THE BEHAVIOR OF FOREIGN EXCHANGE RATES

Transcription

1 THE BEHAVIOR OF FOREIGN EXCHANGE RATES JORGE R. CALDERON-ROSSELL* The World Bank MOSHE BEN-HORIM** University of Florida and Hebrew University Abstract. The analysis of the distribution of foreign exchange rate changes provides a description of the behavior of foreign exchange rates and its determining underlying process. The application of empirical methodologies or further theoretical developments is limited by the nature of this distribution. In this paper, the empirical analysis of major currencies during the flexible exchange rate period suggests that there is no unique distribution representing the behavior of the foreign exchange rate. This, however, is determined both by foreign exchange management policies and the fundamental economic forces. * The analysis of the distribution of foreign exchange rate changes provides a description of the behavior of foreign exchange rates and of the underlying process determining foreign exchange rate. From the investor's point of view, the specification of this distribution is very helpful in assessing the riskiness of foreign exchange holdings. The form of the distribution and the parameters that describe it suggest the risk of investing in foreign assets. The probability of gaining or losing in foreign exchange transactions depends on the assumed distribution, while the sample variance, often used to reflect the variability of foreign exchange rates, might not be an adequate measure of risk. The sample variance is meaningless, for example, in the case of the symmetric stable Paretian distribution. Thus, in the event that foreign exchange rate changes follow a symmetric stable Paretian distribution, mean-variance models could be of limited use in analyzing foreign exchange transactions. The effectiveness of portfolio diversification strategies would also be conditioned by the characteristic exponent of the distribution. The predictability of foreign exchange rates is, in addition, determined by the underlying probability models that best describe the behavior of foreign exchange rate changes. More generally, the authors' findings on the probability distribution of exchange rate changes might influence theoretical foreign exchange rate modeling; in addition, these findings might rule out the use of some empirical methodologies-for example, the application of simple regression techniques to non-normal probability distributions might produce misleading results and would not be appropriate. Regarding the underlying process governing the behavior of the foreign exchange rate, the probability distribution might be indicative of the policies pursued by monetary authorities and, to some extent, of their effectiveness. The study of the distributions of foreign exchange rate changes could, therefore, be INTRODUCTION *Jorge R. Calderon-Rossell is a staff member of the World Bank and has been a faculty member of Columbia University and the University of Florida. He has published mainly in the areas of international finance and financial economics. Dr. Calderon-Rossell has also served as advisor to public and private financial institutions. **Moshe Ben-Horim is Associate Professor of Finance in the College of Business Administration, University of Florida. He is also at the School of Business Administration, the Hebrew University. Dr. Ben-Horim has consulted for governments and public utilities and has written articles on finance and statistics. The authors began this paper during their appointments at the University of Florida, Gainesville. They wish to thank Richard Levich for a number of valuable comments on an earlier draft and to acknowledge the helpful assistance of Teri Blunt in computer programming. The views reported here are those of the authors and do not necessarily reflect those of the institutions named above. Journal of International Business Studies, Fall Palgrave Macmillan Journals is collaborating with JSTOR to digitize, preserve, and extend access to Journal of International Business Studies

2 helpful for governments when they are formulating their foreign exchange management policies. In studying the distribution of daily U.S. dollar prices of the Canadian dollar, the French franc, and the British pound during the relatively flexible exchange rate periods of the 1920s and 1970s (up to 1974), Giddy and Dufey found evidence of non-normality of the distribution of exchange rate changes while reporting changes of the variance over time [10, p. 21]. The distributions had longer tails than those of the normal, and some degree of leptokurtosis. Analyzing the U.S. dollar daily value of the German Deutsche Mark, the British pound, and the Canadian dollar during 1 April April 1975, Burt et al. [3] also found a strong degree of leptokurtosis in the distribution of exchange rate changes while claiming evidence of stationarity. Westerfield [20] studied the weekly foreign exchange rates of the Canadian dollar, the British pound, the Deutsche Mark, the Swiss franc, and the Dutch guilder during the fixed exchange rate regime of the 1960s and the floating regime of the 1970s. From her application of