HEDGE WITH FINANCIAL OPTIONS FOR THE DOMESTIC PRICE OF COFFEE IN A PRODUCTION COMPANY IN COLOMBIA

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1 International Journal of Mechanical Engineering and Technology (IJMET) Volume 9, Issue 9, September, pp , Article ID: IJMET_09_09_141 Available online at ISSN Print: and ISSN Online: IAEME Publication Scopus Indexed HEDGE WITH FINANCIAL OPTIONS FOR THE DOMESTIC PRICE OF COFFEE IN A PRODUCTION COMPANY IN COLOMBIA Miguel Jiménez-Gómez Departamento de Finanzas, Instituto Tecnológico Metropolitano ITM, Colombia Universidad Nacional de Colombia Natalia Acevedo-Prins Departamento de Finanzas, Instituto Tecnológico Metropolitano ITM, Colombia ABSTRACT The financial hedging activities, whose main objective is to reduce investment risk, reduce the volatility of corporate profits. It is common to find companies that cover, through the use of financial derivatives, activities in the balance sheet. Financial options are a financial instrument that grants a right to the buyer and an obligation to the seller to carry out a transaction under previously established price and date conditions. The objective of this paper is to evaluate the benefits of coverage with financial options for the domestic price of coffee in a production company in Colombia. The results show that a lower standard deviation is obtained in the scenario with coverage than in the scenario with coverage. Keywords: Financial options, hedge, coffee. Cite this Article: Miguel Jiménez-Gómez and Natalia Acevedo-Prins, Hedge with Financial Options for the Domestic Price of Coffee in a Production Company in Colombia, International Journal of Mechanical Engineering and Technology, 9(9),, pp INTRODUCTION The two main global crises: the default of the subprime mortgages and the fall of the European sovereign debt, have provoked in the last years exaggerated increase of the volatility. In these circumstances, it is essential that companies establish effective hedging strategies to avoid the harmful consequences of price hops [1]. Due to the above, it is necessary to highlight that the coverage with options is adequate in situations where there is a high uncertainty regarding the cash flows in foreign currency. So this is usually the situation when the cash flows are conditioned, that is, it is not clear if the company will have an account receivable in foreign currency; and where it is feasible that the options are more interesting if the probability that the company has the credit is low and if the editor@iaeme.com

2 Miguel Jiménez-Gómez and Natalia Acevedo-Prins company is especially worried about not having a significant loss [2]. By reducing the volatility of cash flows, companies can reduce the costs of distress. In the world, it is assumed that financial problems have no cost. Therefore, altering the probability of financial difficulties does not affect the value of the company. If financial distress is costly, companies have incentives to reduce their likelihood, and coverage is a method by which a company can reduce the volatility of its profits. By reducing the variance of the cash flows or the profits of the accounting of a company, the coverage decreases the probability, and therefore the expected costs, of financial difficulties [3]. The objective of this paper is to evaluate the benefits of coverage with financial options for the domestic price of coffee in a production company in Colombia. The price of coffee is modeled and to analyze the trend and use a hedging strategy with financial options. Finally, a Monte Carlo simulation is carried out and the effect on financial options is analyzed. 2. METHODOLOGY The price of coffee will be modeled to determine its trend and thus be able to apply a hedging strategy with financial options for a coffee producing company. A Monte Carlo simulation will be conducted to determine the effect of financial options on the coffee producing company. Historical data of the internal price of coffee was used in a monthly cut for 5 years, between the dates of January 1, 2013 and January 1,, to obtain 60 data. For the strike prices of the options, the last coffee load price of the analyzed data will be taken, or the spot price in month zero, for the 6 months that will be projected. To make an assessment of the options and having which is the risk-free rate (IBR) E.A. for 1 month, 3 months and 6 months the rate for the other missing months is searched, where the Bootstrap method or resampling method is used, where basically they are simulation techniques that reuse the observed data to constitute an infinite number from which to extract repeated samples. The unit price without coverage is modeled, with 10,000 random data for the 6 months that are projected, which serve to observe how the price of coffee moves in several areas. For the modeling of the unit price without coverage, it is proposed to look for an average, a 5% percentile and a 95% percentile to observe what will happen with the price in both limits. The above is also done for the price with coverage without the premium payment and with premium VALUATION OF OPTIONS BY THE BLACK-SCHOLES METHOD Since it appeared in the 1970s, the Black-Scholes model has become the most popular method for pricing options and its generalized version has provided mathematically beautiful and powerful results on the price of options. However, they are still theoretical adoptions and not necessarily consistent with the empirical characteristics of the financial performance series [4]. The Black-Scholes formula is given by equations 1 to 4: ( ) ( ) (1) ( ) ( ) (2) ( ) ( ) ( ) ( ) (4) (3) editor@iaeme.com

