX voice broking contributed a hefty 69% to the ICAP group s overall profits. In the context of emerging markets (especially the HKD market), the above percentages can be considered conservative, as ICAP covers more than half of the market share in emerging market securities trading (ICAP, 2007). The market coverage of our dataset, computed as in Bjønees and Rime (2005), is about 40% of the overall HKD spot and forward FX market as reported in BIS (2007). 9 The dataset comprises all of the best and prices for the HKD/USD spot exchange rate, the HKD/USD outright forward rate and all of the best and prices for the HKD- and USD-denominated deposit rates. The forward exchange rates and both the domestic- and foreign-currency denominated deposit rates are relative to three different maturity tenors: one week, four weeks, and 12 weeks. A particular novelty of this unique dataset is that all of the and prices are firm (hence, directly tradable), which is different from most of the previous studies in which all or some of the quotes are indicative. All of the quotes in our dataset are retrieved from ICAP voice-broking record tapes Institutional issues Two important aspects characterize the HKD FX market. The first is that the Hong Kong monetary policy is carried out by means of a currency board. As a consequence the HKD has been tied to the USD since 1983 and in the last two and one-half decades, the value of the HKD/USD spot exchange rate has not moved substantially away from the imposed parity (7.8 HKD per USD), even under the turbulent market conditions of It is instructive to note that this peculiar monetary regime does not hinge on arbitrage practices. In fact, arbitrage pricing in the FX market is independent of the currency regime. The arbitrage conditions tested in this paper should offer, in absence of frictions, riskless profits if the deviations are large enough to cover transaction costs. There is no role for expectations of exchange rates in these conditions as the degree of violation is known at any point in time and any rational trader would exploit such violation (size of trades allowed by the market) regardless of what the central bank is doing. 10 The second important aspect is that the banking market in Hong Kong is highly concentrated. In fact, although there are about The sample period is chosen because of data availability (firm quotes are not available from ICAP before May 17th, 2005). 9 We thank Dagfinn Rime for suggesting this to us. 10 However, as a robustness check we have tested for the possibility that the activity of the Hong Kong Monetary Authority (henceforth HKMA) might have affected arbitrage activities and the size of arbitrage opportunities over the sample period. More specifically we have considered the case of FX intervention dates and dates when policy rates are changed. As for the first case, the ex-post records of the HKMA s FX market activities indicate that during the sample period investigated in this paper, no FX intervention has taken place. In fact official market operations stopped in April 2005 and resumed only at the end of When considering policy rate changes, it is important to emphasize that, given the specific currency regime, the HKMA does not set interest rates but passively follows any federal fund rate changes set by Federal Open Market Committee (FOMC) of the US Federal Reserve. During our sample period 5 FOMC meetings took place which revised US interest rates. In order to check for the possibility that our results may be due to anomalies related to dates where policy interest rates are set, we have carried out a fraction of the empirical analysis using data where the FOMC are removed. The results, not reported to save space, are qualitatively and quantitatively similar to the ones discussed in Section 4.

