1989_arthur j. Raymond and Gordon Weil

Journal of Business Finance & Accounting, 16(4) Autumn 1989, 0306 686X $2.50

DIVERSIFICATION BENEFITS ANDEXCHANGE-RATE CHANGES

ARTHUR J. RAYMOND AND GORDON WEIL*

INTRODUCTION

One of the most widely accepted implications of economic theory is that nationscan increase their welfare through participation in international trade in goodsand services. It has also been demonstrated that the movement of factors ofproduction between nations can generate benefits for the participating coun-tries. A third way in which the residents of different nations can raise theirwelfare by participating in international transactions is through the purchaseand sale of foreign assets, viz. portfolio investment. In fact, movements ofcapital across borders have increased dramatically as barriers to internationalcommunication and cooperation have been relaxed.' This paper investigatesthe potential benefits that arise from international portfolio investment.

In an early and well known article Grubel (1968) demonstrated theoreticallyand empirically that benefits could be realized from international portfolio diver-sification. Since Grubel's paper there have been a number of empirical studiessupporting his initial findings. Levy and Sarnat (1970), like Grubel, generatethe efficient portfolio set and find that it contains foreign assets. Agmon (1972),Lessard (1975a and 1975b), and Solnik (1974), use simple and multiple regres-sion models to demonstrate that a large proportion of the variation of inter-national stock returns is unsystematic and therefore capable of being eliminatedthrough international diversification.^ Solnik (1975) further found that ran-domly chosen portfolios of even modest size, containing as few as five stocks,outperform randomly chosen portfolios of only US stocks, and that maximumrisk reduction occurs with a portfolio with around twenty stocks. That diver-sification benefits occur with such small portfolios is valuable information topotential investors.

The simplest and most straightforward method for showing that internationaldiversification benefits exist is to correlate national asset indices. If the cor-relations are less than one international diversification is beneficial. If one coun-try's returns are low then the overall portfolio's return will probably be pro-tected by off-setting returns in other countries. Thus, the overall variation inreturns risk will be reduced by a portfolio containing foreign assets. Adlerand Dumas (1983), Allan (1982), Errunza (1983), Finnerty and Schneeweis(1979), Grubel and Fadner (1971), Ibbotson et al. (1982), and Joy et al. (1976)

* The authors are respectively, a Lecturer at Tufts University, and Associate Professor at WheatonCollege. (Paper received January 1987, revised October 1987)

455

456 RAYMOND AND WEILhave calculated correlations between various countries for various indices ofassets and found these correlations generally to be low. This consistency inempirical findings is undoubtedly partially responsible for the increased useof internationally diversified portfolios (see Erlich, 1981; and Revey. 1981).Most of the studies referred to above have used rates of return unadjusted forexchange-rate changes, or relied on data drawn from the fixed exchange-rateperiod. Those few studies that do adjust for exchange-rate changes during thefloating period do not emphasize the effect of exchange-rate changes on diver-sification benefits. In fact a new edition of one well known finance text byRodriguez and Carter (1984) notes that the effect of exchange-rate changeson diversification benefits remains unclear.

As part of their investigation of diversification benefits Grubel and Fadner(1971) point out that exchange-rate changes could increase or decrease the diver-sification benefits that would exist in the absence of these changes. In anexpanding economy, for example, it is typical for both rates of return andimports to increase. The resulting exchange rate movement is indeterminant.Hence, exchange rates may move with or against domestic rates of return.Furthermore, in the short run according to the asset market view of exchangerate determination, when higher nominal rates of return are due to domesticinflationary pressures there could be a capital outflow (rather than inflow) ifinvestors expect a weakening of the external value of currency (see Frenkel,1981). In this case too the relation between exchange-rate changes and ratesof return remains unclear. Grubel and Fadner did try to determine empiricallythe effect of exchange-rate changes on their correlations but their data wasrestricted to the fixed-rate period when exchange rates moved by only smallpercentages around par. As might be expected they found no effect ondiversification benefits after adjusting for exchange-rate changes.

