In his classic article on the case for flexible exchange rates, Milton Friedman argued that “on balance it seems to me undesirable for a country to engage in transactions on the exchange market for the purpose of affecting the rate of exchange. I see no reason to expect that government officials will be better judges than private speculators of the likely movements in underlying conditions of trade and, hence, no reason to expect that government speculation will be more successful than private speculation in promoting a desirable pace and timing of adjustment.” 1 In contrast to this view, this paper argues that, in order that the exchange rate should accurately reflect private expectations, official intervention in the foreign exchange market is required to avoid any necessity for the buildup of large open positions by private speculators. The basic rationale for this view is as follows.

Abstract

In his classic article on the case for flexible exchange rates, Milton Friedman argued that “on balance it seems to me undesirable for a country to engage in transactions on the exchange market for the purpose of affecting the rate of exchange. I see no reason to expect that government officials will be better judges than private speculators of the likely movements in underlying conditions of trade and, hence, no reason to expect that government speculation will be more successful than private speculation in promoting a desirable pace and timing of adjustment.” 1 In contrast to this view, this paper argues that, in order that the exchange rate should accurately reflect private expectations, official intervention in the foreign exchange market is required to avoid any necessity for the buildup of large open positions by private speculators. The basic rationale for this view is as follows.

In his classic article on the case for flexible exchange rates, Milton Friedman argued that “on balance it seems to me undesirable for a country to engage in transactions on the exchange market for the purpose of affecting the rate of exchange. I see no reason to expect that government officials will be better judges than private speculators of the likely movements in underlying conditions of trade and, hence, no reason to expect that government speculation will be more successful than private speculation in promoting a desirable pace and timing of adjustment.” 1 In contrast to this view, this paper argues that, in order that the exchange rate should accurately reflect private expectations, official intervention in the foreign exchange market is required to avoid any necessity for the buildup of large open positions by private speculators. The basic rationale for this view is as follows.

In the absence of any official intervention on the foreign exchange market, a deficit (surplus) on the basic balance of payments is necessarily accompanied by a lengthening (shortening) of the open position of private short-term capital transactors. This paper will show that, owing to the risk associated with an open currency position, the expected appreciation of the spot exchange rate will normally differ from the interest rate differential by a risk premium, and that the forward exchange rate will normally differ from the expected future spot rate by a similar risk premium. The greater is the magnitude of the accumulated basic balance of payments deficit or surplus that has to be financed or absorbed by private short-term capital flows, the greater will be the risk premium. Even with an unchanged interest rate differential and an unchanged expected future spot rate, the spot and forward exchange rates will vary owing to changes in the degree of uncertainty with which expectations are held. Since the risk premium required by private speculators under a freely flexible exchange rate has to be paid by current account transactors and long-term capital account transactors, it is argued that official intervention in the foreign exchange market should take place in order to prevent the development of a risk premium. To achieve this, the authorities should not intervene in the foreign exchange market to set the price, but should intervene on a quantitative basis to finance (absorb) the basic balance of payments deficit (surplus)—that is, the authorities should make net purchases (sales) of domestic currency equal to the basic balance of payments deficit (surplus). Only under such official intervention will the current forward rate be an unbiased signal to private and official decision makers of the future spot rate that is expected by the market.

The structure of this paper is as follows. Section I derives a very simple model of the determination of the spot and forward exchange rates in the short run. From this model, the effect of official intervention is obtained and the case for official intervention is discussed. Section II discusses the impact of relaxing certain of the simplifying assumptions. Finally, a summary and conclusion are presented in Section III.

I. The Model

This section begins by deriving the demand functions for spot and forward currency by an individual private capital transactor. The results are then generalized for capital transactors in aggregate and a very simple model is obtained for the determination of the spot and forward exchange rates. From the results of the model, the case for official intervention is then discussed. All capital transactors are assumed to be holding initially a closed foreign currency position. The model is a short-run one in the sense that the current account is assumed to be determined exogenously.