4 W.-M. Fong et al. / Journal of Banking & Finance 34 (2010) licensed banks, only a small number of them are retail banks (i.e. banks that have a network of branches to carry on both retail and wholesale business in the domestic market). In addition, the top three banking groups account for over a half of total customer deposits in Hong Kong (Carse, 2001). As a result, the banks that have an extensive retail deposit-taking network have also a high degree of market power that is exercised by means of a very selective assessment of counterparty credit-worthiness and the imposition of tight credit limits (i.e. trading volumes). This peculiar aspect of the HKD market, associated with its relative lower liquidity (compared to major currencies markets), makes it an interesting case study to investigate how liquidity and credit risk affect the formation of CIP arbitrage deviations. 3. Preliminary analysis 11 LIBOR and Overnight Index Swaps (OIS) daily data are obtained from Bloomberg. In this section measures of market liquidity and credit risk are computed. For each trading day, the measures described below are computed using daily or intraday data. In the latter case, as in previous empirical studies a daily average is used as input for the subsequent estimations (see Roll et al., 2007 and the references therein). Market liquidity has many aspects (immediacy, costs, depth and resiliency) and no empirical measure is able to reflect them all. Our dataset only comprises best and prices for all instruments involved in the CIP arbitrage, hence no information is provided on transaction prices, limit order books and trading volumes. As consequence, we proxy liquidity by means of quoted spreads, daily number of quotations and effective spreads estimated using the procedure suggested by Corwin and Schultz (2008). The liquidity measures employed in the empirical investigation are routinely used in existing studies on market liquidity (see, inter alia, Roll et al., 2007; Corwin and Schultz, 2008; Goyenko et al., 2009 and the references therein). However, they are not immune from criticisms. In fact, spreads capture the implicit cost of trading (see Harris, 2003; Stoll, 2000 and the references therein) but they do not consider other aspects of liquidity. Similarly, the daily number of quotations is usually employed in empirical works on the basis of the notion that liquidity ought to be higher in more active markets (Demsetz, 1968). However, the relationship between liquidity and market activity has been questioned in recent empirical studies (Johnson, 2008). To test for the effect of credit risk on CIP arbitrage deviations we use a measure of the difference in credit risk perception between Hong Kong and US financial institutions. As in Genberg et al. (2009) the measure is computed as the difference between the HKD-denominated LIBOR-OIS spread and the equivalent LIBOR-OIS spread denominated in USD. 11 A positive difference denotes a situation where Hong Kong financial institutions are perceived to be riskier than US financial institutions. This, in turn, generates a credit risk premium that adds to the funding rates in HKD since Hong Kong banks, having to preserve funds on hand, became more cautious in lending to their US counterparties. The use of LIBOR-OIS as reflecting credit risk is currently debated and recent papers use other measures to proxy for credit risk (see, inter alia, Baba and Packer, 2009; McAndrews and Sarkar, 2009; Coffey et al., 2009; Mancini Griffoli and Ranaldo, 2009 and the references therein). In fact, LIBOR-OIS spreads change over time because of changes in credit risk (counterparty risk) exhibited by the banks members of the LIBOR panel and the overall funding liquidity conditions (Giavazzi, 2008; Kotomin et al., 2008; Brunnermeier and Pedersen, 2009). A cleaner measure of credit risk would be represented by the differences in CDS spreads between the Hong Kong and US financial institutions. However, although there are indices of CDS spreads for US financial institution, an equivalent index for Hong Kong financial institutions is not available over the sample period. 