commodity diversification and constrained choice

COMMODITY DIVERSIFICATION ANDCONSTRAINED CHOICE

James Love

In recent years there has been a rapidly expanding literature on theapplications of the Sharpe-Lintner capital-asset-pricing model (CAPM)to international trade.1 The trade problems facing developing countriesprovide a potentially fruitful area of application. This paper considersthe problem of short-run instability in developing countries' exportearnings, which is frequently alleged to adversely affect economicgrowth.2 Conventionally, concentration on a few commodities hasbeen regarded as a major factor contributing to this instability and acase has then been made for diversification of the commodity composi-tion of exports. This policy option has been discussed extensively3 butsimilarities with arguments about diversification and risk in an invest-ment portfolio have not been pursued far. A few authors, notablyBrainard and Cooper,4 Labys and Granger,5 Labys and Perrin6 andLabys,7 have examined the question of instability within a mean-varianceportfolio framework but of these only Brainard and Cooper explicitlyconsidered the relationship between diversification and instability. Ourpurpose is to investigate whether certain elements fundamental to theCAPM may be applied to the analysis of this relationship in the light ofa recent contribution to the theory of finance by Levy.8 It is demon-strated that an approach to analysing the components of instabilitymay be developed which permits closer examination of the effects ofcommodity diversification than has previously been possible.9 Thisapproach is then used to consider the evidence on diversification andinstability for a sample of developing countries.10

This literature is reviewed by Pomery, in Dornbusch and Frenkel (eds.) (1979).2 The arguments about the effects on growth are discussed ¡n Lim (1976). An interesting

recent country study is that by Adams, Behrman and Roldan (1979).Among the significant contributions are: Massell (1964), MacBean (1966), and MacBean

and Nguyen (1980).See Brainard and Cooper (1968).See Labys and Granger (1970).

6 See Labys and Perrin (1976).See Labys (1977).See Levy (1978).An earlier theoretical attempt to analyse the components of instability was made by

Katrak (1976).As in the significant contributions to the debate on diversification and instability, the

approach used here is partial in that it does not consider either the effects of diversification onthe level of earnings over the cycle or arguments for diversification other than those associatedwith the issue of earnings instability.

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146 BULLETIN

PORTFOLIOS OF COMMODITIES AND SECURITIES

The conventional case for commodity diversification is straightforward:the larger is the number of commodities exported, the more even arecommodity shares in total earnings and the greater is the statisticalindependence between changes in earnings from different pairs ofcommodities, the more stable, ceteris paribus, will be a country's totalexport earnings. In an early contribution Massell (1964) pointed outthat instability in proceeds is a function of both external market anddomestic supply factors. The condition of statistical independencecentral to the traditional argument may be reformulated to accommo-date the separate sources of instability, the requirement now beingthat for different pairs of commodities there should be statistical inde-pendence between external market forces and between domestic supplyinfluences. Although in drawing the distinction between market-relatedand supply conditions, Massell highlighted the fact that different in-fluences are at work in determining total instability, little attention hasbeen paid to distinguishing analytically between these potential sourcesof instability. The debate on diversification has been conducted insteadin terms of concentration coefficients and indices of instability basedon deviations from time-trend of total earnings. In contast, the distinc-tion between sources of uncertainty is fundamental to the analysis ofthe effects of diversification in standard portfolio theory.

The Sharpe-Lintner distinction is between market-related, or syste-matic, and unsystematic risk. Given less than perfect correlation amongsecurities' returns, i.e. unsystematic differences in performance acrosscompanies, rational risk-averse investors can reduce their portfolio riskthrough diversification. The limit to the reduction in risk is set by therisk of the market portfolio, which consists of all available risky assets,and, accordingly, the risk of a well diversified portfolio is highly corre-lated with the uncertainty of the market as a whole.

Portfolio management can be assessed within the framework of theCAPM by comparing performance against 'benchmark' portfoliosbased on market return, as represented by an index such as the FinancialTimes Index or Standard and Poor's, and riskless assets, such asTreasury bills. Underlying the CAPM is the assumption that capitalmarkets are perfect, i.e. there are no frictional barriers to the attain-ment of equilibrium positions, and the equilibrium risk-return relation-ship implies two related properties, namely; (a) that all investors' port-folios contain all the risky assets available in the market and (b) thatrisky assets are represented in individual portfolios in the same propor-tions as these assets are available in the market.'