3 Hedge with Financial Options for the Domestic Price of Coffee in a Production Company in Colombia Where, C is the value of a purchase option, European option (Call). P is the value of a put option, European option (Put). S is the sight rate of the currency that is the object of the option. K is the price marked in the option (Strike Price). T is the time expressed in years that still have to pass in the option. r is the domestic interest rate. δ is the foreign interest rate. σ is the volatility of the exchange rate. N is the accumulated normal distribution function. ln is natural logarithm MONTE CARLO SIMULATION This method emerged in 1944, has had many interpretations, received several definitions, therefore, we can say that this method has gone through a long process of evolution and development. Initially, an important issue of the method was to generate large series of random numbers. In the first stage, random numbers were used, and then, with the development of computer technology, this barrier has been eliminated. One of the most interesting works on the Monte Carlo method in the selection of investment projects on cost [5]. The Monte Carlo Method generates artificial values of a probabilistic variable by using a randomly generated random number generator distributed in the interval [0, 1] and also by using the cumulative distribution function associated with these stochastic variables. The simulation of economic decisions can be applied to all the degrees of problems that include operating rules, policies and procedures, such as those related to the adaptation of decisions, the control of decisions and the pricing policy [6]. 3. RESULTS In order to determine the effect of not making coverage with options on the internal price of coffee in Colombia, we start from the grouped data obtained from the National Federation of Coffee Growers (NFC). With the data obtained from NFC, from January 2013 to January, the behavior of the domestic price of coffee is analyzed and it is observed that since this varies and generates high volatility, it causes indecision in both buyers and sellers. Fig 1 shows how the price declines for the month of January 2014 and has an increase in the same year; for November 2016 it is shown how the internal price of coffee has its greatest value within the analyzed time range, revealing as well as a high price speculation for both sellers and buyers editor@iaeme.com

4 01/01/ /05/ /09/ /01/ /05/ /09/ /01/ /05/ /09/ /01/ /05/ /09/ /01/ /05/ /09/ /01/ Miguel Jiménez-Gómez and Natalia Acevedo-Prins $ 1,200,000 $ 1,000,000 $ 800,000 $ 600,000 $ 400,000 $ 200,000 $ - Figure 1 Behavior of the domestic price of coffee. For the put option, as the asset price increases on average $ 5,506 as shown in Table 1, its benefit is maximum. This option provides the company with an expectation of stability in the face of downward movements in the exchange rate, thus facilitating the management of foreign exchange risk and offering a hedge against unfavorable changes in the exchange rate. The put option gives the company the possibility of not selling the product when prices fall, thus taking advantage of the future rise of the same to sell at that time. Month February Table 1 Premium put options. March April May June July Opción Put $22,361 $30,760 $36,876 $41,862 $46,127 $49,893 With this option, the company is protected from the risk derived from the fluctuations experienced in the price of coffee, limiting its losses to the premium while its profits will be unlimited. The premium with coverage for the month of February was $ 767,931, increasing for the month of July by $ 789,150, that is to say, it had an increase of $ 21,219 (see Table 2). Month Prices with coverage Table 2 Prices with coverage including the premium of the put options. February March April May June July $767,931 $771,953 $775,701 $780,383 $784,471 $789,150 When obtaining the results of the price profitability, the model of the Geometric Brownian Movement and the realization of the 10,000 iterations, it is evident that the prices had an increase in the last days, this means that by not covering the profitability generated by the coffee price is minimal, where it is observed in Fig 2 that for month 1 the price is of $ 768,068 and that for month 6 it is of $ 791,410, causing the risk to be higher and negatively impact the profits of the company, since these would cease to be stable and secure. This also leads to the company obtaining a small growth in investment, geographical diversification and access to financial markets editor@iaeme.com

5 Hedge with Financial Options for the Domestic Price of Coffee in a Production Company in Colombia $ 1,100,000 $ 1,000,000 $ 900,000 $ 800,000 $ 700,000 $ 600,000 $ 500, Figure 2 Spot price without coverage Coffee growers expect that on average the price of coffee increases month by month as can be seen in the uncovered spot in Fig 2, and where the 5% and 95% percentiles reveal how the price could be low or high with variations that fluctuate between $ 275,000 in the projected 6 months. With the above scenario, the hedging strategy with financial options is proposed, since benefits are obtained for the coffee producing company, because it is observed that the premium coverage helps the cash flow is not negatively affected, on the contrary It generates financial advantages for the company, since it can obtain a higher profitability. Fig 3 shows that premium coverage for the price of coffee will have an increase in the projected 6 months, and that these will have a minimum variation with respect to the price without coverage; then for a percentile of 95% the prices for the sale of coffee will be high, this being the best context for the coffee company, and in another area is the 5% percentile with low prices with respect to the prices with coverage, showing losses in the cash flow for the company. With the above, it is identified that prices have an increase of $ 30,000 each month, being a good strategy to have coverage in the prices of this product. $ 1,050,000 $ 1,000,000 $ 950,000 $ 900,000 $ 850,000 $ 800,000 $ 750,000 $ 700,000 $ 650, Figure 3 Prices with premium coverage Taking into account the variation of the K, we can observe that when this increases the premium goes up, therefore it is recommended that the strike be lower. Coverage with editor@iaeme.com

