# Exchange rate systems and investor preferences.

I. INTRODUCTION

Dissatisfaction with the performance in the 1980s of floating exchange rates has lead to renewed interest in a system of target zones for foreign exchange rates or a partial return to fixed exchange rates. Consideration of these proposals raises many of the same questions about the economic effects of fixed vs. flexible exchange rates that were addressed in the late 1960s and early 1970s. Although there are several issues of interest, both at the macroeconomic level and at the level of the individual investor, in this paper, we focus on only one: Do floating exchange rates increase the riskiness of international investment positions so that investors would prefer the distribution of returns existing under a fixed exchange rate regime?

This question--whether international financial transactions are more risky under floating than under fixed rates--was a major point of controversy in the debate over the adoption of floating exchange rates. (For a review of the arguments see, for example, Friedman [1953] or Halm [1970].) Once again, this issue has arisen. McKinnon [1988, 86] argues:

I hypothesize that a floating exchange

market is socially inefficient because

private foreign exchange traders face

a huge gap in relevant information;

the relative future purchasing powers

of national fiat monies, none of which

has any intrinsic value, are highly uncertain.

Thus, the assessments of

international investors of whether

dollar, or yen, or mark assets provide

the best combination of yield and

safety are unnecessarily volatile.

We might suppose, then, that this excess volatility will reduce international investment activity relative to what a fixed rate regime would encourage.

McKinnon is by no means alone in the belief that floating exchange rates add an undesirable level of risk to international investment positions (see Edison and Melvin [1990] for a review of this literature); however, there has been little empirical work done on whether the move to floating rates did, in fact, add an undesirable level of risk. Our study is intended to shed light on this issue. Specifically, we ask: Which group of risk averse investors prefers the distribution of returns under a fixed exchange rate regime and which prefers the distribution of returns under a floating exchange rate regime?

We begin by using a stochastic dominance approach to investigate exchange rate risk for twelve countries from the viewpoint of an investor holding currencies. Both U.S. and non-U.S. investors are considered, and we explore the risk-taking characteristics of those investors who would prefer one regime to another. We find that the fixed rate regime should be overwhelmingly preferred by all risk averse investors holding currencies.

Next, we consider the uncovered returns on foreign stocks. Again, we consider both the U.S. and non-U.S. investor. We find that the floating rate regime should be preferred by all risk averse investors. This finding for uncovered stock portfolios indicates that floating rates have not created a level of risk that investors consider excessive.

Before proceeding, we should address the problem of comparing two alternative exchange rate systems over two different time periods. The greater variability of flexible exchange rates in the 1970s and 1980s, compared to the earlier pegged rates is not entirely attributable to the change in the nominal exchange rate regime. The 1970s and 1980s were characterized by more frequent and more serious real shocks to the global economy than was true of the 1950s and 1960s. Because of this difference, we cannot assert, based on a retrospective view of real returns to investors under alternative exchange rate systems, that investors would generally prefer one exchange rate regime to another. At most, we can make inferences regarding which of the past periods investors should have preferred. Would they have preferred the distribution of returns that was available until 1971, or the distribution that was available during the late 1970s and 1980s? This is still a relevant test, as the case for more stable exchange rates is often made by referring to these two periods.

Recognizing that real shocks to the economy will affect the real returns to investors independent of the nominal exchange rate system, there is still persuasive evidence that the nominal exchange rate system itself has a significant effect on real exchange rate variability. Stockman [1983] examined thirty-eight countries, including some that had floating exchange rates prior to 1973 or pegged exchange rates after 1973, to try to separate the effects of the nominal exchange rate system from the effects of greater variability of exogenous shocks. He found that countries pegging their nominal exchange rates to the U.S. dollar after 1973, on average experienced an increase in real exchange rate variability that was less than half of that experienced by countries with floating currencies.

Mussa [1986] offers evidence supporting Stockman's. After examining real exchange rate performance over many countries and time periods, Mussa concludes:

It should be emphasized that this

study does indicate that the choice of

a nominal exchange rate regime has

important economic consequences.

Real exchange rates do exhibit substantially

and systematically different

behavior under different nominal exchange

rate regimes. [p. 202]

These studies simply confirm what many economists already believed. Mussa reviews the typical argument used to explain the difference in real exchange rate variability between floating and fixed exchange rates--slow adjustment of nominal goods prices relative to nominal exchange rates. Under floating rates, the nominal exchange rate adjusts instantaneously to new information while goods prices may adjust more slowly. As a result, the real exchange rate is more variable under a floating than under a pegged exchange rate regime. While alternative stories may be told to explain the higher volatility of real exchange rates under floating, the research to date indicates that the nominal exchange rate regime matters. If it does, we would expect investors to have preferences regarding fixed or floating exchange rates. The simple fact that real exchange rates are more variable under a float does not necessarily imply that risk averse investors would prefer fixed exchange rates. We now turn to an examination of the distribution of returns under fixed and floating exchange rates.

II. DESCRIPTIVE STATISTICS OF RETURN DISTRIBUTIONS

We use the same method to evaluate the distribution of returns under fixed and floating rates for both samples: the pure foreign exchange returns and the realized returns on foreign stock investments. We first calculate four descriptive statistics of the returns: the mean, standard deviation, skewness, and kurtosis. The distributions are evaluated for both U.S. and foreign investors, but only the U.S. distributions are reported here in order to save space. As will be seen below, there is considerable evidence of the non-normality of the returns. Furthermore, it is obvious that there are no truly fixed exchange rates in our sample. The fixed rate period was characterized by a greater probability of large but infrequent exchange rate changes, while the floating rate period was characterized by many small changes.

Pure Foreign Exchange Returns

If [S.sub.i,t] is the spot exchange rate of U.S. dollars per unit of foreign currency i at the end of the month, and [[pi].sub.t] is the U.S. inflation rate, then the percentage change in the exchange rate per month in real dollar terms is

(1) [[??].sub.i,t] = ([S.sub.i,t]-[S.sub.it-1]/[S.sub.i,t-1]-[[pi].sub.t].

