INTERNATIONAL ECONOMIC JOURNAL Volume 10, Number 1, Spring 1996

59

OVERNIGHT COVERED INTEREST PARITY: THEORY AND PRACTICE AMIR KIA* Bank of Canada

This study shows, both theoretically and empirically, that in a world where capital as well as exchange markets are imperfect it is incorrect to employ mid-market rates to estimate CIP relationships. Developing and using the correct specification, we estimated covered interest parity relationships between the overnight U.S. Euro-dollar and Canadian interbank markets, for the 1986-1992 period. It was found that covered interest parity holds for both directions. However, the speed and pattern of adjustments with which potential arbitrage profits are eliminated are not symmetric between U.S. Euro-dollar and Canadian interbank markets. [G15]

1. INTRODUCTION Numerous studies investigated the empirical validity of covered interest parity (CIP) relation in highly efficient markets. The investigation dealt mainly with the size of the raw deviations relative to estimated transaction costs, the existence of potential arbitrage profit and the speed with which this potential arbitrage profit is eliminated. The bulk of these studies focused on the first two points. The general empirical conclusions are that transaction costs cause a narrow neutral band in which CIP may not hold and that profitable trading opportunities are small and short-lived. In relation to the first point, for example, Frenkel and Levich (1975) provide supportive evidence for CIP when compared to estimates of transaction costs; Deardorff (1979) concludes that transaction costs for “one-way arbitrage” cause a narrower neutral band; Callier (1981), Bahmani-Oskooee and Das (1985) as well as Maasoumi and Pippenger (1989) found a neutral band narrower than the one found by Deardorff. Clinton (1988), however, shows that actual transaction costs are very small when short-term swap rates are used. By using mid-market rates in estimations of CIP relationship the existing literature

*I would like to thank Kevin Clinton for his comments on the first version of this paper. Thanks are also due to an anonymous referee and Professor Young Chin Kim, Co-Editor of International Economic Journal, for their helpful comments and suggestions. I also acknowledge the technical assistance of Gordon Lee and Jerry Lawlis. The first version of this paper was presented at the Carleton University Monetary Seminar in May 1993 as well as at the annual meeting of the Canadian Economics Association in June 1993. The opinions expressed in this paper are those of the author and do not necessarily reflect those of the Bank of Canada.

60

AMIR KIA

does not correctly consider the fact that the capital as well as foreign exchange markets are not perfect, i.e., borrowing and lending rates as well as buying and selling prices are different. It only relates the deviation from parity to transaction costs as well as measuring errors. In fact, considering capital and foreign exchange markets imperfections, rates incorporate transaction costs, excluding brokerage fees. Then a deviation from CIP means a potential for arbitrage profit (loss) as well as brokerage costs in the absence of any risk. Transaction costs may be defined as execution costs plus commissions and fees. Commissions and fees are explicit while execution costs are hidden costs of trading. Execution costs exist only when markets are imperfect. They are, however, hidden in the prices. At the equilibrium (ignoring currency swap-interest rate product) one would expect, at each moment of time, either domestic bid interest rate equals foreign offer interest rate plus offer exchange swap rate or the domestic offer interest rate equals foreign bid interest rate plus bid exchange swap rate, but not both. The reason is that bid rates are usually lower than offer rates. It, therefore, follows that estimating a CIP relation using mid-market rates results in a misspecified equation. We will prove this proposition later in the paper theoretically and verify the finding empirically. Moreover, we will prove that when all relating markets are efficient and there is no risk or barrier of any sort, estimating CIP relationships by using traditional midmarket rates setting may result in a violation of the CIP relationships while, in fact, CIP relationships hold. In relation to the second point, it seems that the speed of adjustment and long run movements of funds with which arbitrage profitable trading opportunities are eliminated have not been given a lot of consideration. For instance, by using midmarket rates, the existing literature assumes that the speed and pattern of adjustments with which potential arbitrage profits are eliminated are the same, regardless of the direction of the capital flow. However, it was found in this paper that it is possible for arbitragers to react trivially to small equilibrium errors while reacting substantially to large errors when funds are transferred from one market to another market (e.g., from a large economy to a small economy), but reacting significantly to any equilibrium error when funds are transferred in the opposite direction. Furthermore, when a midmarket rates setting is used, the adjustment toward equilibrium is constrained to be symmetric. That is, the sign of the deviation does not affect the speed at which the short-run disequilibrium is resolved. However, since the adjustment towards equilibrium is driven by arbitrage, one should expect the speed of adjustment to depend on the sign and then the magnitude of the disequilibrium. Namely, there should be an asymmetric adjustment mechanism. This means that a positive deviation from CIP indicates an arbitrage opportunity from Euro-dollar market to Canadian interbank market while a negative deviation from CIP indicates an arbitrage opportunity from Canadian interbank market to the U.S. Euro-dollar market. At the same time, a negative deviation from CIP for the movement of funds from Euro-dollar market to Canada, or a positive deviation from CIP for the movement of funds in the opposite direction, implies the

