Uncertainty and Flexibility in the Brazilian Beef Livestock Sector : the Value of the Confinement Option

In this work, the value of existing operational flexibility is evaluated, its emergence being attributable to the Brazilian livestock alternatives for cattle fattening, i.e. by maintenance in pasture or through confinement. This crucial sector of the Brazilian economy, the second largest in the world, is highly fragmented, features low return margins and is subject to significant uncertainty factors. Confinement increases cattle fattening speed and when compared against maintenance in pasture it maximizes return on investment for farmers. In spite of this, confinement decision making is dependent upon appropriate time management. Confinement also poses risks related to the volatility of feed costs. Through the Real Options management methodology, assessment of financial growth in livestock fattening is directly linked to flexibility of timing in the transfer of cattle from pasture to confinement, with the presence of associated uncertainties. The results indicate that there is a significant increase in financial returns through containment, calculated using the return per head system. They also point to the importance of correct confinement timing to maximize returns.


INTRODUCTION
ccording to USDA (2013) (Department of Agriculture of the United States), Brazil is the world's second largest meat producer since 2009.In 2012, domestic production was 9.2 million tons, representing approximately 16% of the total world production.In the same year, Brazil is also included as the second largest herd in the world, with 197.5 million heads, approximately 19.3 % of all world flock (USDA).
The Brazilian domestic market is among the three largest consumers, with 7.9 million tons in 2012 (USDA).According to estimates by Anualpec (2012), domestic consumption of beef per capita nationally is 34.5 kg per person per annum, similar to countries like the United States (35.3 kg) and Australia (36.1 kg).According to a survey from the Center for Advanced Studies in Applied Economics -(CEPEA / ESALQ, 2014), Gross Domestic Product (GDP) of livestock was R$332.6 billion, representing approximately 30.5 % of total GDP in agribusiness 2013, which shows that livestock has a large representation in the Brazilian economy.
In 2010, the productive line of beef turned over approximately US $ 167.5 billion (BRAZILIAN BEEF, 2011).According to Silveira (2002), the results presented in the cattle sector are due to the intense structural change in recent years occurring through various activities, i.e. the increased application of technology and more efficient management models, ensuring a prominent position on the international scene.
However the majority of producers in Brazil are small to medium sized, and the financial return of margins in the sector are small and subject to uncertainty and the market price of the final product with operating costs.An important and recurring operating decision of producers is when to confine cattle.Such decisions have a strong impact on the profitability of the business because from one perspective confinement increases fattening speed, but on the other hand it also increases production costs.Thus, determining the optimal time for confinement is of critical importance to business success.
The value of this managerial flexibility in an uncertain environment is not captured by the traditional methods of evaluating investments , such as Discounted Cash Flow (DCF ) , as flexibilities requires a system with optional features.The methodology of Real Options, on the other hand, allows the assessment of managerial flexibilities to be built into the projects, processes or companies, in the presence of uncertainty.The objective of this article is to apply the methodology of Real Options to measure the value of strategic confinement timing The beef livestock farming sector was chosen because it has elements common to other sectors of the economy, such as high levels of uncertainty in activity, the existence of managerial flexibility in (farmer) decision making, and the economic and social importance that such activity represents for the country.
This paper is organized as follows: after this introduction, we present the theoretical framework with an overview of the Brazilian livestock sector and Real Options literature reviews and modeling uncertainties for Stochastic Processes.Section 3 shows the model used.
In Section 4, the modeling is demonstrated through the processing of data and the presentation of results.Section 5 presents the conclusions and suggestions for future research.

