A MCDA Application for selecting which Brazilian fruits are best suited to Future Contracts

Danielly Freitas de Almeida Management Engineering Department

Federal University of Pernambuco, UFPE Recife-PE, Brazil

danialmeida_freitas@hotmail.com,

Adiel Almeida-Filho Management Engineering Department

Federal University of Pernambuco, UFPE Recife-PE, Brazil

atalmeidafilho@yahoo.com.br

Abstract— Given the importance of agribusiness for the Brazilian Economy and the requirements of formalization and the degree of professionalization achieved in this sector, this paper considers the use of future contracts to strengthen the marketing of Brazilian fruits. Some of the fruits considered have never been negotiated by using future contracts. However the objective of this paper is to point out which fruits from a set of Brazilian fruits are the most suitable ones when it comes to negotiations that use future contracts. In the case study, a MCDA method was considered that is compatible with this selecting-a-fruit problem. The PROMETHEE I method was used to analyze the following alternatives: banana, guava, orange, apple, papaya, mango, tangerine and grape by considering their performance set against the following criteria: perishability, price oscillation and market size. The main result indicated that the grape is the fruit that best fits into negotiations using the futures markets.

Keywords - Futures Markets, Brazilian Fruits, MCDA, PROMETHEE.

I. INTRODUCTION Given the unpredictability of the future, there is no way to

predict the market of a particular agricultural product when it is harvested. Two possible sceneries can contribute to this inconsistency: shortage of the product caused by natural reasons (blight, frost etc.), which, therefore, leads to prices being increased, thus giving more profit to the producer and, secondly, an abundance of the product brought about by weather conditions favorable to the cultivation of the product, resulting in an oversupply, and thus, its selling price will decrease. As a result, both producers and dealers can be placed in vulnerable situations. The former are at risk from falling prices, since they are the primary sellers and, the latter is under a high risk, since they will intervene in the market between producers and consumers. So, there is a need for both of them to enter an agreement when the product is being planted and set the product at a price that is expected at the end of the harvest [1].

It is as a result of such circumstances that the futures market came into being. It is devised to deal with the risks involved when commodities prices vary by establishing the terms of negotiation between buyers and sellers of a particular item regarding its price, with respect to a deadline in the future that has been previously set.

Thus, the introduction of a given fruit in the negotiations of the futures market can facilitate how its prices are formed in the spot market in Brazil and assist the participants in this market to manage their risks. As there are many different kinds of fruit in Brazil and several conflicting criteria that must be analyzed as to the choice of which best suits negotiations in the futures market, the proper approach to seeking a solution to this selecting-a-fruit problem is reached by applying a multicriteria model. To search for the data that this research was to use, the PROMETHEE I method was chosen, from the PROMETHEE family, as it stands out from the others when it comes to formulating and dealing with the problem suggested in this study. It is an approach in which it is possible to present incomparability between the alternatives, that is, there is an alternative with excellent performance in some criteria and, simultaneously, with poor performance in some other criteria. It also allows non-compensatory assessments and intercriteria to be evaluated by using weights given to the importance of the criteria. In this case, the following fruits were used as alternatives to be analyzed: banana, guava, orange, apple, papaya, mango, tangerine and grape; and the following criteria were used : perishability, oscillations in price and market size.

Given the importance of the agribusiness for the Brazilian economy, this paper suggests that due to the degree of formalization and professionalization achieved in this sector and, also, due to the increased prominence that the global economy has been given in Brazil, there should be negotiations on Brazilian fruits should be set in the futures market. Therefore this paper presents a case study that includes a multiple criteria decision aid approach to indicate which fruit is the most suitable one as to being the subject of negotiations in the futures market. This is with a view to introducing the fruit chosen into the futures market as negotiating its sale therein would help producers and dealers to manage properly the risks of variations in its price and to form its price in an efficient and clear way.

