International trade is largely carried out by exchanging the value of goods and services in the terms of one currency for that of another. Such trade does not make use of a barter trade system and as such we need to account for the fact that virtually every country (or group of countries that form a monetary union) has its own monetary unit or currency. In addition, there are also a number of international transactions that are purely financial in nature, such as trading activity, which may involve the exchange of different currencies.

Hence, the need for a foreign exchange market, where the various national currencies can be exchanged (bought and sold) for one another. The foreign exchange market, like any other concept of a market that is used in economic theory, is not a precise physical place. It is actually formed by banks, brokers and other authorized representatives to whom economic agents apply to buy and sell the various currencies. These representatives of the market are linked by telephone, telex, computer, or by other means and thus the market has an international rather than national dimension.

Over time, the globalisation process has led to a spectacular growth in the volumes of currency that are traded on the foreign exchange market.

# 1 Organisation of the Foreign Exchange Market

In this section, we describe the institutional structure that allows corporations, banks, international investors, and tourists to convert one currency into another.

The foreign exchange market consists of a number of different aspects and is the largest and most liquid market in the world, measured by dollar volume of trade. It is open around the clock (i.e. 24 hours) as the major financial centres where currencies are traded have different geographic locations. Major trading centres, which have been arranged according to relative opening times, include Wellington, Sydney, Tokyo, Osaka, Hong Kong, Singapore, Copenhagen, Frankfurt, Zurich, Paris, London, New York, Chicago and Los Angeles. This market incorporates a multiplicity of heterogeneous market participants and as such it is not surprising to find that the behaviour of exchange rates is relatively complex.

The most important aspect of this market includes the interbank market, which comprises of the wholesale part of the foreign exchange market where banks manage inventories of currencies. This diverse, over-the-counter (OTC) market, does not have a physical trading place where buyers and sellers gather to agree on a price to exchange currencies. Rather, traders, who are employees of financial institutions in the major financial cities around the world, deal with each other via computer or over the phone, with back-office confirmations of transactions occurring at a later point in time.

Since most transactions on the interbank market are made up of large trades with values of $1 million or more, most retail investors and small businesses do not have direct access to this part of the foreign exchange market. As a result, many in need of foreign exchange deal with small regional banks or branches of banks that quote less advantageous rates than those that prevail on the interbank market. Retail investors also participate in the foreign exchange markets through their stockbrokers, who place orders on derivative markets that trade in futures and options contracts. Large multinational corporations (such as Anglo American) and very large money-management firms (such as Investec) would usually have directly access to the foreign exchange interbank market. In addition, some multinational companies also have their own foreign exchange trading desks to manage these transactions. An important recent development that has affected the market is the rapid growth in electronic trading, both in the interbank market (through an electronic brokerage) and on the retail side of the market. To contextualise the various components of the foreign exchange market, we can make use of Figure 1, which is taken from Bekaert and Hodrick (2012). This diagram shows that all the foreign exchange transactions are centered around the interbank market. Figure 1: Structure of the Foreign Exchange Market One interesting feature of this market is that the volume of trading activity has increased rapidly since the 1970s. For example, during 1973 the estimated daily volume of currency trading was between$10 and $20 billion. By the late 1980s, the daily volume had increased to around$500 billion, while in September 1993, the estimated daily volume in all currencies had increased to over $1 trillion. This figure then increased to almost$2 trillion in 2004 and it had almost doubled again in April 2010 when the daily turnover reached $3.9 trillion.1 The Bank for International Settlements (BIS) has since estimated that daily trading volume in 2016 was$5.1 trillion per day,2 and as of April 2019, it had increased to approximately $6.6 trillion per day. This dollar volume of trade dwarfs the corresponding dollar volume of transactions on stock markets such as the New York Stock Exchange (NYSE), where average daily dollar volume was roughly$87 billion in 2015. In addition, it also dwarfs the annual Gross Domestic Product (GDP) of a country like South Africa, which in 2016 was about $$\pm$$ $232 billion3 for the calendar year and$359 billion for 2019.

## 1.1 Communications and funds transfers

The enormous volume of trade in the foreign exchange market requires an extensive communication network between traders and a sophisticated settlement system to transfer payments in different currencies between the buyers and sellers of different currencies. Traders are able to obtain information that is provided by major commercial distributors such as Reuters and Bloomberg. The traders are then able to contact each other, to obtain actual prices and negotiate deals. In addition, they could approach a foreign exchange broker to broker a deal, or they can trade on an electronic brokerage system, where quotes on a screen are transactable. When a trade is agreed upon, banks communicate and transfer funds electronically, using systems such as the Society of Worldwide Interbank Financial Telecommunications (SWIFT), which confirm trades and facilitate payment.

As Cross-Currency transactions may involve the simultaneous exchange of currencies, there is a risk that only one leg of the transaction may be completed, due to the possibility that parties use different systems in different countries that operate out of different time zones. This is known as cross-currency settlement risk, or Herstatt risk. Recently, foreign exchange dealers, encouraged by the BIS, have developed a number of practices to limit settlement risk. These measures include: firstly, banks now have strict limits on the amount of transactions they are willing to settle with a single counterparty on a given day. Secondly, banks have started to engage in a variety of netting arrangements, in which they agree to wire the net traded amounts only at the end of a trading day. Thirdly, settlement risk is eliminated if the exchange of the two monies occur simultaneously in a process known as payment versus payment (PvP).

More recently, we have witnessed the foundation of the Continuous Linked Settlement (CLS) Bank, which is owned by the world’s largest financial groups. CLS is the largest multi-currency cash settlement system, eliminating settlement risk for over half of the worlds foreign exchange payment instructions and its members include central banks, large commercial banks and other large corporations. The CLS daily settlement cycle operates with settlement and funding occurring during a five-hour window when all real time gross settlement systems are able to make and receive payments. This enables simultaneous settlement of the payments on both sides of a foreign exchange transaction. Each member holds a single multicurrency account with CLS, which has a zero balance at the start and the end of trading day. Note that the settlement of the payment instructions and the associated payments are final and irrevocable.

