Incentives for International Currency Diversification by U. S. Financial Investors
Author: Mr. George M. Von Furstenberg1
  • 1 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund
Publication Date:
01 Jan 1981
eISBN:
9781451972672
Language:
English
Keywords:
SP; exchange rate; diversification of portfolio; pound sterling; Norwegian krone; unit of currency; dollar asset; Currencies; Purchasing power parity; Floating exchange rates
Download PDF (1.1 MB)

In recent years, even those segments of the U. S. investing public that are unlikely to incur significant foreign payments obligations1 have at times been advised to consider placing funds into currencies other than the U. S. dollar. The individual U. S. investors were to diversify their interest-bearing money or liquid asset holdings by currency, not for hedging purposes but to increase the return on their portfolios denominated in dollars. This paper examines whether such recommendations would have been well founded. It thus asks whether currency diversification, guided by simple rules, could have been expected to pay over the first seven years of widespread managed floating among major currencies, starting with the second quarter of 1973, and whether it actually did pay.

Abstract

In recent years, even those segments of the U. S. investing public that are unlikely to incur significant foreign payments obligations1 have at times been advised to consider placing funds into currencies other than the U. S. dollar. The individual U. S. investors were to diversify their interest-bearing money or liquid asset holdings by currency, not for hedging purposes but to increase the return on their portfolios denominated in dollars. This paper examines whether such recommendations would have been well founded. It thus asks whether currency diversification, guided by simple rules, could have been expected to pay over the first seven years of widespread managed floating among major currencies, starting with the second quarter of 1973, and whether it actually did pay.

In recent years, even those segments of the U. S. investing public that are unlikely to incur significant foreign payments obligations1 have at times been advised to consider placing funds into currencies other than the U. S. dollar. The individual U. S. investors were to diversify their interest-bearing money or liquid asset holdings by currency, not for hedging purposes but to increase the return on their portfolios denominated in dollars. This paper examines whether such recommendations would have been well founded. It thus asks whether currency diversification, guided by simple rules, could have been expected to pay over the first seven years of widespread managed floating among major currencies, starting with the second quarter of 1973, and whether it actually did pay.

These questions are addressed not to prepare investment advice but to shed light on some larger issues such as the controllability of an economy by its own measures. For if currency diversification of portfolios would have been unambiguously profitable in the past, international asset substitution might spread rapidly to groups of U. S. nationals who have restricted their investments to U. S. dollar assets in the past.2 Any broadening of the inclination to acquire speculative holdings in foreign currencies may alter relations between broadly defined concepts of the national money supply3 and economic activity in the United States and elsewhere. How exactly it will do so may be difficult to predict or to allow for in domestic policy planning and in setting targets for monetary growth. The greater the willingness of investors, and the easier it is for them, to engage in currency diversification of financial holdings, the more excess supply of money in one country is likely to increase the demand for financial assets net of liabilities of other countries, thereby infringing upon monetary and exchange rate management and its intended effects on the economy in several countries.4 To assess the degree of infringement that may be encountered in the future, it is important to determine whether the incentives for international currency diversification may have grown over recent years as experience with floating exchange rates has accumulated.

As internationally covered interest parity appears to hold at almost every instant in continuously adjusting foreign exchange markets,5 individual financial investors may assume a priori that there can be no systematic gain from international currency diversification of their holdings, provided the forward rate is an unbiased predictor of the future spot rate. If they subsume this simple efficiency property, ordinary U. S. investors without a head start on the receipt of “news” that may affect foreign exchange markets would have to expect the same dollar rate of return (ignoring differences in transactions costs) on investments in any of a number of actively traded currencies. However, since foreign exchange risk would be added on investments in all currencies other than the dollar (or currencies pegged to the dollar) from the viewpoint of the risk-averse subclass of investors discussed in this paper, they would shun investments in foreign currencies. Those who reckon their wealth solely in dollars and in terms of what it will buy in the United States would therefore demand foreign currency investments only if the excess of the expected real rate of return in foreign currencies, calculated in dollars, over the real rate of return expected on comparable investments in U. S. dollars is sufficiently large to overcome their risk aversion. Similarly, the residents of any other country who expect to accumulate and to spend in that country would have a natural preference for its currency, as the real rates of return on their portfolios would become more volatile if they ventured out of it.6