OVERNIGHT COVERED INTEREST PARITY

61

absence of profit opportunities. Consequently, in traditional mid-market rates setting the generated equilibrium error is overestimated or underestimated, which results in a biased estimate of speed of adjustment. It was found in this paper that this problem does not exist with our correct specification of CIP relationships. Finally, there is another source of bias in estimating the speed of adjustment in a traditional mid-market rates setting. A small (withing bands) deviation from CIP would not trigger the same adjustment as a larger (outside the bands) deviation since only the latter would imply arbitrage opportunities. This problem will yield biased estimates of the speed of adjustment. However, as we will see in the specification which will be developed in this paper such problem does not exist. The purpose of this paper is to develop the CIP specification which corresponds to the market imperfection assumption (the correct specification) and, using this specification, to estimate short-run and long-run dynamic CIP relationships between U.S. Euro-dollar market and Canadian interbank market for both directions over the period 1986-1992. 1 We will also show, both theoretically and empirically, that using mid-market rates in estimating a CIP relationship results in misleading conclusions. The remaining of the paper is organized as follows: the next section provides the theoretical framework of CIP, Section 3 investigates the CIP relationships and the final section is devoted to conclusions. 2. THEORETICAL FRAMEWORK Let us follow, among others, Clinton (1988), Deardorff (1979) and Frenkel and Levich (1975) and assume that brokerage fees and commissions per transaction are fixed and small so that they may be ignored.2 However, we assume that markets are imperfect, i.e., borrowing and lending rates as well as buying and selling prices are different.3 In the absence of brokerage costs and trade restrictions, an arbitrager who borrows a covered overnight loan from U.S. Euro-market and employs the funds in the Canadian interbank overnight market will find the arbitrage activity profitable if 1 Daily data from Feb. 3, 1986 to April 21, 1992 was used. Euro-dollar London interbank rates are at about mid-day London time and Canadian interbank rate as well as spot and forward rates are at Canada open (8:30 a.m. EST). The data was provided by Financial Markets Department, Bank of Canada. Only one data set on spot exchange rate, at open, is available. This data was collected in such a way to reflect a high probability that trades have taken place. Consequently, observations on spot rate can be bid or offer. Days that were holiday, in London, U.S. or Canada were dropped. Unmatched observations (part of the information missing) were also dropped. The number of observations is 1424. 2 In fact in Canada, for example, each major bank has a section (so-called trading desk) which does the bank’s wholesale transactions without using brokerage services. 3 It should be noted that in their raw deviations calculation, MacDonald and Taylor (1989) correctly specify their net interest parity relationship.