## 1.2 Foreign exchange dealers and brokers

Traditionally, the main participants in the foreign exchange market are the commercial banks, investment banks, and brokerage firms in the major financial cities around the world. Traders at these banks and firms function as foreign exchange dealers, who seek to purchase a foreign currency at a low rate and sell at a higher rate to make a profit. Through this process dealers are simultaneously responsible for “making-a-market” in the currencies in which they specialise. For example, by standing ready to transact with retail customers or other dealers, they provide liquidity to the market, which makes it easier and less costly to match buyers and sellers. When there are large numbers of buyers and sellers, markets are usually very liquid, and transaction costs are low, which would be of benefit to those who would like to make use of the market.

Foreign exchange brokers do not attempt to buy low and sell high. Instead, brokers satisfy the role of a financial intermediary. They match buyers and sellers but do not put their own money at risk. For performing this service, they then receive a brokerage fee on their transactions. Foreign exchange brokers typically have many lines of communication open to various foreign exchange dealers, and they provide information to dealers on the best available prices. Foreign exchange dealers often use these brokers to unwind very large positions in a particular currency in order to preserve their anonymity.

While the brokers continue to play an important role in foreign exchange trading, a large part of the brokering business now happens through computerised trading systems. In the early 1990s, Reuters (now Thomson Reuters), a large financial information provider, and Electronic Brokering Service (EBS), launched the first anonymous electronic brokering systems for trading foreign exchange in the spot market. Trading is then carried out through a network of linked computer terminals among the participating foreign exchange dealers. When using this system currency prices are displayed on computer screens, and deals are completed by keystroke or by automatic deal matching within the system. Before a trade gets executed, either the systems check for mutual credit availability between the initiator of the deal and the counterparty; or each counterparty must have its creditworthiness pre-screened.

Trading in each major currency pair has over time become very highly concentrated on only one of the two systems. The top two traded currency pairs, euro-dollar and dollar-yen, trade primarily on the EBS, whereas the third most traded pair, the pound-dollar, trades primarily on Reuters. As a result, the exchange rates on EBS and Reuters for these particular currency pairs have become the reference rates for dealers across the world. When EBS allowed institutional investors and hedge funds onto its platform in 2005, it confirmed a trend towards the blurring of the distinction between the interbank and retail side of the foreign exchange market. This was later ushered in by the emergence of electronic trading.

## 1.3 Electronic Foreign Exchange Trading

The use of internet platforms lead to the development of a number of Electronic Foreign Exchange Trading (eFX) systems. This is one of the fastest growing segments of the foreign exchange market, representing more than 30% of all trading volume (and more than 50% of the trades in spot markets) during 2010 and such activity continues to rise.

Therefore, it is possible that the old telephone-based system will eventually be supplanted by pure electronic trading, where such platforms may offer multiple quotes from a number of foreign exchange dealers through an electronic communication network (ECN). As with many of the other securities exchanges, an ECN is able to electronically collect and matches buy and sell orders, while also providing the best available prices. Another advantage of an ECN is that it allows for the possibility of straight through processing (STP), where settlement is largely automated, after a trade takes place, which enhances liquidity and reduces trading costs.

There are three different categories of eFX: single bank-sponsored platforms (e.g. Deutsche Bank’s Autobahn), multi-bank portals (e.g. FXConnect and FXall), and independent companies offering electronic trading (e.g. HotSpot and Currenex). In addition, retail aggregators also provide intermediary services, by aggregating bid-offer quotes from the top foreign dealing banks and electronic platforms, which are then streamed to customers on an online platform. These retail aggregators cater to the relatively small accounts and a well-known example is Oanda.

## 1.4 Other participants

With regards to other participants, central banks of various governments may periodically participate in the foreign exchange market as they try to influence the foreign exchange value of their currencies. Other participants include multinational corporations, as they may need to exchange currencies to conduct their international trade; institutional investors who are involved in buying and selling foreign of securities; hedge funds that may speculate on currency movements; and smaller domestic banks that service firms or individuals wanting to exchange currencies.

## 1.5 The costs of transactions

As there are many different types of monetary instruments which may be used to exchange currencies, the respective rate of exchange may be dependent upon the form of currency. For example the exchange rate for cash may be different to the rate that is charged on travellers cheques and these rates may also differ to the rate that pertains to bank transfer orders. These differences depend on various elements that include the costs of transferring funds and the costs for holding these currency balances (i.e. loss of interest and custody costs).

In most instances, a foreign exchange trader is typically responsible for buying and selling a particular currency or a small group of currencies. They would usually hold an inventory or portfolio of positions in those currencies. One reason for this activity in the interbank market is that foreign exchange traders at one bank use foreign exchange traders at other banks to adjust their portfolios in response to transactions that arise from their customers in the corporate market (to maintain an inventory of a particular currency or portfolio position). The repeated passing of inventory imbalances among dealers has been dubbed “hot potato trading” and may be one reason for the large trade volumes that we see on the interbank market.4

Ultimately, traders in the interbank market try to buy and sell various foreign currencies with the goal of generating profits. To do so, they quote two-way prices. The bid rate is the rate at which they want to buy a base currency, and the ask rate is the rate at which they sell base currency. The difference between these two rates is known as the bid-ask or bid-offer spread. The bid price is always less than the ask price because the trader bids for the base currency when they buy it and asks a price for the base currency when they sell it.

The competitive nature of the foreign exchange market and the growth of electronic trading has greatly compressed bid-ask spreads over the last decade. In the interbank market, spreads for major currencies have become negligible. In addition, even in the customer market, bid-ask spreads are now also within 5 pips (for the major currencies of large transaction sizes) where a pip is jargon for the fourth decimal point in a currency quote.

By way of example, if the midpoint of the USDZAR quote is R13.50, and we have a spread of 20 pips then the ask rate is R13.501 and the bid rate is R13.499. Therefore, 1 pip reflects 1/100 of a South African cent in this case. However, to get an idea of transaction costs involved in trading currencies, its usually better to express the bid-ask spread in percentage points, where the spread is computed as:

$\begin{eqnarray} \nonumber \text{Percentage spread} &=& \frac{(\text{ask} - \text{bid})}{\text{midpoint}} \\ \nonumber &=& \frac{(13.501 - 13.499)}{13.5} \\ \nonumber &=& 0.00015 \end{eqnarray}$

Hence, the bid-ask spread represents 0.015% or 1.5 basis points. The cheapest currencies to trade are the major ones like the EUR versus USD (with spreads sometimes as low as 1 pip), the GBP versus USD, and the USD versus JPY. In addition, the “G10” currencies that include the AUD, CHF, CAD, NZD, SEK, and NOK are also highly liquid and typically trade at less than 10 pips, while emerging market currencies trade at higher spreads.