1. derivation of arbitrage and speculation functions

The expected utility derived by the ith individual from the return Ri on his portfolio can be shown to be approximated by2

E[Ui(Ri)]=RieAi2Vi(1)

where Rie is the expected value of the portfolio, Ai is a positive constant, and Vi is the variance E(RiRie)2.

Expected utility is positively related to the expected value of the portfolio but negatively related to the variance or risk on the portfolio. Ai is the coefficient of risk aversion; the greater is the aversion to risk, the greater will be Ai.

The individual is assumed to be a resident of a country whose currency is the “dollar”; to have an initial level of wealth of Wi dollars; and to gain utility from the return on his portfolio measured in dollars. Two riskless forms of investment are assumed to be available to the individual. First, he may hold short-term interest-bearing assets or liabilities denominated in dollars; second, he may hold short-term interest-bearing assets or liabilities denominated in “pounds” covered against exchange risk by appropriate operations in the forward exchange market. One risky form of investment is assumed to be available—he may hold short-term interest-bearing assets or liabilities denominated in pounds uncovered against exchange risk.3

Let the value of his spot purchases of pounds that are covered against exchange risk be equal to ai pounds, and the value of his spot purchases that are uncovered be equal to bi pounds. The individual is assumed to be able to borrow as well as invest in both dollars and pounds, so that there is no constraint on the size or sign of ai and bi. However, the wealth constraint requires that his holdings of financial assets denominated in dollars be equal to Wi - Xs(ai + bi), where Xs is the spot price of one pound in terms of dollars. The individual is assumed to be able to borrow and lend an unlimited amount in each currency without affecting the rate of interest that he faces. It is also assumed that the individual initially has no spot or forward position in pounds, so that his current flow of purchases and sales is identical to his stock of claims and liabilities in pounds.

The total expected value of the individual’s portfolio in terms of dollars is equal to

Rie=aiXf(1+r)+biXie(1+r)+[WiXs(ai+bi)](1+r$)=ai[Xf(1+r)Xs(1+r$)]+bi[Xie(1+r)XS(1+r$)]+Wi(1+r$)(2)

where Xf(Xie) is the forward (expected future spot) price of one pound in terms of dollars; and r$(r) is the rate of interest on financial assets and liabilities denominated in dollars (pounds).

Since there is only one stochastic variable—the future spot rate—the variance of the future value of the individual’s portfolio is simply equal to

Vi=bi2(1+r)2σi2(3)

where σi2 is the variance of the individual’s subjective probability distribution of the future spot rate.

Substituting equations (2) and (3) in equation (1), expected utility equals

E[Ui(Ri)]=ai[Xf(1+r)Xs(1+r$)]+bi[Xie(1+r)XS(1+r$)]+Wi(1+r$)Ai2bi2(1+r)2σi2(4)

It immediately follows from equation (4) that, whenever Xf(1 + r) is not equal to Xs(1 + r$) the individual will engage in covered interest arbitrage to the maximum possible extent (i.e., will make the absolute value of ai as large as possible) in order to maximize expected utility. It is therefore assumed that covered interest arbitrage will ensure that

Xf(1+r)=Xs(1+r$)XfXSXS=r$r1+rr$r(5)

Equation (5) is the well-known interest parity condition: the forward premium on the pound will approximately equal the interest rate differential in favor of the dollar.

Assuming that interest parity holds, expected utility will be maximized when

E[Ui(Ri)]bi=0;2E[Ui(Ri)]bi2<0

The resulting optimal value of bi equals

bi=XieXfAi(1+r)σi2(6)

The individual will be willing to hold pounds on an uncovered basis only if the expected future spot rate for the pound exceeds the forward rate for the pound. Given interest parity, this is equivalent to the condition that the expected appreciation of the spot rate for the pound should exceed the interest rate differential in favor of the dollar. The explanation for this result is simply that, if the expected appreciation were to equal the interest rate differential, the individual could obtain the same expected return without any risk by investing in dollars; investing in dollars would be more efficient than investing on an uncovered basis in pounds. To induce the individual to invest on an uncovered basis in pounds, the expected appreciation of the pound must exceed the interest rate differential against the pound by a risk premium.