Attempts to apply the principles underlying the CAPM tocommodity problems have been limited to date to a concern with

See Levy (1978).

COMMODITY DIVERSIFICATION AND CONSTRAINED CHOICE 147

selecting efficient commodity portfolios, and this has been possibledespite the absence in commodity markets of counterparts to market-return and risk-free assets. Brainard and Cooper considered the possi-bilities for diversification in production based on correlations amongworld prices and Labys and Perrin and Labys were concerned with theselection of commodities for inclusion in an international buffer stockscheme. Accordingly, interest has been focused on risk-return character-istics, where for some given time period return is defined as the meanpercentage change in price and risk is defined as the variance of prices,and attempts were made to identify, first, those commodities minimis-ing risk for given returns and, secondly, the relationships between yieldand risk across commodities. In the absence of bench-mark commodityportfolios, comparisons have been made among risk-return character-istics of various commodity combinations and, where appropriate, theresulting implications for the capital requirements of a buffer stock.

There would appear to be several inter-related factors which accountfor the failure to adapt the concepts relating to portfolio risk to thecircumstances of an individual exporting country which may attempt toreduce the instability in its export earnings by adjusting its allocation ofproductive resources among different commodities. First, investors(and, it may be added, the supra-national buffer stock agency) are, byassumption, free to determine the composition of their portfolios, givenavailable financial resources. Such flexibility does not carry over, how-ever, to the individual exporting country whose export structure isconstrained, on the one hand, by climatic conditions and human andnatural resource endowment and, on the other, by external demandconditions and partner trade policies, usually designed to protectpartners' manufacturing industries. This element of constrained choiceobviously limits the prospects for adaptation from a model predicatedon the assumption that investors operate in a perfect capital market andwith the implicit properties (a) and (b) above. Secondly, the systematicrisk of an investor's portfolio is a function of the variance of the marketreturn, for which there is no counterpart in commodity markets.Thirdly, the alleged, adverse internal consequences for the developingcountries arise from instability in earnings and not from instability inprices alone, and Murray has recently suggested that earningsinstability is mainly due to volume rather than price instability." Thus,the procedure adopted by, for example, Brainard and Cooper of defin-ing risk in terms of the variance of prices alone is inappropriate.12

See Murray (1978)."It may be noted that Murray attempts to distinguish between supply and demand in-

fluences by equating the former with quantity variations and the latter with price variations.Instability is, however, usually defined in terms of earnings and the market-related componentof instability developed here incorporates any impact on earnings of a short-run quantityresponse to changes in world market prices which in Murray's approach would be attributedincorrectly to random supply influences.

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The first two of these problems can now be overcome, however,following the recent paper by Levy. He pointed out that properties(a) and (b) of the CAPM are inconsistent with empirical evidence thatinvestors' portfolios differ in composition and that typical portfolioscontain only a relatively small number of securities. Possible reasons forinvestors holding constrained portfolios are transactions costs, informa-tion costs and the indivisibility of investment. Levy constructed ageneral form of the CAPM based on assumptions that are consistentwith the evidence on asset holdings. In this, more realistic, model theinvestor attempts to minimise the variance of his constrained portfolioand systematic risk is no longer dependent on the variance of marketreturn, but rather on the variance of the return on the selected port-folio. Thus, we now have a model in which the investor, like the export-ing country, operates under constrained choice and in which theconcept of market return is no longer central to the determination ofportfolio risk. There is then a basis for adaptation.