techniques similar to those applied to stock prices, Westerfield suggests that the symmetric nonnormal stable Paretian distribution is the best model to describe the variability of foreign exchange rates. More recently, Rogalski and Vinso [17], using Westerfield's sample, have offered the Student t-distribution with approximately 3.9 degrees of freedom as another alternative. The purpose of this study is to present an empirical analysis of the probability distribution of daily foreign exchange rate changes. The authors have extended the previous studies to include 14 major currencies, focusing on the period 1 July 1974 to 29 July During this period the variability of the flexible foreign exchange rates tended to stabilize after a period of erratic fluctuations that followed the breakdown of the Smithsonian Agreement in [See 1, p. 688.] In the period, however, the variability of foreign exchange rates increased again to the 1973 levels. Several previous studies [10, 17, and 20] measured exchange rate movements as the natural logarithm of exchange price relatives; however, Burt et al. [3] analyzed discrete percentage exchange rate changes. For small exchange rate changes, the two methods produce nearly identical results. The authors selected the discrete formulation in which the daily foreign exchange rate change for country i, xi is defined as2: X ri ri,,t+ t r,t ri, t for i = 1,2,3,...14, (1) ri,t where: xi = daily foreign exchange rate change of currency i; ri, t = daily foreign exchange rate of currency i at day t, expressed as U.S. dollars per foreign currency i unit; and ri, t+ 1 = daily foreign exchange rate of currency i at day t + 1 expressed as U.S. dollars per foreign currency i unit. Under the assumption of stationarity of the distribution of foreign exchange rate changes, the analysis of daily changes can be extended to changes between different holding periods or extended investment horizons. In this paper, however, the focus is only on the one-day holding period. In addition, given that the form of the quotation does not determine the nature of the probability distribution of foreign exchange rate changes, a direct quotation of the foreign exchange rate is used where the unit of account is the U.S. dollar. Therefore, positive values for xi indicate appreciation of foreign currency i vis-a-vis the U.S. dollar, whereas negative values signal a depreciation of the foreign currency i. Under equilibrium conditions the standardized distribution of foreign exchange rate changes expressed in the indirect quotation would be the mirror image of the standardized distribution of the rate changes expressed in the direct quotation. 100 Journal of International Business Studies, Fall 1982

3 In the next section, the skewness of xi's distribution is analyzed. Differences in the skewness of the distribution have been found among groups of currencies. In the third section, the stationarity of the distribution is examined and an attempt is made to reveal the source of the lack of stationarity. Penultimately, the stable Paretian distribution hypothesis is tested and some conclusions are drawn in the last section. One of the major characteristics of the nature of a probability distribution is its degree of asymmetry, or departure from symmetry. The analysis of the symmetry of the probability distributions of foreign exchange rate changes is based on the skewness statistic: Number of observations below the mean Sk=( -1/2) 2n, n (2) where n is the number of sample observations.3 For large samples this statistic is normally distributed with mean 0 and variance 1. In order to analyze skewness and stationarity, the period was divided into 3 subperiods: 1 July June 1975; 1 July July 1976; and 2 August July 1977, labeled subperiods 1, 2, and 3, respectively. For each subperiod the 14 corresponding distributions were observed. Although these subperiods of approximately 365 observations per currency are quite arbitrary, they seem to be appropriate for studying the skewness and stationarity of the foreign exchange rate in different intervals. In principle, under normal conditions and overall stationarity of the period of analysis, which seem to characterize the period under review, any sample subperiod is appropriate for studying variations in the skewness of distributions and for examining stationarity within the period. The value of the Sk statistic for each subperiod is presented in Table 1. Based on SKEWNESS TABLE 1 Skewness Statistic (Sk) Subperiods Group Currency Austrian Schilling Belgian Franc Canadian Dollar Danish Krone Netherlands Guilder Norwegian Krone Deutsche Mark * II French Franc * Swedish Krona * Australian Dollar ** ** Italian Lira ** ** III Japanese Yen ** * Pound Sterling ** ** Spanish Peseta ** * *Significant at 5%. *Significant at 1%. Journal of International Business Studies, Fall

