2CHAPTER 1. SOME INSTITUTIONAL BACKGROUND

1.1International Financial Markets

We begin with a description of some basic international Þnancial instruments and the markets in which they trade. As a point of reference, we view the US as the home country.

Foreign Exchange

Foreign exchange is traded over the counter through a spatially decentralized dealer network. Foreign currencies are mainly bought and sold by dealers housed in large money center banks located around the world. Dealers hold foreign exchange inventories and aim to earn trading proÞts by buying low and selling high. The foreign exchange market is highly liquid and trading volume is quite large. The Federal Reserve Bank of New York [51] estimates during April 1998, daily volume of foreign exchange transactions involving the US dollar and executed within in the U.S was 405 billion dollars. Assuming a 260 business day calendar, this implies an annual volume of 105.3 trillion dollars. The total volume of foreign exchange trading is much larger than this Þgure because foreign exchange is also traded outside the US—in London, Tokyo, and Singapore, for example. Since 1998 US GDP was approximately 9 trillion dollars and the US is approximately 1/7 of the world economy, the volume of foreign exchange trading evidently exceeds, by a great amount, the quantity necessary to conduct international trade.

During most of the post WWII period, trading of convertible currencies took place with respect to the US dollar. This meant that converting yen to deutschemarks required two trades: Þrst from yen to dollars then from dollars to deutschemarks. The dollar is said to be the vehicle currency for international transactions. In recent years crosscurrency trading, that allows yen and deutschemarks to be exchanged directly, has become increasingly common.

The foreign currency price of a US dollar is the exchange rate quoted in European terms. The US dollar price of one unit of the foreign currency is the exchange rate is quoted in American terms. In American terms, an increase in the exchange rate means the dollar currency has depreciated in value relative to the foreign currency. In this book, we will always refer to the exchange rate in American terms.

1.1. INTERNATIONAL FINANCIAL MARKETS

3

The equilibrium condition in cross-rate markets is given by the absence of unexploited triangular arbitrage proÞts. To illustrate, assume that there are no transactions costs and consider 3 currencies–the dollar, the euro, and the pound. Let S1 be the dollar price of the pound, S2 be the dollar price of the euro, and S3x be the euro price of the pound. The cross-rate market is in equilibrium if the exchange rate quotations obey

S1	= SxS2.	(1.1)
	3

The opportunity to earn riskless arbitrage proÞts are available if (1.1) is violated. For example, suppose that you get price quotations of S1 = 1.60 dollars per pound, S2 =1.10 dollars per euro, and S3x = 1.55 euros per pound. An arbitrage strategy is to put up 1.60 dollars to buy one pound, sell that pound for 1.55 euros and then sell the euros for 1.1 dollars each. You begin with 1.6 dollars and end up with 1.705 dollars, which is quite a deal. But when you take money out of the foreign exchange market it comes at the expense of someone else. Very short-lived violations of the triangular arbitrage condition (1.1) may occasionally occur during episodes of high market volatility, but we do not think that foreign exchange dealers will allow this to happen on a regular basis.

Transaction Types

Foreign exchange transactions are divided into three categories. The Þrst are spot transactions for immediate (actually in two working days) delivery. Spot exchange rates are the prices at which foreign currencies trade in this spot market.

Second, swap transactions are agreements in which a currency sold (bought) today is to be repurchased (sold) at a future date. The price of both the current and future transaction is set today. For example, you might agree to buy 1 million euros at 0.98 million dollars today and sell the 1 million euros back in six months time for 0.95 million dollars. The swap rate is the di erence between the repurchase (resale) price and the original sale (purchase) price. The swap rate and the spot rate together implicitly determine the forward exchange rate.

The third category of foreign exchange transactions are outright forward transactions. These are current agreements on the price, quan-

4CHAPTER 1. SOME INSTITUTIONAL BACKGROUND

tity, and maturity or future delivery date for a foreign currency. The agreed upon price is the forward exchange rate. Standard maturities for forward contracts are 1 and 2 weeks, 1,3,6, and 12 months. We say that the forward foreign currency trades at a premium when the forward rate exceeds the spot rate in American terms. Conversely if the spot rate is exceeds the forward rate, we say that the forward foreign currency trades at discount.

Spot transactions form the majority of foreign exchange trading and most of that is interdealer trading. About one—third of the volume of foreign exchange trading are swap transactions. Outright forward transactions account for a relatively small portion of total volume. Forward and swap transactions are arranged on an informal basis by money center banks for their corporate and institutional customers.