Given that systematic risk depends on the variance of the return onassets actually held, the third problem is that of identifying a suitablecounterpart to portfolio return when instability is defined in terms ofearnings. The measure of market conditions used here is based on thevalue of world exports of the commodities the country exports.13 Forany particular commodity one may expect unsystematic or producer-specific influences on earnings to be uncorrelated across countries andto be offsetting in the aggregate. Their aggregate value will approachzero more closely, the larger is the number of countries exporting thecommodity and the more similar are their shares in world exports.There are, of course, certain cases where random disturbances inexports fron a major supplier may exert considerable influence on themarket, Brazilian exports of coffee and Ivorian exports of cocoa beingobvious examples. Care must then be taken in interpreting results onmarket-related and unsystematic earnings for such major suppliers, butfor other exporters such disturbances may be regarded as determiningchanges in market conditions.'4 An additional point which arises fromthe definition of instability in terms of earnings is that comparisons ofthe degree of instability among countries or between different timeperiods for the same country are only possible if the measure of in-stability is independent of the overall level of earnings.15 Thus, as isshown below, our measures of the components of instability, derived

The value of world exports is used as a measure of market conditions in, for example,Kravis (1970).

14 Specifically, one may be unable to distinguish between the components of earningswhere the unsystematic factors specific to the major supplier influence the market for a givenproduct. The more important that country's exports in total world exports of the product andthe more important the product in the country's portfolio, the more highly correlated thecountry's actual earnings will be with the market index for its constrained portfolio.

IS See Massell (1964), p.49.


from the concepts of systematic and unsystematic risk, contain as anelement the mean of the relevant earnings series.16

The well-known market model of standard portfolio theory andLevy's objections to that model are stated briefly in the Appendix. Thefeatures of the constrained portfolio which are relevant here may be setout using the following notation:

R1 = the return on security j= the sensitivity of security j to the return on the con-

strained portfoliou1 = the unsystematic return component for security jm1 = the share of the portfolio's market value represented

by security jm1 = the share of the portfolio's market value represented

security 1k = the number of securities held

= the variance of the return on the constrained portfolio= the variance of the unsystematic return component for

security jcoy (R1, R,) = the covariance between returns of securities ¡ and j

The return on the constrained portfolio may be expressed as:k

Rk=mJRJ (1)/=1

and the conventional market model may be replaced by the time-seriesregression equation

R = a + Ç3,Rkt + U5.

The systematic risk of the constrained portfolio is then given byÑ 2

where the constrained portfolio's beta factor is defined as

k

f3, =/=1

Unsystematic risk for the constrained portfolio, o, is given by

= m7o1 + coy (R1, R,)1=1 /=1 ¡=1

By analogy with Levy's specification of the model and its risk com-ponents, which he employs to re-examine the variance minimisation

16 The mean of export earnings is used here as in the measure referred to by Massell as the'normalized standard error'. See Massell (1964), p. 49.

(5)

Since, by construction, Wg is a sum of weighted values, its variance may

150 BULLETIN

problem underlying the CAPM, we may now derive expressions for themarket-related and unsystematic components of earnings instability.

Let us denote:

x1 = the share of commodity ¡ in the country's total exportearnings

V1 = the index of world market proceeds from commodity ¡,the value for the base year being set equal to 100

g = the number of commodities the country exportsE = the country's earnings from commodity ¡e. = the unsystematic component of the country's earnings

from commodity j= the sensitivity of the country's earnings from commodity

ito the measure of external market conditionsxh = the share of commodity h in the country's total export

earnings= the variance of the measure of external market conditions

c,. = the variance of the unsystematic earnings from com-modity i

cov(e1, E) = the covariance of e and Eh

= the variance of the index of world market proceeds fromcommodity j

For an individual country we define the measure of external marketconditions for its set of exports, Wg, as

gWg XV (6)

i=1

By analogy with equation (2) we may then obtain the following time-series equation in which the country's earnings from commodity ¡ areexpressed in terms of market-related and unsystematic components

E,1 = + ¡3Wgt + cit (7)

The normalised variance of the measure of external market conditionsis given by a,/hgt where h'gt is the average of the Wgt and, by analogywith equation (3), the market-related instability of the country'searnings from its g export commodities is

ßgci2wliVgt (8)

where, by analogy with equation (4), the country's beta factor for itsset of g commodities is

ßg = (9)i=i

be expressed as

cr xa1 + '' XjX, cov(e, Eh) (10)1=1 ¡=1 h1

and substituting from equation (10) into equation (8) we obtain thefollowing for market-related instability

¡g g g \Ißg (+ XjX, cov(e, Eh))/ Wgt (11)

i1 i1h1By analogy with equation (5), the normalised unsystematic or non-market-related instability, o, may be expressed as

g gcr=j XU1+ XXhcoV(El,Eh)/X (12)

\i1 i1 h1 1/

where Î is the mean of the country's time series of total exportearnings.