Similar results to those presented in equations (5) and (6) can also be derived by assuming that the individual is a resident of the country whose currency is the pound and that he gains utility from the return on his portfolio measured in pounds. Such an individual will only be willing to buy dollars on an uncovered basis—that is, bi<0—if the expected appreciation of the pound is less than the interest differential in favor of the dollar.

The aggregate level of uncovered purchases of pounds is obtained by summing equation (6) over all i

Σibi=Σi[XieXfAiσi2(1+r)]b=XeXfAσ2(1+r)(7)

where

b=ΣibiXe=Σi[Xie(Aiσi2)1Σi(Aiσi2)1]aσ2=ΣiAiσi2

Equation (7) introduces the variable Xe—the future spot rate that is expected by the market as a whole. This is defined to be a weighted average of individual expectations where the weights are determined by the reciprocal of the product of an individual’s absolute aversion to risk and his perception of risk. As well as being mathematically convenient, this definition has economic justification. It is generally accepted that an individual’s absolute aversion to risk will be a decreasing function of his wealth. There is, therefore, a presumption that the definition will, in general, give greater weight to the expectations of capital transactors with a high level of wealth than to the expectations of those with a low level of wealth. Also, to the extent that individual expectations which are held with a relatively high degree of certainty represent a relatively high level of information, it is appropriate to give greater weight to those expectations. Obviously, if all individuals had the same aversion to risk and the same perception of risk, the definition of the future spot rate that is expected by the market as a whole would simply be an unweighted average of individual expectations.

2. a simple model of exchange rate determination

When equations (5) and (7) are combined with market-clearing identities for the spot and forward markets, the following simple model of exchange rate determination is obtained:

XfXsXs=r$r1+r
b=XeXfAσ2(1+r)
0=a+b+Ts(8)
0=−a+Tf+Gf(9)

Exogenous: r, r$, Xe, σ2, Gf, T3, Tf

Endogenous: Xf, Xs, a, b

where Ts(Tf) equals the net purchases of pounds for spot (forward) delivery by current account transactors; Gf equals the net purchases of pounds by the authorities in the forward exchange market; and

a=Σiai.

Equations (5), (7), (8), and (9) represent a very simple model of the determination of the spot and forward exchange rates in the short run. Current account contracts are assumed to be denominated in pounds, with the value of spot and forward purchases of pounds by current account transactors being exogenous in the short run. Although current account transactors may readily switch between the spot and the forward markets, it can be assumed that any such switches are motivated by arbitrage or speculative considerations that are implicit in equations (5) and (7). For the sake of simplicity, it is assumed that arbitrageurs do not cover their interest earnings in the forward market;4 purchases of “a” pounds in the spot market are therefore accompanied by sales of “a” pounds in the forward market. Also for the sake of simplicity, it is assumed that the authorities do not intervene in the spot market but confine their intervention to the forward market. This assumption ensures that the domestic and foreign money supplies are unaffected, at least initially, by official intervention and allows the rates of interest to be treated as exogenous variables. The results that are obtained below would remain essentially unchanged if official intervention took place in the spot market only, provided automatic sterilization occurred.

The reduced-form equations of the model are as follows:

a=Tf+Gf(10)
b=TsTfGf(11)
Xf=Xe+Aσ2(1+r)(Ts+Tf+Gf)(12)
Xs=(1+r)(1+r$)[Xe+Aσ2(1+r)(Ts+Tf+Gf)]=(1+r)(1+r$)Xf(13)

Equation (10) reflects the fact that, ex post, capital account transactors will engage in covered interest arbitrage to the extent necessary to clear the forward market.5 Given that excess demand or supply in the forward market is transmitted to the spot market by covered interest arbitrage, equation (11) shows that, ex post, capital transactors will buy pounds in the spot market on an uncovered basis (i.e., capital transactors will take out a long position in pounds) to the extent of the net excess supply of pounds in both the spot and forward markets by current account transactors and the authorities.