62

AMIR KIA

(1 + i ft∗o)(wo t + ) 1 < (1 + i dt ),b

(1)

where ifo*t and idbt are daily offer U.S. Euro-dollar and daily bid domestic interbank rates at time t, respectively.4 Also, wot (= (fot – sb t)/sbt) is the overnight (daily) offer foreign exchange swap rate at time t; fot and sbt are offer overnight forward and bid spot exchange rates at time t, respectively. The exchange rate is defined as the price of a unit of U.S. dollar in terms of Canadian dollar. Since the lending and borrowing rates are different, the arbitrager is charged an offer rate as a borrower and will be paid a bid rate as a lender. In the foreign exchange market he has to pay an offer swap rate since he simultaneously purchases Canadian dollars for today delivery and sells Canadian dollars for tomorrow delivery. Inequality (1) can be rewritten as Wot + (wot )(iot∗ ) + io t∗ < i bt ,

(2)

where Wot, io*t and ibt are offer swap, U.S. Euro-dollar and interbank rates at the annual percentage rate, respectively, all on a 365-day basis, i.e., Wot is equal to wot (36500), io*t is equal to 36500(ifo*t) and ibt is equal to 36500(idbt). Then, U.S. to Canada net covered interest parity (USTCAt) will be defined as, USTCAt = it b- W to - (wo t )(iot∗ ) -

i∗t o.

(3)

For all USTCAt > 0 there is a potential for arbitrage profit from U.S. Euro-dollar market to Canada (domestic country). Similarly, an arbitrage opportunity from Canada to Euro-market is profitable if

iot < Wt b + (wbt )(ibt∗ ) +

i t∗b,

(4)

4 It is assumed that the arbitrager is a trader in a chartered bank and employs the borrowed funds in the interbank market.

OVERNIGHT COVERED INTEREST PARITY

63

where iot, Wb t, wb t and ib*t are offer Canadian interbank, bid foreign exchange swap, bid overnight foreign exchange swap and bid U.S. Euro-dollar rates at time t, respectively. wbt is equal to ((fbt -sot)/ sot) and Wbt is equal to 36500(wbt), where fbt and sot are bid forward and offer spot exchange rates at time t, respectively.5 Here the arbitrager is paying the bid swap rate in foreign exchange market since he is selling Canadian dollars for immediate delivery and purchasing Canadian dollars for the following day delivery. All the above-mentioned rates, except w bt, are annual percentages based on 365 days. Then, Canada to Euro-market net covered interest parity (CATUSt) will be defined as,

CATUSt = i ot - Wbt - (wbt )(ibt∗ ) - i bt∗ ,.

(5)

For all CATUSt < 0 there is a potential for arbitrage profit from Canada to Euromarket. In the absence of brokerage costs, one would expect, on average, in efficient markets, U S T C A t and C A T U S t be zero. However, these two variables cannot simultaneously be zero. If USTCAt and CATUSt are simultaneously zero then we will have ibt = W ot + (wo t )(iot∗ ) +

i t∗o,

iot = Wt b + (wbt )(ibt∗ ) +

i t∗b.

and

(6) (7)

We know that bid rates are lower than their counterpart offer rates in imperfect capital markets. We also know that in both foreign exchange swap and money markets, buying and selling prices are not the same. Consequently, the left hand side of Equation (6) is smaller than the left hand side of Equation (7), while the right hand side of Equation (6) is greater than the right hand side of Equation (7). It, therefore, follows that these two equations cannot simultaneously hold. Namely, since equations (6) and (7) belong to different time frames, it is not possible, theoretically, to add them together. Recalling that a mid-market rate is the average of bid and offer rates, consequently, one cannot use the mid-market data to test for CIP relationship. 5 Note that our foreign exchange swap rates are different than those in the literature, e.g., Clinton (1988). Since a swap transaction is a simultaneous buying and selling, the correct definitions are: the offer rate = wo = (fo-sb)/sb, and the bid rate = wb = (fb-so)/so, while in the literature we have: wo = (fo-so)/so and wb = (fb-sb)/sb. Clearly in the correct definition, wo is larger and wb is smaller than their corresponding values in the literature.

