If Ef is the forward exchange rate , Es the spot rate(sterling ) .Rd is the sterling in the sterling interest rate and Rf is the interest rate in a foreign country (i.e. United State ).
There is incentive for capital to flow between the Two countries when the two side of the equation is not equal ,which is when the sterling’ forward discount is exactly equal to the interest rate differential in favor of London. At this point the forward exchange rate is said to be at interest parity .
Structural Model
Structural model is a more general theoretical view comparing with the Combist approach .As D.T.Llewellyn argued in INTERNATIONAL FINANCIAL INTEGRATION “A formal model of the forward exchange rate may be constructed on the basis of supply and demand schedules for forward exchange by speculator and interest arbitragers.”
In this model , the equilibrium forward rate is determined when the net supply of forward exchange by one group of translator is matched by the net demand from the other. Changes in forward exchange rate and direction of capital flows are determined by factors which induce changes in either the position or slope of speculators’ and arbitrageurs’ demand/supply curve for forward exchange.
This traditional analysis implicitly assumes 1) that speculators and arbitragers deal diect with each other .2) the volume of forward currency made available to arbitragers by either speculators or banks ( if the bank are intervening in forward market )
The basic theoretical model is outlined in Figure 1 .
Forward exchange rate
A S
X1
Pe
E
Pp
M
X0
S A
B D 0 C
As shown in Figure 1,the forward exchange rate is measured on the vertical axis in terms of units of domestic currency per unit of foreign currency (forward sterling price of dollar).The volume of forward exchange supplied and demanded by speculators and arbitrageurs is indicated on the horizontal axis .On the left of horizontal axis ,the arbitragers sale forward exchange / purchase forward sterling and the speculator sale sterling. Conversely on the right. These behavior is associated with a spot capital outflow . In order to explain the determination of forward exchange rate clearly , we need to analysis the role played by either arbitrager or speculator separately .To simplify our analysis we assume that both the spot rate and foreign and domestic interest rate are determined exogenously, and remain constant .
Arbitraguers
AA is the supply and demand curves of interest arbitrage .At point Pp the arbitragers’schedule cuts the vertical axis .Therefore, Pp is the parity level of the forward rate ,at this rate no arbitrage capital flows take place since because the covered interest rate differential is zero .
To the left of the horizontal axis the forward exchange rate is depreciate against its parity level which implies a covered interest differential against domestic assets. Arbitragers purchase forward sterling , sale forward exchange and spot capital out flow. Conversely, to the right of Pp ,arbitragers sale forward sterling ,the capital inflow. Thus the arbitrager’s schedule is demand curve for forward sterling to the left of zero and supply curve to the right of zero. From the shape of AA ,it can be seen clearly that ,as the volume of capital flows increases, an increasingly wide covered interest-rate differential is needed to induce further capitalflows.
For exampl , spot rate is X0 , forward rate is a point below Pp as M. In this situation ,the domestic interest rate is higher than the foreign rate because the parity level of the forward rate (Pp )is at a discount to the spot exchange rate .It can be seen in figure 1.,at a forward rate M below Pp ,we have
which lead on a capital inflow OC with arbitrage selling an amount OC of forward sterling .
The slope of this schedule is important in determining the forward exchange rate and the volume of capital flows. The slope of AA indicates the elasticity of supply of arbitrage funds, i.e.the interest-rate sensitivity of international capital flows. The slop of AA is determined by those factors which determine the interest-rate sensitivity of international capital flows .
The position of AA is determined by the spot exchange rate and the uncovered interest-rate differential between domestic and foreign assets.
Speculators
The speculators’ supply and demand curve is given in figure 1.as SS. Pe is the level of the expected future spot rate that the SS schedule cut the vertical axis .At this point the future spot equal to the forward rate and no speculative sales or purchases of forward exchange are made .To the left of Pe speculators sales forward sterling as the expected future spot rate is depreciated against the current forward rate . Conversely, at forward rate appreciated against the expected spot rate ,speculator purchase forward sterling sales forward foreign currency.
The slope of AA schedule is determined by :1)the degree of the speculator’s confidence about the expected future spot rate .2) the degree of risk-aversion of speculators .The more confident the speculators are the more elastic will be the speculator ‘s schedule .