AGRICULTURAL SECTOR
According to the Anualpec (2012), the number of animals treated in intensive fattening feedlot via increased 67.8 % between 2003 and 2012.However, despite this growth, the number of animals treated in intensive fattening systems is still low, accounting for only about 4% of the total herd.In addition, according to the Ministry of Agriculture, Livestock and Supply (MAPA, 2012), cattle raising is present in all Brazilian states, reinforcing the economic and social importance of the activity in the country.Medeiros and Montevechi (2005) point to the existence of three stages in the production process of beef: raising, breeding and fattening, as can be seen in Table 1.Vitória, v. 12, n. 6, Art. 5, p. 100 -120, nov.-dec. 2015 www.bbronline.com.brAccording to the Agricultural Census (IBGE, 2006) , among establishments with more than 50 heads, approximately 59% of the total herd are located in specialized production units in one or two production steps, which reinforces the horizontalized structure of the process.Silveira (2002) identifies that few producers hold the three stages of production due to cultural factors, location and land prices.In fact, specialization generates lower investment in both capital and the area of development activities (i.e.development being seen in this case as an activity in itself), while at the same time an increase in the cost of activities presents a risk to the production chain.The steps of the production process are developed properties and, according to Barbosa Andrade Souza, Grace, & Pinto (2011), can be divided into two production sub-systems: traditional subsystem (extensive) and an improved subsystem (semiintensive or intensive).In the traditional subsystem, there is a predominance of extensive cattle with heavy reliance on obtaining nutrients through grazing, lack of investment in improvement of pastures and low annual productivity.In improved subsystems, there are increased investments in maintenance, improvement of pastures, use of mineral and nutritional supplementation, and containment systems.These subsystems can identify greater concentration of specialized properties in the stages of growing and fattening, according to Table 1.
In the stage of fattening, Barbosa (2012) reinforces the option of finishing feedlot cattle as a strategy to capture specific market conditions, increasing profitability and increasing production scale of the property.In fact, additional gains from the confinement option is possible due to the flexibility of the commercial environment in which the farmer is inserted.
According IEL report, CNA and SEBRAE (2000), if the market is unfavorable at that moment, the producer has the option not to sell the animal, thus retaining the cattle on pasture or in confinement, thus reducing supply and waiting for an environment more favorable in the near future.
Thus, in properties with improved subsystem features, the farmer has the option to choose the optimal animal fattening process, pasture or confinement, and can determine when to sell the animal within the duration of the fattening stage, as shown in Table 1. Figure 1 shows the decision-making diagram for the farmer in the improved sub-system over the fattening stage.The open points in Figure 1 show the possibility of the farmer's role with the closed points representing the end of flexibility.It may be noted that given the choice of confinement, the option to return the animal to pasture is extinguished because the weight gain obtained in confinement would be reduced given the energy expenditure of the animal's mobility in pasture.However the confinement strategy has restricted access because it requires high initial investment (machinery, buildings etc.) as well as additional food costs, labor, sanitation and other specific costs, further increasing the risk of the activity.
According to Lopes and Magellan (2005), confinement in power represents approximately 30.2% of the total cost of the activity (including the cost of acquiring the animal, representing 66.6 % of total costs).The main feed inputs are grain corn, soybean hulls, sunflower meal, urea and mineral supplement (GUEDES, 2011), which increases the farmer's exposure to market risks such commodities.
As seen in Maya (2003), farmer activity is subject to market uncertainty through the cost of investments and the final product, and the risks inherent in the production process such as climate, pests and genetic mutations.Thus, the skilled livestock manager, with an  A pioneer, Tourinho (1979 ) presents methodology based on the extent of work carried out in Black and Scholes (1973) and Merton (1973) applied in the pricing of the value of options generated by managerial flexibility in the evaluation of projects using real assets (i.e. livestock).This methodology has been called Theory of Real Options (TOR), which allows for the proper assessment of the real value of real projects in uncertain scenarios.Boyle (1988) cites the capacity of the TOR risk model to modulate two uncertainty variables using the methodology of recombinant binomial trees shown in Cox , Ross and Rubinstein (1979).Subsequently, the concept of variable bi-variate tree has been discussed in Copeland and Antikarov (2003) with two modeling uncertainty factors correlated.In Bastian-Pinto, Brandao and Hahn (2009) and Hahn and Dyer (2008) both uncertainty factors (ethanol and sugar prices) are modeled by two processes of Mean Reversion Movement (MRM) adapted to the binomial tree recombinant from the modeling of probabilities supervised and developed by Nelson and Ramaswani (1990).Thus, this approach allows for the application of the TOR methodology in real assets projects involving commodity price correlations.

Project Uncertainty Factors
For this study , we will use two variable objects for pricing of the options described in Confinement costs are the set of ingredients for the animal feed in intensive fattening stage, as an example a kernel of corn, soybean hulls, sunflower meal, urea and mineral supplement (GUEDES, 2011).For Lopes (2008), the total costs of confinement can be segregated into five main components: the acquisition of the animal, food, labor, exercise and

Stochastic Processes
A common form of modeling uncertain variables in investment projects using TOR is geometric Brownian motion (GBM) (PADDOCK; SIEGEL; SMITH, 1988), in which it is assumed that the variable follows a lognormal distribution model of variance growing linearly with time.Dixit and Pindyck (1994) also show that over the short term, the spread of prices are dominated by stochastic shocks, i.e., by a geometric Brownian behavior.However empirical studies of historical data on commodity prices reveal that the average reversion models are more accurate in capturing the real behavior of these variables (HAHN; DYER,