64

AMIR KIA

Furthermore, using mid-market rates in the estimation of CIP relations also implies that speed and pattern of adjustments with which potential arbitrage profits are eliminated are the same regardless of the direction of the capital mobility. However, this may not be true, specially, when the size and structure of the two markets are different. For example, it is possible for arbitragers to react differently to an equilibrium error when funds are transferred from a small to a large economy and vice versa. Thus we can establish the following: PROPOSITION 1: Because of the existence of imperfect capital and exchange markets, there are always two potential and different CIP relationships between two similar securities markets of two countries. This proposition, which in many respects is the key result in this paper, is a very powerful one. It establishes the fact that using mid-market rates to study CIP relationships may generate misleading results. Moreover, from the above analysis we can conclude that: (i) If there is a potential for arbitrage profit it is only in one direction.6 Namely, a potential for arbitrage profit implies that either both USTCAt and CATUSt are positive, which means a potential for arbitrage profit from U.S. to Canada, or both are negative, which means a potential for arbitrage profit in the opposite direction. Note that, at each moment of time, if USTCAt is positive CATUSt must be positive and similarly if CATUSt is negative USTCAt must be negative. However, only values associated with USTCAt > 0 or CATUSt < 0 can be considered as a deviation from CIP. (ii) A zero USTCAt means a positive CATUSt and similarly a zero CATUSt is associated with a negative U S T C A t. This result leads us to the following proposition: PROPOSITION 2: All USTCAt < 0 and CATUS t = 0 or USTCA t = 0 and CATUS t > 0 are associated with CIP. Proposition 2 implies that using mid-market rates in specifying CIP relationships may falsely lead us to believe that CIP relationships do not hold. For example, consider the CIP situation like USTCAt < 0 and CATUSt = 0, i.e., ibt < W ot + (wo t )(iot∗ ) +

i t∗o,

iot = Wt b + (wbt )(ibt∗ ) +

i t∗b.

and

(8) (9)

6 It should be mentioned that Prachowny (1970), using imperfect capital market assumption for both home and foreign securities markets, finds the same result. However, he fails to recognise that currency exchange market is also imperfect.

OVERNIGHT COVERED INTEREST PARITY

65

Adding the left and right hand sides of (8) and (9) and dividing the resulting inequality by 2 to get,

it

59

OVERNIGHT COVERED INTEREST PARITY: THEORY AND PRACTICE AMIR KIA* Bank of Canada

This study shows, both theoretically and empirically, that in a world where capital as well as exchange markets are imperfect it is incorrect to employ mid-market rates to estimate CIP relationships. Developing and using the correct specification, we estimated covered interest parity relationships between the overnight U.S. Euro-dollar and Canadian interbank markets, for the 1986-1992 period. It was found that covered interest parity holds for both directions. However, the speed and pattern of adjustments with which potential arbitrage profits are eliminated are not symmetric between U.S. Euro-dollar and Canadian interbank markets. [G15]

1. INTRODUCTION Numerous studies investigated the empirical validity of covered interest parity (CIP) relation in highly efficient markets. The investigation dealt mainly with the size of the raw deviations relative to estimated transaction costs, the existence of potential arbitrage profit and the speed with which this potential arbitrage profit is eliminated. The bulk of these studies focused on the first two points. The general empirical conclusions are that transaction costs cause a narrow neutral band in which CIP may not hold and that profitable trading opportunities are small and short-lived. In relation to the first point, for example, Frenkel and Levich (1975) provide supportive evidence for CIP when compared to estimates of transaction costs; Deardorff (1979) concludes that transaction costs for “one-way arbitrage” cause a narrower neutral band; Callier (1981), Bahmani-Oskooee and Das (1985) as well as Maasoumi and Pippenger (1989) found a neutral band narrower than the one found by Deardorff. Clinton (1988), however, shows that actual transaction costs are very small when short-term swap rates are used. By using mid-market rates in estimations of CIP relationship the existing literature

*I would like to thank Kevin Clinton for his comments on the first version of this paper. Thanks are also due to an anonymous referee and Professor Young Chin Kim, Co-Editor of International Economic Journal, for their helpful comments and suggestions. I also acknowledge the technical assistance of Gordon Lee and Jerry Lawlis. The first version of this paper was presented at the Carleton University Monetary Seminar in May 1993 as well as at the annual meeting of the Canadian Economics Association in June 1993. The opinions expressed in this paper are those of the author and do not necessarily reflect those of the Bank of Canada.