When there is current account equilibrium and the authorities refrain from official intervention (i.e., Ts + Tf = 0; Gf = 0), equations (12) and (13) show that the forward rate will equal the expected future spot rate, while the spot rate will be such that the expected appreciation of the spot rate will approximately equal the interest rate differential against the currency. Since capital transactors will maintain a closed position in pounds, there will be no element of risk premium in the spot and forward rates.

To the extent that a current account deficit or surplus emerges in the absence of official intervention, equations (12) and (13) show that the forward rate will differ from the expected future spot rate, and that the expected appreciation of the spot rate will differ from the interest rate differential. If there is a current account deficit, the forward rate will be less than the expected future spot rate. Since a current account deficit is necessarily accompanied by capital transactors taking out a long position, the expected appreciation of the spot rate has to exceed the interest differential against the currency by a risk premium. Similarly, if there is a current account surplus, the forward rate will exceed the expected future spot rate sufficiently to compensate capital transactors for taking the risk associated with the holding of a short position in the currency.

3. the case for official intervention

Equation (12) shows that, if current account disequilibrium does emerge under a flexible exchange rate, the forward rate will only equal the expected future spot rate if the authorities intervene in the foreign exchange market and purchase an amount of domestic currency equal to the current account deficit. It is likely that such an intervention policy would increase the welfare of current account transactors for the following reasons:

(1) In the absence of official intervention, the actual profit that is earned by capital transactors on their long or short positions is necessarily paid by current account transactors. If there is a current account deficit, current account transactors in aggregate will be net sellers of pounds. However, since the forward rate will be less than the expected future spot rate, current account transactors will only be able to cover their exchange risk by selling pounds in the forward market at a lower rate than the expected future spot rate.6 If the authorities intervene to prevent the buildup of open positions by capital transactors, current account transactors will be able to cover exchange risk without any expected cost. Provided that private transactors hold unbiased expectations of the future spot rate, the authorities could intervene in the foreign exchange market to eliminate the risk premium without incurring any long-run profit or loss.

(2) In the absence of official intervention, changes in the level of uncertainty, σ, with which private expectations are held will influence the exchange rate even when the interest rate differential and the expected future spot rate remain unchanged. Official intervention to eliminate a risk premium will therefore eliminate the variability in the exchange rate that would otherwise be caused by changes in uncertainty.

(3) Forward prices are likely to be used by private individuals as indicators of the future spot prices that are expected by the market as a whole. Decisions concerning future activity may be based on current forward prices. Only by official intervention can it be ensured that the forward exchange rate is an unbiased signal to private transactors of the future spot rate that is expected by the market.

II. Qualifications

The model presented in the previous section contained a number of simplifying assumptions. This section discusses the extent to which the results are likely to be affected when a number of these assumptions are relaxed. The section also discusses certain real world considerations.

(1) The model assumed that capital transactors gain utility from the return on their portfolios measured in terms of their home currencies7 and therefore perceive risk whenever they hold foreign currencies on an uncovered basis. Although this assumption is appropriate for the many banks and other corporations whose future disbursement needs are denominated principally in their home currencies, the assumption is less appropriate when future disbursement needs have a significant foreign currency component. An individual wealth holder is likely to perceive risk only when the currency composition of his portfolio differs from the currency composition of his future disbursement needs. To overcome this problem at a theoretical level, it could be assumed that the future disbursement needs of residents in terms of foreign currencies are equal to the future distribusement needs of nonresidents in terms of the domestic currency. The conclusion of the previous section concerning the magnitude of official intervention necessary to avoid a risk premium would then still hold.

