Hedging aluminium and electric power
Strategies and products empirically tested
Remco Uittenbroek Groningen
Hedging aluminium and electric power
Strategies and products empirically tested
Aluminium Delfzijl B.V.
University of Groningen
Faculty of Economics and Business Department of Finance Author R.R. Uittenbroek Ceramstraat 10a 9715JN Groningen r.r.uittenbroek@student.rug.nl / r.r.uittenbroek@gmail.com Student number: 1336797
Supervisor University of Groningen Dr. Auke Plantinga
Supervisors Aluminium Delfzijl B.V. Drs. P.C. Hölscher
PREFACE
I started my internship at Aldel at the end of August in 2008 to write my master thesis, which is the final requirement to obtain my master’s degree. This was the beginning of a very interesting period for me, but even more for Aldel. The reason: the economical crisis.
From the moment I just started the aluminium price went down from an almost all-time high record to an almost all-time low record at the end of 2008. Besides that, the electric power prices were sky high due to the high oil price in the same period. But this is not the mayor problem that Aldel had to cope with. The demand for aluminium worldwide collapsed and Aldel was not able to sell all the produced aluminium. On top of that Aldel was for sale, because the owner at that moment wanted to divest its aluminium activities. After a intensive due diligence process Klesch & Company signed a Share Purchase Agreement in the beginning of 2009. The employees of Aldel were relieved, because one of the alternatives of the former owner was closing the business. Although it is not the best period for Aldel to look back at, for me it was very special to experience this from within the organisation.
I had my own struggles during this period, although of an whole other degree. To understand the implementation of the subject at Aldel was a real challenge. I knew merely the basics of the subject, and the additional theory and literature I found on this subject was mainly focused on merchant banks and traders. As a result, matching the implementation to the theory was not easy. Furthermore, with the research I had to keep in mind that I had to fulfil both the assignment Aldel gave me and the thesis requirements of the University. In the end, I think I’ve learned more than someone possibly could without such an internship. I’ve learned the theory of the subject, experienced the practice of the subject, and made a link between the theory and practice.
Writing this thesis would not have been possible without the help of some people. First I would like to thank Peter Hölscher for sharing valuable information of the firm and for his vision on this subject. Furthermore I would like to thank Jan van der Schaaf and Sake Fokkens for their explanation of the implementation and execution of the hedge strategy of Aldel. Also, I would like to thank my roommates at Aldel for the enjoyable working environment: Herman van der Laan, Peter Koop, and Maria Koers.
Auke Plantinga, my supervisor at the university of Groningen, deserves a special thanks too. With his subtle feedback he pushed me each time a bit more in the right direction. I would also like to thank Cor Hendriks, who was the liaison for me between practice and theory. Last but not least: I would like to thank my family, girlfriend, and friends for their support.
I had a great time during my internship and I am satisfied with the result of my thesis. I hope everyone enjoys reading this report and learns something about hedging.
MANAGEMENT SUMMARY
The goal of this research is to seek for performance improvements of the current hedge strategy of Aldel. First I determine whether the current strategy outperforms a no hedge strategy, and if an alternative unconditional hedge strategy outperforms the current strategy. Next I test what the potential performance increase is if the conditions of the current strategy are optimally altered, and what the benefits and threats are of hedging the aluminium and electric power price independently. At last I test alternative products with all the above. I use data of aluminium and electric power futures contracts for the delivery years 2004 until 2008. To have more variation in the price developments of aluminium and electric power I run two different Monte Carlo simulations creating each one hundred different price developments of aluminium and electric power for three years.
I find that the conditional simultaneous hedge strategy outperforms the no-hedge strategy with the historical data and with one of the two simulations, while I do not find that the unconditional simultaneous hedge strategy outperforms the conditional simultaneous hedge strategy. Furthermore I find proof that there is a room for improvement of the conditional hedge strategy of Aldel with all datasets: the increase in EBIT with historical dataset is on average 7.1 million, while with the simulations this is up to 41.8 million. Next I find that hedging the aluminium and electric power price independently could improve the results even more; the results suggest an potential improvement between 12.7 and 14.2 million. However, the potential losses are of the same extent as the potential profits.
It is not possible to draw a conclusion about the performance of the conditional, unconditional, and simultaneous hedge strategy using the alternative products, because the results highly differ between the datasets. If following the independent hedge strategy using the put option and collar the EBIT is lower in all datasets in the best case scenario, and better in worst case scenario.
