research on futures markets: issues, approaches, and...

Research on Futures Markets: Issues,Approaches, and Empirical Findings

Steven C. Blank

This paper presents a brief assessment of the recent futures and options literature withreference only to agricultural markets. The discussion centers on the markets' socialvalue and economic value to firms. Issues currently unresolved are highlighted, insome cases by presenting hypotheses contrary to standard positions. Overall, thecurrent literature describes these markets as having positive social value and servinguseful functions at the firm level, but existing theory and empirical methods arecriticized for many weaknesses.

Key words: futures, literature survey, options.

Futures market research and its resulting lit-erature have increased in volume tremen-dously over the past decade. The successfulintroduction of financial and industrial prod-ucts on futures markets and the legalization oftrading options on futures have attracted mar-ket analysts from nonagricultural disciplines.These researchers brought with them a differ-ent perspective for viewing futures marketswhich has greatly expanded the number andtype of issues being evaluated. In particular,futures market analysts with a business financebackground are much more common than adecade ago. These researchers have begun ap-plying methodologies and testing hypothesesfound only in the finance literature of the 1970s.To facilitate dissemination of the new wave offutures research results, entirely new journalshave appeared during the 1980s, such as TheJournal of Futures Markets and The Review ofFutures Markets. Along with new contribu-tions in traditional outlets for agricultural fu-tures research, these journals have expandedand altered the nature of the futures literature.

The changing composition of futures re-search brought on by the changing composi-tion of futures trading activities can give theimpression that the economic purpose andfunctions of futures markets also may have

Steven C. Blank is a visiting associate professor in the Departmentof Agricultural Economics at the University of California, Davis.

This is Giannini Foundation Research Paper No. 897.

changed in recent years. However, the fact thatfutures exchanges have expanded their productlines to attract customers from nonagriculturalsectors of the economy has not altered theavailability or operation of "agricultural" fu-tures markets. Still, questions remain concern-ing how the new research focus and literaturehave affected the list of topics considered tobe important in futures markets for agricul-tural products. This can be seen by comparingthis paper to earlier surveys of futures litera-ture (such as those by Gray and Rutledge;Leuthold and Tomek; and Kamara).

Therefore, the objective of this paper is topresent a brief assessment of the issues, meth-ods, and results reported in the recent litera-ture, with reference only to agricultural futuresand options markets. These topics are dis-cussed in the sections below, followed by anoutline of future directions the literature maytake.

Issues

Economic analyses of futures markets contin-ue to center around two basic questions: Dothe markets have social value, and economicvalue to firms? Issues related to these questionsare summarized below.

Social Value Issues

Economists tend to credit market instrumentswith positive "social value" if they are judged

Western Journal of Agricultural Economics, 14(1): 126-139Copyright 1989 Western Agricultural Economics Association

Research on Futures Markets 127

to be contributing to pricing efficiency and/orimproving resource allocation (Kamara). Ka-wai supports the long-held view that, in theory,futures have potential for much social valuethrough gains in both pricing and allocationperformance. The steady stream of empiricalevaluations of potential markets (such as thatby Miller, Smith, and Williams) implies thatmarket improvements are expected with theintroduction of futures trading in product mar-kets, thereby implying social value for futures.Also, a number of papers have evaluated theuse of futures as policy tools designed to alterresource allocation (Chavas, Pope, and Kao;Kahl 1986; Kawai). It is likely that policy-related research will be prominent in theliterature for some time because the U.S. De-partment of Agriculture currently is conduct-ing a national pilot program aimed at encour-aging more farmers to use futures and optionsmarkets.

Recent assessments of futures market pric-ing efficiency have considered issues rangingfrom factors affecting price variance (Kenyonet al.; Helms and Martell) to identifying risklevels and risk premiums (Ehrhardt, Jordan,and Walkling; Elam and Vaught; Hartzmark;Hayenga et al.; Lien; Rzepczynski; So). Inparticular, the existence of "normal back-wardation"' and its expected effects on pricerelationships and risk premiums are still beingdebated.2

Although new models are being introduced,research on options pricing efficiency contin-ues to center on evaluating the "Black Model"3

(Jordan et al.; Koop; Wilson, Fung, and Ricks;Wolf, Castelino, and Francis). However, re-

Normal backwardation has been defined in different ways sinceKeynes first described the concept as a situation in which spotprices are higher than forward prices for a commodity. It is some-times defined as the process where a futures price is a systematicallydownward biased estimate of an expected spot price over time. Ithas come to be accepted as a situation where, on average, futuresprices rise over the life of a futures contract so that the currentfutures price is lower than its expected value in later periods (Lien).

2 Issues debated concerning backwardation are empirical ques-tions and, therefore, are discussed in the section on research ap-proaches.

3 The Black model of option pricing is based upon "European"options, which may be exercised only at the end of trading for theoption, rather than "American" options which may be exercisedat any time prior to the end of trading. Models have since beendeveloped that are directly appropriate to American options, butthese models are much more complex and produce estimates ofoption premiums that are very similar to those produced by theBlack model. The Black model estimates option premiums basedupon values of five variables: current price of the associated futurescontract, the option strike price, number of days to option ma-turity, volatility of the associated futures contract price, and theinterest rate on a relatively safe investment.

cent studies have noted that actual premiumsfor options on agricultural futures contracts arenot expected to always equal premiums pre-dicted by the Black Model as thought earlier.Instead of defining the existence of discrep-ancies between the two premiums as evidenceof market inefficiency, analysts are now tryingto identify what factors cause the differences(Hauser and Neff; Wilson, Fung, and Ricks).This means that new definitions of efficiencyare needed for options markets.