12,13 Table 1 reports preliminary statistics based on calculations of CIP arbitrage deviations (Panel A), credit risk measures (Panel B) and liquidity measures (Panel C). A preliminary look at the intraday data suggests the need for a synchronization of the quotes in different markets to compute CIP deviations, as the HKD/USD forward and the two deposit markets are comparatively less active than the HKD/USD spot market. To obtain a time series of contemporaneous quotes for the different instruments, we construct our synchronized data as follows: First, we exclude days with few observations (such as weekends and public holidays). After these adjustments the number of trading days range between 157 (four weeks maturity) and 159 (one and 12 weeks maturity). Second, we retain the active time period within each day (i.e. between 7:00 and 17:00 Hong Kong time). 14 Third, for each instrument, we generate a 15-second interval time series of prevailing quotes. Then, for each maturity tenor, we consolidate all of the 15-second interval time series to form a synchronized sample. Finally, to mitigate a possible problem of stale quotes, we delete all observations in which either the spot or forward prevailing and were quoted more than 5 min previously, or in which either the HKD or USD deposit prevailing and prices were quoted more than one hour previously. 15 Using this synchronized sample, we then compute the daily average of these deviations. 16 The summary statistics of daily CIP deviations are reported in Table 1, Panel A for all maturity tenors. All figures are expressed in pips. In line with Taylor (1987), per-period average CIP deviations increase with maturity tenors. Furthermore average 12 In fact, the CDS market in Hong Kong is relatively small (Genberg et al., 2009) and over the sample period investigated in this paper only CDS spreads for 9 non-financial companies are available. A simple comparison between the US financial CDS index and the simple average of the 9 Hong Kong CDS spreads would be inappropriate since the average rating of the 9 Hong Kong companies is generally higher than the rating of the average company included in the US index. Hence, the difference between the levels of the two series would not be zero on average and this would induce a bias in subsequent estimations. We thank Mico Loretan and Eli Remolona for useful discussions on the CDS market in Hong Kong. 13 Another way to interpret the effect of counterparty risk on arbitrage profits is suggested in Gârleanu and Pedersen (2009). In a theoretical setting, they demonstrate that CIP may fail because it requires capital (margin) to trade and profit from CIP deviations. Our interpretation is also consistent with this line of reasoning since a higher counterparty risk is likely to induce higher and binding margin requirements which, in turn, may prevent arbitrage activity and allow positive CIP deviations to persist over time. See also Darvas (2009). 14 It is worth noting that the market we analyze, during the sample period is mostly voice-intermediated. Therefore trading does not necessarily occur over 24 h as in electronic-intermediated markets and it makes sense in this context to define an opening and closing time. 15 Overall, the number of intraday observations obtained by applying this synchronization scheme is larger than 12,000 for all maturity tenors, with a maximum of about 28,000 observations at the 12 weeks maturity. In order to check for the robustness of our results with respect to the selected synchronization scheme, in Section 5 we compute CIP deviations using other data synchronization filters and adjustments. 16 It is instructive to note that, on the basis of various conversations with several proprietary traders and desk managers, it is possible to conduct arbitrage trades through the voice broker. In fact ICAP does act as one of the main intermediaries in both foreign exchange (spot and forward) and deposit market in Hong Kong. Hence, when a positive CIP deviation is detected, an arbitrageur may complete a set of arbitrage trades by contacting the relevant voice-brokers responsible for different desks. However these trades do not occur often since, as we detail in Section 4, additional aspects must be taken into account (such as effective brokerage fees and settlements costs and credit limits imposed on various traders). In order to check our results with respect to the effect of stale prices or nonsynchronous trading in the four markets involved in CIP arbitrage strategies, we carry out some robustness checks in Section 5.