Evidently, therefore, U. S. investors would not believe that the expected real rates of return must be the same on all currencies or that exchange markets are simply efficient7 if they were to accept advice to diversify their financial holdings internationally. They may be moved to do so once it has been demonstrated to them that exchange-adjusted interest returns were often higher on certain foreign currencies than on U. S. dollars. If this happened with a sufficient degree of regularity, they may come to regret not having invested some part of their financial assets in Japanese yen, Swiss francs, deutsche mark, or any other major currency that appreciated faster than predicted on the basis of interest and/or purchasing power parity in recent years.8 Such investors may therefore project past performance into the future and then decide whether the difference in expected real rates of return would have warranted and whether it may yet warrant the additional risks incurred by any departure from domestic currency investments.9

I. Selection of Multiple Currency Portfolios

To implement this calculation, individual investors are assumed to go through the following steps:

(1) After choosing international financial instruments with negligible default risk and a maturity of three months or less to compare, as detailed in the Appendix, investors, who are assumed to roll over their investments continuously, first convert the average quarterly nominal yields offered on foreign assets, ni0, to dollar rates of return realized during the subsequent quarter, si1. The formula used in this conversion for each quarter is

si1=(1+ni0)(ei1/ei0)−1(1)

where ei is the average U.S. dollar price per unit of currency i in quarter 1 (more generally, t + 1) or 0 (t + 0), as indicated by the second subscript.

(2) The resulting nominal dollar rates of return realized on investments in currency i are then converted to average quarterly real rates, ri1 using the U. S. consumer price index (CPI),

ri1=(1+si1)(CPI0/CPI1)−1(2)

(3) Starting with the real rates realized in the second quarter of 1973, investors accumulate experience with floating exchange rates for five quarters, through the second quarter of 1974, before forming the first expectation of real dollar rates of return to be earned on foreign currencies. This expectation applies to the third quarter of 1974. With each quarter that passes, they augment the number of quarterly observations whose past average yields the real rate of return expected for the next quarter, thereby lengthening the averaging period from a fixed starting point. While the implied process of how expectations are formed is primitive, it is hard to see what, other than the spectacle of superior past performance, could have attracted ordinary U.S. investors and their counselors to foreign currencies in the first place.

(4) Similarly, investors form the first variance-covariance matrix of real rates of return10 for the third quarter of 1974 on the basis of the second quarter 1973 through second quarter 1974 experience and then recalculate this matrix each quarter as additional observations are added.11 Thus the variance-covariance matrix of real returns is estimated on the basis of the rates realized during the second quarter of 1973 through the first quarter of 1980 to determine the currency selection to be made in the course of the first quarter of 1980 for returns to be realized in the second quarter of 1980, the last quarter considered in this paper.12

(5) Individual U. S. investors employ the mean-variance selection rule13 to determine the degree of currency diversification that would raise the risk-adjusted dollar rate of return expected on their portfolio above that available on three-month Eurodollar deposits. The latter were chosen as the basis for comparison, since they yield more than three-month treasury bills, federal funds, or domestic certificates of deposit bearing related rates. Individual investors are assumed to have net asset positions that are positive or zero in any currency, so that short sales (except short sales or borrowing “against the box”) are not allowed.14 Ordinary U. S. investors are not likely to obtain foreign currency loans to invest in dollar assets or to borrow more dollars than they retain so as to invest more than their entire net worth in foreign currencies.