Firm-Level Issues

Futures markets were established to have eco-nomic value for firms by facilitating forwardpricing of products. Questions receiving atten-tion deal with how to use the markets to gainthe greatest benefit. It appears that empiricalresearch has dealt with separate questionswhich fit together in a logical progression fromhedging, to determining optimal hedge ratios,to placing hedges into a portfolio framework,to seeking decision rules to aid in marketingdecision making.

Traditional hedging was the focus of mostearly firm-level futures market research. Thecentral issue was "to hedge or not to hedge?"Despite Working's arguments to the contrary,it often was assumed that risk reduction wasthe primary goal of hedgers. This meant thatmany empirical analyses simply sought to de-termine whether futures and spot prices weresufficiently correlated to allow producers to re-duce their risk exposure by forward pricingusing futures. If price correlation was foundregularly over a period or season, strategieswere developed which most often recom-mended full, one-period hedging over that timespan.

The next issue addressed concerned risks noteliminated by hedging. Correlation betweenspot and futures prices could not be perfect fornumerous economic reasons.4 Therefore, basis5

4 In general, arbitrage forces spot and futures prices of storableand nonstorable products together at the time of futures contractdelivery. During the life of a futures contract for a storable product,arbitrage keeps futures prices at or below a level equaling spot priceplus per unit carrying costs. Nonstorable product futures prices areexpected to reflect spot prices anticipated at a later date whichmay have different supply and demand conditions operating thanthose operating at present, so correlation between spot and futuresprices may be low (Blank, Carter, and Schmiesing).

5 Basis is the difference between spot and futures prices, or be-tween prices of two different futures contracts. Although the price"spread" between two futures contracts is not usually referred toas basis, its behavior is quite similar to basis in some markets.This is especially true if one of the futures contracts is the "nearby."

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risk remained and hedging the entire spot po-sition (a ratio of one for hedged output to spotoutput) was not the lowest risk strategy. As aresult, analysts began estimating "optimal"hedge ratios for particular products (Bond,Thompson, and Geldard; Kahl 1983; Karp;Peterson and Leuthold 1987; Sheales and To-mek).

Analysts studying basis risk recognized thatit was more relevant to evaluate the two com-ponents which together generated basis (spotand futures prices) rather than basis itself. Thisled to the idea of studying hedgers' positionsin spot and futures markets as a two-productportfolio (Berck; Berck and Cecchetti; Brooksand Hand; Brown; Gjerde; Peterson and Leut-hold 1987). This method of evaluation wasexpanded to cover more than two-productportfolios. In particular, cross hedging6 was as-sessed as a risk-reducing strategy (Blank; Bond,Thompson, and Geldard; Witt, Schroeder, andHayenga; Wilson; Zacharias et al.).

The usual Johnson-Stein approach to port-folio modeling describes spot/futures portfo-lios as a means of risk reduction, so determi-nation of the optimal hedge is the goal of suchstudies.7 However, basis is just one source ofrisk affecting portfolios. For example, Grantconcludes that it is impossible to derive anoptimal hedge ratio when both price and quan-tity uncertainty are present, a conclusion whichquestions the entire exercise of calculatinghedge ratios.

These problems lead to issues concerninghow to identify and use risk in decision mak-ing. In particular, much empirical researchseeks to determine whether there are usefultechnical trading methods (Brandt; Irwin andBrorsen; Kenyon and Cooper; Kenyon andClay; Lukac, Brorsen, and Irwin; Peterson andLeuthold 1982; Tesar). Draper's comment onthe paper by Koop notes that technical systemsare common, despite claims by academics thatsuch systems are of "no value" because theyviolate the concepts of market efficiency. Thefact that technical systems are so widespread,especially in futures trade literature (see almostany issue of Futures Magazine), implies thatmany people believe price risk levels vary;

6 Cross hedging involves holding spot and futures positions intwo or more products which are not identical.

7 Johnson and Stein applied the Markowitz two-product port-folio model to spot and futures markets. Using the full covariancemodel, the approach provides a method to identify the lowest riskportfolio for each level of return.

therefore, positive rates of potential return areoccasionally available to traders who can iden-tify and capture them.

Finally, the debate over trading systems andoptimal hedging ratios raises questions con-cerning the relevant range of the ratio itselfand the choice of which market to use whenhedging: forward cash, futures, or options.Technical trading systems generate price fore-casts with different "confidence levels," usu-ally expressed informally as the probability thatprices will move in the direction forecast by asystem (Brandt). Logically, the hedging deci-sion may depend on price level expectationsand the degree of confidence in the forecastunderlying the expected price. A short hedgerconfident of an impending price decline mightfind that a high hedge ratio using forward cashcontracts will produce the most profit. Strongexpectations of a favorable price increase maydictate that options be used for hedging. Fu-tures may prove to be the best hedging vehicleonly when confidence in a forecast price trendis not strong or when the forecast is for a "flat"trend in price movements. For example, in hercomments concerning the paper by Tesar, Pecknotes that although Working described threeforms of commercial usage of futures (opera-tional convenience, anticipatory pricing, andarbitrage), anticipatory pricing appears to bethe sole commercial use of options. She notesthat options are preferred when price expec-tations are strong, but options are not replacingfutures in other uses.