In this paper we attempt to update the work of Grubel and Fadner by draw-ing on data from the more recent floating exchange rate era, rather than fromthe pegged rate period. Since our data are drawn entirely from that periodit is necessary to create the relevant data that would have existed had exchangerates not moved as they in fact did. That set of data, a counter-factual, pro-vides the benchmark to which we compare the actual experience during thefioating period. We have constructed the counter-factual situation under theassumption that nations pursued sterilized intervention so that during the periodunder consideration the exchange rate changes actually observed have beeneliminated without affecting asset returns since the monetary base isunchanged.^ Our tests are based on ex-post share price indices of industries inAustralia, Ganada, Spain, the UK, and the US.* The resuhs indicate that fora US investor international diversification is superior to purely domestic diver-sification. However, in this sample the observed exchange-rate movements havetended to reduce the diversification benefits from what would have arisen hada pegged regime existed (viz. had the central banks followed our counter-factualof sterilized intervention.)

DIVERSIFICATION BENEFITS AND EXCHANGE-RATE CHANGES 457

THEORY

If risk is priced in international markets then the gain to be realized from aninternationally diversified portfolio is a more efficient risk-return tradeoff.^ Ifportfolio risk is measured by the variance of the portfolio's return then the poten-tial for diversification benefits is indicated by the weighted covariances of everypairwise combination of assets' returns. Total diversification benefits, excludingpurely domestic diversification, include those realized from diversifying withinforeign countries and across foreign countries as well as those that would berealized from holding just one foreign asset. The rate of return on an assetfor an investor in county 1 of an n country world is r^.^ and can be written as

( l + r , J = ( 1 + U * (l+-t) (1)where 4m is the nominal rate of return on asset m in country k measured ink'5 currency, and e^. is the appreciation of currency k relative to country I.*"Of course for X: = 1, t = 0. If J^m * * ~ 0 , the exchange-rate adjusted rateof return can be approximated by

nm = hm + * (2)The return on a world portfolio is

Tp = W * R (3)where Wisa. vector whose elements are the proportions of wealth held in eachasset and i? is a vector of assets' rates of returns as approximated by r^ n,. Therisk associated with the world portfolio, measured by its variance, is

VAR {Tp) = W * C * W (4)where C is the variance-covariance matrix of all assets' returns. For large port-folios each element of W approaches 1/^ where s is the number of assets in theworld. The benefits of total (not just international) diversification depend uponthe size of the covariance terms the off-diagonal elements of C. Note thatsince a correlation coefficient is essentially a standardized covariance it islegitimate to measure potential diversification benefits in terms of covariancesas well as correlation coefficients.

The covariance terms of C are of the form GOV (r^^ r,^), and are of fourtypes: (I) between domestic assets {k = j = 1, and m ^ h); (II) between assetsin the same foreign country {k = j ^ 1, and m r^h); (III) between foreignassets in different countries {k ^j ^ 1); and (IV) between domestic and foreignassets {k = 1 ^ j). Expanding the covariance between domestic and foreignassets from equation (2), which measures the extent to which international diver-sification is beneficial, gives

e]) (5)where k = 1 5^ 7- How exchange-rate changes affect the covariance of nominal

458 RAYMOND AND WEIL

rates of return alone, depends upon GOV(i,[,n, ,) the co-movement ofnominal domestic rates of return with exchange rates. This is the argumentgiven by Grubel and Fadner and explained in the previous section. Expand-ing the other types of covariances reveals that exchange-rate changes affect otherdiversification benefits through the covariance of exchange-rate changes witheach other as well as with rates of return. Because there are no strongtheoretical arguments about the co-movement of rates of return and exchangerates with each other, the effect of exchange-rate changes on diversificationis an empirical question.

DATA AND RESULTS

Our data are indices of monthly share prices for 49 US industries and 67 foreignindustries for the period January 1976 to January 1979. Nominal rates of returnwere calculated as simple monthly rates. Letting 4^, be the value of the shareprice index for industry m in country k at the time t, the nominal rate of returnwas calculated as

'kml = {hml-\lhmt)-'^ (6)The rates of return, measured in dollars, were calculated by adjusting the indexlevels by the exchange rate and then calculating simple monthly rates of returnof the adjusted index. Define Ei^t as the dollar price of foreign currency; ofcourse, for the US Ei^, = 1.