4 the skewness of the distributions, foreign currencies were classified in 3 groups. In the first group (I), the skewness statistic Sk was not statistically different from zero for all currencies and subperiods. Therefore, there is strong evidence to conclude that the distributions of all currencies in this group were symmetric during the period of study. In the second group (II), the distribution of changes in the foreign exchange rate of these currencies was close to being symmetric except for at least 1 subperiod. Three out of 9 subperiods showed some degree of skewness, at a 5 percent significance level. In the case of the Deutsche Mark, skewness was positive in the third subperiod, while the skewness of the French franc and Swedish krona was negative in the second subperiod. Finally, in the third group (III), the skewness statistic suggests strongly that all the distributions in these groups were asymmetric. With the exception of the distribution of the Japanese yen with positive asymmetry, all other distributions showed signs of negative skewness. In group III, mainly during subperiods 2 and 3, the likelihood of Type I error is reduced to a significance level of 1 percent, which suggests strongly the asymmetry of the distributions of the foreign exchange rate changes classified under this group. During the period of study, the Deutsche Mark and the Japanese yen, with signs of positive skewness, appreciated vis-a-vis the U.S. dollar, while the Italian lira, the pound sterling, and the Spanish peseta, with a negative skewness, depreciated vis-a-vis the U.S. dollar. It seems, therefore, that the skewness of the distribution of foreign exchange rates is related to the trend value of the currency. This trend might not, however, be anticipated and can be of short duration as in Group II currencies, or it can be a sustained trend as in the case of Group III currencies. Whereas from the theoretical point of view these patterns should be the result of economic causes, the grouping of these currencies on the skewness of the probability distributions suggests also that the management policies of foreign exchange rates are determining factors in the behavior of foreign exchange rates. TABLE 2 Mann-Whitney Z Statistic for Strict Stationarity (xi) Compared Subperiods Group Currency 1 versus 2 2 versus 3 Austrian Schilling * Belgian Franc * ** Canadian Dollar ** ** Danish Krone * * Netherlands Guilder * * Norwegian Krone * Deutsche Mark * * II French Franc * * * Swedish Krona * Australian Dollar ** Italian Lira ** III Japanese Yen * Pound Sterling Spanish Peseta ** *Significant at 5%. *Significant at 1%. 102 Journal of International Business Studies, Fall 1982

5 After the collapse of the Bretton Woods system and subsequently of the Smithsonian Agreement, major currencies of industrial countries entered into a managed floating system subject to different policies. Most European countries entered into an agreement to maintain the foreign exchange rates within established limits, while other countries such as Italy, Japan, and the United Kingdom were following more independent policies in managing their foreign exchange rates. Therefore, the groupings shown in Table 2 suggest that the control regime of foreign exchange rates is a determining factor of foreign exchange behavior. Most countries whose currencies are in Group I and II were managing their foreign exchange rates under the "European Snake" agreement. Although currencies in Group II show some short duration drifts, they are very close to the symmetry shown by Group I currencies. On the other hand, Group III currencies were following more independent foreign exchange regimes. Although the literature has paid attention to policy prescriptions for different management approaches in exchange rates, empirical research has basically neglected these different policies in managing the "dirty float." Evidently, based on the preceding discussion, both the economic causes of foreign exchange rate determination and the policies for managing the foreign exchange rate are important factors determining its actual behavior. The differences between Group I and II, and Group III currencies indicate a substantial difference in foreign exchange adjustments. Nevertheless, the grouping of skewed distributions seems to support the policies for managing the foreign exchange rate as the most plausible explanation determining the behavior of foreign exchange rates. Economic forces would have an effect on this behavior under the guidelines and policies established by monetary authorities. Evidently, this situation implies some effectiveness of governments' control of foreign exchange markets. The extent of this control vis-a-vis the underlying economic forces is still a subject for further research. The analysis of skewness presented in Section II implies some differences in the stationarity of the probability distributions between the groups of currencies and, probably, of the underlying process determining foreign exchange rates. Whereas currencies of Group I appear to have symmetric distributions in each subperiod, therefore suggesting stationarity, the distribution of currencies of Groups II and III changed skewness between subperiods, with currencies of Group III showing more definite trends. In general, if the probability distribution is strictly stationary, then parameter values estimated-with data from period k will be statistically consistent with parameter values