5 1102 W.-M. Fong et al. / Journal of Banking & Finance 34 (2010) CIP deviations are different when computed at the or the side of the market. In fact, for all three maturities, CIP deviations are always positive, on average, at the side while they are always negative at the side. In all cases the figures are significant at the 5% statistical level. 17 However, it is important to note that negative average CIP deviations do not imply that CIP arbitrage is prevented in continuous time. In fact, as in Akram et al. (2008), the maximum of the distribution of intraday CIP deviations, even at the side of the market, is positive suggesting that some profitable arbitrage opportunities may be present. Table 1 Panel B reports summary statistics of the credit risk measure. Average daily LIBOR-OIS spreads are positive for both currencies and their value increases with maturity tenors. HKDdenominated spreads are higher than USD-denominated spreads. This suggests that, over the sample period, Hong Kong financial institutions are perceived to be riskier than US financial institutions. The differences between the two spreads, reported at the bottom of Panel C, are all significant at conventional statistical level and close to 0.15% per annum across the three maturities investigated. The summary statistics of liquidity measures are reported in Table 1 Panel C. As we are interested in measures of liquidity conditions of the four markets, an aggregation of the individual markets liquidity measures is carried out. More specifically, aggregate measures are computed as simple arithmetic average (EW) or weighted average (VW) of the individual markets liquidity measures where, in the latter case, the weights assigned to each market are computed in terms of their daily average turnover as reported in BIS (2007). Daily quoted spreads and effective spreads computed as in Corwin and Schultz (2008) are expressed in pips and exhibit an increasing pattern as maturity increases. The daily number of quotations is instead fairly similar across maturities. The aggregation scheme does not affect the summary statistics since the differences between EW and VW variables, with the exception of the number of quotations, are also small in size. 4. CIP arbitrage profits, liquidity, credit risk and additional trading costs 4.1. CIP arbitrage profits 17 As pointed out in Akram et al. (2008) the existence of statistically significant negative average CIP deviations may be due to the fact that market makers may price instrument more conservatively than CIP conditions would imply, fearing that some of the instruments may move in way to generate arbitrage opportunities. Table 1 Summary statistics. Mean Median Standard deviation Panel A: CIP deviations 1 week 6.32 ** 6.55 ** ** ** weeks ** ** ** ** weeks ** ** ** ** Panel B: credit risk measures USD spreads 1 week ** ** weeks ** ** weeks ** ** HKD spreads 1 week ** ** weeks ** ** weeks ** ** Spread (HKD USD) 1 week ** ** weeks ** ** weeks ** ** Panel C: aggregate liquidity measures Quoted spreads 1 week VW 5.34 ** 5.24 ** 1.13 EW 3.55 ** 3.46 ** weeks VW 5.64 ** 5.61 ** 0.85 EW 4.96 ** 4.91 ** weeks VW 6.08 ** 6.03 ** 0.85 EW 7.89 ** 7.80 ** 0.79 Number of quotations 1 week VW ** ** EW ** ** weeks VW ** ** EW ** ** weeks VW ** ** EW ** ** CS liquidity measure 1 week VW 3.99 ** 3.13 ** 3.05 EW 2.48 ** 1.99 ** weeks VW 6.67 ** 5.36 ** 4.64 EW 5.04 ** 4.34 ** weeks VW 8.80 ** 7.92 ** 5.05 EW 8.93 ** 8.27 ** 4.32 The table reports summary statistics of daily CIP deviations, credit risk measures and liquidity measures computed over the sample period May 17th, 2005 to December 30th, Panel A: CIP deviations are daily averages of intraday CIP deviations computed by synchronizing the time series of quotes of the four markets from the raw tick data, as described in the text (Section 3). CIP deviations are expressed in pips. Panel B: credit risk measures over the three maturity tenors are HKD- and USD-denominated Libor-OIS spreads computed using daily mid-quotes. Spread (HKD USD) denotes the difference between HKD-denominated Libor-OIS spread minus the USD-denominated Libor-OIS spread. Credit risk spreads are expressed in percentage per annum. Panel C: quoted spreads are daily average of differences between intraday best and prices for each instrument involved in the arbitrage strategy. Number of quotations is the daily number of quotations recorded for each instrument involved in the arbitrage strategy. CS liquidity measure is the Corwin and Schultz s (2008) measure computed for each instrument using intraday highest and lowest quotations. Bid spreads and CS measures are expressed in pips. All aggregate liquidity measures are computed assigning either equal weights (EW) to