The exchange rate and inflation data are taken from the International Monetary Fund's International Financial Statistics data tape. The fixed rate period is defined as the period from January 1961 (the earliest month stock price data are available) to March 1971. The stochastic dominance program used below requires that an equal number of observations be used for each period, so the floating period data run from October 1978 to December 1988 (the most recent period available for all stock prices used). Our sample includes the exchange rates of twelve countries: Austria, Belgium, France, Germany, Italy, Japan, the Netherlands, Norway, South Africa, Spain, Switzerland and the United Kingdom. Table I gives estimates of the mean, standard deviation, skewness, and kurtosis for the monthly exchange rate changes from the U.S. investor's perspective. The last row of Table I includes statistics for an equally weighted portfolio of all the currencies in the table.

Table I suggests that the distributions changed considerably between the pegged and floating rate periods. With the exception of Japan, the mean of the distribution is higher for the fixed period and the standard deviation is higher for the float. Based on mean and variance alone, we expect U.S. investors to have a strong preference for the distribution of returns experienced under the fixed exchange rate regime.

Table I also illustrates the non-normality of the distribution of exchange rate changes. The kurtosis statistic for a normal distribution is expected to have a value of zero. We find that kurtosis is much greater than that under fixed exchange rates, suggesting a distribution more peaked than normal; the kurtosis statistics for the floating period are positive, but much lower. Furthermore, the skewness statistic indicates that the fixed rate period distributions are also more skewed than those for the floating rate period. In summary, our evidence supports the intuitive conclusion that the fixed rate period was characterized by a greater probability of large exchange rate changes, while the floating rate period was characterized by many small changes. Since exchange rates are never truly fixed, the question is which distributions would investors prefer?

Table I is based on the point of view of U.S. investors holding foreign currency. We do not report descriptive statistics for other countries' investors due to space constraints. However, the evidence is generally similar to that found for U.S. investors.

Returns to Holding Foreign Stocks

The previous section analyzed the distribution of returns to the international investor holding an open position in a foreign currency. While such pure foreign exchange returns are interesting and provide a basis for comparison to earlier studies, they are likely to be misleading. Generally we expect the typical international investor to hold an earning asset in foreign currency. We will now examine the distribution of returns on positions in shares of foreign stock. For instance, the domestic return for a U.S. investor holding country i stock shares is

(2) [[??].sub.it] = [[(1 + [R.sub.i,t])[S.sub.i], t/[S.sub.i,t-1]] - 1 - [[pi].sub.t]

where [R.sub.i,t] is the nominal share price appreciation in month t, in country i.

Stock prices are recorded on a national market index basis by the IMF and are listed on the International Financial Statistics data tape. Stock price data are available for seven of the twelve countries considered in the last section. Table II reports the descriptive statistics for the real returns to U.S. investors holding foreign shares. As before, we examine the individual country returns and the return on an equally weighted portfolio of foreign stocks. In all cases except Japan, the floating exchange rate returns have a higher mean and a higher standard deviation. A U.S. investor holding Japanese shares would have realized a higher standard deviation over the fixed rate period than was realized under floating exchange rates.

Table II is based on the point of view of U.S. investors holding foreign stocks. As with the currency returns, we do not report descriptive statistics for other countries' investors due to space constraints. However, the evidence is generally similar to that for U.S. investors.

III. GENERALIZED STOCHASTIC DOMINANCE METHODOLOGY

In order to provide a ranking of distributions, we use the most flexible of the commonly used stochastic dominance criteria: generalized stochastic dominance (GSD) developed by Meyer [1977a]. GSD is a generalized version of first, second, and third degree stochastic dominance, as well as stochastic dominance with respect to a function. (For discussion and applications, see McCarl [1988], Meyer [1977b], and Raskin and Cochran [1986].)

The GSD approach begins with the assumption that the group of investors under consideration is made up of individuals who are expected utility maximizers and whose preferences can be represented by a von Neumann-Morgenstern utility function, u(x). Groups of investors are defined by placing lower and upper bounds on the Arrow [1971]-Pratt [1964] measure of absolute risk aversion. In particular, let U[[r.sub.1](x),[r.sub.2](x)] be the group of investors whose expected utility functions satisfy

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

for all x. That is, U[[r.sub.1](x),[r.sub.2](x)] is the subset of all investors whose risk preferences are bounded above and below by risk aversion functions [r.sub.1](x) and [r.sub.2](x) respectively. By varying [r.sub.1](x) and [r.sub.2](x) we can vary the group of investors under consideration.

Given a description of a group of investors, we say that the distribution of returns under fixed exchange rates, F(x), stochastically dominates the distribution of returns under floating exchange rates, G(x), if and only if expected utility under F(x) is greater than expected utility under G(x) for all investors in the group. Formally, F(x) stochastically dominates G(x) (G(x) stochastically dominates F(x)) if and only if

(3) [[integral].sup.b.sub.a] [G(x)-F(x)]u'(x)dx [greater than or equal to] ([greater than or equal to] 0)

for all investors in the group U[[r.sub.1](x),[r.sub.2](x)].

The condition stated above requires a consensus by all investors in the group defined by [r.sub.1](x) and [r.sub.2](x)]; however, checking for such a consensus is impossible since there is an infinity of agents with expected utility functions in this group. Fortunately, we can circumvent this problem if we can identify the utility function within the specified interval, denoted by [u.sub.0](x), that is most likely not to prefer F(x) to G(x). If it can be said for this investor that expected utility under F(x) is greater than under G(x), this implies it must be so for all other investors with utility functions in the specified interval.

The GSD theorem proved by Meyer [1977a] gives us a simple way to find [u.sub.0](x) and, thus, to rank the distributions. According to the theorem, the expected utility function that minimizes

[[integral].sup.b.sub.a][G(x)-F(x)]u'(x)dx

must be such that

[r.sub.0](x) = [r.sub.1](x) if

[[integral].sup.b.sub.y][G(x)-F(x)u'(x)dx < 0,

and

[r.sub.0](x) = [r.sub.2](x) if

[[integral].sup.b.sub.y][G(x)-F(x)u'(x)dx [greater than or equal to] 0.

Since [r.sub.0](x) completely represents a given investor's preferences, we can find [u.sub.0'] and check if the expected utility from distribution F(x) is greater than the expected utility from distribution G(x). Thus, we determine whether F(x) stochastically dominates G(x) for all investors in the group U[[r.sub.1](x),[r.sub.2](x)].