As these differences are usually very small, the examples that are contained below largely assume that there is only one exchange rate for each foreign currency. Therefore, we largely exclude the effects of the bid-ask spread on transactions.

# 2 The exchange rate

The exchange rate is a price of one currency in terms of another. Since two currencies are involved, there are two different ways of giving the quotation for foreign exchange. One is called the direct or price quotation system, and defines the exchange rate as the number of units of domestic currency per unit of foreign currency. When taking South Africa as the home country, we could quote exchange rates as, R 13.24 per US dollar, R 0.12 per Japanese yen, R 15.50 per euro, etc. This amounts to defining the exchange rate as the price of foreign currency in terms of domestic currency.

The alternative method makes use of the indirect or volume quotation system, and it defines the exchange rate as the number of units of foreign currency per unit of domestic currency, which is obviously the reciprocal of the previous case. Once again, when using South Africa as the home country, we would have 0.076 US dollar per South African rand, 8.37 Japanese yens per South African rand, 0.065 euros per South African rand, etc. With this definition the exchange rate is the price of domestic currency in terms of foreign currency.

In what follows we will adopt the direct or price quotation system, and a good piece of advice is to always ascertain which definition is being (explicitly or implicitly) adopted, to avoid confusion.

Rather than write out the full name of these currencies, contractual parties use abbreviations that were established by the International Organization for Standardization (called ISO from the Greek word equal). For example, the notation for the U.S. dollar is USD, the euro is EUR, and the South African rand is ZAR.

If it takes 13.24 South African rand to purchase 1 U.S. dollar, we can write ZAR13.24 = USD1, or ZAR13.24/USD. Note that we treat the slash symbol (/) as a divisor in a ratio to indicate the amount of the first currency that is necessary to purchase one unit of the second currency. In practice, you will encounter foreign exchange quotations, such as USDZAR, in which the first currency in the quote is the base currency and the second currency is the numerator currency or “quote currency”. In other words, if you type USDZAR into Google, it will return the price of the U.S. dollar in terms of South African rands, or how many South African rands you can buy with one U.S. Dollar (which makes use of a direct quotation). Indeed, most practitioners in South Africa, including dealers and brokers, would make use of the term USDZAR, when quoting the exchange rate for these currencies.

When quoting against the U.S. dollar, we make use of two additional terms, where the European quote refers to the amount of foreign currency needed to buy dollars. This is due to the fact that most former European currencies, such as the Deutsche mark and the French franc, were quoted this way relative to the dollar. Similarly, the phrase American quote refers to the dollar price of a foreign currency, which is the number of dollars it takes to purchase one unit of foreign currency.

The focus on the U.S. dollar exchange rates in comparison to other currencies of the world is in most cases warranted, because the U.S. dollar is a vehicle currency, which implies that it is actively used in many international financial transactions around the world. Exchange rates between two currencies that do not involve the dollar are often called cross-rates. Although there appears to be a trend toward more cross-rate transactions, it is estimated that 88% of all transactions use the dollar. Some analysts have suggested that the euro, which replaced 11 different currencies in Europe in 1999, may someday replace the dollar as a vehicle currency, but it still has a long way to go, as a BIS survey of foreign exchange activity that was published in 2019, suggests that about 32% of all trades involved the euro during that year.

Given the variety of potential trades that could arise, it is worthwhile noting that triangular arbitrage is a process that keeps cross-rates (such as euros per British pound) in line with exchange rates quoted relative to the U.S. dollar. A trader can conduct triangular arbitrage in many ways. For example, they may start with euros, buy pounds with the euros, then simultaneously sell those pounds for dollars and sell those dollars for euros. In other words, instead of exchanging just two currencies, the trader exchanges three (hence the term “triangular” arbitrage). If the number of euros the trader has at the end of these three transactions is greater than the number of euros at the beginning, then the trader has earned a profit.

If such transactions can be done profitably, the trader can generate pure arbitrage profits to earn risk-free returns. Obviously, in perfectly competitive financial markets, one would not be able to earn arbitrage profits for very long. If the euro price of the pound were not equal to the euro price of the U.S. dollar multiplied by the U.S. dollar price of the pound, arbitrage activity would immediately restore equality between the quoted cross-rate and the cross-rate implied by the two dollar quotes.

## 2.1 Rates of change

As exchange rates are relative prices, it would imply that there are always two ways to describe the same situation. For example, if we are told that currency $$x$$ has depreciated, we may infer that the value of currency $$x$$ has declined in terms of a foreign currency, such that a greater amount of currency $$x$$ is required to buy one unit of foreign currency. Similarly, this would also imply that a smaller amount of foreign currency is required to buy one unit of currency $$x$$. Hence, the foreign currency would have appreciated, relative to currency $$x$$ in this case.

The terms appreciation and depreciation are typically used to describe changes in flexible exchange rates, where they are able to fluctuate freely in response to changes in demand and supply. This terminology would also usually apply to those exchange rates that are subject to a managed framework, where the central bank of a country would make a number of transactions on the foreign exchange market to alter the value of the domestic currency. This framework is currently employed by the South African Reserve Bank, although it would only usually enter the foreign exchange market in extreme cases.

Alternatively, the government authorities of a particular country may fix or peg the exchange rate of their currency relative to a foreign currency. Discrete changes in the values of exchange rates under such a fixed exchange rate system are termed devaluations or revaluations, for corresponding downward and upward movements.

The rate of appreciation or depreciation of one currency relative to another can be calculated as the percentage rate of change of the exchange rate. For example, if the USDZAR exchange rate moves from R14 to R15 per dollar, then we can show that the % change may be calculated as follows:

$\begin{eqnarray} \nonumber \% \; \text{Change in the rand} &=& \frac{(\text{New exchange rate} - \text{Old exchange rate})}{\text{Old exchange rate}} \\ \nonumber &=& \frac{(15 - 14)}{14} \\ \nonumber &=& 7.14 \% \end{eqnarray}$

In this case, the South African rand is said to have depreciated by 7.14%.

