III Measuring Exchange Rate Variability

International Monetary Fund
Published Date:
July 1984
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The fundamental uncertainty in business is that unforeseen fluctuations in revenues relative to costs will make a particular transaction or activity uneconomic. When revenues and costs are in different currencies, possible exchange rate movements are clearly an important dimension of this uncertainty. They are not, however, necessarily an independent source of uncertainty, nor do they affect different enterprises in the same way.

The simplest kind of international transaction is the basic trading transaction of nineteenth century textbooks, whereby a trader makes a contract to buy a fixed quantity of goods at a given price in one country, and to sell them after, say, 90 days, at a fixed price in another country. His profit is the difference between the purchase price and the selling price (less freight, insurance, and interest costs), and the only source of uncertainty is the exchange rate at which he can translate his sales revenue in foreign currency into local currency to repay his borrowing. It is the possibility that the nominal exchange rate will move by an unknown amount during the life of his contract that is the proper measure of the uncertainty he faces.

Where forward markets exist, of course, the nature of the uncertainty faced by traders is transformed. A forward market represents, in effect, a “guaranteed” forecast of the exchange rate that will prevail at the end of the contract period, which a trader can take advantage of by payment of a small margin around the forward rate. Since currency uncertainty can be removed from the short-term trading transaction by payment of this margin, the “cost” of such uncertainty cannot be higher than the cost of purchasing insurance against it.1

Since spreads between bid and offer rates in the 3-month forward market have rarely exceeded 0.2 of 1 percent for major currencies (see Chart 1), the implicit cost of short-term exchange rate uncertainty would appear to be too small to have a significant effect on aggregate trade flows. Spreads for forward contracts of 12 months’ maturity have generally been larger, reflecting the relative “thinness” of this market. Nevertheless, spreads for the major currencies are generally well under 1 percent (so that the cost for a one-way transaction is under 1/2 of 1 percent of the central rate).

Chart 1.Selected Industrial Countries: Spreads Between Buying and Selling Rates in Forward Exchange Markets, 1974–821

1 Averages of daily rates; exchange rates are U.S. dollars per unit of local currency in the New York foreign exchange market.

Most international trading activity, however, has a longer time horizon than that corresponding to the shipment of goods. It generally involves the commitment of resources, and the development of markets, for an extended period of time. During this time, domestic production costs and foreign selling prices will both change in local currency terms. The key question, therefore, is whether, and by how much, fluctuations in exchange rates offset or accentuate these uncertainty-producing movements in production costs and sales receipts. The answer to these questions requires the adjustment of nominal exchange rate relationships to take account of changes in prices and costs. This in turn presents the problem of choosing suitable indices to capture the particular costs and prices that are most relevant from the point of view of traders.

It is also relevant that the “commitment period” for resources varies widely among activities. The decision to market excess production of a homogeneous commodity with a well-developed international market (e.g., a primary commodity or raw material) can be effected at short notice, and then not repeated if market conditions change. The decision to take advantage of market conditions to sell a manufactured product for which domestic demand falls short of established production capacity requires an investment in developing market outlets that is not worthwhile unless sales are expected to continue for some time. Finally, the decision to create new production capacity to meet foreign demand may entail a commitment to investment in plant and equipment, as well as labor force training, that will continue for a period of many years.

Enough has been said so far to indicate that different kinds of uncertainty are important for different kinds of international enterprise. There is no unique measure of “exchange rate variability” that can be used as a proxy for the uncertainty and adjustment costs that traders face as a result of exchange rate movements (Lanyi and Suss, 1982). In what follows, four dimensions of variability are presented and discussed. They are then combined in various ways to produce proxies for exchange rate uncertainty. The behavior of these proxies–over time and among countries, as well as relative to the other proxies–is discussed later in the section (and in more detail in Appendix I). These measures are used in the empirical analysis presented later in the paper.

Dimensions of Exchange Rate Variability

Nominal vs. Real Exchange Rates

Since the focus of this paper is on the impact of exchange rate variability on trade, the rate that has significance in this connection is the one that is of primary interest to traders. To a large extent, as noted above, this depends on the time dimension of the economic decisions that are being considered. In the very short term, say the period between the contract to supply goods that have already been produced and their actual delivery to a foreign purchaser, all costs and prices are known except the nominal exchange rate. It is, therefore, fluctuations in the nominal exchange rate that introduce uncertainty into traders’ decisions. Once the time period concerned is lengthened, it becomes apparent that other prices become variable also. A decision to produce more in the expectation of foreign sales involves uncertainty about the price in foreign exchange which such sales will realize, as well as the exchange rate at which given foreign exchange receipts can be converted into domestic currency. And a decision to increase domestic production capacity involves uncertainties about the future cost of factors of production (labor and other inputs) as well as the price to be received for final sales.