for period j. Stationarity permits us to make probability assessments of the future value of the foreign exchange rate based on parameter estimates from past data. Because of all this, a more in depth analysis of stationarity is necessary. Strict stationarity4 is defined in terms of the probability function as: STATIONARITY P(xt,...,xt + k) = P(xt + m,...,t + k + m), (3) where t is any point in time, and k and m are any pair of integers.5 The Mann- Whitney U test6 between consecutive subperiods was applied to test for strict stationarity. These results are shown in Table 2. The grouping of currencies in this table and hereafter follows the same classification as in Table 1. Based on the evidence shown in Table 2, the hypothesis that the probability distributions did not change from one subperiod to the next was rejected. With the exception of the pound sterling, the distribution of foreign exchange rate changes varied at least once between consecutive subperiods at the 5 percent significance level. Distributions of currencies in Groups I and II, however, showed more variations than those of Group III. Whereas in the first two groups the distributions changed between every subperiod, in the third group the distributions Journal of International Business Studies, Fall

6 changed only once. Again this pattern seems to reflect the differences in foreign exchange policies pursued by monetary authorities of the respective countries. The asymmetry of the distributions and their relative stationarity, in particular during subperiods 2 and 3, seem to suggest that countries of Group III currencies were either more consistent in their policies or subject to more persistent economic forces than those in the other groups. Given that government policies and controls are likely, however, to be bound by the economic forces determining equilibrium foreign exchange rates, noticing the currencies included in Group III that were subject to a continuous pressure to depreciate or appreciate during the period of analysis, and observing further the asymmetry of these currencies (Table 1), it is plausible to infer that within the period of the study, governments from countries with currencies in Group III were trying to restrain the underlying economic forces determining foreign exchange rates. This implies that foreign exchange rates of currencies in Group III during the period of analysis could have been subject to more stringent controls or government intervention relative to the economic forces governing them. The lack of strict stationarity may, however, be the result of changes in at least one of the parameters of the distribution. In order to examine stationarity of the mean and standard deviation, additional tests for each of the currencies were conducted. For this, the following transformed variables were examined: and yi = xi- Xi, (4) W = Xi/Si. (5) By performing Mann-Whitney U tests on yi, and wi, one can indirectly assess the effect of changes in the mean and/or the standard deviation on strict stationarity.7 If, for example, the U test on xi shows that a given distribution has changed between 2 subperiods, but the test on yi shows no significant change between the same subperiods, the conclusion will be that it is the shift in the mean of the distribution that was the main cause of the change in the distribution of xi. On the other hand, if both xi and yi changed between subperiods, it may be concluded that the change in xi was caused by changes of parameters other than the mean of the distribution. Similarly, if xi changed between subperiods, but wi = xi/si did not, the change in the standard deviation of the distribution of xi is suggested to be the main cause of the change in the distribution of xi. If both xi and wi show significant changes between subperiods, the change in xi was caused by changes of parameters other than the standard deviation. The result of the Mann-Whitney U tests on yi and wi are exhibited in Tables 3 and 4. From contrasting the results of Tables 2 and 3, it is found that when the effect of the change in the mean was removed (equation 4), the currencies in Groups I and II showed a marked drop in the Mann-Whitney Z value, meaning that the major factor contributing to the high Z values for xi (Table 2) for the currencies in Groups I and II was shifts in the means of the distributions between subperiods. Supporting evidence for this conclusion is also derived from Table 4, where the Z values of the Mann-Whitney tests of wi = xi/si are presented. By contrasting the results of Tables 2 and 4, we find that the values in Groups I and II are remarkably close, indicating that the sample standard deviation of these currencies was relatively stationary through the 3 subperiods. The tests for the few currencies in Group III that showed lack of strict stationarity were rather mixed. However, from examining Tables 1 and 2, it is evident that the lack of strict stationarity exhibited by some of the currencies of Group III is mainly the result of changes in the skewness of these distributions. Once more these findings point to the policies of foreign exchange management followed by monetary authorities of the respective countries in combination with the underlying economic forces as the major explanation for the behavior of the 104 Journal of International Business Studies, Fall 1982