## 2.2 Continuously Compounded Rates of Appreciation

In certain instances, we might also want to describe the rate of appreciation using a compounded monthly basis, while still expressing the percentage change at an annual rate. For example, if we want to calculate the annualised value of appreciation of the dollar then we would make use of the following expression:

$\begin{eqnarray} \nonumber (\text{USDZAR}\; 14.00) \Big[1 + ( \eta /12) \Big]^{12} = (\text{USDZAR} \; 15) \end{eqnarray}$

where $$\eta$$ is the rate of appreciation. To solve for $$\eta$$, we first divide both sides by USDZAR 14.00 and then take the (1/12) power of each side:

$\begin{eqnarray} \nonumber \Big[1 + ( \eta /12) \Big] &=& \Big[(\text{USDZAR} \; 15) \; / \; (\text{USDZAR} \; 14) \Big]^{1/12} \\ \nonumber \eta &=& \Big(\big[(\text{USDZAR} \; 15) \; / \; (\text{USDZAR} \; 14) \big]^{1/12} -1 \Big) \times 12 \\ \nonumber &=& 0.0692 \end{eqnarray}$

This provides an answer of $$\eta =$$ 0.0692, or an annualised compound monthly rate of appreciation for the dollar of 6.92%. To calculate the annualised compound monthly rate of depreciation of the rand, relative to the dollar, we could assume that the equivalent values for the ZARUSD are $$1/14$$ and $$1/15$$, respectively. This would imply that the depreciation of the rand could then be calculated as follows:

$\begin{eqnarray} \nonumber (\text{ZARUSD} \; 0.07142857) \Big[1 - (\delta / 12)\Big]^{12} = (\text{ZARUSD} \; 0.0\dot{6}) \end{eqnarray}$

where after using similar steps, $$\delta =$$ 0.0688 or 6.88%.

If we drive the compounding interval to one that is infinitely small, we will eventually be able to derive the continuous rate of appreciation of the dollar relative to the rand. Continuous compounding uses the symbol $$e$$, which represents the base of the natural logarithm, where $$e \sim$$ 2.71828.

In this case the annualized continuously compounded rate of appreciation of the dollar is the value of $$\eta$$ that satisfies the expression:

$\begin{eqnarray} \nonumber (\text{USDZAR} \; 14.00)e^{\eta} = \text{USDZAR} \;15.00 \end{eqnarray}$

To solve for the value of $$\eta$$, we then take the natural logarithm of both sides of the equation to derive the following result:5

$\begin{eqnarray} \nonumber \eta = \log (\text{USDZAR} \; 15.00) - \log (\text{USDZAR} \; 14.00) = 0.069 \end{eqnarray}$

which is equivalent to 6.9%. Similarly, to calculate the annualised continuously compounded rate of depreciation of the rand, we could again assume that the equivalent values for the ZARUSD are $$1/14$$ and $$1/15$$, respectively. To complete this calculation we need to find the value of $$\delta$$ that satisfies the following expression:

$\begin{eqnarray} \nonumber (\text{ZARUSD} \; 0.07142857)e^{-\delta} = \text{ZARUSD} \; 0.0\dot{6} \end{eqnarray}$

To solve for the value of $$\delta$$, we take the natural logarithm of both sides of the equation and derive the following result:

$\begin{eqnarray} \nonumber \delta = - \Big[ \log (\text{ZARUSD} 0.0\dot{6}) - \log (\text{ZARUSD} 0.07142857) \Big] = 0.069 \end{eqnarray}$

which is equivalent to 6.9%. Note that with continuous compounding, the rates of appreciation of the dollar and depreciation of the rand are equivalent.

In finance, we often work with natural logarithms to perform continuous compounding exercises. For example, banks usually quote interest rates at annual rates such as 10%, and they specify a compounding period, which might be annual, semiannual, monthly, daily, or even continuously. Of course, when interest is credited to our account more frequently you will then be able to earn more interest on previously credited interest. In the following table we show that if the quoted interest rate is 10%, at the end of 1 year, we will have the following amounts, depending on the compounding interval:

Compounding Interval $$\hspace{3cm}$$ Amount in 1 Year
Annual [1 + 0.1] = 1.1
Semiannual [1 + (0.1/2)]2 = 1.1025
Quarterly [1 + (0.1/4)]4 = 1.1038
Monthly [1 + (0.1/12)]12 = 1.1047
Daily [1 + (0.1/365)]365 = 1.10516

Table 1: Compounding Rates

Note that the return from continuously compounding at an interest rate, $$i$$, is obtained by taking the limit of the following expression as the number of compounding intervals, where $$n$$ goes to infinity:

$\lim_{n \rightarrow \infty} \big(1 + (i / n) \big)^n = e^i$

In this example, a 10% annual interest rate that is continuously compounded will provide an amount of money after 1 year of $$e$$0.1 = 1.10517 times the amount invested.6 Note that practitioners sometimes write $$exp( i )$$ rather than $$e^i$$, where both imply that they are looking to raise the number $$e$$ to the $$i$$th power.

Hence, raising the number $$e$$ to a power tells you the rate at which your principal grows when it is continuously compounded at a particular interest rate. This implies that the exponential function can be used to describe other growth rates, such as rates of appreciation or depreciation of currencies and rates of inflation. For example, if the value of the South African rand relative to the US dollar were to grow at a continuous rate of $$5\%$$ during the course of a year, then for a starting value of R13.50, the expected exchange rate at the end of the year would be calculated as follows:

$\begin{eqnarray} \nonumber (\text{USDZAR}_{end}) = (R 13.50) \; e^{0.05} = R 14.19 \end{eqnarray}$

## 2.3 The real exchange rate

In general, real magnitudes are obtained from the corresponding nominal magnitudes after we eliminate the change that is due to price changes, which can be done in a variety of ways. In the case of exchange rates the question is slightly more complicated, due to the fact that the exchange rate is intrinsically a nominal concept. This has lead to development of a number of different definitions for the real exchange rate.7

The oldest notion for the real exchange rate, and the one that we will use in much of what follows, is defined as the nominal exchange rate multiplied by the ratio of price levels. For example, if we would want to calculate the real exchange rate for the South Africa rand relative to the euro, we would use the following expression:

$\begin{eqnarray} \text{RS}_{t,\text{R} / {\unicode{0x20AC}}} =\frac{S_{t,{\text{R}}/ {\unicode{0x20AC}}} \times P_{t,{\unicode{0x20AC}}}}{P_{t,{\text{R}}}} \tag{2.1} \end{eqnarray}$

where $$S_{t,{\text{R}}/ {\unicode{0x20AC}}}$$ is the spot exchange rate, while $$P_{t,\text{R}}$$ and $$P_{t,\text{euro}}$$ are the price levels in South Africa and in Europe. This definition is obviously linked to the concept of Purchasing Power Parity (PPP) and this connection will be discussed at a later point in the course.