all markets or weights computed in terms of daily average market turnover (VW). ** Denote significant at 5% statistical level. In this section, we compute positive CIP arbitrage opportunities that satisfy Eq. (3) and associate them with the measures of liquidity and credit risk discussed in the previous section. Table 2 shows the percentage of positive CIP deviations out of all of the observations obtained at intraday level. Across maturity tenors, we find that the average percentage of positive arbitrage deviations ranges between 8% and 84%. Furthermore, arbitrage at the price of CIP is much more frequent (73% on average across maturities) than the arbitrage at the price (16%). This finding is not novel in the literature. In fact Akram et al. (2008) reports for the Japanese yen (JPY)/USD CIP arbitrage a similar pattern. This phenomenon can be explained in different ways. One possible explanation suggested in Akram et al. (2008) relies on the quoting practices of both currencies. In fact, for both JPY/USD and HKD/USD the USD is not the quoting currency. A different and perhaps more interesting explanation can be provided by looking at the concentration of the banking system. In fact, looking at both Table 2 and Panel A, the existence of a large number of arbitrage opportunities which seems to be positive on average indicates that some frictions are in place and prevent arbitrage forces to operate. If access to liquidity in the HKD market is restricted by the selectivity of the major Hong Kong retail banks, positive arbitrage deviations at the side (which require borrowing in the HKD deposits market, selling HKD for USD in the spot FX

6 W.-M. Fong et al. / Journal of Banking & Finance 34 (2010) Table 2 Frequency of positive arbitrage opportunities. 1 week Total dev 12,861 12,861 Profitable dev % share weeks Total dev 22,277 22,277 Profitable dev 14, % share weeks Total dev 28,709 28,709 Profitable dev 24, % share 84 8 Average % share This table shows the frequency of intraday positive CIP arbitrage deviations computed as in Eq. (3) in the main text. Total dev represents the number of all intraday deviations (including non-positive) computed using the synchronization scheme described in Section 3 of the main text. Profitable dev records the number of profitable intraday deviations. % share are the profitable deviations as the percentage of all deviations. See notes to Table 1. market, lending in the USD deposits market and selling USD for HKD in the forward market) would survive for a long time since arbitrageurs would not be able to exploit them because of the credit limits (trading volumes) present in the HKD deposit market. 18 However, the unexpectedly high frequency of positive deviations reported in Table 2 is not sufficient evidence of substantial profitable opportunities, as deviations may have a skewed distribution, i.e. positive deviations may be frequent and small in size. To better quantify the economic value of these deviations, we report the mean values of the positive CIP deviations in Table 3. Average arbitrage profits are computed as per-period returns and annualized returns. 19 At face value, the average profits from CIP arbitrage are handsome, and as in Taylor (1987) per-period returns increase with maturity. Annualized rates do not share this increasing pattern and range between 0.187% (12 weeks at the side) and 0.742% (1 week at the side) per annum The role of market liquidity and credit risk The figures reported in Table 3 take into account transaction costs (i.e. spreads) but they do not tell us whether they may be just reflecting liquidity and credit risk premia demanded by market participants to carry out transactions in the HKD market. In order to test this conjecture, in the spirit of Baba and Packer (2009), we estimate the following linear factor model: PCD i t;k ¼ a þ bliq t;k þ ccrd t;k þ e t;k where PCD i t;k denotes the daily average of positive CIP deviations at the maturity tenor k computed at the i =, side of the market on the trading day t, LIQ t and CRD t are aggregate liquidity measures and the HKD USD LIBOR-OIS spread (credit risk measure) computed on the same day t respectively, and e t is an error term. The parameters b and c denote the sensitivity of positive CIP arbitrage deviations to market liquidity and credit risk variations. When liquidity is poorer, positive arbitrage deviations increase because of an increasing liquidity premium. This would imply a b > 0 18 This finding is also consistent with a situation where funding liquidity conditions are tighter in the HKD deposit market. 