In order to implement the GSD theorem, we must (i) estimate F(x) and G(x), and (ii) specify [r.sub.1](x) and [r.sub.2](x) and calculate expected utilities. Since we do not know the functional form underlying the return distributions, we use the data described in section II of this paper to generate "empirical" distributions. These empirical distributions are used to approximate F(x) and G(x). (Since we have no priors as to the nature of the true distribution, statistical tests for goodness of fit do not exist.)

We use the GSD program developed by McCarl [1988] to order the return distributions. Although, in general, the upper and lower bounds on the risk preference interval can be either increasing or decreasing functions of the random variable, for computational ease we assume that they are constants. That is, we assume that

(4) [u.sub.0](x)=[-e.sup.-rx] r > 0 = x r = 0

This particular specification of upper and lower bounds has become standard in the literature dealing with GSD.

Before proceeding to the results, we must have some idea of what values of the risk aversion parameter, r, represent extremely risk averse behavior. One way to illustrate the meaning of specific values of r is to calculate certainty equivalents. Suppose, for example, we consider the certainty equivalent of a risky investment yielding an annual rate of return of 20 percent with probability .5 and a zero rate of return otherwise. Table III reports the certain return required for indifference between the certain payoff and the risky investment for a variety of values of r. For instance, an individual with a risk aversion parameter of unity would be indifferent between the risky opportunity with an expected return of 10 percent and a certain return of 9.5 percent, while an individual with a risk aversion parameter of 10 would be indifferent between the risky opportunity and a certain return of 5.7 percent. Thus, a risky aversion parameter of 10 indicates extremely high risk aversion. In fact, in a survey of the literature dealing with empirical investigations of the Arrow-Pratt measure of absolute risk aversion, Raskin and Cochran [1986] find that most researchers consider a risk aversion parameter between 5 and 10 to indicate strong risk aversion.

IV. EMPIRICAL RESULTS

Table IV displays the second degree stochastic dominance (SSD) rankings for U.S. investors. To save space, we do not report the SSD rankings for non-U.S. investors; however, the results are much the same. In ten of the thirteen cases for the currency returns, fixed exchange rates are preferred, while for Japan, Spain, and the U.K. the ranking is not unanimous. The stock returns all yield ambiguous rankings, except for the Japanese stocks where the distribution of returns under floating exchange rates is preferred. The ambiguous rankings suggest that risk averse investors will not all agree on the preferred exchange rate regime. To explore the nature of this disagreement we must turn to generalized stochastic dominance.

Table V gives the preferences of U.S. investors over different ranges of risk aversion for the pure foreign exchange returns. By varying the degree of risk aversion, we can observe the switch in preference from one regime to another over different classes of investors. For all cases except Japan, from the risk neutral investor through those with a risk aversion parameter of 10, fixed exchange rates are preferred. This indicates that only extremely risk averse investors would prefer floating exchange rates when holding currencies. In the case of Japan, at low levels of risk aversion the float is preferred. For absolute risk aversion greater than three, fixed exchange rates are preferred when holding yen. This is the case where the mean return is higher under the float. Table VI reports the preferences for non-U.S. investors, that is, investors who are holding equally weighted portfolios of twelve foreign currencies (all other currencies in the table plus the U.S. dollar). In most cases, fixed exchange rates are preferred by all risk averse investors. How ever, in three cases the results differ. Italian investors with absolute risk aversion parameters of 8.7 or more prefer floating exchange rates. For investors from the Netherlands, all risk averse investors would prefer the distribution of returns under the float. South African investors prefer floating exchange rates up to a low level of absolute risk aversion (r = 0.5) and then switch their preference to fixed exchange rates.

Two points may be made with regard to the results listed in Tables V and VI. First, investors in different countries will not all agree on the preferred exchange rate regime. Second, investors in a single country may disagree on the preferred exchange rate regime. For example, moderately risk averse U.S. investors holding Japanese yen prefer the distribution of returns associated with floating exchange rates, but those investors exhibiting a greater degree of risk aversion prefer fixed exchange rates.

The rankings for U.S. investors holding foreign stocks are listed in Table VII. Estimating the stochastic dominance rankings over different ranges of risk aversion, we find a preference for floating exchange rates at low to moderate levels of risk aversion for all portfolios and a shift in preference to fixed rates at high levels of risk aversion in five cases. This finding suggests that critics of floating exchange rates may overstate their case when arguing that investors prefer the distribution of returns under fixed exchange rates. As a general statement applying to U.S. investors, this is only true of very risk averse investors holding concentrated portfolios comprised of stocks of either Austria, Germany, Italy, the Netherlands, or Spain. Those holding portfolio diversified across all seven countries prefer a floating regime over the full range of risk aversion considered.

Table VIII explores shifts in preferences over different ranges of risk aversion for non-U.S, investors holding portfolios of stocks of seven countries (the other countries in the table plus the U.S.) Floating exchange rates are preferred over all ranges, except for the U.K. British investors, at a high level of absolute risk aversion (r = 8.8), prefer fixed exchange rates. The results of Table VIII generally indicate that it is simply not accurate to claim that investors prefer the distribution of returns realized under fixed exchange rates.

The real returns to holding foreign shares of stock provide a much different result than did the pure foreign exchange returns. The foreign exchange returns yielded a preference for fixed exchange rates by all risk averse investors for most portfolios and countries. Once the investor is assumed to hold securities denominated in foreign currency, rather than just actual foreign currency, the results change dramatically. Now, floating exchange rates are generally preferred by investors of most countries. When preferences switch as risk aversion changes, fixed exchange rates are preferred by only the most risk averse investors.

The different results for investors with open positions in foreign stocks compared to investors with open positions in currencies reflect the fact that under a floating regime, exchange rate changes typically reduce the variability of stock returns across countries. We expect a greater degree of exchange rate depreciation in a country where nominal returns on stocks or bonds exceed those of other countries. (However, as noted by Adler and Dumas [1983], exchange rate variability tends to be greater than stock price variability, and changes in exchange rates do not offset changes in stock prices completely.)