According to an alternative definition, the real exchange rate could be described by the (domestic) relative price of tradable and non-tradable goods,

$\begin{eqnarray} \nonumber \text{RS}_{t, \text{T/NT}} = \frac{P_{t,\text{T}}}{P_{t,\text{NT}}} \end{eqnarray}$

The rationale for this definition is that, in a two-sector (tradables-nontradables) model, the balance of trade depends on $$P_{\text{T}}/P_{\text{NT}}$$, since this relative price measures the opportunity cost of domestically producing tradable goods, and the ex ante balance of trade depends on the ex ante excess supply of tradables. According to the Harrod-Balassa-Samuelson hypothesis, the long run PPP holds only for traded goods, and the real exchange rate in the long run is a function of the relative productivity of traded to non-traded goods in the home and foreign countries.

This definition relies on the assumption that the real exchange rate should give a measure of the external competitiveness of a country’s goods (if non-traded goods are also present, only tradables should be considered). However, it is by no means obvious which index should be taken. In the simple exportables-importables model of trade the real exchange rate reduces to the notion of terms of trade defined in the theory of international trade, namely

$\begin{eqnarray} \text{RS}_{t, \text{TOT}} = \pi = \frac{P_{t,\text{EX}}}{S_t \times P_{t,\text{M}}} \tag{2.2} \end{eqnarray}$

where $$P_{t, \text{EX}}$$ represents export prices (in terms of domestic currency), $$P_{t, \text{M}}$$ import prices (in terms of foreign currency), and $$S_t$$ the nominal exchange rate of the country under consideration. From the point of view of the consumer, $$\pi$$ represents the relative price of foreign and domestic goods on which (in accordance with standard consumer theory) demand will depend. From the point of view of the country as a whole, $$\pi$$ represents the amount of imports that can be obtained in exchange for one unit of exported good (or the amount of exports required to obtain one unit of imports). Therefore, an increase in $$\pi$$ is also defined as an improvement in the terms of trade, as it means that a greater amount of imports can be obtained per unit of export (or, equivalently, that a smaller amount of exports are required per unit of import).

The terms of trade $$\pi$$ can serve both the domestic and the foreign consumer (country) for the relevant price-comparison, because the prices of domestic and foreign goods are expressed in domestic currency (for which we have a reciprocal). In addition, it should also be noted that (2.1) is related to (2.2) since exports are an essential part of domestic output and prices, $$P_{t,\text{EX}} = P_{t,{\text{R}}}$$, while imports are related to foreign output and prices $$P_{t,\text{M}} = P_{t,{\unicode{0x20AC}}}$$.

Another definition for the real exchange rate takes the ratio of unit labour costs at home, $$W_{h}$$, to unit labour costs abroad, $$W_{f}$$, expressed in a common monetary unit through the nominal exchange rate, $$S_t$$. Hence, this expression would take the form

$\begin{eqnarray} \nonumber RS_t = S_t \left( \frac{W_{f}}{W_{h}} \right) \end{eqnarray}$

Note that the real exchange rate in this case would suggest that an increase (decrease) would imply an improvement (deterioration) in the external competitiveness of domestic goods. In fact, ceteris paribus, a decrease in domestic unit labour costs relative to foreign unit labour costs is reflected (in both perfectly and imperfectly competitive markets) by a decrease in the relative price of domestic goods with respect to foreign goods. The same result is obtained when, at given $$W_{f}/W_{h}$$, the exchange rate depreciates (i.e. the nominal exchange rate $$S_t$$ increases).

## 2.4 The effective exchange rate

The concept of an effective exchange rate must not be confused with the real exchange rate, since the effective exchange rate can be either nominal or real.

While the (nominal or real) exchange rate involves two currencies only, it may be desirable to have an idea of the overall external value of a currency, namely with respect to the rest of the world (or a subset of it)8 and not only with respect to another country’s currency. The presence of flexible exchange rates makes it difficult to ascertain the behaviour of the external value of a currency. In fact, in a flexible regime, a currency may simultaneously depreciate with respect to one (or more) foreign currency and appreciate with respect to another (or several others).

In such a situation it is necessary to have recourse to an index number, in which the bilateral exchange rates of the currency under consideration with respect to all other currencies enter with suitable weights. This index is called an effective exchange rate. To provide an example of these calculations, lets begin with the nominal effective exchange rate, which is given by the formula:

$\begin{eqnarray} \nonumber R_{E,i}= \sum_{j=1, j\neq i}^{n} w_{j}R_{j,i}, \hspace{1cm} \sum_{j=1, j\neq i}^{n}w_{j}=1 \end{eqnarray}$

The respective variables in this expression refer to:

• $$R_{E,i} =$$ (nominal) effective exchange rate for currency $$i$$
• $$R_{ji} =$$ nominal exchange rate of currency $$i$$ with respect to currency $$j$$
• $$w_{j}=$$ weight given to currency $$j$$ in the construction of the index; by definition, the sum of the weights equals one.

Usually the effective exchange rate is given as an index number with a base of 100 and it is presented in such a way that an increase (decrease) in it means an appreciation (depreciation) of the currency under consideration with respect to the other currencies as a whole.

Unfortunately it is not possible to determine the weights unambiguously. Hence, many effective exchange rates exist in theory; however, the weights are usually derived from the share of foreign trade of country $$i$$ with country $$j$$. Effective exchange rates are computed and published by the International Monetary Fund, central banks and private institutions.

If we carry out the same operation with the use of real rather than nominal bilateral exchange rates, we shall of course obtain the real effective exchange rate. This will provide a measure of the overall competitiveness of domestic goods on world markets rather than with respect to another country’s goods.

# 3 Foreign exchange contracts

Many different types of trades can be conducted in the foreign exchange market. The spot market has traditionally been a very important part of the market for the immediate exchanges of currencies. Another part of the interbank foreign exchange market involves trade in swaps and forward contracts. These transactions involve the exchange of currencies in the future. Together the spot and the forward market constitute the foreign exchange market. Another important type of contract involves derivative securities that would include foreign currency futures and options. These aspects of the market are in what follows.