60

AMIR KIA

does not correctly consider the fact that the capital as well as foreign exchange markets are not perfect, i.e., borrowing and lending rates as well as buying and selling prices are different. It only relates the deviation from parity to transaction costs as well as measuring errors. In fact, considering capital and foreign exchange markets imperfections, rates incorporate transaction costs, excluding brokerage fees. Then a deviation from CIP means a potential for arbitrage profit (loss) as well as brokerage costs in the absence of any risk. Transaction costs may be defined as execution costs plus commissions and fees. Commissions and fees are explicit while execution costs are hidden costs of trading. Execution costs exist only when markets are imperfect. They are, however, hidden in the prices. At the equilibrium (ignoring currency swap-interest rate product) one would expect, at each moment of time, either domestic bid interest rate equals foreign offer interest rate plus offer exchange swap rate or the domestic offer interest rate equals foreign bid interest rate plus bid exchange swap rate, but not both. The reason is that bid rates are usually lower than offer rates. It, therefore, follows that estimating a CIP relation using mid-market rates results in a misspecified equation. We will prove this proposition later in the paper theoretically and verify the finding empirically. Moreover, we will prove that when all relating markets are efficient and there is no risk or barrier of any sort, estimating CIP relationships by using traditional midmarket rates setting may result in a violation of the CIP relationships while, in fact, CIP relationships hold. In relation to the second point, it seems that the speed of adjustment and long run movements of funds with which arbitrage profitable trading opportunities are eliminated have not been given a lot of consideration. For instance, by using midmarket rates, the existing literature assumes that the speed and pattern of adjustments with which potential arbitrage profits are eliminated are the same, regardless of the direction of the capital flow. However, it was found in this paper that it is possible for arbitragers to react trivially to small equilibrium errors while reacting substantially to large errors when funds are transferred from one market to another market (e.g., from a large economy to a small economy), but reacting significantly to any equilibrium error when funds are transferred in the opposite direction. Furthermore, when a midmarket rates setting is used, the adjustment toward equilibrium is constrained to be symmetric. That is, the sign of the deviation does not affect the speed at which the short-run disequilibrium is resolved. However, since the adjustment towards equilibrium is driven by arbitrage, one should expect the speed of adjustment to depend on the sign and then the magnitude of the disequilibrium. Namely, there should be an asymmetric adjustment mechanism. This means that a positive deviation from CIP indicates an arbitrage opportunity from Euro-dollar market to Canadian interbank market while a negative deviation from CIP indicates an arbitrage opportunity from Canadian interbank market to the U.S. Euro-dollar market. At the same time, a negative deviation from CIP for the movement of funds from Euro-dollar market to Canada, or a positive deviation from CIP for the movement of funds in the opposite direction, implies the