7 TABLE 3 Mann-Whitney Z Statistics for y' Compared Subperiods Group Currency 1 versus 2 2 versus 3 Austrian Schilling Belgian Franc Canadian Dollar Danish Krone Netherlands Guilder Norwegian Krone Deutsche Mark II French Franc Swedish Krona Australian Dollar ** ** Italian Lira ** IIl Japanese Yen Pound Sterling * Spanish Peseta ** ** *Significant at 5%. *Significant at 1%. TABLE 4 Mann-Whitney Z Statistic for wi Compared Subperiods Group Currency 1 versus 2 2 versus 3 Austrian Schilling * Belgian Franc * ** Canadian Dollar ** * I Danish Krone * * Netherlands Guilder ** * * Norwegian Krone * Deutsche Mark * II French Franc * * Swedish Krona * Australian Dollar Italian Lira * III Japanese Yen Pound Sterling Spanish Peseta ** * *Significant at 5%. *Significant at 1%. Journal of International Business Studies, Fall

8 distribution of foreign exchange rate changes. After the breakdown of the Smithsonian Agreement, most currencies in Groups I and II entered into a new agreement to maintain the currencies of their respective currencies floating under a band, the "European Snake." Based on the evidence shown above, currencies of those countries were changing mean between subperiods while the sample standard deviation remained unchanged. The stationarity of the standard deviation of the European currencies would suggest that the snake arrangement permitted the effective control of the dispersion of the foreign exchange rates but not necessarily of their overall level. On the other hand, countries of Group III currencies subject to major economic forces that were continuously exerting pressure on the level of the rates were probably actively intervening in the foreign exchange market to restrain further changes in their foreign exchange rates. Countries of currencies in Group III appear to have been holding up the overall mean of the probability distribution while facing continuous drifts that made them asymmetric. In summary, the distribution of foreign exchange rate changes of Groups I and II can be characterized to be symmetric, subject to location shifts-that is, changes of the mean-and to have a constant sample standard deviation (or variance). On the other hand, distributions in Group III are asymmetric and mostly stationary. In the few instances where these distributions shifted, it was the result of changes in the skewness of the distribution. STABLE Studying the behavior of security and commodity prices, Mandelbrot [13] ques- PARETIAN tioned the Gaussian hypothesis and offered the "Stable Paretian Distributions" DISTRIBUTIONS as an alternative. Extending even further the analysis of these distributions, Fama and Roll examined the behavior of stock prices [6, 7, 8] and of interest rates [18]. Westerfield [20] used similar techniques for the analysis of foreign exchange rate behavior. Rogalski and Vinso [17] proposed the Student "t" distribution with approximately 3.9 degrees of freedom as an alternative description for the floating period of the 1970s. This distribution, however, theoretically has a coefficient of kurtosis lower than the normal while the moment coefficient of kurtosis is undefined. Therefore, the Student "t" distribution around 3.9 degrees of freedom has a lower peakedness than the normal and fails to explain the high peakedness of the empirical distributions of foreign exchange rate changes reported in other studies. Because of this, only the stable Paretian hypothesis is examined for this sample of 14 currencies. In general, the stable Paretian family of distributions is defined by the logarithm of the characteristic function (that is, the second characteristic function of the random variable x): logekx (t)= log e [ I eitxdf(x)]= i6t -yltl [1 + i /(t/ltl) tan (ovr/2)] (6) -00 where x is the random variable, i is - 1, t is a real number, and F is the cumulative distribution function. The rest of the parameters are those of the stable Paretian distribution: the characteristic exponent oc(0< oc < 2), the location parameter 6 (the mean when oc >1), the index of skewness 0(- 1 <fi + 1), and the scale parameter c, (y = c)). For the symmetric case (, = 0), the logarithm of the characteristic function is: logexx(t) = it - yltl (7) The characteristic exponent oc defines a particular distribution among the stable Paretian family. When oc =2, the relevant stable Paretian distribution is the normal distribution, whereas when oc = 1, the distribution is the Cauchy distribution. In the interval 0< oc <2, the tails of the stable Paretian are thicker than those of the normal distribution. In this interval the variance does not exist (that is, is not defined), while the mean exists as long as oc> Journal of International Business Studies, Fall 1982