Then I',^, = 4^, * (7)becomes the index of industries prices measured in dollars and

rkmi = {IU-x'Hm)-'^ (8)becomes the simple monthly return measured in dollars.*

In order to determine the effect of exchange-rate changes experienced dur-ing the period of fioating rates on diversification benefits the co-movement ofrates of return, as measured by the correlation coefficient, was estimated bothin dollar terms (from (8)), and then in local currency units (from (6)) accord-ing to our country-factual scenario.

Rates of Return Measured in Home Currency UnitsTable 1 gives the average correlation coefficient between all industries in thecountry listed vertically and the country listed horizontally with returnsmeasured in home currency units.' The diagonal gives the average correla-tion coefficients for returns within countries and so is a measure of diversifica-tion within each country. From a US portfolio holder's point of view the US/USentry in the table is a type I correlation coefficient. The other diagonal entries


Table 1

Average Gorrelation Goefficients of Rates of Return Within and AcrossGountries Measured in Local Gurrency Units

US

UK

CAN

SP

AUS

US

0.4974(1176)

UK

0.0677(1568)0.6814(496)

CAN

0.256(1225)0.022(800)0.4533(300)

SP

0.0848(245)

-0.349(160)0.0233

(125)0.4882(10)

AUS

0.2564(245)0.1752

(160)0.1285

(125)0.0710(25)0.4346(10)

The numbers in parentheses are the number of correlation coefficients in the average.

are type II correlation coefficients, correlations among industries within eachcountry. The top row (other than the US/US entry) is made up of type IVcorrelation coefficients, giving correlations between the US and each foreigncountry, and the remaining entries are type III correlations. By inspection,it is apparent that internal correlation coefficients (type I and II) are largerthan cross-country correlations (types III and IV). This suggests by the usualmethod of analysis that international diversification benefits would have existedunder our country-factual scenario for investors in all five countries. Namely,if an investor in any of the countries indicated reduced the relative importanceof domestic assets by adding assets of other countries, overall portfolio risk woulddecline.'" Table 1 also provides some information on other types of diversifica-tion benefits. Taking a US perspective, the fact that type II (foreign internal)correlation coefficients are less than one indicates that it would have been wisefor a US investor to diversify within each foreign country. Type III correla-tion coefficients (between foreign assets in different countries) are also less thanone suggesting diversification into more than one foreign country would havebeen beneficial." Also if we take average correlation coefficients (type I forthe US and type II for the others) as a measure of the internal integration ofdifferent asset markets then our results indicate that, except for the UK, a verysimilar degree of integration exists in all countries.'^

Table 2 lends statistical force to our casual observations concerning inter-national diversification benefits. The table contains t-statistics for the differencebetween the average US internal correlation coefficient and the average


Table 2

^-Statistics for Difference Between the Average Type I Gorrelation Goefficientand Type IV Gorrelation Goefficients with Returns Measured in Home

Gurrency Units

UK CAN SP AUS

US 70.23 31.29 32.08 18.1(2742) (2399) (1419) (1419)

Numbers in parentheses are degrees of freedom.All differences are significant at the 99 per cent level.

US/foreign correlation coefficients. In all cases the average US/foreign cor-relation coefficient is less than the average US domestic correlation coefficientindicating the presence of international diversification benefits.

We should be clear on our methodology. The results just presented did notmake any adjustment for the actual exchange rate changes that took place overthe time period. This should not be taken to imply that we believe that USinvestors do not consider exchange rate changes when they consider the benefitsand costs of purchasing a foreign asset. Rather, to find the effect that exchangerate changes have had on diversification benefits we have constructed a counter-factual scenario in which the central bank of each nation is presumed to havepursued sterilized intervention thereby holding their exchange rates constant.With sterilized intervention the monetary base is unaffected so asset returnswould be the same as was produced without intervention. In such a situationthere is no need to convert rates of return out of domestic currency values.Thus the results present a benchmark to which we compare the actual correla-tion coefficients observed during our sample period. In the next section theresults of tests are reported when rates of return have been adjusted for exchangerates, and a comparison is then possible. Furthermore, much of the literatureon this subject rests on calculations similar to those presented above. A com-parison of the present results with those found in the studies noted in the firstsection will reveal that other studies also found that diversification benefits doexist for the international investor, when rates of return are measured in localcurrency units.