V. CONCLUSIONS

We now return to the initial question that motivated this study: Did floating exchange rates increase the riskiness of international investment positions so that investors would have preferred the distribution of returns under fixed exchange rates? In our analysis of pure foreign exchange returns, the answer was generally "yes." If we consider only the investor speculating in the foreign exchange markets, we conclude that fixed exchange rates are preferred. While this result is interesting to compare to previous work, there is good reason to doubt its importance. Few investors would hold substantial levels of a non-earning asset like foreign currency.

Considering the more typical investor's behavior of holding open positions in foreign securities, where exchange rate changes serve to reduce the riskiness of investing in different countries, we conclude that floating exchange rates are preferred. Only for high degrees of risk aversion do some investors' preferences switch to fixed rates.

We conclude, then, that floating exchange rates did not increase the riskiness of international investment positions to the point where investors should prefer the distribution of returns under fixed exchange rates. Only investors with a relatively high aversion to risk would prefer fixed to floating exchange rates.

REFERENCES

Adler, Michael and Bernard Dumas. "International Portfolio Choice and Corporation Finance: A Synthesis." Journal of Finance, June 1983, 925-84.

Arrow, K. J. Essays in the Theory of Risk Bearing. Chicago: Markham, 1971.

Edison, Hall J. and Michael Melvin. "The Determinants and Implications of the Choice of an Exchange Rate System," in Monetary Policy in an Era of Change, edited by W. Haraf and T. Willett. Washington: American Enterprise Institute, 1990, 1-44.

Friedman, Milton. "The Case for Flexible Exchange Rates," in Essays in Positive Economics. Chicago: The University of Chicago Press, 1953, 157-203.

Halm, George N. Approaches to Greater Flexibility of Exchange Rates. Princeton: Princeton University Press, 1970.

McCarl, Bruce. "Generalized Stochastic Dominance: An Empirical Examination." Unpublished paper, Department of Agricultural Economics, Texas A & M University, 1988.

McKinnon, Ronald I. "Monetary and Exchange Rate Policies for International Financial Stability: A Proposal." The Journal of Economic Perspectives, Winter 1988, 83-104.

Meyer, Jack. "Choice Among Distributions." Journal of Economic Theory, April 1977a, 326-36.

--."Further Applications of Stochastic Dominance to Mutual Fund Performance." Journal of Financial and Quantitative Analysis, June 1977b, 235-42.

Mussa, Michael. "Nominal Exchange Rate Regimes and the Behavior of Real Exchange Rates: Evidence and Implications," in Real Business Cycles, Real Exchange Rates, and Actual Policies, edited by K. Brunner and A. H. Meltzer. Carnegie-Rochester Conference Series on Public Policy, vol. 25, 1986.

Pratt, J. "Risk Aversion in the Small and in the Large." Econometrica, January/April 1964, 122-36.

Raskin, R. and M. Cochran. "Interpretations and Transformations of Scale for the Pratt-Arrow Absolute Risk Aversion Coefficient: Implications for Generalized Stochastic Dominance." Western Journal of Agricultural Economics, December 1986, 204-10.

Stockman, Alan C. "Real Exchange Rates Under Alternative Nominal Exchange Rate Systems." Journal of International Money and Finance, August 1983, 147-66.

MICHAEL MELVIN and MICHAEL B. ORMISTON *

* Department of Economics, Arizona State University. We are grateful to Richard Sweeney and two anonymous referees for their comments and suggestions. Ali Kutan provided helpful research assistance.

Dissatisfaction with the performance in the 1980s of floating exchange rates has lead to renewed interest in a system of target zones for foreign exchange rates or a partial return to fixed exchange rates. Consideration of these proposals raises many of the same questions about the economic effects of fixed vs. flexible exchange rates that were addressed in the late 1960s and early 1970s. Although there are several issues of interest, both at the macroeconomic level and at the level of the individual investor, in this paper, we focus on only one: Do floating exchange rates increase the riskiness of international investment positions so that investors would prefer the distribution of returns existing under a fixed exchange rate regime?

This question--whether international financial transactions are more risky under floating than under fixed rates--was a major point of controversy in the debate over the adoption of floating exchange rates. (For a review of the arguments see, for example, Friedman [1953] or Halm [1970].) Once again, this issue has arisen. McKinnon [1988, 86] argues:

I hypothesize that a floating exchange

market is socially inefficient because

private foreign exchange traders face

a huge gap in relevant information;

the relative future purchasing powers

of national fiat monies, none of which

has any intrinsic value, are highly uncertain.

Thus, the assessments of

international investors of whether

dollar, or yen, or mark assets provide

the best combination of yield and

safety are unnecessarily volatile.

We might suppose, then, that this excess volatility will reduce international investment activity relative to what a fixed rate regime would encourage.

McKinnon is by no means alone in the belief that floating exchange rates add an undesirable level of risk to international investment positions (see Edison and Melvin [1990] for a review of this literature); however, there has been little empirical work done on whether the move to floating rates did, in fact, add an undesirable level of risk. Our study is intended to shed light on this issue. Specifically, we ask: Which group of risk averse investors prefers the distribution of returns under a fixed exchange rate regime and which prefers the distribution of returns under a floating exchange rate regime?

We begin by using a stochastic dominance approach to investigate exchange rate risk for twelve countries from the viewpoint of an investor holding currencies. Both U.S. and non-U.S. investors are considered, and we explore the risk-taking characteristics of those investors who would prefer one regime to another. We find that the fixed rate regime should be overwhelmingly preferred by all risk averse investors holding currencies.

Next, we consider the uncovered returns on foreign stocks. Again, we consider both the U.S. and non-U.S. investor. We find that the floating rate regime should be preferred by all risk averse investors. This finding for uncovered stock portfolios indicates that floating rates have not created a level of risk that investors consider excessive.

Before proceeding, we should address the problem of comparing two alternative exchange rate systems over two different time periods. The greater variability of flexible exchange rates in the 1970s and 1980s, compared to the earlier pegged rates is not entirely attributable to the change in the nominal exchange rate regime. The 1970s and 1980s were characterized by more frequent and more serious real shocks to the global economy than was true of the 1950s and 1960s. Because of this difference, we cannot assert, based on a retrospective view of real returns to investors under alternative exchange rate systems, that investors would generally prefer one exchange rate regime to another. At most, we can make inferences regarding which of the past periods investors should have preferred. Would they have preferred the distribution of returns that was available until 1971, or the distribution that was available during the late 1970s and 1980s? This is still a relevant test, as the case for more stable exchange rates is often made by referring to these two periods.