6 Miguel Jiménez-Gómez and Natalia Acevedo-Prins financial options provides the contract buyer with the right, but not the obligation, to buy or sell an asset or financial instrument at a fixed price in a predetermined future month or sooner. That means that the maximum risk for the buyer of an option is limited to the premium paid. One of the best reasons for financial options is the fact that it is possible to make significant profits, without necessarily having to have large sums of money. On the other hand, according to the standard deviations made, it is identified that there is less volatility in the price when coverage is used, which decreases the risk of loss and increases the profitability of the money and makes the price of coffee more stable (see Table 3). As shown in the Table 3, for the month of April the deviation with coverage is $ 72,045 and on the other hand without coverage it is $ 106,700, which indicates that the coverage causes the price of coffee to move in a considerable range and that is present favorable opportunity; since if the volatility decreases the premium increases. Month Standard deviation price with coverage Standard deviation price without coverage February Table 3 Standard deviations of prices March April May June July $38,426 $56,643 $72,045 $83,617 $95,953 $107,799 $60,395 $86,819 $106,700 $123,739 $139, ,074 Finally, to examine the scenario with coverage with options and compare it with the scenario without coverage, it can be seen in the graph that since the 5th percentile with coverage is above the 5th percentile without coverage, this means that the risk decreased. On the other hand, it is observed that the 5th and 95th percentiles with coverage are less dispersed; therefore, premium coverage generates positive benefits, this being the best option; The possibility of suffering losses is lower, as is our financial risk (see Fig 4). $ 1,150,000 $ 1,050,000 $ 950,000 $ 850,000 $ 750,000 $ 650,000 $ 550, Figure 4 Spot prices with coverage and without coverage 4. CONCLUSIONS When not covering the sale of coffee, the difference between the 5% and 95% percentiles is on average $ , which causes a much wider distance between them and the risk increases; On the other hand, the use of coverage shows that the difference between the 5% and 95% percentiles is on average $ 213,075, proving that this is the best alternative for the editor@iaeme.com

7 Hedge with Financial Options for the Domestic Price of Coffee in a Production Company in Colombia company. Since it should be remembered that what is intended is that both percentiles are narrower to provide less uncertainty against price fluctuations. When analyzing the average of the unitary price with coverage, an average of the differences is made in each of the months and it is observed that this is of $ 4,240, on the contrary the average of the average of the unit price without coverage is of $ 5,233; being this higher. The foregoing demonstrates that the use of financial options reduces the volatility levels of the asset price, due to its versatility, the control of risk that they allow and the improvement of market expectations. Fig 4 shows how the scenario with coverage with options and without coverage behaves, within the 5% percentile with coverage shows an increase on average of $ 725,923, and the 5% percentile without coverage on average $ 616,572, this means that on average the risk is reduced. REFERENCES [1] E. Bajo, M. Barbi, and S. Romagnoli, Optimal corporate hedging using options with basis and production risk, North Am. J. Econ. Financ., vol. 30, pp , [2] S. Winkel, in Economics Hedging strategies for currency risk, [3] D. M. Sprčić, M. Tekavcic, and Z. Sevic, A review of the rationales for corporate risk management: fashion or the need?, Int. J. Econ. Sci. Appl. Res., vol. 1, pp , [4] X.-T. Wang, E.-H. Z. Zhu, M.-M. Tang, and H.-G. Yan, Scaling and long-range dependence in option pricing II: Pricing European option with transaction costs under the mixed Brownian fractional Brownian model, Elsevier B.V. All rights Reserv., p. 7, [5] M. Jiménez-Gómez, N. Acevedo-Prins, and D. Rojas, Cobertura cambiaria con derivados financieros: caso empresa exportadora en Colombia, in Finanzas, modelación y riesgo, N. Marín, Ed. Medellín, 2017, p [6] M. Jiménez-Gómez and N. Acevedo-Prins, Aplicación del método de Opciones Reales en la valoración de parque eólico en Colombia, in Gestión del Riesgo Financiero Contribuciones desde Latinoamérica, Optimal Research Group, Ed. Medellín,, p editor@iaeme.com