In other words, as the planning horizon of traders is lengthened, the relevant exchange rate becomes that between domestic costs of production and foreign sales prices converted into domestic currency. From such a perspective, it is clear that stability in the real rate of exchange (somehow defined) is more likely to reduce the uncertainty facing traders than mere stability of nominal rates. Thus, the comparisons and time series presented in this paper will focus on nominal magnitudes only when short-term variability is being considered, and will give more emphasis to variability in real rates when longer time periods are involved.

The choice of the price index to be used in making real exchange rate calculations is not simply an esoteric and technical matter. Reference to an inappropriate price index can systematically affect judgments on the scope and direction of movements in real exchange rates (Williamson, 1983). It is generally argued (Artus, 1978) that the index used should attempt to measure costs of production of tradable goods, rather than actual prices, since the forces of competition will tend to equalize the latter among countries through changes in profit margins. This consideration has led to the adoption of indices of unit labor costs in manufacturing industry (normalized for cyclical changes in productivity) as a proxy for the competitiveness measure that is most relevant for exchange rates. Such indices, however, have problems of their own, notably the difficulty of incorporating secular shifts in productivity and the incomplete coverage of the traded goods sector (which also includes important parts of agriculture, mining, and services). For the latter reason, it can also be useful to refer to the more broadly based gross domestic product (GDP) deflator as a proxy for cost and price changes that influence external competitiveness.

Bilateral vs. Effective Exchange Rates

Each individual trade transaction takes place between two countries, and therefore involves only one bilateral exchange rate. Thus, it might seem that the appropriate measure of uncertainty facing traders is some average of the variability in individual bilateral exchange rates (Lanyi and Suss, 1982). In other words, if the fluctuations in currency A against both currency B and currency C are X percent, then the proper measure of variability for the combined trade with B and C is also X. Such reasoning overlooks the actual and potential diversification that characterizes international trading relationships. If currency B has a systematic tendency to rise against A when C falls, the average or effective exchange rate for A may be much more stable than either of the two bilateral rates. For traders dealing with both foreign countries, it is the effective exchange rate that best reflects the aggregate uncertainty in their future income stream.

It becomes clear, therefore, that the choice between bilateral and effective rates depends to a considerable extent on whether one wishes to measure the uncertainty facing the economy as a whole or that facing individual traders, and the degree to which individual traders are diversified. (It should be noted that diversification applies to import sources as well as to export destinations. Bilateral exchange rates would be the appropriate focus of concern when imports are dominated by a single major supplier.)

For illustrative purposes, the calculations presented in Appendix I, and discussed later in this section, cover the variability both of effective exchange rates and of the weighted average of bilateral rates. Since the bulk of trade in the major industrial countries is undertaken by diversified enterprises, the effective rate is probably a better measure of the influence of exchange rate factors on trading uncertainty; however, it needs to be borne in mind that a significant proportion of producers (probably including a relatively greater number of small enterprises) will have a high degree of export concentration.

Time Period of Variability

One of the most difficult issues in choosing a measure of exchange rate variability is the time period over which such variability is to be measured. The average period-to-period movement in an exchange rate is likely to be quite different depending on whether day-to-day, quarter-to-quarter, or year-to-year swings are considered. Actually, two issues are involved. Since exchange rates display serial correlation (i.e., the level of the rate in any period is strongly correlated with its level in the previous period), it is important to assess both how much the exchange rate has shifted since the previous period and how far it has moved relative to some average or trend.

Since exchange rates vary continuously, it might seem appropriate to measure variability over very short periods (i.e., for practical purposes, day to day). Transactions take place at individual moments in time, and the possibility of exchange rate movements from day to day imposes uncertainties on traders, even if these very short-term fluctuations are quickly reversed.

While this is true, and such short-term uncertainties undoubtedly impose costs, it can be doubted whether these are the most significant adverse aspect of exchange rate variability. Trade transactions are usually not entered into for settlement within one or two business days. A much more normal practice would be a contract covering a period of, say, three months. In this case, a more important uncertainty for the trader would be the degree to which an exchange rate was likely to change between the date at which a contract was entered into and the date at which it matured.