OVERNIGHT COVERED INTEREST PARITY

61

absence of profit opportunities. Consequently, in traditional mid-market rates setting the generated equilibrium error is overestimated or underestimated, which results in a biased estimate of speed of adjustment. It was found in this paper that this problem does not exist with our correct specification of CIP relationships. Finally, there is another source of bias in estimating the speed of adjustment in a traditional mid-market rates setting. A small (withing bands) deviation from CIP would not trigger the same adjustment as a larger (outside the bands) deviation since only the latter would imply arbitrage opportunities. This problem will yield biased estimates of the speed of adjustment. However, as we will see in the specification which will be developed in this paper such problem does not exist. The purpose of this paper is to develop the CIP specification which corresponds to the market imperfection assumption (the correct specification) and, using this specification, to estimate short-run and long-run dynamic CIP relationships between U.S. Euro-dollar market and Canadian interbank market for both directions over the period 1986-1992. 1 We will also show, both theoretically and empirically, that using mid-market rates in estimating a CIP relationship results in misleading conclusions. The remaining of the paper is organized as follows: the next section provides the theoretical framework of CIP, Section 3 investigates the CIP relationships and the final section is devoted to conclusions. 2. THEORETICAL FRAMEWORK Let us follow, among others, Clinton (1988), Deardorff (1979) and Frenkel and Levich (1975) and assume that brokerage fees and commissions per transaction are fixed and small so that they may be ignored.2 However, we assume that markets are imperfect, i.e., borrowing and lending rates as well as buying and selling prices are different.3 In the absence of brokerage costs and trade restrictions, an arbitrager who borrows a covered overnight loan from U.S. Euro-market and employs the funds in the Canadian interbank overnight market will find the arbitrage activity profitable if 1 Daily data from Feb. 3, 1986 to April 21, 1992 was used. Euro-dollar London interbank rates are at about mid-day London time and Canadian interbank rate as well as spot and forward rates are at Canada open (8:30 a.m. EST). The data was provided by Financial Markets Department, Bank of Canada. Only one data set on spot exchange rate, at open, is available. This data was collected in such a way to reflect a high probability that trades have taken place. Consequently, observations on spot rate can be bid or offer. Days that were holiday, in London, U.S. or Canada were dropped. Unmatched observations (part of the information missing) were also dropped. The number of observations is 1424. 2 In fact in Canada, for example, each major bank has a section (so-called trading desk) which does the bank’s wholesale transactions without using brokerage services. 3 It should be noted that in their raw deviations calculation, MacDonald and Taylor (1989) correctly specify their net interest parity relationship.

62

AMIR KIA

(1 + i ft∗o)(wo t + ) 1 < (1 + i dt ),b

(1)

where ifo*t and idbt are daily offer U.S. Euro-dollar and daily bid domestic interbank rates at time t, respectively.4 Also, wot (= (fot – sb t)/sbt) is the overnight (daily) offer foreign exchange swap rate at time t; fot and sbt are offer overnight forward and bid spot exchange rates at time t, respectively. The exchange rate is defined as the price of a unit of U.S. dollar in terms of Canadian dollar. Since the lending and borrowing rates are different, the arbitrager is charged an offer rate as a borrower and will be paid a bid rate as a lender. In the foreign exchange market he has to pay an offer swap rate since he simultaneously purchases Canadian dollars for today delivery and sells Canadian dollars for tomorrow delivery. Inequality (1) can be rewritten as Wot + (wot )(iot∗ ) + io t∗ < i bt ,

(2)

where Wot, io*t and ibt are offer swap, U.S. Euro-dollar and interbank rates at the annual percentage rate, respectively, all on a 365-day basis, i.e., Wot is equal to wot (36500), io*t is equal to 36500(ifo*t) and ibt is equal to 36500(idbt). Then, U.S. to Canada net covered interest parity (USTCAt) will be defined as, USTCAt = it b- W to - (wo t )(iot∗ ) -

i∗t o.

(3)

For all USTCAt > 0 there is a potential for arbitrage profit from U.S. Euro-dollar market to Canada (domestic country). Similarly, an arbitrage opportunity from Canada to Euro-market is profitable if

iot < Wt b + (wbt )(ibt∗ ) +

i t∗b,

(4)

4 It is assumed that the arbitrager is a trader in a chartered bank and employs the borrowed funds in the interbank market.

OVERNIGHT COVERED INTEREST PARITY

63

where iot, Wb t, wb t and ib*t are offer Canadian interbank, bid foreign exchange swap, bid overnight foreign exchange swap and bid U.S. Euro-dollar rates at time t, respectively. wbt is equal to ((fbt -sot)/ sot) and Wbt is equal to 36500(wbt), where fbt and sot are bid forward and offer spot exchange rates at time t, respectively.5 Here the arbitrager is paying the bid swap rate in foreign exchange market since he is selling Canadian dollars for immediate delivery and purchasing Canadian dollars for the following day delivery. All the above-mentioned rates, except w bt, are annual percentages based on 365 days. Then, Canada to Euro-market net covered interest parity (CATUSt) will be defined as,

CATUSt = i ot - Wbt - (wbt )(ibt∗ ) - i bt∗ ,.