9 Westerfield [20] suggested that foreign exchange rate changes during the floating period of the 1970s followed a symmetric stable Paretian distribution with characteristic exponent in the interval 1 < oc <2, more precisely close to 1.4. Therefore, the Kolmogorov-Smirnov statistic8 to test the hypothesis that the distributions are indeed stable Paretian was applied to each one of the 14 currencies over the entire period of analysis: 1 July 1974 through 29 July For the theoretical distribution the authors used the Fama and Roll [7] tables for standardized symmetric stable distributions for 12 different values of oc in the interval 1 < oc <2. The Kolmogorov-Smirnov test9 was performed for the 12 values of the characteristic exponents previously selected. The values of the test statistic for c = 1.0, o= 1.5, and oc =2.0 are presented in Table 5. The evidence seems to suggest again that the behavior of the foreign exchange rate changes varies between currencies. The results for the currencies in Groups I and II lend support to previous findings that the returns distributions are stable Paretian with characteristic exponent 1 < c <2; the hypothesis that oc = 1.5 could not be rejected at the 5 percent level for any of these currencies, while the hypotheses that oc = 1.0 and oc = 2.0 were rejected in most cases at 5 percent significance level. As the table shows, however, the currencies in Group III differ significantly in their distributions of the foreign exchange rate changes. Using the Kolmogorov-Smirnov test, the authors rejected the null hypothesis for the currencies in Group III at the 1 percent significance level and concluded that these returns distributions are not symmetric stable Paretian. Based on the fourth moment (available upon request), as reported in other studies, the distributions of the currencies in Group III have exhibited a high degree of leptokurtosis, substantially greater than the stable Paretian distributions, while showing also a high.degree of asymmetry. Perhaps these distributions could still be stable Paretian but of the asymmetric family. Testing this hypothesis, however, would require the theoretical development of the parameters TABLE 5 Kolmogorov-Smirnov Statistic: DI max Hypotheses Ho: a = 1 (Cauchy) Ho: a = 1.5 Ho: a =2 (Normal) Group Currency Hi: a 1 Hi: a 1.5 Hi: ac2 Austrian Schilling 4.99* * Belgian Franc * Canadian Dollar 4.96* Danish Krone 5.36* * Netherlands Guilder 5.16* * Norwegian Krone Deutsche Mark 5.57* * II French Franc 5.99** ** Swedish Krona 4.89* * Australian Dollar 17.42** 17.46** 17.40** Italian Lira 16.95** 16.97** 16.91** III Japanese Yen 8.61* 8.63** 8.58** Pound Sterling 11.83** 11.86* * 11.85** Spanish Peseta 16.29** 16.09* * 16.0** *Significant at 5%. *Significant at 1%. Journal of International Business Studies, Fall

10 of those distributions that are not yet available. Nevertheless, the differences between the probability distributions reported here provide evidence regarding the different behavior of foreign exchange rates under different foreign exchange policies and underlying economic forces. CONCLUSIONS The analysis of the empirical probability distribution of fourteen daily foreign exchange rate changes during the flexible exchange rate period leads to two major generalizations: (1) there is no unique distribution that represents the behavior of the foreign exchange rate of major currencies; and (2) the evidence seems to suggest that the behavior of foreign exchange rates is strongly determined by both the foreign exchange rate management policies pursued by the monetary authorities of the respective countries and the underlying economic forces determining foreign exchange rates. In this study, 14 major currencies could be classified under two major broad groups representing two basic distinct foreign exchange rate management policies. The first major group (I and II) is characterized by symmetric distributions, nonstationarity of the mean, almost stationary sample variance, and most likely following a symmetric stable Paretian model with a characteristic exponent close to oc = 1.5. The second major group (III) is characterized, however, by almost stationary asymmetric distributions, and following other than a symmetric stable Paretian distribution. During the sample period most countries of currencies in the first major group (I and II) were following a foreign exchange rate policy designed to restrict exchange rate variability to predetermined limits-that is, the "European Snake" agreement. On the other hand, countries of currencies in the second major group (III) were attempting to restrain further drifts of the foreign exchange rate while facing substantial economic pressures to adjust toward equilibrium rates. In analyzing covered interest arbitrage Frenkel and Levich [9] suggest classifying periods by the degree of turbulence rather than by the legal arrangement of the exchange rate regime. Although the analysis of the behavior of foreign exchange rate changes discussed in this paper is made under the same legal arrangement of the exchange rate regime, the results show-similarly to the Frenkel and Levich study-a different behavior between groups of currencies that were subject to a different "degree of turbulence." This turbulence has been associated here with the underlying economic forces determining foreign exchange rates and the governments' policies for its management. In