Rates of Return Measured in DollarsTables 3 and 4 contain the same information as Tables 1 and 2 respectively,except that rates of return are measured in dollars as defined by equation (8).When measured in dollars there are still benefits to international diversifica-tion. All of the average correlation coefficients between US assets and foreignassets are lower than the average correlation coefficient among US assets only.


Table 3

Average Correlation Coefficients of Rates of Return Within and AcrossCountries Measured in Dollars

US

UK

CAN

SP

AUS

US

0.4974(1176)

UK

0.0843(1568)0.7657(496)

CAN

0.2763(1225)0.0393(800)0.5617(300)

SP

0.0465(245)0.0426

(160)-0.0809

(125)0.6541(10)

AUS

0.2510(245)0.1992

(160)0.2814

(125)0.1124(25)0.5939(10)

The numbers in parentheses are sample sizes.

Table 4

^-Statistics for the Difference Between the Average Type I CorrelationCoefficient and Type IV Correlation Coefficients with Returns Measured

in Dollars

UK CAN SP AUS

US 68.2 30.5 35.3 18.9(2742) (2399) (1419) (1419)

The numbers in parentheses are degrees of freedom.All differences are significant at the 99 per cent level.

The ^ratios reported in Table 4 further indicate that each of these differencesis indeed statistically significant. A US investor who holds an internationallydiversified portfolio, subject to exchange risk, will still have lower risk thanif the portfolio contained only US assets. As would be expected, type II andtype III correlation coefficients are less than one as in the previous sub-section.An internationally diversified portfolio should contain more than one asset ineach foreign country and more than one foreign country's assets. Thus thefour types of correlations labelled type IIV can alternatively be viewed asfour sources of diversification benefits. However, it is the correlation betweenUS and foreign assets that determine if international diversification ultimatelypays.

462 RAYMOND AND WEILTable 5 addresses the central question of this paper. It presents ^-statistics

for the difference in the average type II, III, and IV correlation coefficientsthat result from including exchange-rate changes in the analysis. Each


terms that include the exchange rate are forced to become zero. The resultsreported in Table 5 are essentially generated by subtracting from those equa-tions noted above (with exchange rate terms held to zero) the same equationthis time with the observed variation in exchange rates. The results of thosesubtractions are almost invariably negative. We could describe a limited amountof exchange rate flexibility by setting free those terms forced to zero. Sincethose terms are positive, for the time period studied, the exercise must reducethe negative values from our subtractions that are reported in Table 5. Hencewe might conclude that by permitting limited fiexibility in the exchange ratewe find that fioating exchange rates reduce diversification benefits a bit lessthan when the alternative is absolutely fixed rates, but never that it increasesdiversification benefits.

There is, however, a problem with the above approach. Implicitly we haveassumed that permitting the exchange rate to vary would have no effect onrates of return. From a larger, general equilibrium, perspective, we wouldexpect rates of return as well as other economic variables to follow a differentpath when exchange rates vary than when they are held constant throughsterilized intervention. Thus we should recognize that when sterilized interven-tion is not practiced and exchange rates do vary to some limited extent, themovement in rates of return will also be affected. Hence the conclusions ofthe preceeding paragraph (which do not account for any difference in the pathsof rates of return) cannot bear too much weight. If we try to pin down moreclosely the diversification benefits when exchange rates vary a limited amountwe encounter the insurmountable problem of having to postulate, and test,any number of different potential scenarios. The different scenarios beingmotivated in large part by the actions of the Central Bank, the Treasury, andthe expectations of investors. Since the actions of each of these agents is nearlyimpossible to predict we are unable to argue convincingly that one scenariois necessarily a more likely outcome than another. Thus we feel it is best touse as our basis for comparison the unambiguous and limiting case of absolutelyfixed exchange rates.