## 3.1 The spot market

The spot market for the foreign exchange of currencies relates to the exchange of two currencies on the spot (i.e. for immediate delivery). In most instances, this transaction would be reflected by an immediate change in the demand deposits of banks that are denominated in the two currencies. It is worth noting that although it may be the possible to earn arbitrage profits on the spot market, due to time lags or other possible frictions, the reality is that these discrepancies are incredibly small, which would imply that it is unlikely that any potential profit will exceed the transaction costs.

A number of important rules are associated with trades on the interbank spot market. For example, when the trade involves the U.S. dollar, these rules dictate that spot contracts are settled after 2 business days. One business day is necessary because of the back-office paperwork involved in any financial transaction. The second day is then needed because of the time zone differences around the world. All transactions need to be settled within this time frame.9

## 3.2 The forward market

The forward foreign exchange market (or the forward market, for short) is the market for exchanges of currencies in the future. The main function of the forward exchange market is to provide economic agents who are engaged in international transactions (whether these are commercial or financial) an opportunity to cover themselves against the exchange rate risk that is due to possible future variations in the spot exchange rate. If it were the case that the spot exchange rate were permanently and rigidly fixed, then the agent who is about to make or receive a foreign currency payment in the future (or, more generally, who has liabilities and/or assets in foreign currency) does not incur any exchange risk. However, as most exchange rates will change over time, as is usually the case, an exchange rate risk will usually arise.

From the point of view of the agent who has to make a future payment in foreign currency (for example, an importer who will need to paid after a period of time for the goods that are ordered now), the risk is that the exchange rate will depreciate at the time of the payment. In this case the purchaser will have to pay out a greater amount of domestic currency to purchase the required amount of foreign currency. From the point of view of the agent who is to receive a future payment in foreign currency, the risk is that the exchange rate will have appreciated at the time of the payment, in which case they will get a smaller amount of domestic currency from the sale of the given amount of foreign currency.

Naturally the agent who has to make a future payment in foreign currency will benefit from an appreciation of the domestic currency and, similarly, a depreciation will benefit the agent who is to receive a future payment in foreign currency. However, if we exclude the category of speculators and only consider economic agents who are risk averse, then such an agent will assign a greater weight on the eventuality of a loss than on a gain derived from future variations in the exchange rate. This would be achieved with the aid of some form of hedging transaction. For example, to hedge against currency risks, the agent would enter into an additional contract that provides a profit when the underlying transaction on the spot market results in a realised pecuniary loss. To evaluate the costs and benefits of hedging for a future transaction involving foreign currencies, the hedging party must have some way to quantify the degree of uncertainty it faces about future spot exchange rates. It accomplishes this by figuring out the likelihood of observing various ranges for future exchange rates.

The need for some form of hedging transaction arises whenever the liabilities and assets of an agent that are denominated in foreign currency are not matched. Of course, this exact balance must hold for each of the foreign currencies that the agent holds. These positions are usually described with financial jargon, where to have no open position in foreign exchange would imply that you have neither a long position (more assets than liabilities in foreign currency) nor a short position (more liabilities than assets in foreign currency).

## 3.3 Derivative contracts

Foreign currency futures and options can be used for hedging or speculative purposes. Since the profits and losses earned on futures and option contracts, as well as those earned on forward contracts, depend on how the spot exchange rate evolves over time, all these instruments are termed derivative securities. Hence, derivative securities are securities whose values depend on the values of other, more basic underlying variables, which pertain to the spot exchange rate in this case.

As with other instruments in the foreign exchange market, much of the trade in futures contracts and options are conducted by banks. Commercial and investment banks deal aggressively in foreign currency options in order to meet the demands of their corporate and institutional customers, who use them to hedge their foreign exchange risks. In addition to banks, hedge funds and other investors trade foreign currency futures and options purely for speculative purposes (in order to earn a profit).

# 4 Recent Developments on the Foreign Exchange Markets

One of the best sources for current information relating to the foreign exchange market may be obtained from the Bank of International Settlements Triennial Central Bank Survey. The most recent edition of this report was compiled in 2019 and you may view it at the following website: https://www.bis.org/statistics/rpfx19.htm.

In terms of some of the highlights of the most recent report, it has been noted that transactions involving currencies of emerging market economies (EMEs) continue to gain market share, reaching 25% of overall global turnover. In contrast with previous periods the turnover in the Chinese renminbi, grew only slightly faster than the aggregate market and retains its position as the eighth most traded currency.

While the volume of spot trades increased relative to 2016, the expansion was not as strong when compared with other instruments. Hence the share of spot trades continued to fall, to 30% in 2019. In contrast, FX swaps continued to gain market share, accounting for 49% of total foreign exchange market turnover. Trading of forwards also increased and FX trading with “other financial institutions”, (i.e. those other than reporting dealers), again exceeded inter-dealer trading volumes and account for 55% of the global turnover. This was due to a higher share of trading with non-reporting banks as well as with hedge funds and proprietary trading firms (PTFs), while trading with institutional investors declined.

During 2019, sales desks in five countries, which include the United Kingdom, United States, Hong Kong, Singapore and Japan, facilitated 79% of all foreign exchange trading.

# 5 Crytocurrencies

Less than 10 years after their inception, cryptocurrencies have emerged from obscurity to attract intense interest on the part of businesses and consumers, as well as central banks and other authorities. They garner attention because they promise to replace trust in long-standing institutions, such as commercial and central banks, with trust in a new, fully decentralised system founded on the blockchain and related distributed ledger technology (DLT).

For the trust to be maintained in this system, honest network participants need to control the vast majority of computing power, as each and every user needs to verify the history of transactions and the supply of the cryptocurrency needs to be predetermined by its protocol. Trust can evaporate at any time because of the fragility of the decentralised consensus through which transactions are recorded. Not only does this call into question the finality of individual payments, it also means that a cryptocurrency can simply stop functioning, resulting in a complete loss of value. Moreover, even if trust can be maintained, cryptocurrency technology comes with poor efficiency and vast energy use. In adidtion, most cryptocurrencies cannot scale with transaction demand, are prone to congestion and greatly fluctuate in value. Institutions such as the Bank of International Settlements (BIS) suggest that the decentralised technology of cryptocurrencies, however sophisticated, is a poor substitute for the solid institutional backing of money.

However, the underlying technology could be used in other applications, such as the simplification of administrative processes in the settlement of financial transactions. However, such uses of this technology would still need to be tested.