addition to these differences between currencies, some variations of these factors were also evident within the period or subperiods analyzed for each currency. The apparent differences between the probability distribution of foreign exchange rate changes reported here seem to suggest also that unless some compensatory factors modifying the structure of foreign exchange distributions are present, some degree of segmentation may exist in foreign exchange markets. The differences in the groups of currencies would imply a characterization between segments of the foreign exchange market. Nevertheless, to study this segmentation hypothesis further, an acceptable theory of international markets integration needs to be developed. From the investor's point of view, the currencies of interest need to be examined in light of the foreign exchange rate management policies pursued by the respective monetary authorities relative to the underlying economic forces. Under the flexible exchange rate assumption, this is an additional dimension to the foreign exchange risk. Monetary authorities might resort to different foreign exchange rate policies which could modify the behavior of foreign exchange rates. Disregarding this new element of risk, usually neglected in the empirical literature, in- 108 Journal of International Business Studies, Fall 1982

11 vestors would need to assess their strategies in dealing with currencies under the two major groups. The evidence seems to indicate that currencies in the first major Group (I and II) within boundaries are allowed to follow floating rates. These rates, however, do not follow a stationary process. Therefore, for an investor participating in these markets, it may be a fair, but extremely risky, game. Although the sample variance is stationary, this is irrelevant if the distribution follows a symmetric stable model with a characteristic exponent around a= 1.5 that does not have a defined variance. In addition, the location of the distribution is subject to continuous shifts. Under these circumstances, any forecasts and actual rates would coincide only by chance. On the other hand, investing in currencies in the second major group (III), with the skewness of their distribution, would be similar to entering in a biased game. Although theoretical arguments could be advanced to further discuss biases of skewed distributions, empirical research would be necessary to recommend particular investment strategies. Nevertheless, it is expected that investors would decide whether or not to engage in these markets depending upon the risk aversion of the investor and the nature of the asymmetry of the distribution. If other factors held constant (for example: international interest rates), currencies with negative means and negative asymmetry would be avoided, except by risk-lovers, while currencies with positive means and positive asymmetry would be preferred. In this case, the tendency of these currencies seems to be more amenable to a forecasting exercise. Besides the behavior of foreign exchange rates, however, the analysis of investment opportunities needs to take into account other factors which have been omitted here. The pay-off of the investment, the value judgment, horizon period, portfolio, and consumption preferences, and the time value of money or foreign exchange are some additional factors that would have to be taken into account in assessing investment opportunities of foreign exchange markets. The actual behavior of the foreign exchange market, in general, has eluded the ideal theoretical assumptions undertaken in the literature. The fact that the International Monetary System was fragmented after the collapse of the Bretton Woods system and the breakdown of the Smithsonian Agreement has not been fully explored in the empirical literature. Different policies for managing the foreign exchange rate bounded by the underlying economic forces appear to result in different probability distributions of foreign exchange rates. Serious doubts are raised, therefore, regarding empirical studies developed under the assumption of the traditional normal distributions of foreign exchange rate changes. Mean-variance models might have led to misleading results. In future research, the simple extension of stock market analysis to the behavior of foreign exchange markets needs to be justified and analyzed to account for the major factors that intervene in the international arena. Thus, because the current behavior of foreign exchange markets remains elusive, further work is called for on foreign exchange rate determination models that will enhance our understanding of international financial markets. 1. A data file of about 800 daily exchange rates was developed for each of 14 currencies re- FOOTNOTES ported in the International Financial Statistics, published by the International Monetary Fund. These daily exchange rates are the market rates of the respective countries. The South African Rand was excluded because its behavior is a de facto adjustable fixed exchange rate. 2. The discrete formulation imparts a small upward bias to the percentage change calculation; for example, if an exchange rate moves from 1.00 to 1.01 and back to 1.00 in two days, the average change, is 0.0 percent when the calculation is based on the logarithm of exchange rate relatives. The average daily change is percent when the calculation is based on discrete exchange rate changes. This difference is insignificant. Furthermore, most of our exchange rate movements are less than 1.0 percent. For $(ri,t), the U.S. investor Journal of International Business Studies, Fall