II. FUTURES MARKETS The futures market aims to establish negotiations between

buyers and sellers of a particular item at a specific price, under a deadline in the future that has been previously set. It is part of the derivates market because negotiations of future contracts depend on the physical market of the corresponding product

2012 IEEE International Conference on Systems, Man, and Cybernetics October 14-17, 2012, COEX, Seoul, Korea

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having been created to deal with the needs of producers and dealers in order to manage the risks, should there be changes in the price of the item. In other words, there is an underlying assumption that a certain minimum level of the product can be supplied. Souza (1996) states that the reason why the futures market exists, is because it offers the possibility of transferring risks [1].

The main participants of future markets are hedgers, speculators and arbitrageurs. Hedgers are agents who participate in the physical and futures market, and aim to acquire protection by means of exploiting the risks of variations in fixed prices. Given the volatility in the market, there are speculators who seek to acquire positions in the market by betting on high or falling prices and who accept the risks of these varying while at the same time they aim to make capital gains to cover variations in the prices of commodities. Finally, there are arbitrageurs, who seek to make profits by simultaneously buying and selling the same or an extremely similar commodity in different markets [1, 2].

In the futures market, prices are formed in a transparent, efficient and clear way, and control, automatically, the imperfections of how they have been formed. Therefore, entering a futures contract would enable distortions to be reduced in either the scope of the market or in the financial scope. However, before seeking to enter a futures contract, studies must be undertaken to rule out the possibility of this leading to failures similar to those that have been occurring lately [1, 3].

There are several criteria that must be taken into account if a futures contract is to be successful. Among them, according to the authors [3, 4, 5], aspects that can influence the use of future contracts and that stand out regarding commodities are: storage and useful life: the commodity should be storable for a considerable period of time; uniformity: the commodity must have a minimum variation with respect to its quality and standardization; the failure of existing fixed-term contracts: the need for a futures contract only exists if there are likely to be gaps when negotiating fixed-term contracts; the absence of external intervention: governmental agents or private agents should not influence the formation of commodity prices; the size of the physical market: a large number of participating companies, a great number of negotiations and the high frequency of negotiation allow enormous variation in prices and, therefore, the need for a hedge; oscillation in cash prices: if cash prices should oscillate widely, they attract hedgers and speculators because the former need to decrease the risk of oscillation and the latter are interested in profiting from the oscillations, and; competition in the market: the success of a futures contract can be influenced by the existence of similar contracts. Negotiations on the same stock exchange or on the foreign stock exchange of a futures contract may lead to failure in negotiations for a futures contract.

III. MULTICRITERIA In complex sceneries of decision-making, the choices to be

made are significant, the consequences are long-term and can affect many people. The Multicriteria Decision Aid (MCDA) approach aims to help decision makers organize and

summarize information such that they can feel more secure about the decisions made, thus reducing the possibility of errors [6].

A distinction is made between multicriteria methods that are compensatory and those that are non-compensatory. Compensatory methods balance their criteria between different amounts, that is, an alternative with a bad criterion can be compensated for by another other criterion that results in a good evaluation and uses constants of scale. Non-compensatory methods between the criteria do not make up for the disadvantage of a criterion in relation to an advantage over another criterion. They need information about the relative importance of criteria. An alternative with a bad criterion cannot interfere in the final result even if there is another criterion with a very good evaluation [7].

Multicriteria Decision Aid Methodology provides several methods to solve different problems. The choice of a particular method depends on several requirements, such as questions related to the size and characteristic of the problem, the decision maker’s preferences and so on. The multicriteria methodology helps to find the “the best solution to which a commitment should be made” since the “optimal solution” will not always be feasible for all objectives simultaneously [8].

IV. REVIEW OF THE LITERATURE MCDA approaches has been applied in several contexts,

such as maintenance [9, 10, 11, 12, 13], risk evaluation [14, 15, 16, 17], outsourcing and logistics [12, 18] , project management [19, 20, 21], water resources management [22, 23 , 24] and many others.