2008).
The Mean Reversion Movement (MRM) is a Markov process in which the direction and intensity of deviation are dependent on the current price, which in turn converges to an average of market equilibrium which is assumed to be the price long-run average.The single factor Ornstein-Uhlenbeck process is the simplest form of MRM, which is defined by Equation (1): Where xt is the modeled variable, η the mean reversion speed, the long-term equilibrium level for which xt converges, σ the volatility of the process and dz a Wiener process.The expected value and variance of the process are given by Equations ( 2) and (3) (PINDYCK; DIXIT, 1994): Equations ( 2) and (3) show that when: t tends to infinity, then: Var [x t ], tends to : o 2 2h unlike what occurs in the GBM where the variance tends to infinity as the time increases.Thus, the variance of the MRM process has a lower dispersion than the GBM model having characteristics of a non-stationary series, namely the average and variance changes with time.Thus, determining the stationarity of whether or not the series can contribute to the choice most suitable to the process for modeling the variable.

Selection of the Stochastic Process
One of the main verification tests of the existence of stationarity in a time series is the Dickey-Fuller test (ADF).This test unit infers the existence of root, whereby the null hypothesis (H0) that there unit root in the series, i.e., b = 1, by linear least squares regression.
If you can not reject the null hypothesis, we conclude that the series has a unit root and follows a random diffusion process.If the null hypothesis is rejected, there are indications that the series is a stationary process, in which the mean and variance are constant over time, featuring a mean reversion.The ADF test was applied in the representative time series of farmer uncertainty variables in the fattening stage: market prices of Livestock Cattle (CEPEA / ESALQ, 2014) and confinement costs (BIGMA, 2012), both measured in Reais per sign (R$ / @).
The EViews software was used for the augmented Dickey-Fuller test (ADF) with the deflated series in natural logarithm of Livestock Cattle Prices and Costs of Confinement.This was done using the option "intercept" in the test equation for series of Livestock Cattle prices, and the option "trend and intercept" for series of Cost of Confinement, in order to better accommodate the data series.However, for both series, the test was performed without the addition of lags or differentiation.The reason for this is that in studies involving derivatives (such as Real Options), the calculations of optimizations along the uncertain paths of the underlying asset, are carried out by backward induction (or from future to present).For this reason, the stochastic processes are modeled with Markov processes, in which the next step depends only on the last value of the series, regardless of the trajectory of this hitherto.For this reason, the search for stationarity should be performed on the natural logarithm of series without introduction of differentiation.
The t-statistic for the Livestock Cattle price series does not allow rejection of the null hypothesis of a unit root at a significance level of 5% (critical value: -3.425 ), indicating that the series presents suitability for Brownian motion.However, for variable "Confinement costs", the t-statistic shows that the series presents mean reversion behavior, as can be seen in the test results below: • Price of Livestock Cattle -t-statistic: -2.245 • Cost of Confinementt-statistic: -3.630 Pindyck (1999 ) argues that the ADF test is not sufficient to determine the choice of the stochastic process, and recommends using another approach that reflects the series behavior of the feature before price shocks, in that temporary impacts in the series show a behavior of mean reversion.To this end he suggests using the variance ratio test in equation form (4).

R =
1 Var ( P t+k -P t ) k Var ( P 1 -P ) (4) The variance ratio test measures the variance of the behavior of the series as the number of lags k increases.In the MGB case, in which the variance grows linearly with k , the ratio Rk approaches 1 with k's growth.On the other hand, if the ratio initially increases, stabilizing thereafter at a level below 1, there is evidence of a steady process of mean reversion.The variance ratio test of the uncertainty factors of the Fattening Activity via Confinement systems was applied.The result is shown in Figure 3 and corroborates the assumption of mean reversal for both series.Overall, the tests (ADF and Variance Ratio) support the hypothesis that the factors of uncertainty pricing in Livestock Cattle and Confinement Costs can be modeled as mean reversion stochastic processes.Mean reversion processes have higher computational complexity compared to the MGB, given the greater difficulty of bringing the results to bear through the recombinant binomial tree structure.

APPROACH OF RECOMBINANT BINOMIAL TREE TO THE MEAN REVERSION PROCESS
Ramaswany and Nelson (1990) propose a method that approximates the discrete continuous Ornstein-Uhlenbeck model using a recombinant binomial tree.This model uses a The additive binomial step (o Ornstein -Uhlenbeck process is an MRM arithmetic) is shown in Figure 4 .In order to demarcate, the probabilities above are within the range [1:0], Nelson and Ramaswami (1990) censor the existing probabilities that are out of range, preventing negative probabilities and / or above 100%.Equation ( 6) summarizes the conditions: Since the probability of ascent and descent of each node of the tree is dependent on the recombinant xt, level, the result converges weakly into an MRM (HAHN; DYER, 2008).
However, in order to review the binomial tree with a risk-free discount rating, we need to modify the MRM for a risk neutral process.Therefore, it is necessary to penalize the longterm average by the normalized risk premium of variable xt, represented by: λx/η (DIXIT; PINDYCK, 1994).Thus, Equation (7) depicts the Equation ( 6) adjusted for risk neutrality:

