THE THEORY OF FORWARD EXCHANGE badly needs a systematic reformulation. Traditionally, the emphasis has always been upon covered interest arbitrage, which forms the basis of the so-called interest parity theory of forward exchange.1 Modern economists, of course, recognize that operations other than interest arbitrage, such as hedging and speculation, also exert a determining influence upon the forward exchange rate,2 but a systematic theory of forward exchange which explains precisely how the interplay of all these different types of operation jointly determine the forward exchange rate and how the forward exchange market is linked to the spot exchange market still appears to be lacking.
The purpose of this paper is to work out a more comprehensive and systematic theory of forward exchange, which would enable us better to understand the behavior of the forward exchange rate and to deduce the likely consequences of government intervention in the forward exchange market.
Mr. Tsiang, economist in the Special Studies Division, is a graduate of the London School of Economics, and was formerly Professor of Economics in the National Peking University and the National Taiwan University. He is the author of The Variations of Real Wages and Profit Margins in Relation to Trade Cycles and of several articles in economic journals.
See, e.g., Henry Deutsch, Transactions in Foreign Exchanges (London, 1914), p. 174, and J.M. Keynes, Tract on Monetary Reform (London, 1923), pp. 122–32.
See Keynes, op. cit.; P. Einzig, The Theory of Forward Exchange (London, 1937); League of Nations, Economic Intelligence Service, Monetary Reviews (Geneva, 1937), Section B, “The Market in Forward Exchanges,” pp. 42–51; C.P. Kindleberger, “Speculation and Forward Exchange,” Journal of Political Economy, Vol. XLVII (April 1939), pp. 163–81, and International Economics (Homewood, Illinois, 1953), Chap. 3, pp. 39–57; F.A. Southard, Jr., Foreign Exchange Practice and Policy (New York, 1940), Chap. III, pp. 75–111; A.I. Bloomfield, Capital Imports and the American Balance of Payments, 1934–1939 (Chicago, 1950), Chap. II, pp. 39–85; J.E. Meade, The Theory of International Economic Policy, Vol. 1, The Balance of Payments (London, 1951), Chap. XVII; J. Spraos, “The Theory of Forward Exchange and Recent Practice,” The Manchester School of Economic and Social Studies, Vol. XXI (May 1953), pp. 87–117; and M.N. Trued, “Interest Arbitrage, Exchange Rates, and Dollar Reserves,” The Journal of Political Economy, Vol. LXV (October 1957), pp. 403–11.
As defined by Professor Kindleberger, an excess of uncovered claims over liabilities in foreign exchange is called a “long position”; an excess of debts over assets, a “short position.” See Kindleberger, International Economics (cited in footnote 2), p. 40.
The central banks usually reserve the right to intervene in their forward exchange markets for the purpose of influencing the forward rate for any particular foreign currency. In some cases, e.g., in the Danish and Swedish forward markets for U.S. dollars, the central banks concerned actually buy and sell forward dollars at their respective official spot buying and selling rates, with a certain discount for forward purchases and a certain premium for forward sales. However, at least one central bank, namely that of Belgium, has announced that it presently does not intervene in the forward markets for U.S. and Canadian dollars. Recently, there has been a debate going on in the United Kingdom with regard to the question of whether or not the authorities should intervene in the forward market.
Op. cit., pp. 87–89.
Spraos contends that the usual verbal formulation of the interest parity theory is consistent with his more rigorous formulation only if Ib, is negligibly small (op. cit., pp. 88–89). In making this assertion, however, he is not doing justice to the usual verbal formulation; for what is neglected there is simply the term pIb which is a product of p, the forward premium (or discount), usually a small percentage, and Ib, the short-term interest rate in the foreign country per three months, another small percentage. Therefore, pIb, can be negligibly small, even when Ib, is not negligibly small.
Keynes, op. cit., p. 128. Keynes’ original estimate of the minimum sensibile was readily endorsed by Einzig (op. cit., p. 172), Bloomfield (op. cit., pp. 52–53), and Spraos (op. cit., p. 95).
Spraos, op. cit., p. 88.
Keynes, op. cit., p. 129.
For a speculator—and indeed for hedgers as well—the maturity of a forward contract does not mean that the contracted amount of foreign exchange will actually be delivered against full payment in local currency. A matured forward contract is usually settled by the contracting parties taking the profit, or paying the loss, implied in the difference between the contracted forward rate and the actual current spot rate at the moment of maturity.
Let us define the shift operator E in such a way that
Dt+1 = EDt and Dt−1 = E−1 Dt.
When E is applied to equation (18), that equation can be rewritten as
That is rjt(E–λj)=γjEDjt
Spraos, op. cit., pp. 92-95.
Thus speculators’ aggregate demand will be negative at the forward rate equal to
The sale of sterling for local currency by the U.S. monetary authorities is equivalent to the purchase of dollars with local currency by the British monetary authorities. To avoid confusion, however, we must continue to call one currency (say, sterling) the foreign exchange and the other (say, dollars) the domestic currency.
See John Spraos, “Exchange Policy in the Forward Market: Case for an Official Peg,” A.E. Jasay, “Case for Official Support,” and anonymous, “Case for the Status Quo,” all in The Banker, Vol. CVIII (April 1958). See also A.E. Jasay, “Making Currency Reserves ‘Go Round,’” The Journal of Political Economy, Vol. LXVI (August 1958), and “Forward Exchange: The Case for Intervention,” Lloyds Bank Review (October 1958).
See “Case for the Status Quo” (cited in footnote 16), pp. 234–35.
It may, however, have some remote indirect effect upon arbitragers’ demand for spot exchange. For the maturing of forward commitments previously entered into would alter, to some extent, the risk position of the speculator concerned and thus might affect his willingness to make new speculative purchases and sales, as indicated in equations (18) and (21). Indirectly, this might affect the spot exchange market through the forward rate, with interest arbitragers acting as the link between the two markets. However, as equation (18) shows, the effects of past commitments upon the marginal risk of a speculator diminishes in weight with the proximity to maturity, so that the eventual maturing of a forward contract should not have any abrupt effect upon the marginal risk of the speculator concerned.
The deferred effects on the spot exchange market of an official intervention in the forward exchange market appear to be totally neglected by the participants on both sides of the debate on forward exchange (see articles in The Banker, cited above in footnote 16).