MATHEMATICS OF SELECTION

With a maximum of (n − 1) foreign currency investments to consider in relation to investments in the nth currency, the U. S. dollar, the objective function is linear in the expected real portfolio rate of return, r, and its variance, var r. The portfolio share of the ith currency, with expected yield ri is denoted by ai ≧ 0, with the share of the nth currency determined residually an=1−∑i=1n−1ai. Taking account of the nonnegativity constraints and the fact that products of the unknown portfolio shares appear in the variance-covariance matrix yields a quadratic programming problem. The portfolio shares, ai are to be selected so as to maximize the risk-adjusted real rate of portfolio return, R, expected with assigned values of the coefficient of risk aversion, b. For programming purposes, the problem of maximizing R = r − b var r anew each quarter is converted to the equivalent problem of minimizing

D=bvarr−r(3)

subject to

ai ≧ 0, i = 1 … n

using quarterly changing values of

r=∑i=1n−1airi+(1−∑i=1n−1ai)rn

and

varr=∑i=1n−1ai2varri+∑i=1n−1∑j≠in−1aiajcovarrij+2∑i=1n−1ai(1−∑i=1n−1ai)covarrin+(1−∑i=1n−1ai)2varrn

The matrix input required to solve this problem for the n − 1 unknown portfolio shares, a, takes the form (S) = [A] (a) + (C), where (S) is a vector of slack variables such that an element of S is zero only if the corresponding element of (a) is nonnegative in the optimal program.15 The elements of the coefficient matrix [A] and the vector of constants, (C), are derived from the first-order conditions as explained later on. Ignoring the nonnegativity constraints, the first-order conditions derived for R with the definitions in (3) are, for any i,

∂R/∂ai=(ri−rn)−2baivarri−2b∑j≠in−1(ajcovarrij)−2b(1−∑i=1n−1ai)covarrin+2b∑i=1n−1(aicovarrin)+2b(1−∑i=1n−1ai)varrn=0

Hence, dividing through by 2b, changing the sign, and expressing var ri as covar rii yields

∂D/∂ai=−[(ri−rn)/2b+(varrn−covarrin)]+∑j=1n−1(covarrij−covarrjn−covarrin+varrn)aj(4)

The first term is the ith element in the vector of constants, (C), and the n − 1 elements in the ith row of the coefficient matrix [A] are contained in parentheses in the second term solved for each column j.16 The generation of these inputs is completed by going through all the i from 1 to n − 1 and repeating the entire operation each quarter as additional information is obtained.

II. Indicated Currency Diversification and Its Results

The solutions to the nonlinear programming problem are shown in Tables 1, 2, and 3 for values of the coefficient of risk aversion, b, ranging from 1 to 0.25. A b of 1 indicates a required rate of compensation of 1 unit of expected real rate of return per unit increase in its variance, while this rate of compensation falls to one quarter if b is 0.25.17 Although both the Belgian franc and the French franc survived the initial screening for inclusion in the selection program, as detailed in the Appendix, positive currency shares were never indicated for these currencies. Hence only the deutsche mark, Japanese yen, Netherlands guilder, Norwegian krone, Swiss franc, and pound sterling are shown as alternatives to U. S. dollar investments in these tables.

Table 1.

Optimal Currency Shares(a)with Risk Aversion Coefficient(b)of 1, Third Quarter 1974–Second Quarter 1980l

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All rows add to 1.

Table 2.

Optimal Currency Shares (a) with Risk Aversion Coefficient (b) of 0.5, Third Quarter 1974–Second Quarter 19801

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All rows add to 1.

Table 3.

Optimal Currency Shares (a) with Risk Aversion Coefficient (b) of 0.25, Third Quarter 1974–Second Quarter 19801

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All rows add to 1.

As expected, the dollar share is always higher, the greater the degree of risk aversion. If b were infinite, U. S. investors would not venture out of the dollar at all. This is because the covariances between the real rates of return on foreign currencies are positive and very large compared with covariances involving the real rate of return on the dollar, as illustrated in Table 4. The real rate of return on the U. S. dollar has been so stable that its variance is often only about one hundredth of the variance of the real dollar rate of return on foreign currencies. These currencies, in turn, have tended to rise or fall together against the dollar, making the covariance of their real dollar rates of return very high. Hence, all the currencies included in the optimal program at more moderate degrees of risk aversion must necessarily offer a higher expected return to overcome specified degrees of risk aversion. The smaller the degree of such aversion, the greater the diversification out of the dollar, until finally only the currency with the highest expected real dollar rate of return would be picked if risk aversion were zero.