19 Annualized returns are computed using the assumptions that 1 pip represents HKD100 per USD1 million traded, 1 USD is exchanged at the rate of 7.8 HKD and a 365 day-a-year convention is employed. ð4þ Table 3 Average positive arbitrage opportunities. Per-period returns Annualized returns 1 week (0.99) (1.20) (0.0006) (0.0008) 4 weeks (2.30) (2.76) (0.0004) (0.0005) 12 weeks (5.24) (6.64) (0.0003) (0.0004) This table shows the average of all of positive CIP deviations. Per-period returns are reported in pips. Annualized returns are computed using the assumptions that 1 pip represents HKD100 per USD1 million traded, 1 USD is exchanged at the rate of 7.8 HKD and a 365 day-a-year convention is employed. Annualized returns are reported in percentages per annum. The values in parenthesis are asymptotic standard errors calculated using autocorrelation and heteroskedasticity variance covariance matrices (Newey and West, 1987). when liquidity is proxied by spreads and b < 0 when liquidity is proxied by the daily number of quotations. When credit risk increases against Hong Kong financial institutions, credit risk premia are demanded by market participants. This affects the cost of HKD funds which, in turn, causes positive CIP deviations to increase. This would imply the parameter c to be positive. The results of the estimation are reported in Table 4. Panel A C reports the value of the parameter estimates when liquidity measures are proxied by quoted spreads, number of quotations and effective spreads respectively. Some interesting patterns can be retrieved: First, the sign of the estimated parameters b and c is consistent with our initial prior. In fact, the poorer the market liquidity and the higher the perceived credit risk against Hong Kong financial institutions, the larger the positive CIP deviations. Second, across maturity tenors and at both the and side of the market, credit risk measures are found to affect positive CIP deviations significantly at conventional statistical level. Third, market liquidity seems to affect positive CIP deviations only at very short maturities (i.e. 1 week). Fourth, the results are insensitive to the different aggregation schemes used to construct aggregate liquidity measures. With respect to the economic significance of the estimated parameters, if the HKD USD LIBOR-OIS spread increases by 1 bp, on average across maturities, positive CIP deviations increase by 0.6 pip at the side and 0.8 pip at the side. If liquidity decreases, for example when the effective spread increases by 1 pip, positive CIP deviations increase by an average of 0.6 pip at the side and 1.1 pip at the side. These results are consistent with the notion that CIP deviations are not only due to transaction costs but they also incorporate risk premia demanded by market participants to provide liquidity in an illiquid market and carry out transactions with less credit-worthy counterparties. Eq. (4) also provides us with some additional insights with regards to residual CIP arbitrage profits which may accrue to arbitrageurs once liquidity and credit risk premia are also explicitly taken into account. In fact, these residual arbitrage profits can be measured by the estimated parameter a in Eq. (4), which may be interpreted as a proxy of daily average positive CIP deviation adjusted for market liquidity and credit risk. Table 5 reports the estimated residual CIP arbitrage profits expressed as per-period and annualized returns. It is interesting to note that, on average across different specifications and maturity tenors, residual arbitrage profits are lower than the positive CIP deviations reported in Table 3. This reinforces the previous finding that the positive CIP deviations computed by taking into account and prices, contain liquidity and credit risk premia. Once