In the extreme, if confidence is very highconcerning expected price movements, themost profitable hedge ratio could be greaterthan one or less than zero. This range has beenconsidered irrelevant to agricultural hedgersby researchers because it represents market ac-tivities that increase, rather than reduce, risks.This limitation in past research reflects the de-bate over what is hedging versus speculation.It assumes that hedgers are highly risk averseand use futures and options markets only toreduce risk exposure. A contrary opinion isthat farmers reveal a preference for some (pro-duction) risk by choosing farming over alter-native investments for their labor and capitaland that it is rational for agricultural marketparticipants to use futures and options marketsas vehicles to adjust their total level of riskexposure up or down as dictated by their utilityexpectations. As market conditions becomemore favorable, a producer (for example) may

128 July 1989


want to increase expected utility by increasingoutput, which would increase his total level ofproduction risk if it could be done. If it is toolate to plant additional acreage (or no addi-tional acreage is available), futures or optionstransactions would enable the producer to"market" the desired amount of additionaloutput and have an opportunity to gain higherlevels of utility. In such a case, raising the hedg-ing ratio above one reflects the same type ofproduction decisions which lead to producingless than 100% of capacity in other cases (byleaving some acreage fallow)-the decisionsreflect an assessment of expected utility basedupon some confidence level in a forecast. Thesemarketing decisions are analogous to decisionsof an investor selecting the desired portfoliofrom those along the "borrowing" or "lend-ing" sections of the capital market line whichis tangent to the mean-variance efficient fron-tier.

A new debate appears to be developing overthe effects of margin calls on hedgers. Manyanalysts have ignored margin requirements ofhedgers either because they assumed hedgerswould have an established line of credit witha lender to cover calls as needed, or becausethey assumed the interest expense on marginswas zero since T-bills or some other interest-producing security could be used as collateralfor margin requirements while hedges wereheld. For example, in a recent issue of TheJournal of Futures Markets, Peterson andLeuthold (1987) exclude margin call effectsfrom their analysis of cattle hedging strategies,describing them as trivial. Yet, in the sameissue of the Journal, Kenyon and Clay findmargin effects to be significant when hedginghogs due to the capital liquidity problems theycan create for high-risk producers. Clearly,more firm-level analysis of this issue is needed.

Research Approaches

Hypotheses concerning pricing efficiency andimproving resource allocation through risk re-duction have been the center of most empiricalresearch addressing issues of the markets' so-cial value. Questions involved in this type ofanalysis include whether the markets respondquickly (efficiently) to information and wheth-er the response is "accurate" in that resultingprice levels make resource allocations moreefficient. The various hypotheses have been

tested using methods often applied to equitymarkets in the finance literature, as noted inthe following sections. Firm-level decisions fo-cus on profitability and, therefore, so does re-search regarding these decisions.

Social Value Analyses

Efficient capital market theory provides alter-native efficient market hypotheses (EMHs). Forfutures markets these have all led to researchapproaches focusing on pricing efficiency as areflection of the level of informational effi-ciency in the markets (examples include: Car-ter; Chavas and Pope; Epps and Kukanza;Hudson, Leuthold, and Sarassoro; Murphy;Shonkwiler). The null hypothesis is expressedin three forms (Schwartz pp. 293-302):

(a) Weak form: The information contained inthe past sequence of price movements isreflected in current prices.

(b) Semistrong form: All public informationis reflected in current prices.

(c) Strong form: All information is reflectedin current prices.

Empirical tests of the weak form EMH mostoften have evaluated time series of spot andfutures price data by using the equation

(1)or

(2)

St = a + PF,_I + e,

F, = a + -F, t + et,

where St is the spot price, Ft is the price at timet of a futures contract expiring at some time t+ i, Ft,_ is the previous period's price for thesame contract, et is an error term at time t, anda and f are, respectively, the intercept andregression coefficient relating the two prices.Data used have been both price levels and pricechanges, but in most studies published re-cently, price change data are used to reducestatistical problems. Since transforming theoriginal price level data into price changes usu-ally produces stationary series, ordinary leastsquares (OLS) is most often used to estimatethe regression equation. The (joint) hypothesesimplied in the weak-form model are tested bysimply computing t-statistics for Ho: a = 0 and3= 1.

Studies by Maberly and by Elam and Dixonhave criticized use of pricing efficiency testsbased in equation (1), noting that results can

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be misleading.8 Elam and Dixon note that inearlier empirical work estimates of a typicallybecome larger and estimates of : becomesmaller as the time to maturity of a futurescontract increases. They attribute these resultsto an inherent bias in the OLS estimates of aand 3 rather than inefficient pricing. They alsopresent Monte Carlo evidence to argue thatthe customary F test of the joint hypothesis a= 0 and : = 1 is not valid, concluding that anew test is needed.

Different versions of the weak-form test havebeen evaluated through applications of otherestimation techniques. For example, Canarellaand Pollard tested the EMH within the frame-work of the theory of the rational expectationshypothesis (REH) using a vector autoregres-sion approach. The REH states that futuresmarket participants use all available infor-mation when making forecasts of the futurespot price. The hypothesis can be written inthe form of equation (1) above. However, Can-arella and Pollard note that a number of sta-tistical problems are encountered when esti-mating the single-equation model which make3 inefficient. They used a modified Full Infor-mation Maximum Likelihood (FIML) proce-dure to estimate a two-equation system usingfirst differenced data (necessitated by the au-toregressive structure of the spot and futuresprice data). The two equations took the generalform:

(3) S,= (aiS,) + (biFt) + u,a=l b=l

(4) Ft = (ciS,_i) + 2 (diFi) + v,,c=l d=l

where the current spot price (St) and futuresprice (F,) are each specified as a function oflagged values of the two time series; a, b, c, dare regression coefficients; and ut and v, areerror terms. By jointly estimating the twoequations with and without cross-equationconstraints, the likelihood ratio test statisticcould be computed for use in hypothesis test-ing. Using data from 1960-82, Canarella andPollard found that this procedure led to sta-tistical support for the EMH for five agricul-tural futures markets: corn, wheat, soybeans,soybean oil, and soybean meal. They notedthat other studies (such as Just and Rausser)

8 See the paper by Buccola in this issue for more detail on thetopic of pricing efficiency.

have produced similar results concerning im-plications for the effectiveness of technicaltrading systems' forecasting performance rel-ative to that of futures markets.