Table 4.

Variance-Covariance Matrix and Average Quarterly Real Dollar Rate of Return (in Per Cent) on Short-Term Investments in Seven Currencies, for Third Quarter 1973–First Quarter 1980, and Elements of Matrix [A], First Quarter 19801

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The elements of matrix [A] are very close to the corresponding elements of the variance-covariance matrix, showing that this matrix is dominated by the variance-covariance matrix for the real dollar rates of return on foreign currencies (covar rij in equation (4)). The matrix actually entered in the program also contained the Belgian franc and the French franc, but the corresponding matrix elements are not shown, since these currencies never appeared in the quarterly solutions. Matrix [A] for the first quarter of 1980 is used to determine the optional currency composition on which interest is realized in the second quarter of 1980, the final quarter considered in this paper. The full matrix is, of course, symmetric around the principal diagonal.

The results shown in Tables 1, 2, and 3 lie between these extremes as the average quarterly share indicated for the U. S. dollar falls from 95 per cent when b is 1 to 85 per cent when b is 0.25. Furthermore, the lower the degree of risk aversion, the more interesting the Swiss franc and the Netherlands guilder would have looked over the period examined. The frequency with which the deutsche mark, Japanese yen, and pound sterling appear in the optimal program is affected far less by changing degrees of risk aversion. Norway owes its entry into the optimal program largely to the strong appreciation of the krone in the wake of the first oil price shock, raising the expected real dollar rate of return on that currency.

To investigate how much the indicated degree of currency diversification would have been expected to pay investors to overcome specified degrees of risk aversion, and how much it should actually have paid, some further calculations are required. If there should appear to be a systematic difference between the expected and the actual payoff from currency diversification, then the U. S. investor would have been misled by the decision calculus attributed to him. In particular, the assumption that the averages of the quarterly real dollar rates of return realized on foreign currencies from the time of transition to generalized floating to quarter t yield unbiased predictors of the real rate of return realized in quarter t + 1 would have proved false.

To examine this, the investor is endowed with a principal of $100 that he invests during the third quarter of 1974 in accord with the currency diversification indicated for that quarter in Tables 1, 2, and 3. As real returns are realized during the subsequent quarter, he reinvests principal and interest in the currency proportions shown for the fourth quarter of 1974 at a specified degree of risk aversion and continues in this way each quarter. The real values of principal and interest so realized, either actual or expected, can then be compared with each other and with the growth in the real dollar value of the portfolio that would have been experienced if the U. S. investor had remained in dollars exclusively. This last comparison series is shown in column 1 of Table 5 and is followed by the actual and hypothetical compound growth series that would have been realized with the currency diversification indicated for degrees of risk aversion ranging from b = 1 to b = 0.25, respectively.

Table 5.

How the Real Value of $100 Would Have Grown from Third Quarter 1974 to Second Quarter 1980 If It Were Invested with Interest in U. S. Dollars or, Alternatively, in Several Currencies

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The currency distributions associated each quarter with the corresponding coefficients of risk aversion are shown in Tables 1, 2, and 3.

If the investor’s expectation of future real dollar rates of return, generated from lengthening past averages, is unbiased, he would do better than expected in some quarters and worse than expected in other quarters. Still, in the long run he would come out about as expected, as unexpected gains and losses would tend to average out. The period examined here is too short to permit firm conclusions. Yet it may be significant that the investor’s actual real wealth, while at first somewhat larger, is much smaller than expected at the end of the period in mid-1980,18 with the difference being higher, the lower the degree of risk aversion shown in Table 5. If one interprets this evidence as indicating that the investor’s real rate-of-return expectations were biased upward by his extrapolation of past averages, one would have to conclude that he did not receive the risk compensation required to warrant the degree of currency diversification actually engaged in at any value of b, although his real wealth rose faster than it would have if it had been invested in dollars alone. Although he would have expected the real value of the alternative portfolios invested in several currencies to be between 1 and 5 per cent higher by the second quarter of 1980 than that of a portfolio invested exclusively in dollars,19 he would have found himself actually gaining only between 1 and 2 per cent.