However, at a realistic level, it is important to consider explicitly the enormous financial wealth and future disbursement needs of the oil exporting countries. The oil exporting countries are unable to hold their financial wealth in terms of their home currencies, and presumably gain utility from the return on their portfolios measured in terms of a single or a composite foreign currency. If, for example, all oil exporting countries gained utility from the value of their wealth measured in terms of, say, U. S. dollars, a risk premium on the dollar would only emerge in the absence of all official interventions in dollars to the extent that the U. S. current account deficit differed from the surplus earned by the oil exporting countries. Alternatively, if the oil exporting countries gained utility from the value of their wealth measured in special drawing rights (SDRs), each country whose currency was included in the SDR basket could expect to receive a capital inflow without incurring a risk premium equal to the surplus of the oil exporting countries times the weight of the country in the SDR basket. It would obviously be very difficult to estimate the capital inflow to each currency that would occur in the absence of risk premiums owing to the actions of capital transactors who gain utility from the value of their wealth measured in currencies other than their home currency. However, it is probably reasonable to assume that, for as long as the price of oil is set in terms of U. S. dollars, the oil exporting countries will only be willing to hold significant amounts of short-term funds in most currencies other than the U. S. dollar if a risk premium can be earned on such funds.

(2) The demand for spot and forward pounds by current account transactors has been assumed to be exogenous. Under this assumption, the magnitude of official purchases of pounds necessary to prevent the development of a risk premium is fixed; any change in the exchange rate will be reflected in a change in the number of dollars that need to be sold by the authorities rather than in the number of pounds purchased by the authorities. However, if all trade contracts were denominated in dollars rather than pounds, so that the dollar value of the current account was exogenous, any change in the exchange rate would necessitate an offsetting change in the magnitude of official purchases of pounds. In reality, trade contracts are denominated in both domestic and foreign currencies. If the deficit on all current account transactions denominated in domestic currency were, say, £ 100 million, while the deficit on all current account transactions denominated in foreign currency were, say, $200 million, the authorities would need to buy £(100 + 200/X) million (which is identical to selling $(100 X + 200) million) in order to prevent the development of a risk premium, where X is the exchange rate faced by the authorities when they intervene.

(3) It has been implicitly assumed that the authorities actually know the value of the current account payments balance at any point in time. Given that physical trade flows normally pass through customs before they give rise to payments flows, a country where customs data are reported expeditiously is likely to have a reasonable idea of the magnitude of official intervention that is required on, say, a month-to-month basis to prevent the development of a risk premium. The question remains, however, as to what should be the official intervention strategy on a day-to-day (or even an hour-to-hour) basis. Essentially, the authorities have two choices. They can either spread their intervention evenly throughout the month or they can intervene actively to smooth out day-to-day fluctuations subject to the constraint that their total monthly purchases of domestic currency equal the current account payments deficit for the month. Given that nonsynchronization of purchases and sales by current account transactors will give rise to daily pressures in the exchange market, the latter intervention policy seems preferable.

(4) The model assumed that a capital transactor will add greater risk to his portfolio by investing on an uncovered basis in a foreign currency than he will by investing in his home currency. As far as short-term investment is concerned, the assumption is probably realistic; the return on short-term interest-bearing financial assets denominated in the home currency is likely to be essentially riskless. However, the assumption may not be correct for long-term portfolio investments. For example, if the price level in a foreign country were stable and the exchange rate were expected to offset the inflation rate differential, investing in bonds denominated in the foreign currency would be similar to investing in indexed bonds denominated in the currency of the home country.8 If indexed bonds did not exist in the home country, foreign bonds might be thought preferable to domestic bonds. In general, long-term investment is unlikely to be significantly affected by a risk premium on, say, the three-month forward rate. Whereas a 1 per cent risk premium on the three-month forward rate will influence the return on a three-month investment by 1 percentage point, it will influence the return on a one-year investment by ¼ of a percentage point, and will influence the annual return on a ten-year investment by 140 of a percentage point. In the short run, it is reasonable to assume that both the current account and the long-term capital account are exogenously determined. The official strategy to eliminate risk premiums should, therefore, be to buy an amount of domestic currency in the foreign exchange market equal to the value of the combined deficit on the current account and the long-term capital account—that is, an amount equal to the deficit on the basic balance of payments.