Recognizing that real shocks to the economy will affect the real returns to investors independent of the nominal exchange rate system, there is still persuasive evidence that the nominal exchange rate system itself has a significant effect on real exchange rate variability. Stockman [1983] examined thirty-eight countries, including some that had floating exchange rates prior to 1973 or pegged exchange rates after 1973, to try to separate the effects of the nominal exchange rate system from the effects of greater variability of exogenous shocks. He found that countries pegging their nominal exchange rates to the U.S. dollar after 1973, on average experienced an increase in real exchange rate variability that was less than half of that experienced by countries with floating currencies.

Mussa [1986] offers evidence supporting Stockman's. After examining real exchange rate performance over many countries and time periods, Mussa concludes:

It should be emphasized that this

study does indicate that the choice of

a nominal exchange rate regime has

important economic consequences.

Real exchange rates do exhibit substantially

and systematically different

behavior under different nominal exchange

rate regimes. [p. 202]

These studies simply confirm what many economists already believed. Mussa reviews the typical argument used to explain the difference in real exchange rate variability between floating and fixed exchange rates--slow adjustment of nominal goods prices relative to nominal exchange rates. Under floating rates, the nominal exchange rate adjusts instantaneously to new information while goods prices may adjust more slowly. As a result, the real exchange rate is more variable under a floating than under a pegged exchange rate regime. While alternative stories may be told to explain the higher volatility of real exchange rates under floating, the research to date indicates that the nominal exchange rate regime matters. If it does, we would expect investors to have preferences regarding fixed or floating exchange rates. The simple fact that real exchange rates are more variable under a float does not necessarily imply that risk averse investors would prefer fixed exchange rates. We now turn to an examination of the distribution of returns under fixed and floating exchange rates.

II. DESCRIPTIVE STATISTICS OF RETURN DISTRIBUTIONS

We use the same method to evaluate the distribution of returns under fixed and floating rates for both samples: the pure foreign exchange returns and the realized returns on foreign stock investments. We first calculate four descriptive statistics of the returns: the mean, standard deviation, skewness, and kurtosis. The distributions are evaluated for both U.S. and foreign investors, but only the U.S. distributions are reported here in order to save space. As will be seen below, there is considerable evidence of the non-normality of the returns. Furthermore, it is obvious that there are no truly fixed exchange rates in our sample. The fixed rate period was characterized by a greater probability of large but infrequent exchange rate changes, while the floating rate period was characterized by many small changes.

Pure Foreign Exchange Returns

If [S.sub.i,t] is the spot exchange rate of U.S. dollars per unit of foreign currency i at the end of the month, and [[pi].sub.t] is the U.S. inflation rate, then the percentage change in the exchange rate per month in real dollar terms is

(1) [[??].sub.i,t] = ([S.sub.i,t]-[S.sub.it-1]/[S.sub.i,t-1]-[[pi].sub.t].

The exchange rate and inflation data are taken from the International Monetary Fund's International Financial Statistics data tape. The fixed rate period is defined as the period from January 1961 (the earliest month stock price data are available) to March 1971. The stochastic dominance program used below requires that an equal number of observations be used for each period, so the floating period data run from October 1978 to December 1988 (the most recent period available for all stock prices used). Our sample includes the exchange rates of twelve countries: Austria, Belgium, France, Germany, Italy, Japan, the Netherlands, Norway, South Africa, Spain, Switzerland and the United Kingdom. Table I gives estimates of the mean, standard deviation, skewness, and kurtosis for the monthly exchange rate changes from the U.S. investor's perspective. The last row of Table I includes statistics for an equally weighted portfolio of all the currencies in the table.

TABLE I Descriptive Statistics--Exchange Rate Changes for U.S. Investors (Fix [1/61-3/71] Listed First, Float [10/78-12/88] Listed Second) Country Mean Sta-Dev. Skewness Kurtosis Austria -.002561 .0087 -3.0071 7.9495 -.003097 .0374 .1704 .2966 Belgium -.002584 .0091 -2.8977 7.2459 -.005655 .0383 .3530 .5888 France -.003540 .0127 -4.9596 31.7510 -.006873 .0362 .1804 .6074 Germany -.001450 .0120 -.3031 6.9023 -.003353 .0376 .3808 .3381 Italy -.002621 .0087 -2.9765 7.6193 -.008077 .0322 .2398 .1761 Japan -.002602 .0091 -2.8838 7.1111 -.000642 .0380 .4293 .0761 Netherlands -.002190 .0105 -.4802 11.6142 .003648 .0378 .1221 1.8648 Norway -.002606 .0088 -2.7686 6.9570 -.006380 .0306 .4396 .5262 S. Africa -.002577 .0091 -3.1065 8.0345 -.011723 .0477 -.2741 5.1863 Spain -.003744 .0151 -6.5132 53.2251 -.008156 .0308 .4822 .4900 Switzerland -.002588 .0094 -2.7601 6.9886 -.003601 .0416 .2600 .8192 U.K. -.003764 .0146 -6.0105 46.7177 -.004834 .0361 .7190 1.5765 All 12 -.002735 .0091 -2.8676 6.8735 Currencies -.005503 .0322 .3751 .1191 Note: Only for South Africa and the 12 currency portfolio is the difference between the means for fixed and floating rates statistically significant at the 5% level. All of the differences between the standard deviations are statistically significant at the 5% level.

Table I suggests that the distributions changed considerably between the pegged and floating rate periods. With the exception of Japan, the mean of the distribution is higher for the fixed period and the standard deviation is higher for the float. Based on mean and variance alone, we expect U.S. investors to have a strong preference for the distribution of returns experienced under the fixed exchange rate regime.

Table I also illustrates the non-normality of the distribution of exchange rate changes. The kurtosis statistic for a normal distribution is expected to have a value of zero. We find that kurtosis is much greater than that under fixed exchange rates, suggesting a distribution more peaked than normal; the kurtosis statistics for the floating period are positive, but much lower. Furthermore, the skewness statistic indicates that the fixed rate period distributions are also more skewed than those for the floating rate period. In summary, our evidence supports the intuitive conclusion that the fixed rate period was characterized by a greater probability of large exchange rate changes, while the floating rate period was characterized by many small changes. Since exchange rates are never truly fixed, the question is which distributions would investors prefer?