## 5.1 The elusive promise of decentralised trust

Cryptocurrencies aspire to be a new form of currency and promise to maintain trust in the stability of their value through the use of technology. They consist of three elements. First, a set of rules (the “protocol”) that takes the form of computer code that specifies how participants can transact. Second, a ledger that stores the history of transactions. And third, a decentralised network of participants that update, store and read the ledger of transactions following the rules of the protocol. With these elements, advocates claim, a cryptocurrency is not subject to the potentially misguided incentives of banks and sovereigns.

Such cryptocurrencies combine three key features. First, they are digital, aspiring to be a convenient means of payment and relying on cryptography to prevent counterfeiting and fraudulent transactions. Second, although created privately, they are no one’s liability, i.e. they cannot be redeemed, and their value derives only from the expectation that they will continue to be accepted by others. And, last, they allow for digital peer-to-peer exchange.

Compared with other private digital moneys such as bank deposits, the distinguishing feature of cryptocurrencies is the digital peer-to-peer exchange, where cryptocurrency transfers can in principle take place in a decentralised setting without the need for a central counterparty to execute the exchange.

## 5.2 Distributed ledger technology in cryptocurrencies

The technological challenge in digital peer-to-peer exchange is the so-called “double-spending problem”. Any digital form of money is easily replicable and can thus be fraudulently spent more than once, since digital information can be reproduced more easily than physical banknotes. For digital money, solving the double-spending problem requires, at a minimum, that someone keep a record of all transactions. Prior to cryptocurrencies, the only solution was to have a centralised agent do this and verify all transactions.

Cryptocurrencies overcome the double-spending problem via decentralised record-keeping through what is known as a distributed ledger. The ledger can be regarded as a file (think of a massive spreadsheet) that starts with an initial distribution of cryptocurrency and records the history of all subsequent transactions. An up-to-date copy of the entire ledger is stored by each user (this is what makes it “distributed”). With a distributed ledger, peer-to-peer exchange of digital money is feasible: each user can directly verify in their copy of the ledger whether a transfer took place and that there was no attempt to double-spend.

While all cryptocurrencies rely on a distributed ledger, they differ in terms of how the ledger is updated. One can distinguish between two broad classes, with substantial differences in their operational setup, as displayed in Figure 2.

Figure 2: Centralised ledger and permissioned/permissionless decentralised ledgers

One class is based on “permissioned” DLT. Such cryptocurrencies are similar to conventional payment mechanisms in that, to prevent abuse, the ledger can only be updated by trusted participants in the cryptocurrency - often termed “trusted nodes”. These nodes are chosen by, and subject to oversight by, a central authority, which could be the firm that developed the cryptocurrency. Thus, while cryptocurrencies based on permissioned systems differ from conventional money in terms of how transaction records are stored (decentralised versus centralised), they share with it the reliance on specific institutions as the ultimate source of trust.

In a much more radical departure from the prevailing institution-based setup, a second class of cryptocurrencies promises to generate trust in a fully decentralised setting using “permissionless” DLT. The ledger that records these transactions can only be changed by a consensus of the participants in the currency: while anybody can participate, nobody has a special key to change the ledger. Bitcoin makes use of a permissionless distributed ledger, termed the “blockchain”, which is updated in groups of transactions called blocks. Blocks are then chained sequentially via the use of cryptography to form the blockchain. This concept has been adapted to countless other cryptocurrencies.

Blockchain-based permissionless cryptocurrencies have two groups of participants: “miners” who act as bookkeepers and “users” who want to transact in the cryptocurrency. At face value, the idea underlying these cryptocurrencies is simple: instead of a bank centrally recording transactions (Figure 3, left-hand panel), the ledger is updated by a miner and the update is subsequently stored by all users and miners (right-hand panel).

Figure 3: Valid transactions in a centralised ledger/bank account and in a permissionless cryptocurrency

Miners are genearly responsible for updating the ledger by a process of matching transactions. In essence, this involves digging up rare numbers via laborious computations, which require costly equipment and electricity, for which they receive a fee or newly minted cryptocurrency. Since all the miners and users of a cryptocurrency would be able to verify all ledger updates, this induces miners to include only valid transactions. Valid transactions need to be initiated by the owners of funds and must not be attempts to double-spend. If a ledger update includes an invalid transaction, it is rejected by the network and the miner’s rewards are voided. The protocol also specifies rules to achieve a consensus on the order of updates to the ledger. This is generally achieved by creating incentives for individual miners to follow the computing majority of all other miners when they implement updates. Such coordination is needed, for example, to resolve cases where communication lags lead to different miners adding conflicting updates.

With these key ingredients, it is costly - though not impossible - for any individual to forge a cryptocurrency. To successfully double-spend, a counterfeiter would have to spend their cryptocurrency with a merchant and secretly produce a forged blockchain in which this transaction was not recorded. This would require a substantial share of the mining community’s computing power as you would need to enter this false transaction on the majority of the ledgers that are held by miners and users.

## 5.3 Assessing the economic limitations of permissionless cryptocurrencies

Two of the major limitations of cryptocurrencies relate to the fact that they are relatively inefficient and are subject to a potential breach of trust. For example, the total electricity use of Bitcoin mining equalled that of mid-sized economies such as Switzerland, and other cryptocurrencies also use ample electricity (Figure 4, left-hand panel). Put in the simplest terms, the quest for decentralised trust has quickly become an environmental disaster.

Figure 4: Energy consumption and scaling issues

In addition, cryptocurrencies are not sufficiently scalable, as the ledger for the Bitcoin blockchain has growing at around 50 GB per year. To keep such a ledger on the computers of all miners and users is going to become problematic and with the increase in size, the time needed to verify all transactions may no longer be manageable (Figure 4, centre panel).

Figure 5: Transaction fees over time and in relation to transaction throughput

The second key issue with cryptocurrencies is their unstable value, which can erode our sense of trust. This arises from the absence of a central issuer with a mandate to guarantee the currency’s stability. Well run central banks succeed in stabilising the domestic value of their soveriegn currency by adjusting the supply of the means of payment in line with transaction demand. They do so at high frequency and they are also able to satisfy this function during times of market stress.

This contrasts with a crytocurrency, where generating some confidence in its value requires that supply be predetermined by a protocol. Any fluctuation in demand would then translate into changes in valuation. This means that crytocurrency valuations are extremely volatile (Figure 6, left-hand panel) and the inherent instability is unlikely to be fully overcome by better protocols or financial engineering.