III. Conclusion

During recent years, interest in foreign currency investments appears to have spread to groups of U. S. investors who had previously felt secure in domestic issues and paid scant attention to interest rate and exchange rate developments abroad. The record has shown that investors in short-term, interest-bearing instruments of uniformly low default risk could have done much better over the first seven years of floating exchange rates if they had invested in assets denominated in some other currencies besides dollars.20 However, if investors had decided to diversify only after real rate-of-return differentials had emerged that would yield adequate compensation for risk if they continued into the future, the investors would have been disappointed by the actual investment results in the end.

There are several reasons why past differences in the average real dollar rate of return may not vanish quickly. Runs in the exchange value of currencies have often been observed to extend over periods of several quarters. Some purchasing power relationships have shown drifts that have caused some of these relations to be adjusted for trend in empirical studies of the dollar exchange value of foreign currencies and its determinants, and constant risk premiums have sometimes been interposed between the forward rate and the expected future spot rate.21 Even in a world of complete purchasing power parity, discounts or premiums may be observed relative to the expected future spot rate if the nominal interest-bearing securities of two countries have different degrees of market risk.22 Nevertheless, there is no firm theoretical support for assuming that past differences in the real dollar rates of return will continue undiminished to the extent that they can be attributed to unexpected exchange rate developments.

Residents of other countries without direct foreign payments obligations will have a natural preference for their currency as a financial investment vehicle, just as U. S. investors have for the dollar. Exchange rate volatility always tends to deter portfolio diversification by currency, as the variance of real rates of return is increased in all currencies except the one in which the utility calculus is conducted. However, to the extent that these countries are more exposed to price and credit developments in other countries,23 this preference may be less. Residents of other countries may therefore be more prone to diversify than U. S. investors.24 On the other hand, should the kind of U. S. investor discussed in this paper ever have a strong and reasoned incentive to diversify out of the dollar, the incentives for the rest of the world would be that much greater.25 So far, however, the existence of any such incentive has not been confirmed.

APPENDIX

A number of foreign currency instruments were considered to determine which of them might possibly interest U. S. investors who would invest abroad for the sole purpose of increasing the dollar rate of return on their portfolios. To be able to focus on this objective in the simplest manner, all securities are chosen to be of comparable maturity and negligible default risk. The maturity of the deposits or treasury bills, largely selected from the Fund’s International Financial Statistics (IFS), ranges from overnight deposits to a maximum of three months, with the new issue rates averaged by quarter.

The instruments and rates identified in Table 6 comprise all major market rate series on practically risk-free, short-term instruments that have been available publicly at least since the first quarter of 1973. While foreign nationals have not always been able to invest in these instruments directly, it may be assumed that comparable rates could be obtained by such nationals on deposits negotiated either in the issuing country or in the Eurocurrency markets.

Table 6.

Short-Term Interest Rates Used to Construct Average National Rates Quoted Each Quarter from First Quarter 1973 to First Quarter 1980 and Realized from Second Quarter 1973 to Second Quarter 19801

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Asterisks denote rates used in currency selection problem solved in Section II.

To narrow the list of 15 interest rates in 12 currencies shown in Table 6 down to manageable proportions, it was decided to drop those instruments that did not yield the highest average dollar rate of return in even a single quarter past the third quarter of 1974, where the average extends from the second quarter of 1973 onward. The interest-bearing instruments of Canada, Italy, and South Africa were eliminated on this basis. For the United Kingdom and the United States, the respective Eurocurrency rates were the highest of several rates examined. Hence these two rates and the rates shown for Belgium, France, the Federal Republic of Germany, Japan, the Netherlands, Norway, and Switzerland were used in the portfolio selection program, for a total of nine currencies.

*

Mr. von Furstenberg, Chief of the Financial Studies Division of the Research Department, was formerly Professor of Economics at Indiana University and a Senior Staff Economist of the U. S. President’s Council of Economic Advisers.