(5) It was assumed in the model that capital transactors were initially holding closed positions. As a result, a current account deficit (surplus) was necessarily associated with the development of a long (short) position in the currency in the absence of official intervention. In reality, private short-term capital transactors will initially be holding an open position equal to the accumulated deficit on the basic balance of payments less the accumulated total of official purchases of domestic currency in the spot and forward markets. In order to remove any element of risk premium in the spot and forward rates, it would be necessary for the authorities to intervene once and for all to eliminate the initial open position that was being held.9 Thereafter, it would be necessary to intervene on a continuing basis and to buy an amount of domestic currency equal to the basic deficit on the balance of payments.

(6) An intervention strategy that ensures that the exchange rate accurately reflects the expectations of private speculators will obviously be inappropriate if speculators’ expectations are not formed on the basis of underlying conditions of trade and, as a result, differ significantly from traders’ expectations. Under such conditions, it is preferable for the authorities to set the price in the foreign exchange market rather than to intervene on a quantitative basis only.10 Moreover, it is possible that the official intervention strategy examined in this paper could reduce the extent to which speculators form their expectations on the basis of underlying conditions of trade. If it is anticipated that any impact of the basic balance of payments on the exchange rate will always be offset by official intervention, individual speculators may begin forming their expectations more on the basis of what they believe other speculators are expecting and less on the basis of underlying balance of payments considerations—that is, expectations may be formed more on an extrapolative basis and less on a “rational” basis. However, it seems reasonable to assume that speculators will believe that the authorities neither will be able nor will wish to continue the intervention strategy indefinitely if the exchange rate is not such as to provide medium-term equilibrium in the basic balance of payments.

(7) The previous analysis has suggested that the size of the risk premium on a currency will depend not only upon the magnitude of the accumulated basic balance of payments deficit or surplus that has to be financed or absorbed by private individuals but also upon private individuals’ perceptions of and aversions to the risk involved in holding an open position in the currency. Although the analysis was concerned with exchange risk, other types of risk are also likely to exist. In particular, holders of long spot positions in a currency face the risk that exchange controls may be imposed that would restrict the convertibility of their spot balances. Obviously, the magnitude of risk that is perceived to be involved in holding alternative currencies will vary; the level of risk involved in holding the currency of a country with unstable underlying economic and political conditions is likely to be much greater than is involved in holding the currency of a country with stable underlying economic and political conditions. The greater is the risk that is perceived to be involved in holding a currency, the greater will be the reluctance of private individuals to hold that currency and hence the greater will be the need for the authorities to finance the basic balance of payments deficit. Whereas, at one extreme, a significant risk premium is unlikely to develop on the U. S. dollar/deutsche mark exchange rate even when there are large imbalances on the U. S. and German basic balances, at the other extreme there are many less developed countries that have little choice but to finance officially their entire basic balance of payments deficits. In the category between these two extremes are included countries such as the United Kingdom and Italy, where large risk premiums would probably exist if the authorities did not finance the major part of their accumulated basic balance of payments deficits.