Figure 6: Volatility of select cryptocurrencies and number of cryptocurrencies

This outcome is not coincidental. Keeping the supply of the means of payment in line with transaction demand requires a central authority, typically the central bank, which can expand or contract its balance sheet. In a decentralised network of cryptocurrency users, there is no central agent with the obligation or incentive to stabilise the value of the currency: whenever demand for the cryptocurrency decreases, so does its price.

Further contributing to unstable valuations is the speed at which new cryptocurrencies - all tending to be very closely substitutable with one another - come into existence, where the proliferation of new releases and failures ensures that we are unable to produce reliable estimates of the number of cryptocurrencies in circulation (Figure 6, right-hand panel). Recalling the private banking experiences of the past, the outcome of such liberal issuance of new moneys would not contribute towards stability.

In addition, permissionless cryptocurrencies cannot guarantee the finality of individual payments, which would also contribute towards a further erosion of trust. One reason is that although users can verify that a specific transaction is included in a ledger, there have been occassions where rival versions of the ledger were established. This can result in transaction rollbacks, for example when two miners update the ledger almost simultaneously. Since only one of the two updates can ultimately survive, the finality of payments made in each ledger version is probabilistic.

Figure 7: Mining concentration and bitcoin value during a temporary fork

Not only is the trust in individual payments uncertain, but the underpinning of trust in each crytocurrency is also fragile. This is due to “forking”, which is a process whereby a subset of crytocurrency holders coordinate on using a new version of the ledger and protocol, while others stick to the original one. In this way, a cryptocurrency can split into two subnetworks of users. While there are many recent examples of this, an episode on 11 March 2013 is noteworthy as an erroneous software update led to incompatibilities between one part of the Bitcoin network mining on the legacy protocol and another part mining using an updated one. Once news of this fork spread, the price of Bitcoin tumbled by almost a third (Figure 7, right-hand panel).

Overall, decentralised cryptocurrencies suffer from a range of shortcomings. The main inefficiencies arise from the extreme degree of decentralisation: creating the required trust in such a setting wastes huge amounts of computing power. In addition, this form of decentralised consensus is vulnerable to sudden erosions of trust. While some of these issues might be addressed by novel protocols and other advances, most would appear to be inherently linked to the fragility and limited scalability of such decentralised systems.

## 5.4 Beyond the bubble: making use of distributed ledger technology

While cryptocurrencies do not work as money, the underlying technology may have promise in other fields. A notable example is in low-volume cross-border payment services in a few niche settings, where the benefits of decentralised access exceed the higher operating cost of maintaining multiple copies of the ledger. For example the World Food Programme’s blockchain-based Building Blocks system, which handles payments for food aid serving Syrian refugees in Jordan is an excellent example of a successful application. This system was contained to be relatively small in size and it was also centrally controlled by the World Food Programme to reduce transaction costs, when compared to bank-based alternatives.

Permissioned cryptopayment systems may also have promise with respect to small-value cross-border transfers, which are important for countries with a large share of their workforce living abroad. Global remittance flows total more than 540 billion annually (Figure 8, left-hand and centre panels) and current mechanism for international payments involve multiple intermediaries, leading to high costs (right- hand panel). That said, while cryptopayment systems are one option to address these needs, other technologies are also being considered, and it is not clear which will emerge as the most efficient one. Figure 8: Indicators of the volume and cost of remittances # 6 Conclusion Trading activity in the foreign exchange market continues to increase and recent innovations have made this market more accessible. The market accommodates a diverse selection of trading needs for a large array of heterogeneous market participants. The institutional framework of this market effects the behaviour of several financial variables and it has also influenced most developed and developing economies in one way or another. # 7 References Bekaert, Geert, and Robert J. Hodrick. 2012. International Financial Management. New York: Prentice Hall. Chinn, M. D. 2006. “A Primer on Real Effective Exchange Rates: Determinants, Overvaluation, Trade Flows and Devaluation.” Open Economies Review 17: 15–143. Hinkle, E. L., and P. Montiel. 1999. Exchange Rate Misalignment: Concepts and Measurement for Developing Countries. Oxford: Oxford University Press for the World Bank. International Settlements, Bank of. 2016. “Triennial Central Bank Survey of Foreign Exchange and Otc Derivatives Markets in 2016.” Bank of International Settlements. Lipschitz, L., and D. McDonald. 1992. “Real Exchange Rates and Competitiveness: A Clarification of Concepts, and Some Measurements for Europe.” Empirica 19: 37–69. Lyons, R. 1997. “A Simultaneous Trade Model of the Foreign Exchange Hot Potato.” Journal of International Economics 42: 275–98. Marsh, I. W., and S. P. Tokarick. 1996. “An Assessment of Three Measures of Competitiveness.” Weltwirtschaftliches Archiv 132: 700–732. 1. One trillion is equal to 1 000 000 000 000.↩︎ 2. This is down from5.4 trillion in April 2013. This represents the first decline in FX spot trading activity, since 2001. However, activity in FX derivatives has continued to increase. Trading in OTC interest rate derivatives averaged $2.7 trillion per day in April 2016, up from$2.3 trillion in April 2013 (International Settlements (2016)).↩︎

3. When using an exchange rate of R13.24 to the US dollar.↩︎

4. This term was coined by Lyons (1997).↩︎

5. The natural logarithm is denoted “$$\log$$” in this calculation.↩︎

6. The natural logarithm of 1.10517 is 0.1 because raising 2.71828 to the 0.1 power is 1.10517.↩︎

7. For surveys see, e.g., Lipschitz and McDonald (1992); Marsh and Tokarick (1996); Hinkle and Montiel (1999); Chinn (2006).↩︎

8. Where most countries use the currencies of their main trading partners.↩︎

9. Several exceptions to the 2-business-day rule are noteworthy. First, for exchanges between the U.S. dollar and the Canadian dollar or the Mexican peso, in these cases the rule is 1 business day. Second, if the transaction involves the dollar and the first of the 2 days is a holiday in the United States (but not in the other settlement centre), the first day is counted as a business day for settlement purposes. Third, Fridays are not part of the business week in most Middle Eastern countries, although Saturdays and Sundays are. Hence, Middle Eastern currencies transacted on Wednesday settle on Saturday, not on Friday.↩︎