(5)

For all CATUSt < 0 there is a potential for arbitrage profit from Canada to Euromarket. In the absence of brokerage costs, one would expect, on average, in efficient markets, U S T C A t and C A T U S t be zero. However, these two variables cannot simultaneously be zero. If USTCAt and CATUSt are simultaneously zero then we will have ibt = W ot + (wo t )(iot∗ ) +

i t∗o,

iot = Wt b + (wbt )(ibt∗ ) +

i t∗b.

and

(6) (7)

We know that bid rates are lower than their counterpart offer rates in imperfect capital markets. We also know that in both foreign exchange swap and money markets, buying and selling prices are not the same. Consequently, the left hand side of Equation (6) is smaller than the left hand side of Equation (7), while the right hand side of Equation (6) is greater than the right hand side of Equation (7). It, therefore, follows that these two equations cannot simultaneously hold. Namely, since equations (6) and (7) belong to different time frames, it is not possible, theoretically, to add them together. Recalling that a mid-market rate is the average of bid and offer rates, consequently, one cannot use the mid-market data to test for CIP relationship. 5 Note that our foreign exchange swap rates are different than those in the literature, e.g., Clinton (1988). Since a swap transaction is a simultaneous buying and selling, the correct definitions are: the offer rate = wo = (fo-sb)/sb, and the bid rate = wb = (fb-so)/so, while in the literature we have: wo = (fo-so)/so and wb = (fb-sb)/sb. Clearly in the correct definition, wo is larger and wb is smaller than their corresponding values in the literature.

64

AMIR KIA

Furthermore, using mid-market rates in the estimation of CIP relations also implies that speed and pattern of adjustments with which potential arbitrage profits are eliminated are the same regardless of the direction of the capital mobility. However, this may not be true, specially, when the size and structure of the two markets are different. For example, it is possible for arbitragers to react differently to an equilibrium error when funds are transferred from a small to a large economy and vice versa. Thus we can establish the following: PROPOSITION 1: Because of the existence of imperfect capital and exchange markets, there are always two potential and different CIP relationships between two similar securities markets of two countries. This proposition, which in many respects is the key result in this paper, is a very powerful one. It establishes the fact that using mid-market rates to study CIP relationships may generate misleading results. Moreover, from the above analysis we can conclude that: (i) If there is a potential for arbitrage profit it is only in one direction.6 Namely, a potential for arbitrage profit implies that either both USTCAt and CATUSt are positive, which means a potential for arbitrage profit from U.S. to Canada, or both are negative, which means a potential for arbitrage profit in the opposite direction. Note that, at each moment of time, if USTCAt is positive CATUSt must be positive and similarly if CATUSt is negative USTCAt must be negative. However, only values associated with USTCAt > 0 or CATUSt < 0 can be considered as a deviation from CIP. (ii) A zero USTCAt means a positive CATUSt and similarly a zero CATUSt is associated with a negative U S T C A t. This result leads us to the following proposition: PROPOSITION 2: All USTCAt < 0 and CATUS t = 0 or USTCA t = 0 and CATUS t > 0 are associated with CIP. Proposition 2 implies that using mid-market rates in specifying CIP relationships may falsely lead us to believe that CIP relationships do not hold. For example, consider the CIP situation like USTCAt < 0 and CATUSt = 0, i.e., ibt < W ot + (wo t )(iot∗ ) +

i t∗o,

iot = Wt b + (wbt )(ibt∗ ) +

i t∗b.

and

(8) (9)

6 It should be mentioned that Prachowny (1970), using imperfect capital market assumption for both home and foreign securities markets, finds the same result. However, he fails to recognise that currency exchange market is also imperfect.

OVERNIGHT COVERED INTEREST PARITY

65

Adding the left and right hand sides of (8) and (9) and dividing the resulting inequality by 2 to get,

it