In line with the reformulation of the traditional argument to accom-modate Massell's distinction between external market and domesticinfluences, the potential impact of diversification on, first, the market-related component of instability may be demonstrated by assumingthat for each pair of commodities market-related earnings are uncorre-lated, that commodities account for equal shares in total earnings andthat is the average value of u. Then (11) becomes:

13g (!Uj)/1Ï7g (13)

Thus, as the number of commodities exported is increased market-related instability will be reduced, ceteris paribus.

Likewise, to demonstrate thé potential effect of diversification onunsystematic instability we assume that for each pair of commoditiesunsystematic earnings are uncorrelated, that commodities' shares intotal earnings are equal and that is the average value of 4. Then(12) becomes:


(1/g) d2-e (14)

Thus, as additional commodities are exported, ceteris paribus, unsyste-matic instability will be diminished.

The empirical relationship between diversification and earningsinstability may be examined by making comparisons between two timeperiods. The extent to which a country has diversified its export struc-ture may be measured by, first, calculating the widely-used Gini-

152 BULLETIN

Hirschman coefficient for each period.17 This coefficient is defined as

c xt (15)

A diversification factor may then be estimated as the ratio of the coeffi-cient for the second period to that for the first. Total instability in acountry's earnings, which may be denoted by 4, is given by the sum ofthe market-related and unsystematic components and behaviourbetween two time periods may be observed by again estimating theratio of the value for the second period to that for the first. The sameprocedure may be followed for the components of instability.

This approach can now be applied to data on export earnings for asample of countries to consider (j) the relationship between diversifica-tion and instability in earnings and (ii) the relative importance ofmarket-related and unsystematic influences in determining totalinstability.

SAMPLE

A sample of 30 developing countries was selected on the basis of theavailability of consistent and fairly comprehensive data on exportearnings over the period 1948_75.18 For purposes of comparison theperiod was divided into two sub-periods of equal length, 1948-61 and1962-75. The indices of market conditions for the countries' com-modity sets were calculated from data on world export proceeds.'9

RESULTS

The results are presented in Table I. The values obtained for thediversification factor, D, range from 0.51 for Maxico to 1.20 forIndonesia. Exports of all but eight countries became more diversified,i.e. D < 1. Increased concentration was associated with expandedpetroleum exports for Ecuador, Indonesia, Nigeria, Trinidad-Tobago

17 This is the most widely-used of the measures of concentration and is the most approp-riate for our present concern. See MacBean and Nguyen (1980), p. 356.

The countries included in the sample are those for which data are available on com-modities accounting for at least 80 per cent of total earnings in both periods. Commoditieswere identified at the three-digit level of the SITC. Data were taken principally from variousissues of United Nations, Yearbook of International Trade Statistics and also from variousissues of IMF, International Financial Statirtics.

19 Estimates of world trade in the commodities exported by the countries in the samplewere taken from various issues of FAO, Trade Yearbook, Commodity Review and Yearbookof Fishery Statistics. For commodities such as coffee and cocoa the estimates included thevalue of semi-processed products but these generally account for only small proportions of thetotal world value of exports. Published estimates are not available for certain types of products,notably metals and minerals, and the estimates used here were compiled from the value of themajor suppliers' exports.


TABLE 1Measures of Diversification and Instability and the Shares of the Market-Related

Component in Total In stability

and Tunisia with greater dependence on traditional mineral exports forChile and Peru and with greater dependence on traditional agriculturalcommodities for the Dominican Republic.20 Given this fairly wide-spread commodity diversification, the conventional argument suggeststhat we might expect to find offsetting marked-related and unsyste-matic influences contributing to greater earnings stability.

20 increased concentration on primary products for the Dominican Republic may beexplained by the rapid expansion of that country's sugar exports following the shift in USdemand away from Cuba after 1959. See Grissa (1976).