TABLE OF CONTENTS Preface ... iii Management Summary ... iv Table of contents ... v 1 Introduction ... 1
1.1 Research goal, questions and design ... 2
2 Aldel ... 5
2.1 Primary Process ... 5
2.1.1 Primary process ... 5
2.1.2 The aluminium and electric power exchanges ... 5
2.1.3 Business plan ... 6
2.2 Hedge Strategy Aldel ... 7
2.2.1 Hedge strategy ... 7
2.2.2 Reason to focus on the long term hedges ... 8
3 Literature ... 9
3.1 Motives for corporate hedging ... 9
3.1.1 Hedging lowers the probability of incurring financial distress costs ... 9
3.1.2 Hedging results in tax benefits ... 9
3.1.3 Hedging reduces agency and borrowing costs ... 10
3.2 Hedge strategies and products ... 11
3.2.1 Hedging simultaneously increases the profits and reduces risk for cattle feeders ... 11
3.2.2 Selective hedging is profitable with informational advantage ... 11
3.2.3 Add options if profits are not linear in price, or if options are underpriced ... 12
4 Data ... 14
4.1 Data description ... 14
4.1.1 Aluminium and electric power ... 14
4.1.2 Dollar to euro conversion ... 15
4.1.3 Option premiums and volatility ... 15
4.2 Calculations related to hedge products ... 15
4.2.1 Futures and dollar to euro conversion ... 15
4.2.2 Option volatility and premium ... 16
4.2.3 Swap: electric power price based on aluminium price ... 18
4.3 Overview ... 18
5 Methodology ... 21
5.1.1 Profit/loss on the hedging products ... 22
5.2 Conditional and unconditional hedge strategy ... 22
5.3 Determining the room for improvement of the hedge conditions ... 23
5.4 Determining the potential of the independent hedge ... 24
5.5 Alternative hedge products ... 24
5.6 Comparing the strategies and products ... 25
5.7 Monte Carlo Simulation ... 25
5.7.1 Geometric Brownian motion ... 25
5.7.2 Ornstein–Uhlenbeck process (Mean Reverting) ... 26
5.7.3 Model input variables ... 27
5.8 Other assumptions ... 30
6 Results ... 32
6.1 Performance of the unconditional and conditional hedge ... 32
6.2 Room for improvement for the conditional simultaneous hedge strategy ... 33
6.3 Potential benefits and threats of the independent hedge strategy ... 35
6.4 EBIT change if using alternative hedging products ... 37
6.4.1 With the conditional and unconditional simultaneous hedge strategy ... 37
6.4.2 Alternative products with the simultaneous hedge strategy ... 39
6.4.3 Alternative products with the independent hedge strategy ... 42
7 Conclusion and recommandations ... 44
7.1 Implications and recommendation for further research ... 46
References ... 48
1 INTRODUCTION
In this research I find that there are potential improvements for the current hedge strategy of the Dutch aluminium smelter Aluminium Delfzijl BV (Aldel) to increase the EBIT while it still protects the firm against the adverse movements of aluminium and electric power prices. First I review the performance of the current hedge strategy of Aldel against a no-hedge strategy and an unconditional hedge strategy. Furthermore I investigate to what extent the current conditional simultaneous hedge strategy can be improved, and what potential benefits and threats an independent hedge strategy gives. Finally, I test the performance of the strategy of Aldel with options and swaps, and identify the performance increase or decrease with these products compared to futures in the best and worst cases.
Aluminium producers sell products based on price quotations of primary aluminium contracts on metal exchanges since the mid 80s, plus a premium or discount relating to the location of the producer, the grade of their products, delivery conditions, and other specifiable factors (Figuerola-Ferretti and Gilbert, 2005). The most important exchange for aluminium is the London Metal Exchange (LME). Producers do not have the ability to directly control the prices of their product and therefore have to concentrate on reducing costs (Figuerola-Ferretti, 2005). One of the major costs of producing pure aluminium, besides for example the costs of alumina, anodes, and labour, is electric power. Electric power represents about 20% to 40% of the cost of producing aluminium, depending on the location of the smelter and the contract the firms has with an electric power supplier. Large electric power consumers in the Netherlands are able to choose their own supplier since 1998 due to the liberalization of the power market in the European Union. The liberalization starts in 1996 with the Electricity Directive (EU, 1996) and subsequent directives in 2003 (EU, 2003a; EU, 2003b).
According to Bartram (2005), commodity prices exhibit higher volatility than (most) foreign exchange rates, interest rates, and equity prices during the period 1987-1995, thus represent a major source of financial risk to an aluminium smelter. An aluminium smelter that focuses primarily on its core business is less diversified and as a consequence price volatility highly affects the financial result of the firm. This risk is manageable by using derivatives. Authors on risk management split managing risk into hedging and speculating: hedging is the process of trying to reduce the dependence of firm value on a risk exposure, while speculating means a firm increases the dependence on a risk exposure. Surveys show that the overwhelming majority of non-financial European firms use derivatives for the purposes of hedging (e.g. Bodnar, de Jong, and Macrae, 2003; De Ceuster et al., 2000; Mallin, Ow-Yong, and Reynolds, 2001). Forward and future contracts, options, swaps, and other derivates are available at over-the-counter-markets, exchanges and bilateral agreements to reduce the risk a firm faces from potential future movement in a market variable (Hull, 2006).
discovery of an enormous gas field in Slochteren (close to Delfzijl) in 1958, the Dutch Minister of Economic Affairs decides to sell electric power for reduced prices to the industry in the Netherlands. A few years later, in 1966, Hoogovens, Billiton, and Alusuisse build an aluminium smelter in Delfzijl to produce aluminium for customers in The Netherlands. The contract with the government concerning the supply of cheap electric-power based on gas expires two decades later. This caused the continuation of Aldel to depend on several occasions on the negotiation of new contracts with local electric power suppliers. Today, over 40 years after starting the production process, the price of electric power and aluminium depends on volatile markets, Aldel supplies aluminium to customers in whole Europe, and the firm faces world-wide competition from aluminium producers.