Studies using semistrong form tests of theEMH are typified by the paper by Gross. Hesays that a market is defined to be efficient ifthere exists no profitable trading strategy. Us-ing this definition, semistrong form tests ofefficiency focus on comparing price forecastingerrors of econometric models with that of fu-tures prices. This method is an improvementover the weak-form test but still has a majorshortcoming. Although the forecasting modelis reestimated for every new observation (pieceof information) which is added, the hypothesistest (using mean squared error usually) resultsare still dependent upon the analyst's choiceof model. Therefore, mixed results are likelyfrom different studies. For example, Garcia etal. find no inefficiency in live cattle; Leutholdand Hartmann are somewhat inconclusive onthe efficiency of hog markets; and Gupta andMayer decide that futures markets for coffee,cocoa, sugar, copper, and tin are efficient. Dueto this shortcoming of the semistrong formtest, Rausser and Carter argue that finding amodel which forecasts better than futures pricesis a necessary, but not sufficient, condition forinefficiency.

Empirical examples of strong-form tests offutures markets are rare due to lack of data.The test of asymmetry in market informationamong participants requires an analyst to iden-tify forms of "insider trading" which produceabnormal returns to one or more groups oftraders. Although trade publications occasion-ally have reported the differences in averagereturns going to professional futures tradersand to nonprofessionals, 9 it is not clear wheth-er this performance disparity is due to differ-ences in information available to each groupor to differences in trading skill.

Empirical tests of the "accuracy" of futuresmarkets' response to information have soughtto identify bias in the pricing process. Bias inthe form of normal backwardation has beenanalyzed since Keynes first defined it. Al-

9 Nonprofessionals usually are considered to be people whoseprimary source of income is something other than futures trading.The data published by the Commodity Futures Trading Commis-sion concerning positions held by "large" and "small" traders givesome indication of differences in performance of various groupsof traders but offer no explanation of information flows in themarkets.

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though Berck and Cecchetti showed that theKeynes-Hicks hypothesis of a risk premiumoffered by commodity storers to attract spec-ulators need not hold true, even in theory, em-pirical investigations of the issue continue toappear in the literature.

Dusak was the first to use the Capital AssetPricing Model (CAPM) to test hypotheses re-lated to normal backwardation (Ehrhardt, Jor-dan, and Walkling). The CAPM methodologycompares the performance of a particular assetto the performance of the market as a wholeto estimate the degree of "systematic" risk inthat asset and whether a market-determinedrisk premium exists. Dusak found no system-atic risk in grain futures. A later study by Car-ter, Rausser, and Schmitz (CRS) criticized Du-sak's use of the Standard and Poor's 500 Indexas the only measure of futures market perfor-mance. CRS used an equally weighted indexincorporating futures and stock markets andfound that systematic risk was present in grainfutures pricing behavior. The CRS approachto developing a relevant index was criticizedby Marcus and by Baxter, Conine, and Ta-markin. Both of those studies proposed dif-ferent weightings heavily favoring the stockmarket component in the market index and,consequently, joined Dusak in concluding thatno systematic risk existed in grain futures. Fi-nally, separate studies by So and by Elam andVaught used a range of weightings for the mar-ket index and found low (statistically insignif-icant) systematic risk and zero risk premiumsin crop and livestock futures markets, respec-tively. However, Elam and Vaught noted thatsignificant risk would be detected if the weight-ing given to futures in the index was increasedsufficiently.

Alternate approaches to evaluating back-wardation are illustrated in the papers by Lienand by Murphy. Lien defined backwardationas rising futures prices over time and proposedthat it was due to seasonality in the actions oflong and short hedgers. It was implied thatspeculators need not be attracted. They comewhen profitable price changes are expected,E(Pt+,) # P,, and seasonal changes in inven-tory levels will create these situations. The factthat Lien found no support for the "inventoryeffect" in corn or wheat futures markets im-plies that those markets are efficient year-round. Murphy came to a similar conclusion,finding no seasonality using spectral analysisof CAPM risk and return in crop and livestock

futures contracts. In that study, a market port-folio of stocks, bonds, and T-bonds was used,purposely ignoring agricultural assets, becausethe portfolio is for speculators (who are as-sumed to be interested only in futures tradingnot marketing agricultural products).

Although futures are risky in Keynes' con-cept of total risk, they are found to be risklessin the CAPM because their beta is low, usuallynot significantly different from zero, as in thestudies cited. Beta is a commonly used mea-sure of the degree of variability in returns ofan asset compared to variability in returns ofthe market as a whole. Tests for the CAPMtypically regress excess returns for the futurescontract on excess returns for the market, usingan equation of the form

(5) R - Rft = a + 3[E(Rmt) - Rf] + et,

where, at time t, Ri is the return on futurescontract i, Rf is the risk-free return, E(Rm) isthe market's expected return, a is expected tobe zero, f is the estimate of beta (systematicrisk), and e is the asset-specific disturbanceterm (unsystematic risk). In this form of theequation, a beta of zero indicates that the assetdoes not have any systematic risk; f > 0 in-dicates the presence of systematic risk.