While three months may be a typical contract/settlement lag for individual transactions, it is much less than the normal planning horizon for strategic decisions to participate (or refrain from participating) in international trade. A manufacturer who contemplates developing a foreign market or markets will have a stream of receipts in foreign currency, and a stream of payments in local currency, extending over a number of years. Day-to-day variability in exchange rates will be of little concern to such an enterprise, since the law of large numbers will ensure that random daily fluctuations in the rate tend to be self-canceling. Even quarterly fluctuations that reverse themselves from period to period may not be regarded as of great significance.

This consideration leads on to the importance of sustained deviations from trend, as well as period-to-period movements, in introducing uncertainty into trade. If exchange rates move by an average of, say, 2 percent a month, but in a random manner, this may well be an easier type of uncertainty for businesses to absorb than where monthly movements are held to, say, 1 percent, but tend to cumulate through a succession of such movements in the same direction before undergoing a reversal.

Since manufacturers and traders face different planning horizons, depending on the nature of the activity in which they are engaged, there can be no single “correct” measure of the most appropriate time period for gauging exchange rate variability. In the statistical analysis presented here, evidence is provided of monthly and quarterly period-to-period movements in exchange rates. Deviations of monthly and quarterly exchange rates from their average, or trend, levels are also considered.

Actual vs. Predicted Movements

The fact that exchange rates move does not, of course, mean that such movements involve uncertainty. To the extent that exchange rate developments are foreseen and reflected in forward market quotations, they are perfectly consistent with a well-functioning mechanism for allocating resources. This consideration suggests use of deviations between actual and predicted (on the basis of earlier forward quotations) exchange rates as the relevant measure of exchange rate uncertainty.

Once forward exchange rates are brought into the analysis, it can be argued that a better measure of the uncertainty cost of exchange rate variability is the cost of insuring against it. This cost is reflected by the spread between bid and offer quotations for forward exchange contracts (not the forward premium or discount, since the cost of a forward premium to one party is the benefit of a forward discount to the other, if the bid/offer spread is ignored).

Before proceeding to a discussion of some of the evidence on variability, it is worth noting one other difficulty in the way of generating statistical estimates of variability. Traditional measures of variance, such as the standard deviation, have well-defined properties that make them particularly useful for analysis. However, as Westerfield (1977) points out, these properties depend on assumptions about the underlying statistical series that are not borne out in the case of exchange rates. The “skewness” of the distribution, particularly in the fixed rate period when the bulk of the observed variance is accounted for by individual discrete exchange rate changes, means that observed standard deviations do not necessarily have the normal properties. For this reason, most of the tables in Appendix I present data in the form of average changes rather than in standard deviations.

Exchange Rate Variability, 1960–83

The foregoing discussion implies that there are a large number of potential measures of variability. Several of these are presented, using data for the major industrial countries, in Appendix 1. (For another presentation and discussion of exchange rate variability, see Kenen, 1979.) The footnotes to the tables indicate the definitions that have been used in their construction. Interpretation of these results, however, requires some simplifying organizational structure. The following discussion is grouped around a series of frequently asked questions concerning exchange rate variability:

–Has exchange rate variability (however defined) increased in the floating rate period compared with what it was before?

–Has there been a “learning” process during the floating rate period, such that volatility has tended to diminish as experience with floating rates accumulates?

–Are some currencies more prone to fluctuations than others? Specifically, are countries that participate in cooperative exchange rate arrangements shielded from volatility?

–Have exchange rate movements tended to offset price movements, so that real exchange rate fluctuations are systematically smaller than fluctuations in nominal rates?

–Are deviations of exchange rates from medium-term trends greater or less than would be expected on the basis of their short-term volatility?

Volatility in Floating vs. Fixed Rate Period

There is no doubt that, on almost any definition of exchange rate variability, fluctuations in exchange rates have been greater in the decade since floating was adopted than they were in the period of the 1960s. The weighted average of monthly changes in nominal effective exchange rates (see Appendix I, Table 4) among the major industrial countries was 0.2 percent during the period 1961–70, and averaged almost 1.2 percent over the period 1974–83, a sixfold increase. Quarterly movements in nominal exchange rates, which are somewhat larger than average monthly movements, have also increased about sixfold. The variability of real exchange rates was somewhat greater than that of nominal exchange rates during the late 1960s, and the increase between then and the more recent period has been proportionately smaller. Nevertheless, the weighted average of changes in real rates has still been 2½-3 times greater in the period 1974–83 than in the decade of the 1960s. Indeed, for no year after 1974 is the average variability of the seven major currencies less than for the year of greatest variability in the period to 1970.

Is There a “Learning” Process?