Table I is based on the point of view of U.S. investors holding foreign currency. We do not report descriptive statistics for other countries' investors due to space constraints. However, the evidence is generally similar to that found for U.S. investors.

Returns to Holding Foreign Stocks

The previous section analyzed the distribution of returns to the international investor holding an open position in a foreign currency. While such pure foreign exchange returns are interesting and provide a basis for comparison to earlier studies, they are likely to be misleading. Generally we expect the typical international investor to hold an earning asset in foreign currency. We will now examine the distribution of returns on positions in shares of foreign stock. For instance, the domestic return for a U.S. investor holding country i stock shares is

(2) [[??].sub.it] = [[(1 + [R.sub.i,t])[S.sub.i], t/[S.sub.i,t-1]] - 1 - [[pi].sub.t]

where [R.sub.i,t] is the nominal share price appreciation in month t, in country i.

Stock prices are recorded on a national market index basis by the IMF and are listed on the International Financial Statistics data tape. Stock price data are available for seven of the twelve countries considered in the last section. Table II reports the descriptive statistics for the real returns to U.S. investors holding foreign shares. As before, we examine the individual country returns and the return on an equally weighted portfolio of foreign stocks. In all cases except Japan, the floating exchange rate returns have a higher mean and a higher standard deviation. A U.S. investor holding Japanese shares would have realized a higher standard deviation over the fixed rate period than was realized under floating exchange rates.

TABLE II Descriptive Statistics--Share Price Changes for U.S. Investors (Fix [1/61-3/71] Listed First, Float [10/78-12/88] Listed Second) Country Mean Sta-Dev. Skewness Kurtosis Austria -.000563 .0484 4.4471 35.0154 -.003792 .0606 1.2266 2.8922 Germany -.001234 .0490 .6271 2.0195 .003121 .0573 -.0908 1.0586 Italy -.005917 .0460 .4337 .6576 .011067 .0783 .1524 .9311 Japan .003371 .0701 -.1752 4.0187 .013964 .0565 .2558 -.3075 Netherlands -.001233 .0411 -.1732 .0828 .005477 .0543 -.1794 .9290 Spain .005517 .0353 -.7916 -.7916 .00823 .0789 .1946 1.5492 U.K. -.000308 .0461 -.497 .5838 .007438 .0544 .1368 1.1331 All 7 -.000005 .0261 -.1515 1.0090 Stocks .007581 .0451 .1700 .8690 Note: Only for Italy is the difference between the means statistically significant at the 5% level. All of the differences between the standard deviations are statistically significant at the 5% level.

Table II is based on the point of view of U.S. investors holding foreign stocks. As with the currency returns, we do not report descriptive statistics for other countries' investors due to space constraints. However, the evidence is generally similar to that for U.S. investors.

III. GENERALIZED STOCHASTIC DOMINANCE METHODOLOGY

In order to provide a ranking of distributions, we use the most flexible of the commonly used stochastic dominance criteria: generalized stochastic dominance (GSD) developed by Meyer [1977a]. GSD is a generalized version of first, second, and third degree stochastic dominance, as well as stochastic dominance with respect to a function. (For discussion and applications, see McCarl [1988], Meyer [1977b], and Raskin and Cochran [1986].)

The GSD approach begins with the assumption that the group of investors under consideration is made up of individuals who are expected utility maximizers and whose preferences can be represented by a von Neumann-Morgenstern utility function, u(x). Groups of investors are defined by placing lower and upper bounds on the Arrow [1971]-Pratt [1964] measure of absolute risk aversion. In particular, let U[[r.sub.1](x),[r.sub.2](x)] be the group of investors whose expected utility functions satisfy

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

for all x. That is, U[[r.sub.1](x),[r.sub.2](x)] is the subset of all investors whose risk preferences are bounded above and below by risk aversion functions [r.sub.1](x) and [r.sub.2](x) respectively. By varying [r.sub.1](x) and [r.sub.2](x) we can vary the group of investors under consideration.

Given a description of a group of investors, we say that the distribution of returns under fixed exchange rates, F(x), stochastically dominates the distribution of returns under floating exchange rates, G(x), if and only if expected utility under F(x) is greater than expected utility under G(x) for all investors in the group. Formally, F(x) stochastically dominates G(x) (G(x) stochastically dominates F(x)) if and only if

(3) [[integral].sup.b.sub.a] [G(x)-F(x)]u'(x)dx [greater than or equal to] ([greater than or equal to] 0)

for all investors in the group U[[r.sub.1](x),[r.sub.2](x)].

The condition stated above requires a consensus by all investors in the group defined by [r.sub.1](x) and [r.sub.2](x)]; however, checking for such a consensus is impossible since there is an infinity of agents with expected utility functions in this group. Fortunately, we can circumvent this problem if we can identify the utility function within the specified interval, denoted by [u.sub.0](x), that is most likely not to prefer F(x) to G(x). If it can be said for this investor that expected utility under F(x) is greater than under G(x), this implies it must be so for all other investors with utility functions in the specified interval.

The GSD theorem proved by Meyer [1977a] gives us a simple way to find [u.sub.0](x) and, thus, to rank the distributions. According to the theorem, the expected utility function that minimizes

[[integral].sup.b.sub.a][G(x)-F(x)]u'(x)dx

must be such that

[r.sub.0](x) = [r.sub.1](x) if

[[integral].sup.b.sub.y][G(x)-F(x)u'(x)dx < 0,

and

[r.sub.0](x) = [r.sub.2](x) if

[[integral].sup.b.sub.y][G(x)-F(x)u'(x)dx [greater than or equal to] 0.

Since [r.sub.0](x) completely represents a given investor's preferences, we can find [u.sub.0'] and check if the expected utility from distribution F(x) is greater than the expected utility from distribution G(x). Thus, we determine whether F(x) stochastically dominates G(x) for all investors in the group U[[r.sub.1](x),[r.sub.2](x)].