There are important articles that on using the PROMETHEE method in the financial field. In [25] is presented a case study on the calculation of the fairest percentages for sharing the European budget. [26] presents a new method for portfolio design so that investment companies can plan scenarios. [27] assesses and classifies a set of companies for investment opportunities. [28] conducts a quality evaluation to measure the performance of Turkish hospitals. [29] using financial data evaluates Greek companies engaged on agricultural food production and in the field of marketing. [30] selects attractive portfolios under an investor´s constraints and, consequently, maximizes returns and minimizes risk. [31] obtains a classification performance of the agrifood business in accordance with profitability, solvency and performance managerial ratios. [32] assess the performance of a bank regarding the bank´s overall performance and exposure to risk. [33] chooses the best investments, using 15 criteria. [34] uses goal programming to select potential companies to support public funds financially under political and budgetary constraints. [35] selects high stocks for investments in the Tehran Stock Exchange (TSE).

V. APPLICATION OF THE PROMETHEE I METHOD The problems included in this paper aim to select a fruit

that is the best fit for negotiations in the futures market by applying a multicriteria model. Since there are many kinds of fruit to choose from and this choice is driven by the desire to

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meet several objectives that are linked to criteria that allow each alternative to be analyzed. For this purpose, a multicriteria approach was chosen because this methodology aims to help the decision makers organize and summarize the information such that can feel more secure about the decision made, thus reducing the possibility of errors. It also evaluates several alternatives for tackling multiple objectives simultaneously.

The PROMETHEE I method, from the PROMETHEE family, was chosen because it stands out from the others since it formulates and deals with the problem put forward in this study. It sets out an approach in which it is possible to show incomparability between the alternatives, that is, where an alternative has an excellent performance in some criteria and simultaneously, a poor performance in other criteria. It also enables non-compensatory and intercriterion assessments to be made by using weights for the criteria to denote their degree of importance. The steps from PROMETHEE I method will be given below and are drawn from [6, 7, 36].

Step 1 - Defining the decision agent: The decision agent chosen was a specialist who acts on the Brazilian futures market and has extensive knowledge of how it functions.

Step 2 - Defining a decision matrix with “m” alternative and “n” criteria: A decision matrix was compiled with the alternatives (banana, guava, orange, apple, papaya, mango, tangerine and grape) versus criteria (perishability, prices oscillation and market size). Table I presents the decision matrix data.

TABLE I. DECISION MATRIX

Alternatives Criteria

Perishability (days) Oscillations in Price (%)

Market size (000’s of reais)

Banana 21 11.987528 3,160,292

Guava 21 15.207568 213,482

Orange 60 13.458927 4,695,049

Apple 210 21.169922 943,761

Papaya 23 24.649907 1,348,294

Mango 21 19.538326 602,125

Tangerine 28 20.574047 524,944

Grapes 180 32.853500 1,612,043

Weights 6 4 8 Source: compiled based on data from Embrapa, Ceasa,-BA and IBGE. These fruits were chosen because they are the main fruits

produced in Brazil. Moreover their production is feasible all year round in Brazil and their trade balance is favorable. The choice of criteria was based on either the fruit being apt to or not being apt to interfering in the success of a particular futures contract.

The data about the perishability of the fruits are related to their lifetime i.e. the point at which a fruit becomes perishable if it exceeds its determined limit of useful life. The useful life of each fruit was defined from data collected from the Brazilian Agricultural Research Corporation (EMBRAPA). The size of the fruit market was derived from the value of fruit production in Brazil, in 2009. These data were collected from the Brazilian

Institute of Geography and Statistics (IBGE) and represent the share of these fruits in national production in reais (R$). The prices of the monthly quotations of fruit were taken from the Bahia Center for Food Supply (Bahia-Ceasa) from 2007 to 2010. Bahia was chosen because it is the state that is the largest exporter of fruit, accounting for 20% of total exports and is one of the biggest fruit producers in Brazil. The formula of the standard deviation was used to calculate the volatility of prices.

Step 3 – Defining the preference function for each criterion: There are six models from which the decision maker defines his/her preference function for each criterion. They are used to define the intensity of his/her preference. The decision maker chooses the function model and defines the required parameters. The criteria of price volatility and market size were defined as true criteria (there is no parameter to be defined. The criterion of perishability was defined as the preference threshold (p=90), by the decision maker who used a questionnaire.