7 1104 W.-M. Fong et al. / Journal of Banking & Finance 34 (2010) Table 4 Arbitrage profits: liquidity or credit risk? Liquidity Credit risk R 2 Panel A: liquidity = quoted spread 1 week VW ** (0.325) ** (0.001) 0.27 EW ** (0.510) ** (0.001) weeks VW * (0.577) ** (0.002) 0.26 EW (0.704) ** (0.002) weeks VW (0.754) ** (0.003) 0.27 EW (0.646) ** (0.003) week VW ** (0.687) ** (0.001) 0.24 EW ** (1.000) ** (0.001) weeks VW (0.626) ** (0.001) 0.27 EW (0.711) ** (0.001) weeks VW (1.008) ** (0.005) 0.24 EW (0.802) ** (0.005) 0.24 Liquidity (10 7 ) Credit risk R 2 Panel B: liquidity = number of quotations 1 week VW * (0.916) ** (0.001) 0.24 EW * (3.334) ** (0.001) weeks VW (1.868) ** (0.002) 0.25 EW (6.638) ** (0.002) weeks VW (3.929) ** (0.003) 0.28 EW (11.933) ** (0.003) week VW ** (1.469) ** (0.001) 0.23 EW ** (5.118) ** (0.001) weeks VW (1.950) ** (0.001) 0.27 EW (6.884) ** (0.001) weeks VW (3.281) ** (0.001) 0.24 EW (11.753) ** (0.005) 0.24 Liquidity Credit risk R 2 Panel C: liquidity = CS liquidity measure 1 week VW * (0.284) ** (0.001) 0.31 EW * (0.523) ** (0.001) weeks VW (0.259) * (0.001) 0.33 EW (0.395) * (0.001) weeks VW (0.430) * (0.001) 0.31 EW (0.461) * (0.002) week VW * (0.487) ** (0.001) 0.27 EW ** (0.770) ** (0.001) weeks VW (0.295) ** (0.001) 0.23 EW (0.431) ** (0.001) weeks VW (0.784) * (0.005) 0.27 EW (0.703) * (0.005) 0.27 The table reports the results of the estimation of Eq. (4). The variable used to measure credit risk in all Panels is the HKD USD LIBOR-OIS spread constructed as discussed in Table 1 while estimations using the three proxies for aggregate liquidity are reported in Panels A, B and C respectively. Values in parenthesis are asymptotic standard errors calculated using autocorrelation and heteroskedasticity variance covariance matrices (Newey and West, 1987). * Denotes parameter estimates significant at 10% level. ** Denotes parameter estimates significant at 5% level. these premia are taken into account the amount of residual profits available to arbitrageurs is smaller. More specifically residual profits are not available at the 1 week maturity, as the estimates are negative or statistically insignificant, and the positive ones range between 0.12% (12 weeks at the side) and 0.36% (12 weeks at the side) per annum. Table 5 Residual arbitrage profits. BA NQ CS Average Panel A: CIP deviations () Per-period returns 1 week [ 2.4, 4.4] [0.1, 2.5] [1.9, 0.5] 4 weeks [7.1,5.1] [129, 10.3] [18.9, 16.6] 12 weeks [64.0, 62.0] [64.8, 62.2] [73.9, 71.5] Annualized returns 1 week [ 0.158, 0.291] [0.002, 0.169] [0.128, 0.030] 4 weeks [0.119,0.086] [0.210, 0.177] [0.313, 0.280] 12 weeks [0.373, 0.328] [0.376, 0.331] [0.427, 0.382] Panel B: CIP deviations () Per-period returns 1 week [ 15.2, 17.2] [ 13.5, 16.1] [ 11.6, 14.0] 4 weeks [12.8, 10.8] [12.7, 10.1] [14.1, 11.7] 12 weeks [22.3, 20.3] [22.0, 19.4] [24.8, 22.4] Annualized returns 1 week [ 0.913, 1.247] [ 0.813, 1.160] [ 0.693, 1.013] 4 weeks [0.231, 0.164] [0.224, 0.157] [0.249, 0.182] 12 weeks [0.152, 0.085] [0.149, 0.082] [0.135, 0.128] This table shows residual profit computed as the intercept a in Eq. (4) reported in the main text. BA, NQ and CS denote parameter estimates obtained using aggregate spreads, number of quotations and Corwin and Schultz s (2008) measures of liquidity respectively. Average denotes the arithmetic average of the parameter estimates across the three different specifications. See also notes to Table Additional trading costs The results reported so far indicate that small residual arbitrage profits are available to arbitrageurs even after adjusting for prices and liquidity and credit risk premia. A logical question to is then whether the profits reported in Table 5 represent the genuine compensation provided to arbitrageurs for their activity (Deardorff, 1979; Grossman and Stiglitz, 1980). Those figures, albeit incorporating the effect of the and prices and liquidity and credit risk, do not include additional trading costs (i.e. brokerage fees and settlement costs). It is well known among market practitioners that voice-broking intermediated FX markets are characterized by a large variability of trading costs and estimates for broker s fees are very hard to get (Mavrides, 1992, p. 15). These costs are applied with different magnitudes to different market participants with different credit-worthiness and, in some cases, even to the same market participants for different financial instruments or different market conditions. 20 Thus, it is difficult to pin down a unique number that unambiguously represents the amount of additional trading costs in this market and ready estimates are not available. In order to provide an educated guess of the additional roundtrip arbitrage costs faced by market participants in the HKD FX market, we borrow two estimates computed in a similar context by Cheung and Chan (1994, p. 25) and Akram et al. (2008, p. 20 This is also corroborated by the anecdotal evidence provided by several FX chief dealers in Hong Kong during informal conversations.