The equilibrium forward rate is point E and the volume of capital flow are determined at OA in Figure 1.At this rate the net demand for forward sterling by interest arbitragers is met by the net supply for forward sterling by speculators. This because at E the forward rate is appreciated against the expected future spot rate Pe ,thus the arbitragers purchase OD amount of forward sterling associated with the capital outflows and the speculators sales OD amount of forward sterling .
If the equilibrium were in the right hand segment of Figure 1.,the expected future spot rate Pe would be appreciated against the interest rate parity level of forward rate Pp. In this case, the equilibrium in the forward market would imply a capital inflow with consequent sales of forward sterling by arbitragers matched by demand for forward sterling by speculators.
In figure 1. the equilibrium forward rate E is different from the interest rate parity level Pe. Therefore arbitrageurs will forgoing profitable investment opportunities if the elasticity of arbitrage schedule is less than perfect. Furthermore, the parity theory can be upheld if
1)The arbitrage schedule AA is infinitely elastic ,which mean the supply of potential arbitrage fund is infinite. 2)The expected future spot rate is equal to the parity level .Since the two schedule intersect on the vertical axis there is zero capital flows .
“ The closer is the expected future spot rate to the parity level of the forward rate the greater the probability that the forward rate will be close to parity irrespective of the elasticity of the two schedule”
Combist approach
The Combist analysis differs in important detail from the structural model discussed before . The traditional analysis implicitly assumes either that the speculators and arbitragers deal direct with each other ,or that banks act solely as brokers .The Combist approach is an alternative analysis of the forward exchange market offered by banks.
In combist approach ,banks perform an equilibrating arbitrage role in the forward market. Covered arbitrage transactions by non-banks have no net effect upon the spot rate ,reserves or domestic money supply as they are offset by equal and opposite spot transactions by banks.
The interest-rate-parity theory is the center of the Combist approach .The equilibrium in Combist approach is determined by the bank’s automatic response in the spot market to their non-bank customers’ sales or purchases in the forward market .This equilibrating mechanism ensures that the forward rate dose not deviate from its parity level. There is no meaningful unique non-bank arbitrage function the supposed response of non-banks to intrinsic premium or discount .The forward exchange rate is always at its parity level with respect to euro currency interest rates .This factor is induced by the automatic adjustment by bank transactions .
The banks’ automatic respond is the central feature of forward exchange operations in the Cambist approach.
1) matching the customer’s demand (supply) with an equal and opposite customer supply (demand) .However, the bank can’t always find the chance to match it in this way .
2)Bank sell spot whatever the customer is selling forward since they have to buy forward from its customer. This transaction is in order to avoid creating an undesired open speculative forward position.
However ,a bank will not be forced into a speculative position by the impact of the customer’s transactions. Bank offer forward facilities to customers without being forced into open speculative positions through two main method out lined below:
1)The swap method (currency swap)
Currency swap involves an inter-bank transaction where a bank sells a currency spot to another bank and simultaneously buys the currency back forward.
2) The Euro-currency Mechanism
the bank will do series transaction to avoid potential risk from the response forward transaction to customers.
- borrows in the euro market the currency being sold forward by its customers
- sells the currency spot for the currency being bought by the customer
- invests the proceeds of the spot sale in the appropriate euro-currency market.
In the Combist approach , banks provide forward facilities in a perfectly competitive foreign-exchange market through banking mechanism ,and equilibrium is determined automatically. As a consequence the forward rate can never deviate from its parity level. Indeed, dealers quote forward exchange rate on the basis of observes euro currency interest-rate differential.
Conclusion
There is therefore no inherent significant conflict between the two model. There is no important analytical difference between bank and non-bank arbitrage ,and the two forward exchange mechanism do not differ in any significant respect.
“In particular ,the precise mechanism of arbitrage has little analytical significance .The structural model may therefore be betaken as a reasonable representation of the forces operating in the market.”, D.T.Llewellyn argued in INTERNATIONAL FINANCIAL INTEGRATION.
Reference
1. chapter 4 & 5 International financial integration Professor. D.T.Llewellyn
2 Grubel, Herbert G. (Herbert Gunter), Forward exchange, speculation and the international flow of capital , Stanford University Press, 1966
3 International Finance Heather D. Gibson