1

The ordinary U. S. investor, whose portfolio choices are addressed in this paper, may be affected by exchange rate movements in consumption, for instance because the dollar costs of foreign travel or of the import and import substitute components of personal consumption expenditures in the United States may be changed.

2

For the derivation of optimal portfolios of noninterest-bearing foreign currencies and of foreign currencies and common stocks, see Haim Levy and Marshall Sarnat, “Exchange Rate Risk and the Optimal Diversification of Foreign Currency Holdings,” Journal of Money, Credit and Banking, Vol. 10 (November 1978), pp. 453–63. See also R. Stafford Johnson, Charles W. Hultman, and Richard A. Zuber, “Currency Cocktails and Exchange Rate Stability,” Columbia Journal of World Business, Vol. 14 (Winter 1979), pp. 117–26.

3

The substitutions relevant for this paper are between interest-bearing monies or liquid assets denominated in different currencies. In the theoretical literature, however, currency substitution is a term often reserved for money that bears no interest so as to allow the focus to be shifted simply to the inflation differentials that countries can maintain in view of the prevailing degree of substitution with foreign currencies. See, for instance, Marc A. Miles, “Currency Substitution, Flexible Exchange Rates, and Monetary Independence,” American Economic Review, Vol. 68 (June 1978), pp. 428–36. See also M. A. Akhtar and Bluford H. Putnam, “Money Demand and Foreign Exchange Risk: The German Case, 1972–1976,” Journal of Finance, Vol. 35 (June 1980), pp. 787–94; and Bluford H. Putnam and D. Sykes Wilford, “Exchange Rate Determination with Currency Substitution,” Business Economics, Vol. 15 (May 1980), pp. 16–19.

4

For detailed discussions, see Morris Goldstein, Have Flexible Exchange Rates Handicapped Macroeconomic Policy? Special Papers in International Economics, No. 14, International Finance Section, Princeton University (June 1980); Jacques R. Artus and John H. Young, “Fixed and Flexible Exchange Rates: A Renewal of the Debate,” Staff Papers, Vol. 26 (December 1979), pp. 654–98; Harvey A. Poniacheck, Monetary Independence under Flexible Exchange Rates (Lexington, Massachusetts, 1979); Stephen J. Turnovsky, “On the Insulation Properties of Flexible Exchange Rates,” Revue Economique, Vol. 30 (July 1979), pp. 719–46; and Ralph C. Bryant, Money and Monetary Policy in Interdependent Nations, The Brookings Institution (Washington, 1980).

5

Any deviations are quickly arbitraged away by specialists other than the investor considered here. See Richard M. Levich, The International Money Market: An Assessment of Forecasting Techniques and Market Efficiency, Contemporary Studies in Economic and Financial Analysis, Vol. 22 (Greenwich, Connecticut, 1979). Thus, if covered interest parity holds, the investor discussed in this paper is functionally indistinguishable from “speculators who [consciously] keep open positions based on the difference between their expectation of future spot rates and corresponding forward rates.” See Maurice D. Levi, “Underutilization of Forward Markets or Rational Behavior?” Journal of Finance, Vol. 34 (September 1979), pp. 1013–17, especially p. 1013.

6

Variations in the real rate of return are limited in each country in its own currency by fundamental economic and technological relationships governing the demand for and supply of productive capital in conjunction with the prevailing system of financial intermediation.

7

Hansen and Hodrick have explained that rejection of the simple efficiency hypothesis, which states that the forward exchange rate is equal to the mathematical expectation of the corresponding future spot rate conditioned on the information set available at the beginning of the time span, is not immediately translatable into rejection of the efficiency or rationality of the foreign exchange market if economic agents are risk averse. Rather, simple efficiency is a composite hypothesis of rational expectations, risk neutrality, and competitive markets without transactions costs. See Lars Peter Hansen and Robert J. Hodrick, “Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis,” Journal of Political Economy, Vol. 88 (October 1980), pp. 829–53; and Robert E. Cumby and Maurice Obstfeld, “Exchange-Rate Expectations and Nominal Interest Differentials: A Test of the Fisher Hypothesis,” National Bureau of Economic Research, Working Paper No. 537 (Cambridge, Massachusetts, August 1980).