Recent futures literature has followed equitymarket analyses in noting weaknesses of theCAPM. In particular, reliance on a market in-dex as the basis for comparison is consideredto be a major shortcoming of the CAPM forfutures markets. As a result, So concludes thatArbitrage Pricing Theory (APT) is more the-oretically sound than the CAPM.

In one of the first applications of APT toagricultural futures, Ehrhardt, Jordan, andWalkling (EJW) find a high degree of system-atic risk, yet excess returns (risk premia) arezero for corn, wheat, and soybeans. This con-clusion is intuitively more reasonable thanthose produced by CAPM analyses which maylead more researchers to adopt this method-ology.

The APT assumes that the return on an assetequals an expected return plus a linear com-bination of zero-mean disturbances to under-lying factors, plus a zero-mean, asset-specificdisturbance (EJW). The equation to be esti-mated takes the form:

(6) Rit = Fot + Bil(Rt- Rft + DIt)+ ... + Bik(Rkt- Rft + Dkt) + eit,

where Rit is return on an asset, defined as (Pit

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- Pi,t_l)/Pi,t,_ (EJW calculated it over a two-week period); Rft is the risk free rate; Fot is theintercept (expected to be zero in an efficientmarket); Dkt is a zero-mean disturbance to fac-tor k; Bik is a measure of sensitivity to thedisturbance (systematic risk coefficient); andet is a zero-mean, security-specific disturbance(nonsystematic risk).

The factors (Rkt - Rft + Dkt) as well as thecoefficients (Fot and Bk) in an APT model areestimated from the correlation matrix of se-curity returns by using factor analysis. Onlyfactors which are significant for pricing the fu-tures contracts of interest are used in the anal-ysis. Generally, a subjective procedure judgingthe improvement in a Chi-squared statisticand/or the percentage of variance explained isused to decide whether factors are to be in-cluded in the equation. Despite this weaknessin its procedure, the APT is considered to havegreater power than does CAPM in testing nor-mal backwardation hypotheses of systematicrisk and risk premia.

In the few years since options on agriculturalfutures have been available, a sizable body ofliterature has developed concerning the pricingefficiency of those markets (examples includeCatlett and Boehlje; Hauser and Andersen;Hauser and Eales; Koop; Ogden and Tucker;Tesar; Webb). The methodology used in mostearly work concentrated on evaluating the per-formance of individual markets compared tothe Black-Scholes Model of option pricing. Thismeant modifying the weak-form tests in equa-tions (1) and (2) and using statistics such asmean squared error in hypothesis tests. How-ever, recent studies (Hauser and Neffis an ex-ample) have noted that discrepancies betweenactual premiums and Black premiums are ex-pected to exist because American options arecompared to European options on the basis ofthe Black model. Black's model was developedassuming the option is European, meaning thatit can be exercised only at maturity. Americanoptions can be exercised at any time. There-fore, their premiums should reflect the privi-lege of early exercise. Wilson, Fung, and Rickspoint out that this means the existence of sig-nificant discrepancies implies neither marketinefficiency nor the model's inaccuracy. It sim-ply indicates that the right to exercise an optionearly may have some positive value.

New approaches to defining and testing forpricing efficiency of options markets are typ-ified by Ogden and Tucker's study of currency

futures options. They apply a methodologywhich tests the efficiency of an options marketby determining whether arbitrage relation-ships are maintained in prices. They specifysix arbitrage conditions applicable to Ameri-can options which should not be violated inan efficient market. They point out that anysuch violations represent unexploited risklessarbitrage profit opportunities. Although theprocedure does not yet appear in the empiricalliterature for agricultural options, it is likely tobe applied widely as analysts reconsider thedefinition of efficiency for options markets.

Firm-Level Analyses

Individual firms use futures as part of man-agement strategies aimed at hedging cash po-sitions of a single product and spreading riskthrough the development of a portfolio ofproducts. Central to these management deci-sions is an understanding of the optimal hedgeratio. Deriving this ratio is an empirical is-sue-it cannot be estimated theoretically. Also,a number of versions of the optimal ratio havebeen specified and estimated using differentmethods (examples include Bond and Thomp-son 1985, 1986; Bond, Thompson, and Lee;Hayenga et al.; Nelson and Collins; Wilson;Witt, Schroeder, and Hayenga). The strengthsand weaknesses of each estimation method arestill being debated. Therefore, this section firstwill present some of the most widely used sin-gle-product optimal hedge ratio models beforediscussing multiple-product portfolios.

Two questions are being debated concerningempirical estimation of hedge ratios: What isthe decision maker's objective when hedging?,and What type of data should be used? Thefirst question arises from the debate overwhether hedging is a risk-minimizing or util-ity-maximizing activity. The second questioncomes from debate over theoretical, statistical,and practical concerns about the estimationprocess itself. Depending on which data areused, the choice of equations to be estimatedwill vary. Three types of data have been usedin estimating hedge ratios: price differences,percentage change, and price levels (Witt,Schroeder, and Hayenga).