Short-Term Debt

A Eurocurrency is a foreign currency denominated deposit at a bank located outside the country where the currency is used as legal tender. Such an institution is called an o shore bank. Although they are called Eurocurrencies, the deposit does not have to be in Europe. A US dollar deposit at a London bank is a Eurodollar deposit and a yen deposit at a San Francisco bank is a Euro-yen deposit. Most Eurocurrency deposits are Þxed-interest time-deposits with maturities that match those available for forward foreign exchange contracts. A small part of the Eurocurrency market is comprised of certiÞcates of deposit, ßoating rate notes, and call money.

London Interbank O er Rate (LIBOR) is the rate at which banks are willing to lend to the most creditworthy banks participating in the London Interbank market. Loans to less creditworthy banks and/or companies outside the London Interbank market are often quoted as a premium to LIBOR.

Covered Interest Parity

Spot, forward, and Eurocurrency rates are mutually dependent through the covered interest parity condition. Let it be the date t interest rate

1.1. INTERNATIONAL FINANCIAL MARKETS

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on a 1-period Eurodollar deposit, it be the interest rate on an Euroeuro deposit rate at the same bank, St, the spot exchange rate (dollars per euro), and Ft, the 1-period forward exchange rate. Because both Eurodollar and Euroeuro deposits are issued by the same bank, the two deposits have identical default and political risk. They di er only by the currency of their denomination.1 Covered interest parity is the condition that the nominally risk-free dollar return from the Eurodollar and the Euroeuro deposits are equal. That is

	Ft
1 + it = (1 + i )	St	.	(1.2)
t

When (1.2) is violated a riskless arbitrage proÞt opportunity is available and the market is not in equilibrium. For example, suppose there are no transactions costs, and you get the following 12-month eurocurrency, forward exchange rate and spot exchange rate quotations

it = 0.0678, it = 0.0422, Ft = 0.9961, St = 1.0200.

You can easily verify that these quotes do not satisfy (1.2). These quotes allow you to borrow 0.9804 euros today, convert them to 1/St = 1 dollar, invest in the eurodollar deposit with future payo 1.0678 but you will need only (1 + it )Ft/St = 1.0178 dollars to repay the euro loan. Note that this arbitrage is a zero-net investment strategy since it is Þnanced with borrowed funds. Arbitrage proÞts that arise from such quotations come at the expense of other agents dealing in the international Þnancial markets, such as the bank that quotes the rates. Since banks typically don’t like losing money, swap or forward rates quoted by bank traders are routinely set according to quoted eurocurrency rates and (1.2).

Using the logarithmic approximation, (1.2) can be expressed as

it ' it + ft − st

(1.3)

where ft ≡ ln(Ft), and st ≡ ln(St).

1Political risk refers to the possibility that a government may impose restrictions that make it di cult for foreign investors to repatriate their investments. Covered interest arbitrage will not in general hold for other interest rates such as T-bills or commercial bank prime lending rates.

6CHAPTER 1. SOME INSTITUTIONAL BACKGROUND

Testing Covered Interest Parity

Covered interest parity won’t hold for assets that di er greatly in terms of default or political risk. If you look at prices for spot and forward foreign exchange and interest rates on assets that di er mainly in currency denomination, the question of whether covered interest parity holds depends on whether there there exist unexploited arbitrage proÞt opportunities after taking into account the relevant transactions costs, how large are the proÞts, and the length of the window during which the proÞts are available.

Foreign exchange dealers and bond dealers quote two prices. The low price is called the bid. If you want to sell an asset, you get the bid (low) price. The high price is called the ask or o er price. If you want to buy the asset from the dealer, you pay the ask (high) price. In addition, there will be a brokerage fee associated with the transaction.

Frenkel and Levich [63] applied the neutral-band analysis to test covered interest parity. The idea is that transactions costs create a neutral band within which prices of spot and forward foreign exchange and interest rates on domestic and foreign currency denominated assets can ßuctuate where there are no proÞt opportunities. The question is how often are there observations that lie outside the bands.