8

For analyses of the possible nonmonetary causes and the persistence of deviations from purchasing power parity, see Jacob A. Frenkel and Michael L. Mussa, “The Efficiency of the Foreign Exchange Market and Measures of Turbulence,” American Economic Review, Papers and Proceedings, Vol. 70 (May 1980), pp. 374–81; Alan C. Stockman, “A Theory of Exchange Rate Determination,” Journal of Political Economy, Vol. 88 (August 1980), pp. 673–98; and Jeffrey A. Frankel, “On the Mark: A Theory of Floating Exchange Rates Based on Real Interest Differentials,” American Economic Review, Vol. 69 (September 1979), pp. 610–22.

9

Even sophisticated international investors with no particular local habitat are assumed to share this conception in Rudiger Dornbusch, “Exchange Rate Economics: Where Do We Stand?,” Brookings Papers on Economic Activity: 1 (1980), pp. 143–85, especially pp. 165–67. On the basis of the average real dollar rates of return, calculated by use of a dollar price index of manufacturers in world trade over the first six years of generalized floating, he finds that a speculative position in deutsche mark would be indicated that is motivated by the difference in mean real yields. Dornbusch notes, however, that his argument may overstate the case, particularly if much of the differential in mean real returns reflects unanticipated deutsche mark appreciation. Past differences in nominal rates of return, expressed in an import-weighted basket of currencies, are used without discussion of their predictive significance in Avraham Ben-Bassat, “The Optimal Composition of Foreign Exchange Reserves,” Journal of International Economics, Vol. 10 (May 1980), pp. 285–95. By contrast, systematic differences in expected yields can arise only on account of exchange risk when international currency diversification problems are solved by finding the minimum variance portfolio, as in James P. Healy, “The Asset Market Determination of Exchange Rates in a Multi-Country Setting,” unpublished doctoral dissertation (Princeton University, June 1980) (see especially chapter VI).

10

The importance of using real rather than nominal rates in the construction of the variance-covariance matrix, if that matrix is not to be unduly sample specific, should be emphasized. If there are common trends or synchronized fluctuations in the rates of inflation of several countries, nominal interest rates, transformed into the reference currency, will change in unison, thereby creating higher degrees of positive covariance than would be observed in the corresponding real rates that are relevant.

11

As exchange rate volatility appears to have been greatest early in the period of floating, the elements of this matrix tend to decline at a decreasing rate as additional observations are added. The matrix calculated with the largest number of observations is shown in Table 4.

12

Because investments are assumed to be staggered, with portions rolled over each business day, real rates of return are realized as three-month investments mature successively during any quarter for possible reinvestment in different currencies. No time is allowed to elapse between the receipt of data, their processing to indicate the optimal currency composition, and the implementation of the programming solution, although such maximum response speed can only be approximated in practice.

13

The limited generality of that rule, as well as its continued attractiveness if investment returns are normally distributed, are both explained in Vijay S. Bawa and Lewis M. Chakrin, “Optimal Portfolio Choice and Equilibrium in a Lognormal Securities Market,” pp. 47–62 in Portfolio Theory, 25 Years After: Essays in Honor of Harry Markowitz, ed. by Edwin J. Elton and Martin J. Gruber, North-Holland/TIMS Studies in the Management Sciences, Vol. 11 (Amsterdam, 1979). Real rates of return on foreign currencies can be assumed to be distributed normally only after the transition to managed floating. Even then, however, a normal distribution may not have been approximated very closely for the Netherlands guilder and the Norwegian krone because of their de facto ties to the deutsche mark being broken from time to time through discrete exchange rate adjustments.

14

For an example of a solution to an international currency diversification problem without restrictions on short sales or foreign borrowing, see Pentti J. K. Kouri and Jorge Braga de Macedo, “Exchange Rates and the International Adjustment Process,” Brookings Papers on Economic Activity: I (1978), pp. 111–50, especially p. 129.