C2D=- (4)2I (gv/'gt)2 (2)2

M1 M2i (4) MR_(ga!t)l 2(U)i

Argentina 0.99 4.141 4.518 1.984 0.83 0.92Bolivia 0.83 6.647 17.783 0.856 0.37 0.93Brazil 0.60 2.542 2.823 2.398 0.34 0.38Burma 0.88 1.014 5.606 0.424 0.88 0.63Chile 1.18 4.111 4.340 1.805 0.91 0.96Colombia 0.69 1.048 1.717 0.744 0.31 0.04Costa Rica 0.73 3.337 3.849 1.481 0.78 0.90Dominican Republic 1.04 4.312 7.157 0.707 0.56 0.93Ecuador 1.05 4.915 27.870 3.071 0.08 0.42EI Salvador 0.60 1.026 0.828 1.729 0.78 0.63Ethiopia 0.96 4.609 0.424 5.776 0.22 0.02Ghana 0.94 2.885 8.721 0.691 0.27 0.82Guatemala 0.52 1.618 1.707 1.000 0.52 0.58Guyana 0.85 1.636 18.491 0.851 0.04 0.49Haiti 0.81 1.201 2.038 0.047 0.58 0.98Honduras 0.72 7.188 35.253 1.933 0.16 0.77Indonesia 1.20 4.021 6.880 3.554 0.17 0.27Jamaica 0.99 1.583 2.970 1.187 0.22 0.42Mexico 0.51 1.938 2.390 1.776 0.12 0.15Nicaragua 0.75 1.464 0.718 2.791 0.64 0.31Nigeria 1.26 6.144 1.439 11.280 0.52 0.01Panama 0.86 2.919 3.000 2.685 0.83 0.84Paraguay 0.96 2.623 3.691 2.354 0.20 0.28Peru 1.05 12.042 1.790 22.641 0.51 0.08Sri Lanka 0.98 2.858 1.702 3.023 0.12 0.07Sudan 0.91 3.772 5.258 3.539 0.14 0.19Trinidad-Tobago 1.03 4.831 8.133 0.979 0.54 0.91Tunisia 1.25 1.727 1.606 2.041 0.72 0.68Uruguay 0.84 1.242 2.868 0.959 0.15 0.34Venezuela 0.99 1.513 6.537 1.750 0.14 0.01

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From Table 1 it may be seen, however, from the results for theinstability ratio for total earnings, I, that all countries experienced anincrease in total instability, i.e. in all cases I> 1. Values of I rangedfrom 1.0 14 for Burma to 12.042 for Peru. These results are consistentwith the evidence on increases in instability obtained from studiesusing the conventional measures of instability when, as here, the1970's are included in the coverage.21

Inspection of the results in Table 1 indicates no clear relationshipbetween D and I. Recognition of constrained choice, however, high-lights the fact that the argument relevant to an individual exportingcountry, namely, that the greater is the extent of diversification, thegreater will be the stability of earnings, cannot be extended to a sampleof countries. The nature of the constraints defining export possibilitieswill differ among countries and will lead to differences in the market-related and unsystematic changes in instability associated with diversifi-cation. Thus, countries experiencing the greater degree of diversificationare not necessarily those with the more stable earnings. For what it isworth, the correlation coefficient between D and Jis r 0.3 53 which isinsignificant at the 95 per cent level of confidence. Excluding the oil-exporting countries22 does not alter matters, as we then have r = 0.3 54,which is also insignificant at the 95 per cent level.

Turning to the components of instability, we find that the value ofthe market-related component has increased, i.e. MR> 1, for allcountries other than El Salvador, Ethiopia and Nicaragua. Each of thesethree countries had D < 1 and, coincidentally, each is heavily dependenton coffee. Thus, unlike the other countries in the sample with D < 1including coffee-exporters such as Brazil, Colombia, Costa Rica,Guatemala and Haiti, diversification was accompanied in these threecases by stabilizing market-related influences. Given the commodity'boom' of the mid-1970's it might be argued that MR> 1 for mostcountries simply reflects greater instability in commodity marketswhich violates the ceteris paribus assumption of the conventionalargument. But even then there remains the possibility of offsetting non-market-related or unsystematic fluctuations.