8 W.-M. Fong et al. / Journal of Banking & Finance 34 (2010) ). The two estimates are imperfect substitutes of the true additional trading costs. In fact, although Cheung and Chan (1994) investigate the HKD voice-intermediated FX market, their estimates are representative of the trading costs faced by market participants in 1990s. Differently, Akram et al. (2008) reports trading costs on the Reuters D3000 platform for the three major currencies vis-à-vis the USD. Although these estimates are relative to a more recent period, the markets they analyze and the trading venue (i.e. electronic) are different from the one investigated in this paper. Nevertheless, albeit imperfect, the above estimates can provide us with two extreme cases within which the current voice-broking trading costs are located. Residual CIP arbitrage profits and the estimates of additional trading costs are reported in Table 6. Overall, across maturities and on both the and side of the market, additional trading costs do not offset the residual arbitrage profits. In fact, if the largest estimates of trading costs are used, the residual profits net of trading costs range between 0.088% and 0.332% per annum on average. These results suggest that when trading costs deriving from the specific voice-broking environment are incorporated, only a subset of traders those with high creditworthiness or longer and established business relationship with their counterparts will be able to reap genuine arbitrage profits as a compensation for their activity. 5. Robustness In this section we report some robustness checks carried out to assess the sensitivity of our baseline results discussed in Section 4. Our first check relates to the possible bias induced by the synchronization rule applied to intraday data discussed in Section 3. More in particular we assess how the percentage share of positive CIP deviations, their average and the parameter estimates of Eq. (4) change when CIP deviations are computed using a different, and more stringent, synchronization rule. We construct a different sample using the synchronization rule so that CIP deviations are only computed when all instruments are quoted within a minute interval. The results computed using as liquidity measure the value-weighted aggregate quoted spread 21 and reported in Table 7 Panel A and Table 8 Panel A indicate that the baseline results are robust to this alternative synchronization scheme, although the number of usable intraday observations drops substantially. In fact, the percentage shares of positive CIP deviations at both the and side of the market and their average are consistent with the figures reported in Tables 2 and 3. Similarly the parameter estimates reported in Table 8 Panel A are in line with the estimates reported in Tables 4 and 5. A second robustness check on the computation of positive CIP deviations involves the effects of possible nonsynchronous trading in the four markets involved in the CIP arbitrage. To address this issue we adopt the methodology proposed by Jokivuolle s (1995) which allows us to estimate the true value of an index when some of its components are subject to nonsynchronous trading. The results are reported in Table 7 Panel B and Table 8 Panel B. Once again the results are in line with the ones reported in Tables 2 5. Overall, the robustness exercises reported in this section indicate that the key results discussed in Sections 3 and 4 are robust. These baseline results are not affected by stale pricing, the nonsynchronous trading occurring in the markets involved in the arbitrage strategy. 21 The results computed using the remaining two liquidity measures and the EW aggregation scheme are not reported to save space, but available upon request. In all cases the results are consistent with the baseline estimates reported in Tables 2 5. Table 6 Additional trading costs. 6. Conclusions Residual profits (% annualized) Additional trading costs (% annualized) Akram et al. (2008) 4 weeks weeks weeks weeks Cheung and Chan (1994) This table reports the average residual profits from CIP arbitrage as in Table 5 together with estimates of brokerage fees and settlement costs per round-trip transaction. Estimates of brokerage fees and settlement costs are computed using the figures reported in Akram et al. (2008, Appendix A.B, pp ) and Cheung and Chan (1994, Table 2, p. 25). All figures are annualized rates of return. See notes to Tables 3 and 5. Table 7 Data issues and arbitrage opportunities. CIP deviations Panel A: alternative synchronization scheme 1 week Total dev % share Mean (% p.a.) weeks Total dev % share Mean (% p.a.) weeks Total dev % share 78 9 Mean (% p.a.) Average % share Panel B: CIP deviations corrected as in Jokivuolle (1995) 1 week Total dev 12,861 12,861 % share Mean (% p.a.) weeks Total dev 22,277 22,277 % share Mean (% p.a.) weeks Total dev 28,709 28,709 % share Mean (% p.a.) Average % share This table shows the total number of synchronized CIP deviations (Total dev), the frequency of profitable deviations from round-trip arbitrage in the FX market (% share) and the average positive CIP deviation (Mean). The figures are computed using a different synchronization scheme involving the four financial instruments, as discussed in Section 5 of the main text (Panel A) and the correction for asynchronous trading as in Jokivuolle (1995) (Panel B). Average positive CIP deviations are expressed as annualized rate of returns. See Notes to Table 3. In this paper we study the profitability of CIP arbitrage violations and their relationship with market liquidity and credit risk. This analysis is motivated by the growing evidence documenting that FX markets are often characterized by a substantial number of instances in which CIP deviations exceed the transaction cost band coupled with the assumption that such arbitrage deviations