Let the (proportional) transaction cost incurred from buying or selling a dollar debt instrument be τ, the transaction cost from buying or selling a foreign currency debt instrument be τ , the transaction cost from buying or selling foreign exchange in the spot market be τs and the transaction cost from buying or selling foreign exchange in the forward market be τf . A round-trip arbitrage conceptually involves four separate transactions. A strategy that shorts the dollar requires you to Þrst sell a dollar-denominated asset (borrow a dollar at the gross rate 1 + i). After paying the transaction cost your net is 1 − τ dollars. You then sell the dollars at 1/S which nets (1 − τ)(1 − τs) foreign currency units. You invest the foreign money at the gross rate 1 + i , incurring a transaction cost of τ . Finally you cover the proceeds at the forward rate F, where you incur another cost of τf . Let

¯		)(1	− τf ),
C	≡ (1 − τ)(1 − τs)(1 − τ

and fp ≡ (F −S)/S. The net dollar proceeds after paying the transac-

1.1.	INTERNATIONAL FINANCIAL MARKETS						7
tions	costs are	C¯(1 + i )(F/S). The arbitrage					is unproÞtable if
C¯(1 + i )(F/S)		≤	(1 + i), or equivalently if
			f	f¯	(1 + i) − C¯(1 + i )	.	(1.4)
			p ≤	p ≡	C¯(1 + i )

By the analogous argument, it follows that an arbitrage that is long in the dollar remains unproÞtable if

f	p ≥	f		≡	C¯(1 + i) − (1 + i )	.	(1.5)
			p		(1 + i )

[fp, f¯p] deÞne a neutral band of activity within which fp can ßuctuate but still present no proÞtable covered interest arbitrage opportunities. The neutral-band analysis proceeds by estimating the transactions costs

¯	¯
C	. These are then used to compute the bands [fp, fp] at various points

in time. Once the bands have been computed, an examination of the proportion of actual fp that lie within the bands can be conducted.

Frenkel and Levich estimate τs and τf to be the upper 95 percentile of the absolute deviation from spot and 90-day forward triangular arbitrage. τ is set to 1.25 times the ask-bid spread on 90-day treasury bills and they set τ = τ. They examine covered interest parity for the dollar, Canadian dollar, pound, and the deutschemark. The sample is broken into three periods. The Þrst period is the tranquil peg preceding British devaluation from January 1962—November 1967. Their estimates of τs range from 0.051% to 0.058%, and their estimates of τf range from 0.068% to 0.076%. For securities, they estimate τ = τ to be approximately 0.019%. The total cost of transactions fall in a range from 0.145% to 0.15%. Approximately 87% of the fp observations lie within the neutral band.

The second period is the turbulent peg from January 1968 to De-

¯

cember 1969, during which their estimate of C rises to approximately 0.24%. Now, violations of covered interest parity are more pervasive with the proportion of fp that lie within the neutral band ranging from 0.33 to 0.67.

The third period considered is the managed ßoat from July 1973 to

¯

May 1975. Their estimates for C rises to about 1%, and the proportion

8CHAPTER 1. SOME INSTITUTIONAL BACKGROUND

of fp within the neutral band also rises back to about 0.90. The conclusion is that covered interest parity holds during the managed ßoat and the tranquil peg but there is something anomalous about the turbulent peg period.2

Taylor [130] examines data recorded by dealers at the Bank of England, and calculates the proÞt from covered interest arbitrage between dollar and pound assets predicted by quoted bid and ask prices that would be available to an individual. Let an “a” subscript denote an ask price (or ask yield), and a “b” subscript denote the bid price. If you buy pounds, you get the ask price Sa. Buying pounds is the same as selling dollars so from the latter perspective, you can sell the dollars at the bid price 1/Sa. Accordingly, we adopt the following notation.

Sa : Spot pound ask price. 1/Sa : Spot dollar bid price. Sb : Spot pound bid price. 1/Sb : Spot dollar ask price.

ia : Eurodollar ask interest rate. ib : Eurodollar bid interest rate.

Fa : Forward pound ask price. 1/Fa : Forward dollar bid price. Fb : Forward pound bid price. 1/Fb : Forward dollar ask price. ia : Euro-pound ask interest rate. ib : Euro-pound bid interest rate.

It will be the case that ia > ib, ia > ib , Sa > Sb, and Fa > Fb. An arbitrage that shorts the dollar begins by borrowing a dollar at the

gross rate 1 + ia, selling the dollar for 1/Sa pounds which are invested at the gross rate 1 + ib and covered forward at the price Fb. The per dollar proÞt is

(1 + i )Fb − (1 + ia).

b Sa

Using the analogous reasoning, it follows that the per pound proÞt that shorts the pound is

(1 + ib) Sb − (1 + i ).

Fa a

Taylor Þnds virtually no evidence of unexploited covered interest arbitrage proÞts during normal or calm market conditions but he is able to identify some periods of high market volatility when economically signiÞcant violations may have occurred. The Þrst of these is the 1967

2Possibly, the period is characterized by a ‘peso problem,’ which is covered in chapter 6.