CONCLUSION

Our ex-post test using industry data from five countries reinforces the conclu-sion of many other researchers that benefits from international diversificationdo exist. Theoretically, industry returns may be positively or negatively cor-related with exchange-rate changes so that diversification benefits may increaseor decrease as a result of including exchange-rate changes. Our results indicatethat under floating exchange rates international diversification still pays, butnot as much as would have been the case had exchange rates been pegged.'^This result is further reinforced by a comparison of Crubel and Fadner's cor-relation coefficients (from the fixed period) and ours from the fioating period.


While the two data sets are drawn from two very different time periods, coverdifferent industries, and include different countries, on average our correla-tions are slightly higher than those found in their study.

APPENDIXData Sources

The sources of the industry data are:

(1) US: Standard and Poor's Statistical Service, Security Price Index Record 1980.(2) UK: F.T.-Actuaries Share Indices, Financial Times, last day of each month for fmancial

transactions, Jan. 2, 1975-Jan. 31, 1979.(3) CAN: Industry Price Indexes, Statistics Canada, Minister oflndustry. Trade and Com-

merce, March 1979.(4) SP: Moody's International Manual, Moody's Investor Service, Inc., New York, 1982,

Madrid Stock Exchange, p a 51.(5) AUS: Moody's International Manual, Moody's Investor Service, Inc., New York, 1982,

Australia, p a 46.All exchange rate data were taken from 'Supplement on Exchange Rates'. International FinancialStatistics, Supplement Series No. 1, International Monetary Fund, 1981.

NOTES

1 At the time of writingjapan and the United States have announced the relaxation of Japanesecapital restrictions in the interest of promoting efficient world capital markets.

2 Lessard (1975) reports less diversification benefits for the US since the US is such a large partof the world market.

3 It is, of course possible to critique almost any counter-factual scenario. In this case one couldargue that nations may not have had sufficient reserves to undertake the sterilized interventionwe assume.

4 The sample consists of 5 industries in Spain and Australia, 25 industries in Canada, 32 industriesin the UK, and 49 industries in the US.

5 In poorly integrated markets where risk may not be appropriately priced, there may be assetswith returns higher than can be explained by risk. Ehrlich (1981) suggests that this is the viewof many pension fund executives.

6 An exact definition of the rate of return could also include the rate of inflation.7 Type I, II, and III covariances are respectively:

iji,), i = > = I andj , iji,)^COV(ij^, ,)

for k = j ^ I and m ^ h;

for i = j = 1.8 There is a bias in both ij^, and r/^, due to the omission of dividends which was not available

from our sources. However, the use of simple arithmetic rates of return reduces that bias byoverstating rates of return.

9 Our approach is to examine potential diversification benefits on the basis of correlation coeffi-cients of rates of return among all industries (foreign and domestic) in our sample. Thus, thetype of model we employ is what Eun and Resnick (1984) term the 'Full Historical Model'.Their study showed this model to be one of the most accurate approaches to forecasting cor-relation coefficients. Indeed, it is their benchmark for comparing alternative approaches.

10 It is possible to analyze diversification benefits from any country's point of view because the


data is in each country's own units. When exchange rate adjustments are made in the secondpart of this section, so that all returns are measured in dollars, all analysis will have to be fromthe US perspective.

11 If type II and type III correlation coefficients were both equal to one then international diver-sification could be accomplished by holding any one foreign asset, all others would be perfectsubstitutes and so redundant in the portfolio.

12 By taking unweighted averages we are assuming that the relevant portfolio is one made upof equal amounts of equities. Adler and Dumas (1979) point out that any market segmentation(e.g. deviations from purchasing power parity) obscures the concept of an equilibrium or marketportfolio because such a portfolio will differ by nationality. Consequendy, it should beemphasized that our measure of diversification benefits only applies to the equal weight port-folio we have constructed. For very large portfolios, weights approach equality so our analysiscan be construed to be applicable to very large portfolios.

