3.2 Arbitrage under the gold standard

The classical gold standard, which was in operation worldwide from around 1870 until 1914, when it collapsed with the outbreak of the First World War, is basically a system of fixed exchange rates. In this section we examine the process whereby currency arbitrage is conducted under a system of fixed exchange rates, where the rates are determined by the gold values of indi­vidual currencies.

Under the gold standard the fixed exchange rates are determined as follows. The monetary authority in each country fixes the price of gold in terms of the domestic currency and stands ready to buy or sell any amount of gold at that price. This would in turn establish a fixed exchange rate between any two currencies called the "mint parity". The actual exchange rate can only vary above and below the mint parity between certain limits called the "gold points", which are determined by the cost of shipping gold between the two countries in question.

Let us assume that the country whose currency is x is the home country, and the country whose currency is y is the foreign country. Suppose that the price of an ounce of gold is a units of x and b units of y. The mint parity is then given by

(a) USD/GBP

(b) USD/CAD

FIGURE 3.3 Actual and PPP exchange rates.

S^M = - (3.12)

b

Suppose now that the cost of shipping gold between the two countries is a fraction, e, of the value of the gold shipped. From the perspective of the home country, the gold export point, which is the upper limit on the exchange rate, is given by

s^u= bb⁺{-)=(1+e{b) (³-¹³)

The gold export point implies that no resident in the home country would pay more than (1 + e)(a/b) units of x for one unit of y. This is because it is possible to buy (a/b) units of x worth of gold, ship it to the foreign country and

FIGURE 3.4 Exchange rate determination under the gold standard.

sell it for one unit of y. Similarly, the gold import point, which is the lower limit on the exchange rate, is given by

S^L = b - <-) = (1 - e{D (3.14,

The gold import point implies that no resident of the home country is willing to accept less than (1 - e)(a/b) units of x for one unit of y.

The gold export and import points have some implications for the shapes of the supply and demand for currency y curves. The supply curve becomes infi­nitely elastic or horizontal at the gold export point, whereas the demand curve becomes horizontal at the gold import point. In between they have the normal upward and downward sloping shapes, as illustrated in Figure 3.4, which shows that the equilibrium exchange rate S^E is above the mint parity rate, S^M. The exchange rate can move between the gold import and export points, but not outside this range. Thus, the no-arbitrage zone is represented by a band around the mint parity rate.

3.3 Arbitrage between eurocurrency and domestic interest rates

Arbitrage between Eurocurrency and domestic money markets ensures that there is a close relationship (a no-arbitrage condition) between domestic and

Eurocurrency interest rates. In the absence of the bid-offer spread, the no- arbitrage condition would take the form

(3.15)

where i is the domestic interest rate and i* is the Eurocurrency interest rate. If the condition is violated, arbitrage would take the form of borrowing funds in the market where funds are cheap and lending in the market where they are expensive. In the presence of the bid-offer spread, the no-arbitrage condition would take the form

⁽ⁱb ^{, 1} a ⁾ = ⁽C ⁱb⁾

In reality, however, there are factors that prevent the equality of domestic and Eurocurrency rates as indicated by equations (3.15) and (3.16). The condi­tions become

i = i + a and

⁽ⁱb ^{, i}a ⁾ = Oa + ^{b i}b + g⁾

where a > 0, b > 0 and g > 0.

i = i

(3.16)

(3.17)

(3.18)

Figure 3.5 shows the relationship between Eurocurrency and domestic rates. Domestic rates are determined by the demand for and supply of funds in the domestic market, whereas the Eurocurrency rates are determined by the demand for and supply of funds in the Eurocurrency market. In both cases, the bid rate is determined by the demand of market makers and the supply of others (including arbitragers), whereas the offer rate is determined by the demand of others and the supply of market makers. As we can see, the relationship between Eurocurrency and domestic rates is such that

Supply (market makers) Supply (others)	Supply (market makers) Supply (others)
	;
w
Demand (others) Demand (market makers)
	Demand (others) Demand (market makers)

Eurocurrency market

Domestic market

Quantity x Quantity y

FIGURE 3.5 Determination of domestic and Eurocurrency interest rates.

i_a > i*_a > ib > i_b . We can also see that the bid-offer spread in the Eurocurrency market is narrower than the spread in the domestic market, which is normally interpreted to indicate that the Eurocurrency market is more efficient due to the absence of regulatory requirements.

What are the factors that prevent the equality of Eurocurrency and domestic interest rates despite the presence of arbitrage activity? These factors may include transaction costs, capital controls and political risk. Under full and effective capital controls, the domestic and Eurocurrency markets will be completely isolated from each other, preventing arbitrage activity from equating interest rates. Several factors can explain why the Eurocurrency offer rate (lending rate) is lower than the corresponding domestic offer rate:

1. The absence of regulatory requirements in the Eurocurrency market, which makes borrowing and lending cheaper than in the domestic market.

2. Borrowers are of higher quality and credit rating than in the domestic market, which makes the risk premium lower in the Eurocurrency market.

3. Eurocurrency transactions are much larger than domestic transactions, which allows the exploitation of the economies of scale.

4. Eurocurrency transactions can take place out of tax havens, which makes them cheaper to execute.

The Eurocurrency bid rate (deposit rate) is higher than the corresponding domestic bid rate, for the following reasons:

1. It has to be higher to attract domestic deposits.

2. Eurobanks can afford to pay higher deposit rates.

3. The absence of interest rate ceilings in the Eurocurrency market.

4. Eurobanks are more efficient than domestic banks, and they can lend out a larger percentage of deposits.