Step 4 - Defining how to find two alternatives in accordance with each criterion: The differences ( ikδ ) for each pair of alternatives must be calculated, given the criterion ki Sxx :

( ) ( )kjijik xuxu −=δ . (1)

Where ikδ is the difference between the alternative

performance ix and the alternative performance kx related to criterion j.

The function of the relative preference for each criterion j

is calculated by Equation 2.

( ) ( ) ( )( ) ( )ikjkjijjkij PxuxuPxxP δ=−=, . (2)

This step is presented in Table II.

Step 5 – Calculating the preference index ikS of the

alternative ix , compared to the alternative kx :

( ) ( )==

j

ikjj

j

j

kijj

j

ik wj

Pw

wj

xxPwS

δ,. (3)

Where ikS is a value from 0 to 1.

The calculations of the preference index express the intensity of preference of a given alternative over different alternatives, and considers all criteria simultaneously (Table II).

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Step 6 – Calculating the positive +Φ i and negative −Φ i

outranking flux regarding alternative ix :

The positive and negative outranking flux shows respectively, how a given alternative outranks and, at the same time, is outranked by the other alternatives (Table III).

=Φ +

kiki s (4)

=Φ −

kiki s

. (5)

It is important to note that the set of alternatives in discussion interferes in the results of the positive and negative outranked fluxes obtained, that is, the relation of classification between an alternative a and an alternative b can be changed by including or excluding alternatives.

TABLE II. CALCULATION OF THE PREFERENCE INDEX

Pair of alternatives

Alternatives X weight

Pair of alternatives

Alternatives X weight

Pair of alternatives

Alternatives X weight

Pair of alternatives

Alternatives X weight

Banana-Guava 0.44 Orange-Banana 0.81 Papaya-Banana 0.22 Tangerine-Banana 0.24 Banana-Orange 0 Orange-Guava 0.58 Papaya-Guava 0.67 Tangerine-Guava 0.69 Banana-Apple 0.44 Orange-Apple 0.44 Papaya-Orange 0.22 Tangerine-Orange 0.22 Banana-Papaya 0.44 Orange-Papaya 0.58 Papaya-Apple 0.66 Tangerine-Apple 0 Banana-Mango 0.44 Orange-Mango 0.58 Papaya-Mango 0.67 Tangerine-Papaya 0.01 Banana-Tangerine 0.44 Orange-

Tangerine 0.56 Papaya-Tangerine 0.66 Tangerine-Mango 0.24

Banana-Grape 0.44 Orange-Grape 0.44 Papaya-Grape 0 Tangerine-Grape 0 Guava-Banana 0.22 Apple-Banana 0.55 Mango-Banana 0.22 Grape-Banana 0.55 Guava-Orange 0.22 Apple-Guava 1 Mango-Guava 0.66 Grape-Guava 1 Guava-Apple 0 Apple-Orange 0.55 Mango-Orange 0.22 Grape-Orange 0.55 Guava-Papaya 0 Apple-Papaya 0.33 Mango-Apple 0 Grape-Apple 0.66 Guava-Mango 0 Apple-Mango 1 Mango-Papaya 0 Grape-Papaya 1 Guava-Tangerine 0 Apple-Tangerine 1 Mango-Tangerine 0.44 Grape-Mango 1

Guava-Grape 0 Apple-Grape 0.11 Mango-Grape 0 Grape-Tangerine 1 Source: the authors

TABLE III. CALCULATION OF THE POSITIVE AND NEGATIVE OUTRANKING FLUX

ikS Banana Guava Orange Apple Papaya Mango Tangerine Grape +Φ i

Banana - 0.44 0 0.44 0.44 0.44 0.44 0.44 2.66 Guava 0.22 - 0.22 0 0 0 0 0 0.44 Orange 0.81 0.58 - 0.44 0.58 0.58 0.56 0.44 4.02 Apple 0.55 1 0.55 - 0.33 1 1 0.11 4.55 Papaya 0.22 0.67 0.22 0.66 - 0.67 0.66 0 3.13 Mango 0.22 0.66 0.22 0 0 - 0.44 0 1.55 Tangerine 0.24 0.69 0.22 0 0.01 0.24 - 0 1.42 Grape 0.55 1 0.55 0.66 1 1 1 - 5.77

−Φ i 2.84 5.06 2 2.22 2.37 3.95 4.11 1

Source: the authors.