In order to implement the GSD theorem, we must (i) estimate F(x) and G(x), and (ii) specify [r.sub.1](x) and [r.sub.2](x) and calculate expected utilities. Since we do not know the functional form underlying the return distributions, we use the data described in section II of this paper to generate "empirical" distributions. These empirical distributions are used to approximate F(x) and G(x). (Since we have no priors as to the nature of the true distribution, statistical tests for goodness of fit do not exist.)

We use the GSD program developed by McCarl [1988] to order the return distributions. Although, in general, the upper and lower bounds on the risk preference interval can be either increasing or decreasing functions of the random variable, for computational ease we assume that they are constants. That is, we assume that

(4) [u.sub.0](x)=[-e.sup.-rx] r > 0 = x r = 0

This particular specification of upper and lower bounds has become standard in the literature dealing with GSD.

Before proceeding to the results, we must have some idea of what values of the risk aversion parameter, r, represent extremely risk averse behavior. One way to illustrate the meaning of specific values of r is to calculate certainty equivalents. Suppose, for example, we consider the certainty equivalent of a risky investment yielding an annual rate of return of 20 percent with probability .5 and a zero rate of return otherwise. Table III reports the certain return required for indifference between the certain payoff and the risky investment for a variety of values of r. For instance, an individual with a risk aversion parameter of unity would be indifferent between the risky opportunity with an expected return of 10 percent and a certain return of 9.5 percent, while an individual with a risk aversion parameter of 10 would be indifferent between the risky opportunity and a certain return of 5.7 percent. Thus, a risky aversion parameter of 10 indicates extremely high risk aversion. In fact, in a survey of the literature dealing with empirical investigations of the Arrow-Pratt measure of absolute risk aversion, Raskin and Cochran [1986] find that most researchers consider a risk aversion parameter between 5 and 10 to indicate strong risk aversion.

TABLE III Certainty Equivalent of a Risky Opportunity With an Expected Return of 10% r Certainty Equivalents (%) 1 9.5 5 7.6 10 5.7

IV. EMPIRICAL RESULTS

Table IV displays the second degree stochastic dominance (SSD) rankings for U.S. investors. To save space, we do not report the SSD rankings for non-U.S. investors; however, the results are much the same. In ten of the thirteen cases for the currency returns, fixed exchange rates are preferred, while for Japan, Spain, and the U.K. the ranking is not unanimous. The stock returns all yield ambiguous rankings, except for the Japanese stocks where the distribution of returns under floating exchange rates is preferred. The ambiguous rankings suggest that risk averse investors will not all agree on the preferred exchange rate regime. To explore the nature of this disagreement we must turn to generalized stochastic dominance.

TABLE IV Preferences for Fixed versus Floating Exchange Rates Based on Second Degree Stochastic Dominance for U.S. Investors Currency or Stocks of: Currency Stocks Austria Fix * Belgium Fix NA France Fix NA Germany Fix * Italy Fix * Japan * Float Netherlands Fix * Norway Fix NA S. Africa Fix NA Spain * * Switzerland Fix NA U.K. * * All 12 Currencies Fix NA All 7 Stocks NA * * denotes ambiguous choice NA denotes not applicable

Table V gives the preferences of U.S. investors over different ranges of risk aversion for the pure foreign exchange returns. By varying the degree of risk aversion, we can observe the switch in preference from one regime to another over different classes of investors. For all cases except Japan, from the risk neutral investor through those with a risk aversion parameter of 10, fixed exchange rates are preferred. This indicates that only extremely risk averse investors would prefer floating exchange rates when holding currencies. In the case of Japan, at low levels of risk aversion the float is preferred. For absolute risk aversion greater than three, fixed exchange rates are preferred when holding yen. This is the case where the mean return is higher under the float. Table VI reports the preferences for non-U.S. investors, that is, investors who are holding equally weighted portfolios of twelve foreign currencies (all other currencies in the table plus the U.S. dollar). In most cases, fixed exchange rates are preferred by all risk averse investors. How ever, in three cases the results differ. Italian investors with absolute risk aversion parameters of 8.7 or more prefer floating exchange rates. For investors from the Netherlands, all risk averse investors would prefer the distribution of returns under the float. South African investors prefer floating exchange rates up to a low level of absolute risk aversion (r = 0.5) and then switch their preference to fixed exchange rates.

TABLE V U.S. Investor Preferences as a Function of Absolute Risk Aversion for Currency Portfolios Under Fixed or Floating Exchange Rates Currency of: Range where float is Range where fixed preferred to fixed rates preferred to rates float Austria 0-10 Belgium 0-10 France 0-10 Germany 0-10 Italy 0-10 Japan 0-3.0 3.0-10 Netherlands 0-10 Norway 0-10 S. Africa 0-10 Spain 0-10 Switzerland 0-10 U.K. 0-10 All 12 Currencies 0-10

Two points may be made with regard to the results listed in Tables V and VI. First, investors in different countries will not all agree on the preferred exchange rate regime. Second, investors in a single country may disagree on the preferred exchange rate regime. For example, moderately risk averse U.S. investors holding Japanese yen prefer the distribution of returns associated with floating exchange rates, but those investors exhibiting a greater degree of risk aversion prefer fixed exchange rates.

TABLE VI Non-U.S. Investor Preferences as a Function of Absolute Risk Aversion for Currency Portfolios Under Fixed or Floating Exchange Rates Investor of: Range where float is Range where fixed preferred to fixed rates rates preferred to float Austria 0-10 Belgium 0-10 France 0-10 Germany 0-10 Italy 8.7-10 0-8.7 Japan 0-10 Netherlands 0-10 Norway 0-10 S. Africa 0-0.5 0.5-10 Spain 0-10 Switzerland 0-10 U.K. 0-10 Note: Investors of each country hold an equally weighted portfolio of the currencies of the other countries in the table plus the U.S. dollar.

The rankings for U.S. investors holding foreign stocks are listed in Table VII. Estimating the stochastic dominance rankings over different ranges of risk aversion, we find a preference for floating exchange rates at low to moderate levels of risk aversion for all portfolios and a shift in preference to fixed rates at high levels of risk aversion in five cases. This finding suggests that critics of floating exchange rates may overstate their case when arguing that investors prefer the distribution of returns under fixed exchange rates. As a general statement applying to U.S. investors, this is only true of very risk averse investors holding concentrated portfolios comprised of stocks of either Austria, Germany, Italy, the Netherlands, or Spain. Those holding portfolio diversified across all seven countries prefer a floating regime over the full range of risk aversion considered.