Price difference models of hedge ratios varydepending upon the decision maker's goal. Ifthe goal is to minimize the variance of returns,the hedge ratio is

132 July 1989


(7)-Xfrcf

Xc }'fXI

where Xc is the quantity of cash commodity,Xf is the quantity of futures commodity, 10 afis the variance of futures price changes, and ao-is the covariance of cash and futures pricechanges. This hedge ratio can be estimated byregressing cash price changes on futures pricechanges. On the other hand, if the goal is tomaximize expected utility, Kahl (1983) pre-sents the model

(8) d- y c ) \E(F 2 - F,) f

where F1,2 is the futures price expected at thetime a hedge is placed, or lifted, respectively,and 7 is a risk-aversion parameter. Xf is pos-itive (negative) assuming 7 > 0, which will bethe case for a risk-averse person.

Models using percentage change data alsodistinguish between the two possible goals ofhedgers. The hedge ratio when minimizingvariance is

(9)f 0-rcrf

Kc o2rf

where Vi is the total value of the cash (Vc) andfutures positions (Vf), ri is the return from pe-riod 1 to period 2 on the values of the cash(r,) and futures (rf) positions, and the variancesand covariances are now of returns rather thanprices. This hedge ratio is the slope coefficientof a regression of cash percentage price changeson futures percentage price changes. Whenmaximizing expected utility, the hedge ratio is

(10)if _ crf rf

Vc, rc V^r2

using the same notation.For a hedger concerned only with variance

about the expected return in an anticipatoryhedge (there is no current cash position), theoptimal hedge ratio is

After considering statistical,'1 theoretical,and practical questions about the appropriate-ness of using one model over another, Witt,Schroeder, and Hayenga point out that:

In comparing the price difference models with the per-centage change models, the gauge is the degree of lin-earity between the cash price and futures price differ-ences. If the cash price of the commodity to be (cross)hedged responds linearly with the futures price, the pricedifference model would be preferred because a goal isto keep the model as simple as possible. If a definitenonlinear relationship exists between the parties, thepercentage change model may be preferred. (pp. 141-42)

Theoretically, the proper hedge ratio esti-mation technique depends upon the objectivefunction of the hedger and the type of hedgebeing considered. Witt, Schroeder, and Hay-enga conclude that the best method for antic-ipatory and storage hedges, respectively, is aprice-level regression and the price changemodel. If the hedger's objective is to maximizeutility as opposed to minimizing the varianceof returns, then none of these estimation tech-niques will provide the appropriate hedge ra-tio. In that case, factors in addition to cash andfutures price variance will be significant in de-termining the optimal hedge ratio.

When presenting the results of optimal hedgeposition analysis, most empirical studies havegenerated a mean-variance (E-V) efficientfrontier to illustrate the relationship betweenexpected returns and risk (Chavas and Pope;Karp; Levy; Peck). The E-V frontier is simplydefined as the two-dimensional plot of thevariance in returns (usually measured in termsof standard deviations or the coefficient ofvariation) for each level of expected mean re-turns in a single period. The relationship isoften expressed as a preference function suchas the one used by Chavas and Pope:

(12) L = E(r - ()V(r),

(11) af aC2f2XC ~U

This equation is similar in form to equation(7), but in this case the hedge ratio is the regres-sion coefficient of cash price levels regressedon futures price levels during the period whenthe hedger would be closing the futures posi-tion and entering the cash market.

10 A positive (negative) sign preceding either cash or futuresquantity indicates a long (short) position.

where L is the objective function, E and Vdenote mean and variance, respectively, ir isprofit and a is a measure of risk aversion. Itgenerally is used in the context of expectedutility maximization with constant absoluterisk aversion and normality of Tr.

Analysts' assumptions of (a) constant ab-

n They note that generalized least squares procedures may beneeded to produce more efficient estimates of the hedge ratio dueto the influence of autocorrelation in the residuals.

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solute risk aversion on the part of hedgers and(b) a single decision period covering the timea cash position may be held have limited thistype of study. Clearly, the level of risk aversionis significant in its effect on hedge ratio levels,as noted in equation (12) and most other formsof the E- Vfunction. Therefore, empirical workis needed to establish criteria for use in guidingthe selection and/or definition of "optimalhedges" over time for individuals with differ-ent risk attitudes, not just the risk-averse case.These criteria obviously need to include somemeasure of a decision maker's level of riskaversion. This work is progressing through ap-plications of elicitation methods (Wilson andEidman; Halter and Mason; Tauer) but is hin-dered by the unresolved issue of how to mea-sure risk (uncertainty) itself (McSweeny, Ken-yon, and Kramer).

One approach to dealing with the problemof incorporating risk aversion levels into thehedging decision over time was illustrated byKarp. He defined determining optimal dynam-ic hedges as a linear exponential Gaussian con-trol problem. He allowed for differing levelsof risk aversion by generating probability dis-tributions of profits, thereby enabling hedgersto select their desired distribution. This meth-od avoids having to measure risk aversion di-rectly; it simply allows individual decisionmakers to "reveal" their risk preferences asrelated to profits. Karp's approach to selectingoptimal hedges by selecting the strategy whichwill produce the desired probability distribu-tion of profits may imply that profit, not riskreduction, is the goal of hedgers (as argued byWorking). However, a hedger may select a prof-it distribution which has a minimum proba-bility of loss, which can be considered a risk-reduction goal.