Step 7 - Defining a partial pre-order using the pre-orders previously calculated from the following relations:

- ix outranks kx if:

+Φ i > +Φ k and −Φ i < −Φ k or

+Φ i > +Φ k and −Φ i = −Φ k or

+Φ i = +Φ k and −Φ i < −Φ k

- ix is indifferent to kx if:

+Φ i = +Φ k and −Φ i = −Φ k

- ix is incomparable to kx if:

+Φ i > +Φ k and −Φ i > −Φ k or

+Φ i < +Φ k and −Φ i < −Φ k

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From the results obtained, it may be concluded that: The alternative of banana outranks the alternatives of guava, mango and tangerine. The alternative of guava does not outrank any of the alternatives. The alternative of orange outranks the alternatives of banana, guava, papaya, mango and tangerine and is incomparable with the alternative of apple. The alternative of apple outranks the alternatives of banana, guava, papaya, mango and tangerine and is incomparable with the alternative of orange. The alternative of papaya outranks the alternatives of banana, guava, mango and tangerine. The alternative of mango outranks the alternatives of guava and tangerine. The alternative of tangerine overcomes the alternative of guava. The alternative of grape outranks all other alternatives (banana, guava, orange, apple, papaya, mango and tangerine).

Therefore, based on data collected and information obtained from an expert on futures markets, PROMETHEE I was applied and the final result obtained was that grape is the fruit that is best fitted for negotiations in the futures market.

According to the decision maker’s preferences, orange and grape are incomparable to each other due to the absence of clear and positive reasons to justify the preference or indifference relation, that is, there is an alternative with excellent performance in some criteria and, simultaneously, with poor performance in other criteria. By comparing the orange to the apple, which has a longer life, 240 days, a greater price volatility (21.16%) and a market of smaller size (R$ 943,761), while the orange has a useful life of 60 days, a price volatility of 13.45% and a market size of R$ 4,695,040.

In order to check the robustness of the results, a sensitivity analysis was performed that considered possible simulations for parameter variations of up to 20%. From the sensitivity analysis the outcome is that the alternative of the grape was considered as a robust solution for the decision model.

Negotiating the trade of this fruit in the futures market would help both its producers or traders to manage the risks in price variations of grape and its price could be established in an efficient and clear way. It would also control, automatically, the imperfections of how its price is formed.

VI. CONCLUSIONS Given the objectives of this study, it appears that producers

and traders need to manage the risks in their activities and characteristics related to how the market in fruits influences the success or failure of futures contracts. This paper set out by using PROMETHEE I to choose which fruit is best fitted for contracts in the futures market, thus enabling the risks associated with the prices of these products and this market to be managed. It is thus an extremely useful tool for the producers and traders who are susceptible to price variations in their products. The following alternatives were analysed: banana, guava, orange, apple, papaya, mango, tangerine and grape; and set against the following criteria used: perishability, oscillations in price and market size.

The data collected on grape prices were those that had greater oscillation compared with the other fruit selected in this study. The size of the market in grapes, that is, its production

value, is classified as the third largest one, compared with the other fruit studied. Moreover, the criterion of perishability, which defines the useful life of grape is shown to be the second highest one, which may last for up to 180 days, which places it in a good position in relation to the others when it comes to negotiations in the futures market, as shown by the results after using PROMETHEE I in this study.

In order to check if the results obtained in this paper were robust, a sensitive analysis was undertaken using possible simulations for different weights of criteria, and it was observed that the result found that the grape is the best alternative as to which fruit is best negotiated in the futures market, i.e. the initial result had not been changed. Therefore, all the scenarios showed the grape as the best alternative. This enhances the claim that the result obtained has a high level of reliability.

ACKNOWLEDGMENT This paper is part of a research study funded by CNPq (the

Brazilian Bureau that Funds Research) and CAPES (the Brazilian agency that fosters the training and development of Higher Education Personnel).

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