TABLE VII U.S. Investor Preferences as a Function of Absolute Risk Aversion for Stock Portfolios Under Fixed or Floating Exchange Rates Range where float Range where fixed is preferred to rates preferred Stocks of: fixed rates to float Austria 0-5.5 5.5-10 Germany 0-7.7 7.7-10 Italy 0-8.4 8.4-10 Japan 0-10 Netherlands 0-9.8 9.8-10 Spain 0-1.1 1.1-10 U.K. 0-10 All 7 Countries 0-10

Table VIII explores shifts in preferences over different ranges of risk aversion for non-U.S, investors holding portfolios of stocks of seven countries (the other countries in the table plus the U.S.) Floating exchange rates are preferred over all ranges, except for the U.K. British investors, at a high level of absolute risk aversion (r = 8.8), prefer fixed exchange rates. The results of Table VIII generally indicate that it is simply not accurate to claim that investors prefer the distribution of returns realized under fixed exchange rates.

TABLE VIII Non-U.S. Investor Preferences as a Function of Absolute Risk Aversion for Stock Portfolios Under Fixed or Floating Exchange Rates Range where float Range where fixed is preferred to rates preferred Investor of: fixed rates to float Austria 0-10 Germany 0-10 Italy 0-10 Japan 0-10 Netherlands 0-10 Spain 0-10 U.K. 0-8.8 8.8-10 Note: Investors of each country hold an equally weighted portfolio of the stocks of the other countries in the table plus U.S. stocks.

The real returns to holding foreign shares of stock provide a much different result than did the pure foreign exchange returns. The foreign exchange returns yielded a preference for fixed exchange rates by all risk averse investors for most portfolios and countries. Once the investor is assumed to hold securities denominated in foreign currency, rather than just actual foreign currency, the results change dramatically. Now, floating exchange rates are generally preferred by investors of most countries. When preferences switch as risk aversion changes, fixed exchange rates are preferred by only the most risk averse investors.

The different results for investors with open positions in foreign stocks compared to investors with open positions in currencies reflect the fact that under a floating regime, exchange rate changes typically reduce the variability of stock returns across countries. We expect a greater degree of exchange rate depreciation in a country where nominal returns on stocks or bonds exceed those of other countries. (However, as noted by Adler and Dumas [1983], exchange rate variability tends to be greater than stock price variability, and changes in exchange rates do not offset changes in stock prices completely.)

V. CONCLUSIONS

We now return to the initial question that motivated this study: Did floating exchange rates increase the riskiness of international investment positions so that investors would have preferred the distribution of returns under fixed exchange rates? In our analysis of pure foreign exchange returns, the answer was generally "yes." If we consider only the investor speculating in the foreign exchange markets, we conclude that fixed exchange rates are preferred. While this result is interesting to compare to previous work, there is good reason to doubt its importance. Few investors would hold substantial levels of a non-earning asset like foreign currency.

Considering the more typical investor's behavior of holding open positions in foreign securities, where exchange rate changes serve to reduce the riskiness of investing in different countries, we conclude that floating exchange rates are preferred. Only for high degrees of risk aversion do some investors' preferences switch to fixed rates.

We conclude, then, that floating exchange rates did not increase the riskiness of international investment positions to the point where investors should prefer the distribution of returns under fixed exchange rates. Only investors with a relatively high aversion to risk would prefer fixed to floating exchange rates.

REFERENCES

Adler, Michael and Bernard Dumas. "International Portfolio Choice and Corporation Finance: A Synthesis." Journal of Finance, June 1983, 925-84.

Arrow, K. J. Essays in the Theory of Risk Bearing. Chicago: Markham, 1971.

Edison, Hall J. and Michael Melvin. "The Determinants and Implications of the Choice of an Exchange Rate System," in Monetary Policy in an Era of Change, edited by W. Haraf and T. Willett. Washington: American Enterprise Institute, 1990, 1-44.

Friedman, Milton. "The Case for Flexible Exchange Rates," in Essays in Positive Economics. Chicago: The University of Chicago Press, 1953, 157-203.

Halm, George N. Approaches to Greater Flexibility of Exchange Rates. Princeton: Princeton University Press, 1970.

McCarl, Bruce. "Generalized Stochastic Dominance: An Empirical Examination." Unpublished paper, Department of Agricultural Economics, Texas A & M University, 1988.

McKinnon, Ronald I. "Monetary and Exchange Rate Policies for International Financial Stability: A Proposal." The Journal of Economic Perspectives, Winter 1988, 83-104.

Meyer, Jack. "Choice Among Distributions." Journal of Economic Theory, April 1977a, 326-36.

--."Further Applications of Stochastic Dominance to Mutual Fund Performance." Journal of Financial and Quantitative Analysis, June 1977b, 235-42.

Mussa, Michael. "Nominal Exchange Rate Regimes and the Behavior of Real Exchange Rates: Evidence and Implications," in Real Business Cycles, Real Exchange Rates, and Actual Policies, edited by K. Brunner and A. H. Meltzer. Carnegie-Rochester Conference Series on Public Policy, vol. 25, 1986.

Pratt, J. "Risk Aversion in the Small and in the Large." Econometrica, January/April 1964, 122-36.

Raskin, R. and M. Cochran. "Interpretations and Transformations of Scale for the Pratt-Arrow Absolute Risk Aversion Coefficient: Implications for Generalized Stochastic Dominance." Western Journal of Agricultural Economics, December 1986, 204-10.

Stockman, Alan C. "Real Exchange Rates Under Alternative Nominal Exchange Rate Systems." Journal of International Money and Finance, August 1983, 147-66.

MICHAEL MELVIN and MICHAEL B. ORMISTON *

* Department of Economics, Arizona State University. We are grateful to Richard Sweeney and two anonymous referees for their comments and suggestions. Ali Kutan provided helpful research assistance.

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Author: | Melvin, Michael; Ormiston, Michael B. |
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Publication: | Economic Inquiry |

Date: | Jul 1, 1991 |

Words: | 5069 |

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