Portfolio models have increasingly been usedto estimate optimal hedge ratios when morethan one asset is held at a time. Methods forevaluating strategies appropriate in this situ-ation have centered on techniques similar tothose developed by Markowitz and expandedon by Johnson and Stein in the early 1960s(Peterson and Leuthold 1987; Berck; Berck andCecchetti; Wilson). The Johnson-Stein ap-proach tended to support the traditional theoryof hedging which held that the primary mo-tivation for hedging was risk reduction. Defin-ing spot and futures positions as two differentassets, hedging was viewed as a two-productportfolio approach to risk reduction. Johnson-

Stein define the risk-minimizing hedge ratio as

b*= AO,0a

where of is the covariance of spot and futuresprices and af is the futures price variance. Inthis formula the hedge ratio, b*, is the slopecoefficient for a simple regression of spot onfutures price levels. Brown reformulated thismodel to use variances and covariances of ex-pected returns 12 rather than prices.

Applications of portfolio analysis have be-come much more complicated in the numberof products included in the portfolio and inthe estimation techniques used in determininghedge ratios. For example, Peterson and Leut-hold (1987) evaluated some multiple-product(inputs and outputs) and multiple-period hedg-ing strategies available to a cattle feedlot byapplying a discrete nonlinear programmingroutine to the general function

(14) min y z 2 XiXjiji J

where y is a risk aversion parameter; Xi is thepercentage of the total market value of theportfolio invested in i; al- is the variance ofreturns on the ith investment, i = j, or co-variance of returns on the ith and jth invest-ments, i 7 j; and Ri is the mean of returns onthe ith investment.

Cross hedging is a special type of hedge whichhas been analyzed using traditional mean-vari-ance methods as well as portfolio techniques.The study by Zacharias et al. typifies recentapproaches to this firm-level problem. As analternative to mean-variance analysis, theyused a numerical simulation approach in com-bination with stochastic dominance to evalu-ate a variety of cross hedging strategies for arice grower. First-, second-, and third-degreestochastic dominance criteria were used to rankalternatives produced by simulating the equa-tion below for two representative farms:

(15)

where ir is expected net revenue; Ps is expectedspot price at harvest of the cash commodity;Y is expected output; PN is the futures priceused to open the cross hedge; P{ is the expectedfutures price of the commodity; Xis the futuresposition taken; and C(X) are commission and

12 Returns are calculated as in equation (6). A return is simplythe percentage change in price from one period to the next.

134 July 1989

(13)

7r = PY + (P - P)X - C(X),


margin costs as a function of the futures po-sition taken.

Zacharias et al. compare the stochastic dom-inance results to results from a traditionalregression approach to optimal hedge deter-mination. They conclude that the regressionanalysis may or may not be a risk-efficientchoice depending upon the decision criteriaemployed.

In summary, it appears that some key ques-tions remain concerning hedging and analysisof hedges. First, Brown found that the tradi-tional portfolio model is not empirically sup-ported in some agricultural product markets.The implication was that risk reduction is notthe primary motivation for hedging or crosshedging. Therefore, the relative weights ofprof-it seeking and risk reduction in firm-level de-cision making must be determined in some yetto be established manner and applied in em-pirical studies to improve the validity of re-sults.

Finally, the question of whether any of the"optimal hedge ratio" measures can be trulyconsidered "optimal" is being debated. Bond,Thompson, and Lee evaluated a simple hedg-ing rule and concluded that due to the empir-ical estimation processes required, the rule is"indicative" not "optimal."13 Similar esti-mation problems are encountered with vir-tually all hedge ratio measures, implying thatat least a change in the label (dropping "op-timal") is in order.

Turning to options, empirical studies ofhedging strategies using these relatively newmarketing tools are still few in number (ex-amples include Hauser and Andersen; Hauserand Eales; Hauser and Neff; Wolf, Castelino,and Francis). Theoretical and empirical issuesconcerning hedging with options are presentedby Hauser and Andersen. They also contributeto the evolution of empirical methods of anal-ysis by applying alternative definitions of re-turn and risk. By recognizing the unique fea-ture of options (compared to futures contracts)of being able to select price "ceilings or floors"for hedges by selecting a particular strike price,

13 They note that the simple price difference regression modelmay sometimes be inappropriate leading to biased estimates of theoptimal hedge ratio. They also find that "simultaneous equationbias may be present in regressions of spot on futures prices, im-plying biased and inconsistent estimates of the optimal hedgingstrategy." Applying instrumental variable techniques in this casealters the slope coefficient such that it no longer is exactly theoptimal hedge ratio.

Hauser and Andersen argue that evaluatingoptions' hedging performance must centeraround those target prices. They do so by usingHolthausen's target deviation model:

(16)

(17)

RK = (I- a)G'(a) da,

RT= (a - )G'(a) da,Ji

where RK is risk, RT is return, 1 is the target,a and j are risk preference parameters, andG'(a) is a probability density function for out-come a. They conclude that options are es-pecially useful as a marketing tool for agricul-tural producers with price expectations differentfrom those of the market.

Summary of Empirical Findings

In this section the question, "What have welearned about these markets?" is addressed byreviewing some empirical questions askedcontinually by analysts. The "answers" to thesequestions continue to change; therefore, thegoal here is to present only a progress report.

Social issues often center around the ques-tion, "Are the markets 'working'?" The firstissue involved with this question has to dowith whether the markets make efficient useof information.

The results discussed in this paper are mixedconcerning futures market efficiency. The pres-ence of technical trading systems implies thatfutures markets are inefficient. Yet, these trad-ing systems focus mostly on very short-termperiods only. Therefore, it may be that futuresmarkets are "inefficient" only over certain,short periods. Several studies have shown thatthe markets are efficient in the long term (Gar-cia, Hudson, and Waller); however, tradingsystems and hypotheses are tested in the shortterm leading to conclusions of inefficiency.Could it be that the testing time frame is in-appropriate? Information-efficient marketsmay have detectable trends for short periodsat the end of trading for particular contractsdue to "real-world" arbitrage limitations whichare known and used in trading systems.