III. Conclusion

This paper has argued that, if the exchange rate is to reflect private expectations accurately, official intervention in the foreign exchange market is required to avoid any necessity for the buildup of large open positions by private capital transactors. Unless such official intervention occurs, the expected appreciation of the spot exchange rate is likely to differ from the interest rate differential by a risk premium, while the forward rate will also differ from the expected future spot rate by a risk premium. The actual size of the risk premium will be greater, first, the greater is the perception of private individuals of the risk involved in holding an open position in the currency and, second, the greater is the magnitude of the accumulated basic balance of payments deficit or surplus that has to be financed or absorbed by private individuals. Since the risk premium has to be paid by current account transactors and long-term capital account transactors and since the risk premium may cause economic distortions, it is argued that it is appropriate for the authorities to intervene in the foreign exchange market to prevent such risk premiums. The strategy to achieve this is not for the authorities to set the price in the foreign exchange market but rather for them to intervene on a quantitative basis and buy an amount of domestic currency in the spot or forward exchange markets equal to the basic balance of payments deficit.

The findings of the paper have an important bearing on the problem of exchange rate surveillance. To the extent that private short-term capital transactors form their expectations on an accurate assessment of the underlying conditions of trade, official intervention (or nonintervention that reduces the required open position of private short-term capital transactors is appropriate, while any official intervention that increases their open positions is inappropriate.

*

Mr. Day, economist in the Financial Studies Division of the Research Department, is an external graduate of the University of London and received his doctorate from the University of Birmingham.

1

Milton Friedman, “The Case for Flexible Exchange Rates,” Essays in Positive Economics (University of Chicago Press, 1953), p. 188.

2
Expanding by Taylor’s series about the mean, actual utility equals
Ui(Ri)=Ui(Rie)+Ui(Rie)(RiRie)+Ui"(Rie)2!(RiRie)+....
Assuming that expectations are normally distributed, the expected value operator can be applied to both sides, with all moments above the second being dropped.
E[Ui(Ri)]=Ui(Rie)+Ui(Rie)2Vi
Assuming that the utility function is unique up to a positive linear transformation, the function’s origin may be translated to give
E[Ui(Ri)]=RieAi2Vi

where A=Ui(Rie) See, for example, Donald E. Farrar, The Investment Decision Under Uncertainty (Chicago, 1967). With the utility function being unique up to a positive linear transformation, the maximization of the expected utility from the future value of the portfolio is equivalent to the maximization of the expected utility from the return on the portfolio. For a simple discussion of the postulates under which it is possible to assign utility numbers to each alternative sure level of return where the numbers are unique up to a positive linear transformation, and under which the choice of the individual with regard to uncertain outcomes is described by the maximization of expected utility, see Armen A. Alchian, “The Meaning of Utility Measurement,” American Economic Review, Vol. 43 (March 1953), pp. 26-50.

3

A purely speculative forward purchase of pounds is equivalent to a combination of an uncovered spot purchase of pounds and a covered spot sale of pounds.

4

In reality, banks frequently ignore interest earnings when they quote swap rates. See Adam Hepburn, “The Way to True Profit on Interest Arbitrage?” Euromoney (July 1974), pp. 45-47.

5

Banks normally cover the exchange risk associated with any imbalance in the forward facilities that they provide by operations in the spot market. This is covered interest arbitrage undertaken passively.

6

It is assumed that current account transactors hold the same expectations as capital transactors.

7

When an individual gains utility from the value of his wealth measured in, say, U. S. dollars, it is assumed that the individual’s utility is unaffected by changes in the value of his wealth measured in any alternative currency if the U. S. dollar value of his wealth remains unchanged.

8

See William H. White, “The Portfolio Diversification Argument that Flexible Exchange Rates Will Permit Important Interest Rate Effects on Capital Movements” (unpublished, International Monetary Fund, January 2, 1974).

9

The most efficient means of eliminating the initial open position would be to intervene steadily over, say, a three-month period to offset open positions as they matured.

10

It can be argued that it would be preferable under such conditions for the authorities to set the price in the forward exchange market rather than in the spot exchange market. See William H. L. Day, “The Advantages of Exclusive Forward Exchange Rate Support,” Staff Papers, Vol. 23 (March 1976), pp. 137-63.