13 We are referring only to that part of risk of a portfolio due to the co-movement of returns.The question of the effect of exchange rate changes on the variance of returns has not beenaddressed in this paper.

REFERENCES

Adler, M. and B. Dumas (1983) 'International Portfolio Choice and Corporate Finance: A Syn-thesis', Journal of Finance, XXXVIII, 3 (June 1983), pp. 925-984.

Agmon, T. (1972), 'The Relations Among Equity Markets: A Study of Share Price Co-movementin the United States, United Kingdom, Germany andjapan'. Journal of Finance, XXXVII,4 (September 1972), pp. 839-856.

Allan, I. (1982), 'Return and Risk in International Capital Markets', The Columbia Journal of WorldBusiness, Summer, XVII, 2 (Summer 1982), pp. 3-23.

Ehrlich, E.E. (1981), 'International Diversification by United States Pension Funds'. Federal ReserveBank of New York Quarterly Review, VI, 3 (Autumn 1981), pp. 1-14.

Elton, E.J. and M.J. Gruber, eds. (1975), International Capital Markets (Amsterdam, North Holland,1975).

Errunza, V.R. (1983), 'Emerging Markets: A New Opportunity for Improving Global PortfolioPerformance', Financial Analyst's Journal, September/October, 1983, pp. 5158.

Eun, C S . and B.G. Resnick (1984), 'Estimating the Correlation Structure of International SharePrices', The Journal of Finance, XXXIX, 5 (December 1984), pp. 1311-1324.

Finnerty, J.E. and T. Schneeweis (1979), 'The Co-movement of International Assets and Returns',Journal of International Business Studies, X, 3 (Winter 1979), pp. 66-75.

Frenkel, J. A. (1981), 'Flexible Exchange Rates, Prices and the Role of "News": Lessons from thei970's'. Journal of Political Economy, LXXXIX, 4 (1981), pp. 665-705.

Grubel, H.G. (1968), 'Internationally Diversified Portfolios; Welfare Gains and Capital Flows',American Economic Review, LVIII, 5 (December 1968), pp. 1299-1314.

and K. Fadner (1971), 'The Interdependence of International Equity Markets', youma/of Finance (March 1971), pp. 89-94.

Ibbotson, R.G., R.C. Carr and A.W. Robinson (1982), 'International Equity and Bond Returns',Financial Analysts Journal (Ju\ylAugust 1982), pp. 6183.

Joy, O.M., D.B. Panton, F.R. Reilly and S.A. Martin (1976), 'Co-movement of Major Inter-national Equity Markets', The Financial Review, 1976, pp. 121.

Lessard, D. (1975), 'World, Country, and Industry Relationships in Equity Returns', in Eltonand Gruber eds.. International Capital Markets (1975), pp. 279-297.

(1975), 'The Structure and Gains From International Diversification', in Elton Grubered.. International Capital Markets (North Holland, Amsterdam, 1975), pp. 207220.

Levy, H. and M. Sarnat (1970), 'International Diversification of Investment Portfolios', AmericanEconomic Review, LX, 4 (September 1970), pp. 668-675.

Raymond, A.J. (1983), 'Asset Returns Under Fixed and Floating Exchange Rate: A ResearchProposal', Unpublished paper (February 1983).

Revey, P.A. (1981), 'Evolution and Growth of The United States Foreign Exchange Market',Federal Reserve Bank of New York Quarterly Review, VI , 3 (Augumn 1981), pp. 3244.


Rodriquez, R.M. and E.E. Carter (198^) Intemationat Financial Management, 3rd edition (New Jersey,Prentice-Hall. Inc., 1984), p. 587.

Solnik, B.H. (1974), 'The International Pricing of Risk: An Empirical Investigation of WorldCapital Market Structure', Journal of Finance, XXIX, 2 (May 1974), pp. 365-378.

(1975), 'Why Not Diversify Internationally', Financial Analyst's Journal (Juiy/August 1975),pp. 48-54.

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1989_arthur j. Raymond and Gordon Weil