For most measures of monthly or quarter-to-quarter variations in exchange rates, 1973 is the year of greatest variability. However, although there was an apparently systematic trend toward greater stability over the four or five years following the adoption of floating exchange rates, this trend was interrupted at the end of the 1970s. Since 1978, Japan and the United States have experienced notably greater fluctuations in their effective exchange rates (in both nominal and real terms) than prior to that date. Italy and the United Kingdom, by contrast, had greater fluctuations in the external value of their currencies in the middle of the floating period than at the beginning or more recently. There is, therefore, no convincing evidence of any trend toward greater or lesser variability over time.

Intercountry Variations

It has already been noted that different currencies have experienced increases in variability at different times. This suggests that there have been country-specific influences on exchange rate variability as well as common external causes. In addition, some currencies have tended to be relatively more stable than others over time. It is noteworthy that the real effective exchange rates of France, the Federal Republic of Germany, Canada, and Italy have shown considerably smaller quarter-to-quarter variations over the period 1974–83, taken as a whole, than have those of the United States, the United Kingdom, and Japan. This could reflect, in the case of the European currencies, the influence of cooperative monetary arrangements, and, in the case of Canada, the close ties between the Canadian economic and financial system and that of its principal trading partner, the United States.

Exchange Rates and Price Movements

It is generally accepted that prolonged inflation differentials among countries will eventually lead to broadly offsetting movements in the exchange rate between their currencies. The reasons for this relationship are well known (Officer, 1976), and experience during the floating exchange rate period generally bears it out. Among the major currencies, those with the most rapid rates of inflation during the past decade have been Italy, the United Kingdom, and France, and the currencies of these three countries have depreciated most. Japan has been the most successful of the major industrial countries in containing inflation, and the exchange rate for the yen has risen over the floating period.

But while such a relationship can be detected over long periods, when relative prices move by significant amounts, it is much less certain whether the connection is so close in the short or medium term. A comparison of Table 4 and Table 5 in Appendix I suggests that month-to-month changes in real effective exchange rates are broadly similar in size to those in nominal exchange rates. For several countries and in a number of years, the relationship is perverse. A similar result was obtained by Kenen (1979). From this it can perhaps be concluded that movements of nominal exchange rates do not appear to be primarily due to contemporaneous shifts in national price levels. This does not, of course, mean that expectations concerning inflationary developments, and the policies that may be adopted to deal with them, might not themselves have a significant impact on interest differentials and hence on exchange rates.

Deviations from Trends

As may be seen from Tables 4 and 5 in Appendix I, period-to-period movements in exchange rates, though substantially greater in the floating than in the prefloating period, are still relatively small in absolute terms. If the quarterly variability faced by traders was in the range of 2–3 percent suggested by these tables, it could perhaps be assumed that the adverse impact of the resultant uncertainty on trade was relatively limited. What is perhaps more significant is to know the extent to which short-term movements are quickly and systematically reversed, or rather tend to cumulate before ultimately changing direction.

Chart 2 offers a perspective on the issue of deviations from trend by plotting the movements in real effective exchange rates around their medium-term trend, which is defined as a 19-quarter centered moving average. It may be seen that these have become quite large during the floating period. The series have been brought up to the end of 1983 by assuming that the exchange rate for the future period needed to calculate the moving average is the same as the average for the quarters available for the calculation. For Japan, the United States, and Canada, there is clear evidence that swings about the medium-term real effective exchange rate began to be greater in the early 1970s and have, if anything, tended to increase in amplitude in the period since then. For the European economies, variability by this measure appears to have begun earlier, and has not exhibited any very significant tendency to increase. This probably reflects the quite sizable realignment of exchange rates involving European currencies in the 1967–71 period. For all countries, however, the variability in the early and middle 1960s was considerably less than it was subsequently.

Chart 2.Major Industrial Countries: Deviations from Trend in Real Effective Exchange Rates, 1961–831

(In percent)

1 Quarterly data, with the trend exchange rate defined as a 19-quarter centered moving average.

Even the deviation from a 19-quarter centered moving average can understate the degree to which exchange rate swings cause uncertainty. For one thing, the periodicity of a complete cycle may be longer than 19 quarters. Chart 7 in Appendix I, for example, suggests that the behavior of the dollar during the floating rate period includes a trend decline (though with interruptions) throughout the 1970s, followed by an increase from 1980 onward. A second reason for caution about the use of a centered moving average is that the estimate of trend used in Chart 2 requires knowledge of future actual observations, knowledge that market participants will not have at the time. If a moving average of historical observations were used instead (e.g., for the 19 quarters up to the observation quarter), somewhat larger divergences would probably result.

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