The definition of "efficient" may need to bechanged when considering futures markets.Schmiesing, Blank, and Gunn suggest that amore appropriate criterion might be the effi-ciency of the arbitrage process performed by

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a market. (Ogden and Tucker use this ap-proach in judging options market perfor-mance.) Are futures markets "inefficient" be-cause they reflect expectations and not real(local) supply and demand factors for most ofa futures contract's life? Or is the problem thatfutures become "cash" market prices for con-tract delivery points at the end of each con-tract, and this is when prices become more"predictable" (due to arbitrage limitations),which reflects "inefficiency" in current ter-minology? Using the current definition, Garciaet al. conclude that efficiency probably nevercan be proven; we only can fail to disprove it.

The second general question concerning thesocial value of futures markets is "Where isthe money going?" Hartzmark studied incomeredistribution effects of futures trading andfound that commercial (hedging) traders aremost profitable while noncommercial (specu-lative) traders earn negative or zero profits. Henoted that because speculators are not receiv-ing rewards for the risks they absorb, the the-ory of normal backwardation and its exten-sions can be rejected.

The most significant firm level question fac-ing futures market analysts is, "Why do peopletrade?" Intuitively it is obvious that peoplewill continue to use the markets only as longas their business and/or personal goals are beingmet. Since the growing volume of trade indi-cates continued success of the markets, it isclear that traders' goals are being met. Sur-prisingly, analysts still do not agree over whatthose goals are: risk reduction, profit seeking,or a combination of the two (utility maximi-zation). However, evidence seems to be fa-voring the position put forward by Workingdecades ago, that risk-adjusted profits (utility)are the primary goal of traders and, therefore,provide the incentive for market actions taken.As noted earlier, Brown found that the tradi-tional portfolio model is not empirically sup-ported in some agricultural product markets,implying that risk reduction is not the primarymotivation for hedging or cross hedging.Therefore, questions of hedger motivations andgoals urgently need resolution before detailedanalyses of strategies can be undertaken.

A general question facing futures and op-tions market analysts is, "How do we keepscore?" The mixed results of the studies citedhere makes one wonder whether the methodsof analysis currently being used are appropri-ate/relevant to the issues needing attention.

Specifically, concerns have been raised in anumber of studies about the data used in em-pirical work and about the appropriate defi-nitions of "risk" and "return." Data in theform of price levels, absolute and percentageprice change, and returns have all been de-scribed as the "best" input for the statisticalmodel of preference. Also, alternative defini-tions of risk and return have been proposed.In particular, the debate over whether CAPMor APT pricing models are more appropriatefor futures indicates that several theoreticaland empirical issues need additional analysis.

Future Research Directions

When considering the unresolved issues notedabove, two other questions come to mind: "Areacademic and industry analysts going in thesame direction?" and, "Who is leading (fol-lowing)?" To answer these questions, tradepublications were reviewed as well as thescholarly literature cited above. Below is oneopinion of where the two groups are going andhow they might collaborate in the future.

It does not appear that industry and aca-demic researchers are going in the same direc-tion. Analysts in industry focus their researchefforts almost entirely on short-term priceanalysis which leads to price forecastingmodels. On the other hand, academic analystsconsider technical analysis and its resultingforecasting models to be a virtual waste of timebecause those models contradict the efficientmarket hypothesis (as it is now defined). Ac-ademic analyses of trading systems have hadrelatively long-term perspectives-much lon-ger than that of industry models.

The question concerning which group isleading the way in futures and options marketresearch appears to lead to a split decision. Themarkets were developed long ago by industryto fill its needs; academic attention came afterthe markets were well established. Industry-produced research clearly was the leader con-cerning firm-level decisions before the 1980s;until The Journal of Futures Markets appearedin 1981, the volume of scholarly research onfutures was far outweighed by industry re-search output. It appears that industry is stillleading academia in identifying firm-levelproblems and possible solutions. Yet, it makessense that business issues are first found inbusiness publications and then expanded on

136 July 1989


later in academic journals. One significant ex-ception to industry's lead was the developmentof the Black-Scholes model by academics.

Concerning social, macrolevel policy deci-sions affecting these markets, academic anal-ysis has been in the lead, as would be expected.Individual firms and analysts do not oftenspend time on economy-wide issues. How-ever, the shortcoming of academic research isthat too often it ignores the relevant period ofreal business decision making (very short run)and, therefore, is of little direct value to traders(hedgers or speculators).

This leads to the conclusion that academicresearchers can continue to fill the need formacroanalysis of the markets but should alsofocus some attention on the short-run deci-sion-making processes used by hedgers andspeculators. It may be that academic analystshave resources better suited to explaining whyindustry's technical trading systems work forperiods of time. Academic researchers need topay more attention to the "real world" deci-sion calculus of firms, using the same timehorizon as used by agribusiness managers, orthey may miss significant structural attributesof the price-setting process and ultimately reachpoor conclusions concerning policy directions.Industry analysts can assist in this processthrough their knowledge of, and access to, em-pirical data regarding actual decision processesof decision makers. Therefore, increased con-tact between academic and industry analystsin forums such as those sponsored by the fu-tures exchanges can serve as an "arbitrage"process to keep research progressing efficientlyin useful directions.

[Received July 1988; final revisionreceived December 1988.]

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