BI-VARIATE MODELING WITH TWO FACTORS OF UNCERTAINTY FOLLOWING MRM
Bi-variate models allow for the possible connecting up of different stochastic processes different to the two uncertainty variables, that may or may not be correlated.The recombinant binomial lattice approach of Cox et al (1979) for two variables was initially presented by Boyle (1988).Subsequently, He (1990); Ho, Stapleton and Subrahmanyam (1995) Schwartz and Smith (2000) developed a mean reversion model with two factors that adopts two distinct stochastic processes to model the price of a commodity.In the article, it applied an MRM to describe the short-term behavior of this variable, and a GBM to capture the evolution of price equilibrium level over the long-term uncertainty factor.Hahn (2005) adapted the model of Schwartz and Smith (2000) with a bi-variate tree, modeling two uncertainty factors, one being built as a binomial lattice of Cox et al (1979), and the other using the Nelson and Ramaswami approach (1990), converging weakly to a mean reversion process.Bastian-Pinto, Brandão and Hahn (2009) and Hahn and Dyer (2008) apply the bivariate tree model using two MRM processes for two project uncertainty factors using the reviewed model of Nelson and Ramaswami (1990).
In general, in bi-variate models, for each tree node there are four branches with ascent and descent probabilities associated with two variables ( x and y) , as can be seen from Figure 5.
x,y x+Δx, y +Δy x+Δx, y -Δy x-Δx, y +Δy x-Δx, y -Δy Therefor: pu|u + pd|u =1 e pu|d + pd|d =1.This formulation allows for the segregation of the four subdivisions with the joint probabilities in a sequential manner, in which the conditional probability of the variable x can be reviewed again using Equation (7).Bastian-Pinto (2009) adapted to the model of Ornstein-Uhlenbeck mean reversion, those probabilities having already been formatted through the use of risk neutral Equations ( 11):

Figure 1 -
Figure 1 -Diagram of the farmer's decision-making (model) -fattening stage Figure1, could lead to problems in the application of traditional theories of evaluation of investment projects, i.e. because these systems of analysis fail to measure the influence of existing managerial flexibilities in the (livestock) marketplace.

Figure 2 ,
Figure2, which are: The market spot price of Livestock Cattle and confinement costs, both in Reais per Bushel (R$/@).The spot price of Livestock Cattle is the primary variable for the operating cash flow of activity, and this parameter is used to guide much of the decisionmaking process of the farmer (IEL;CAN; SEBRAE, 2000).The price data on the spot market of Livestock Cattle were obtained through the CEPEA site (Center for Advanced Studies in Applied Economics, the Higher School of Agriculture, CEPEA/ESALQ, 2014).
health.For this study we will use the costs in the trough, i.e. feed costs over the other operating costs of the confinement activities.Data on the costs of confinement were obtained from estimates made by Bigma Consulting(BIGMA, 2012), industry specialists in the management of farms, project analysis and production techniques.

Figure 2 -
Figure 2 -Monthly average price of the deflated view (without seasonality) of Livestock Cattle and Cost of Confinement (both in R$/@ ) (Translated Glossary for Chart: Custo de Confinamento = Cost of Confinement.Boi Gordo = Fattened Cattle)

Figure 3 -
Figure 3 -Variance Ratio Test (K-defasagens tempo = K-time lags) (Chart Translation Reference: Razao de Variancia = Variance Ratio, Boi Gordo = Fattened Livestock, Custo Confinamento = Cost of Confinement) simple binomial sequence of length ∆t with n periods, and time horizon T = nΔt.The model also uses probability as a way to manage parts of the binomial tree built by providing consistent results for the application of TOR.Equations (5) describe the values and probabilities of the binomial stochastic process to model the Ornstein-Uhlenbeck mean reversion.

Figure 5 -Where
Figure5-Branching bivariateBrandão and Dyer ( 2011) demonstrated that joint probabilities for x and y can be described as outlined in Equations (8): ì

A
Uncertainty and Flexibility in the Brazilian Beef Livestock Sector: the Value of the Confinement Option 102 used in the beef livestock farming sector in Brazil.And so, this article seeks to highlight if this managerial flexibility (i.e.Real Options) adds, in fact, value to cattle raising, quantifying this value from the simple approach of discounted cash flow.