From Table I we find, however, that the value of the unsystematiccomponent has risen, i.e. U> 1, for all countries other than Bolivia,Burma, Colombia, Ghana, Guyana, Haiti, Trinidad-Tobago andUruguay. Apart from Trinidad-Tobago, these countries had D < 1.Thus, only seven of the 22 countries in the sample whose exportsbecame more diversified experienced reductions in the unsystematiccomponent of instability. The balance of evidence does not support,therefore, even this part of the conventional argument.

21 See Love (1977) and Bigman (1978).22 The oil-exporting countries in the sample are Colombia, Ecuador, Indonesia, Nigeria,

Panama. Trinidad-Tobago, Tunisia and Venezuela.


Generally, the values for MR are greater than for U, the exceptionsbeing El Salvador, Ethiopia, Nicaragua, Nigeria, Peru, Tunisia and SriLanka. The proportionate increases in market-related instability havebeen greater, therefore, than the proportionate increases in the unsyste-matic component and, accordingly, the contributions of the former com-ponent to total instability have risen. The shares of the market-relatedcomponent in total instability in the first and second periods aredenoted in Table 1 by M1 and M2 respectively. From Table 1 it may beseen that M2 > M1 for all but the eight countries just mentioned. How-ever, despite the widespread greater increases in MR, the number ofcountries for which the market-related component accounted for thelarger part of total instability continued to be less than half of thesample. Both M1 > 0.5 and M2> 0.5 for 14 countries. Thus, unsyste-matic factors have been the marginally more important determinantof instability across the sample in both periods. It appears, therefore,that over two-thirds of the countries in the sample have experienceddiversification of the commodity composition of exports which hasbeen accompanied by increases in earnings instability resulting fromincreases in both the market-related and unsystematic components andthat the unsystematic factors represent the principal source ofinstability for just over half the sample.

CONCLUSIONS

Most of the countries in our sample experienced diversification of theirexport structures. Although the conventional argument holds that suchdiversification will lead to greater stability in earnings, our results indi-cate that there were increases in instability across the sample. Generally,these increases resulted from rises in both the market-related and un-systematic components of instability. It follows that the central elementin the case for diversification, namely, that widening the range ofexports will produce offsetting changes in earnings, is not supported bythe empirical evidence. This evidence on the widespread absence ofreductions in either component of instability casts doubt on theefficacy of commodity diversification as a means of reducing earningsinstability.

University of Strathclyde

APPENDIX

In standard portfolio theory the return on security j, R, is divided intotwo components: systematic return, which is dependent on marketreturn, Rm, and unsystematic return, which depends on factors specific

156 BULLETIN

to the company such as managerial abilities and labour disputes. Thus,we have the following time-series regression:

R1 = am + 13,mRmt + 6'jt (A. 1)

Employing the usual definition of risk as the variance of returns,security i's systematic or market-related risk is given by:

!3jm0n (A.2)

where u is the variance of market returns.Unsystematic or non-market-related risk is given by a, the variance

of the residual return factor.The systematic risk of the investor's portfolio is then given by:

p' 2t-'p0m

where the portfolio beta factor, ß,, is defined as:

n= mß1m

¡=1

where n is the number of securities held.Unsystematic portfolio risk, 4, is given by:

4 = mja + mm1 cov(R1, R1) (A.5)/=1 /=1 ¡=1

Levy argues that the evidence on portfolio holdings indicates thatinvestors hold only a few risky assets rather than the market portfolio.This has important implications for the estimation of risk components.Suppose that an investor holds a portfolio with k assets whose randomreturn is Rk while the random return on the market portfolio is Rm.Since the constrained portfolio includes only a few securities, onewould expect the variance of Rm to be smaller than the variance of RLevy describes the relationship between Rk and Rm as follows:

RmRk+ (A.6)

where i1, is an error term.Since the investor holds only k assets the appropriate form of the

time-series regression is

R1 = a + ß/kRkt + uit (A.7)