15

The computer program used to derive the solution is J. A. Tomlin’s “Users Guide for LCPL: A Program for Solving Linear Complementarity Problems by Lemke’s Method,” Systems Optimization Laboratory, Department of Operations Research, Technical Report SOL 76–16 (Stanford University, August 1976). For an analogue, see especially p. 23, problem 3.

16

As pointed out in the note to Table 4, each element is dominated by covar rij, with the other three components shown in the second set of parentheses adding or subtracting very little.

17

To illustrate further, with a b as high as 1, the investor would be indifferent between an investment yielding a certain real rate of return of 0 and one yielding a real rate of return of 1 per cent with a variance of 1, as there would be a chance of about one sixth that the real rate of return will actually turn out to be negative on the latter investment, assuming a normal distribution of returns.

18

In the second half of 1980, the dollar rose against most other major currencies, so that currency diversification might have paid even less.

19

As shown in Table 5, the real value of the undiversified investment in dollars is actually somewhat less in the second quarter of 1980 than at the beginning of the third quarter of 1974, as real interest rates have frequently been negative even on Eurodollar deposits. If the taxation of nominal interest (and nominal capital gains) had been considered, the real value would have shrunk much faster throughout.

20

For a demonstration, see International Monetary Fund, Annual Report 1980 (Washington, 1980), pp. 64–67.

21

See Pentti J. K. Kouri, “International Investment and Interest Rate Linkages under Flexible Exchange Rates,” in The Political Economy of Monetary Reform, ed. by Robert Z. Aliber (New York, 1977), pp. 74–96; Jacques R. Artus, “Methods of Assessing the Long-Run Equilibrium Value of an Exchange Rate,” Journal of International Economics, Vol. 8 (May 1978), pp. 277–99; Hans Genberg, “Purchasing Power Parity Under Fixed and Flexible Exchange Rates,” Journal of International Economics, Vol. 8 (May 1978), pp. 247–76; Alexander K. Swoboda, “Exchange-Rate Flexibility in Practice: A Selective Survey of Experience Since 1973,” forthcoming in Weltwirtschaftliches Archiv.

22

Fama and Farber view a forward exchange contract as an agreement to exchange the future payoffs on nominal bonds denominated in the monies of two countries. “Because there can be differences in the purchasing power risks of the two monies, the real payoffs on the bonds can have different degrees of risk, in which case the bonds are priced to have different expected real returns, and the forward exchange rate is not just the ratio of the expected values of the real payoffs on the bonds.” See Eugene F. Fama and Andre Farber, “Money, Bonds, and Foreign Exchange,” American Economic Review, Vol. 69 (September 1979), pp. 639–49; quotation is from p. 648.

23

Technically, this would raise the components covar rin and covar rjn (where n is the home currency), which are both signed negatively in the elements of matrix [A] shown in equation (4). As the size of these elements falls, currency diversification is encouraged.

24

However, it should not be assumed that the U. S. dollar will necessarily be the chief beneficiary of such substitution, as currencies other than the U. S. dollar, particularly those of neighboring countries, may be the preferred alternative for the residents of some of the smaller foreign countries. If there are informal exchange rate links between such neighboring currencies, the variances of their real rates of return (covar rij with i = j and var rn in equation (4)) may differ less than they would if the reference currency (n) were the dollar.

25

For a theoretical analysis of the possible instability caused by currency substitution, see Lance Girton and Don Roper, “Theory and Implications of Currency Substitution,” Journal of Money, Credit and Banking, Vol. 13 (February 1981), pp. 12–30.

Same Series

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Cover IMF Staff Papers
IMF Staff papers: Volume 28 No. 3
Author: International Monetary Fund. Research Dept.
Volume/Issue:
Volume 1981: Issue 003
Publisher:
International Monetary Fund
ISBN:
9781451972672
ISSN:
1020-7635
Pages:
208
DOI:
https://doi.org/10.5089/9781451972672.024