12 can purchase one money unit of currency i on day t. On day (t + 1) he can convert back and get $(ri,t+ 1). Thus this rate of return for the day in xi as defined earlier. 3. Roll [18], p The concepts of stationarity and stability have to be distinguished with respect to the stable Paretian distributions. Stationarity implies no changes in any of the parameters of the distribution, while stability is specifically related to no changes in the characteristic exponent of the stable Paretian distribution. 5. Nelson [15], p When dealing with two or more empirical distributions, the Mann-Whitney test is the most appropriate [Siegel 19, p. 136]. The test is based on the U statistic which is determined by the number of cases, ni and n2, of each sample and the sum of the ranks, R1 and R2, of each sample. The sampling distribution of U approaches the normal distribution. For more on this test see Conover [4] or Siegel [19]. 7. A direct test of the mean will be to use the Mann-Whitney Test assuming that any difference between the distribution functions is a difference in the location of the distribution. [See Conover 4, page 225.] However, this direct approach is based on an assumption that has to be proved; therefore, to find further evidence of the shifts in the mean the authors developed the tests for the transformed variable, yi. 8. The Kolmogorov-Smirnov test is one of the most powerful goodness-of-fit tests when an empirical distribution is compared with an hypothesized theoretical distribution. Contrary to the chi-square test, the Kolmogorov-Smirnov treats individual observations separately, therefore, it does not lose information through the combining of categories. Because of this the Kolmogorov-Smirnov test may be in all cases more powerful than the chi-square test. [See Siegel (19), p. 51]. 9. The tests were performed on the standardized variables xi - ui Uj i- Ci where ui is the mean of the empirical distribution. The results of these tests are reported in Table 5. In addition, we used the standardized variables U= Xi-6i Ci where 6i is the.5 truncated mean, as was suggested by Fama and Roll [7]. Although this approach could be subject to debate, the authors disregard it considering that the results were very close to those reported in Table 5. REFERENCES 1. Artus, J. R., and Young, J. H. "Fixed and Flexible Exchange Rates: A Renewal of the Debate." IMF Staff Papers, December 1979, pp Bergstrom, H. "On Some Expansions of Stable Distributions." Arkiv for Matematik, February 1952, pp Burt, J.; Kaen, F. R.; and Booth, G. G. "Foreign Exchange Market Efficiency Under Flexible Exchange Rates." The Journal of Finance, September 1977, pp Conover, W. J. Practical Nonparametric Statistics. New York: John Wiley & Sons, Inc., Fama, E. F. "Mandelbrot and the Stable Paretian Hypothesis." The Journal of Business, July 1963, pp "The Behavior of Stock-Market Prices." The Journal of Business, January 1965, pp Fama, E. F., and Roll, R. "Some Properties of Symmetric Stable Distributions." Journal of the American Statistical Association, September 1968, pp "Parameter Estimates for Symmetric Stable Distributions." Journal of the American Statistical Association, June 1971, pp Frenkel, J. A., and Levich, R. M. "Transactions Costs and Interest Arbitrage: Tranquil Versus Turbulent Periods." Journal of Political Economics, November-December 1977, pp Giddy, I. H., and Dufey, G. "The Random Behavior of Flexible Exchange Rates: Implications for Forecasting." Journal of International Business Studies, Spring 1975, pp Granger, C. W. J., and Morgenstern, O. Predictability of Stock Market Prices. Lexington, MA: D. C. Heath & Co., IMF. International Financial Statistics, Mandelbrot, B. "The Variation of Certain Speculative Prices." Journal of Business, July 1963, pp Journal of International Business Studies, Fall 1982

13 14. Mood, A.; Graybill, F. A.; and Boes, D. Introduction to the Theory of Statistics. 3rd ed. New York: McGraw-Hill Book Co., Nelson, C. R. Applied Time Series Analysis for Managerial Forecasting. San Francisco: Holden-Day, Inc., Kaplansky, I. "A Common error concerning Kurtosis." Journal of the American Statistical Association, June 1945, p Rogalski, R. J., and Vinso, J. D. "Empirical Properties of Foreign Exchange Rates." Journal of International Business Studies, Fall 1978, pp Roll, R. The Behavior of Interest Rates. New York: Basic Books, Inc., Siegel, S. Nonparametric Statistics for the Behavioral Sciences. New York: McGraw-Hill Book Co., Westerfield, J. M. "An Examination of Foreign Exchange Risk Under Fixed and Floating Rate Regimes." Journal of International Economics, May 1977, pp Journal of International Business Studies, Fall