Levy argues that the use of equation (A.l) rather than equation (A.7)causes a bias in the estimation of the beta factor. The estimate of ßjm isgiven by:

cov(Ri,Rm)jm var m)


cov(R1, Rk + i4i)

var(Rk + ,1i)

cov(R/,Rk) + cov(R1, iii)

o+ a + 2cov(Rk, Li)Dividing by a and assuming errors to be distributed independently ofthe true values (R1 and Rk), the last term in both the numerator anddenominator will tend to zero as the sample size increases. Thus,

- ID D \/I1J_ 2/ 2\ 2l'jm - cov1, "k)I' ' U/Ukj UkBut since

!3/k = cov(R1, Rk) a (A.1O)

we obtain

l-'Jm 1 +

Hence

1%m <ßjk

The appropriate risk measures are then those given in the text which arederived from equation (A.7) in this Appendix. The corresponding equa-tion in the text is equation (2) in which the k subscript on the jthsecurity's beta factor is dropped for convenience.

REFERENCES

Adams, F. G., Behrman, J. R. and Roldan, R. A. (1979). 'Measuring the Impact ofPrimary Commodity Fluctuations on Economic Development: Coffee andBrazil',American Economic Review, Vol. 69, May, pp. 164-68.

Bigman, D. (1978). 'Levels of Export Instability: Some Methodological Considera-tions and Recent Evidence', presented to the Econometric Society Meeting,Chicago.

Brainard, W. C. and Cooper, R. N. (1968). 'Uncertainty and Diversification inInternational Trade', Food Research Institute Studies, Vol. 8, pp. 257-85.

Grissa, A. (1976). Structure of the International Sugar Market, Paris, DevelopmentCentre Studies, OECD.

Katrak, H. (1976). 'Commodity Concentration and Export Fluctuations: AProbability Analysis', Journal of Development Studies, Vol. 12, pp. 274-76.

Kravis, I. B. (1970). 'Trade as a Handmaiden of Growth: Similarities Between theNineteenth and Twentieth Centuries', Economic Journal, Vol. 71, pp. 850-72.

Labys, W. C. and Granger, C. W. J. (1970). Speculation, Hedging and CommodityPrice Forecasts, Lexington, D. C. Heath & Co.

Labys, W. C. and Perris, Y. (1976). 'Multivariate Analysis of Price Aspects ofCommodity Stabilization', Weltwirtschaftliches Archives, Vol. 112, pp. 5 56-64.

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Labys, W. C. (1977). 'Optimal Portfolio Analysis of Multicommodity StockingArrangements',BULLETIN, Vol. 39, No. 3, August, pp. 219-28.

Levy, H. (1978). 'Equilibrium in an Imperfect Market: A Constraint on the Numberof Securities in the Portfolio',American Economic Review, Vol. 68, September,pp. 643-58.

Lim, D. (1976). 'Export Instability and Economic Growth: A Return to Funda-mentals', BULLETIN, Vol. 38, No.4, November, pp. 311-22.

Love, J. (1977). 'The Decline in Export Instability?',BULLETIN, Vol. 39, No.4,November, pp. 355-59.

Massell, B. F. (1964). 'Export Concentration and Fluctuations in Export Earnings:A Cross-Section Analysis', American Economic Review, Vol. 54, March,pp. 47-63.

Massell, B. F. (1970). 'Export Instability and Economic Structure', AmericanEconomic Review, Vol. 60, September, pp. 618-30.

Murray, D. (1978). 'Export Earnings Instability: Price, Quantity, Supply,Demand?', Economic Development and Cultural Change, Vol. 27, pp. 61-73.

MacBean, A. I. (1966). Export Instability and Economic Development, London,George Allen & Unwin.

MacBean, A. I. and Nguyen, D. T. (1980). 'Commodity Concentration and ExportEarnings Instability: A Mathematical Analysis', Economic Journal, Vol. 90,June, pp. 354-62.

Pomery, J. (1979). 'Uncertainty and International Trade', in Dornbusch, R. andFrenckel, A. (eds.), International Economic Policy: Theory and Evidence,Boston, John Hopkins University Press.

commodity diversification and constrained choice

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