Aldel has a hedge strategy which has the goal to manage the price risks of aluminium and electric power in order to fix the result for a delivery year. Aldel sells aluminium futures contracts on the LME and buys electric power futures contracts via an European energy market (Endex), up to two years before physical delivery. At the moment Aldel buys the electric power futures contracts, which is for delivery of electric power for a whole year, it sells aluminium futures contracts (or the other way around). Consider that volume and all other costs and income are certain for a specific delivery year. If Aldel buys futures contracts for all the required electric power and sells futures contracts of the whole aluminium production volume for the specific delivery year at the same time, the profit is known for the delivery year. The trigger to buy and sell futures contracts is the price of both commodities at that moment. If the combination of the two prices meets a predetermined required profit, the futures contracts are sold and bought. This is the simultaneous conditional hedge strategy.
Yet this hedge strategy has its drawback: it is difficult to determine the required profit. If the required profit is set too high it is not possible to perform the hedge, because the required profit margin is never met. But if Aldel sets the required profit too low opportunity costs can arise (i.e. the profit is fixed at 5 million €, while without a hedge the profit would be 15 million €). Due to unfavourable price movements a profit could not always be met for the past delivery years and for the upcoming delivery years, and the economical crisis that started in 2008 made it even more difficult to make profit in a year.
1.1 Research goal, questions and design
The first question that arises is whether the current hedge strategy of Aldel outperforms a no-hedge strategy. The hedge strategy of Aldel merely seems to offer protection against losses if a required profit is met, and limits the profit at the moment the required profit is met. After all, a hedge strategy does not guarantee the result is higher than the result without hedging (Hull, 2006 ). The first question I answer in this research is:
Research question 1) Does the conditional simultaneous hedge strategy of Aldel outperform a non-hedge strategy?
Literature on hedge strategies often describe an unconditional hedge strategy (see for example: Chen, Lee, and Shrestha, 2003; Hull, 2006). Fixing a hedge exactly twelve months before maturity of the futures contract is an example of the unconditional hedge strategy. The advantage of such strategy is, of course, the lack of difficult to determine hedge conditions. This strategy may minimize the price risk, but does it increase the profit compared to the strategy of Aldel? This leads to the next question, which is:
Research question 2) Does the unconditional simultaneous hedge strategy outperform the conditional simultaneous hedge strategy of Aldel?
If the current strategy limits the profits, and does not offer protection against losses, it also suggests that there is a potential to improve the performance by changing the hedge conditions. But is this true? And to what extent? The third question of my research is therefore:
Research question 3) What is the potential performance increase of the conditional simultaneous hedge strategy if the hedge conditions are optimally altered?
Instead of hedging simultaneously Aldel can choose to hedge the aluminium and electric power price independently of each other. Aldel can for example hedge (fix) the aluminium price at the moment they perceive it as high, even if the electric power price is also high at that moment. Using the simultaneous hedge strategy this would not be possible if the required profit is not met. However, the risk is that the electric power price will increase even more after hedging the aluminium price, or that the aluminium price drops after hedging the electric power price. Therefore I also have the look at the potential losses this strategy may give. Research question four is:
Research question 4) What are the potential benefits and risks of a strategy where the electric power and aluminium prices are hedged independently compared to hedging simultaneous?
Until now the focus was on hedge strategies using futures. In the past, merchant banks offered Aldel to use options and swap in their hedge strategy. An aluminium put option, a combination of an aluminium put and call option (collar), and a swap that makes the electric power price dependent of the aluminium spot price are included in the research.
premium. The costless collar sets a maximum and minimum price around the futures price. Depending on the aluminium spot price at maturity, the EBIT increases or decreases compared to using aluminium futures. With the swap the higher or lower profit also depends on the aluminium spot price at maturity. Aldel would like to know if these hedge products could improve the result of their current strategy. Furthermore I research the potential of the products if the unconditional simultaneous hedge strategy is followed. This leads to research question five:
Research question 5) Does other hedge products improve the performance of the conditional simultaneous hedge strategy and the unconditional hedge strategy?
Each product has its own specific properties and performs best under certain market conditions. Therefore I calculate the EBIT increase or decrease in the best and worst case scenarios if the put option, collar, or swap are used instead of futures, following a strategy that involves hedging simultaneously and hedging independently. The last research question is:
Research question 6) What are the maximum benefits and losses of other hedging instruments compared to futures if hedging simultaneously and independently?
To be clear, I do not develop new hedge strategies or new hedge conditions which Aldel is able to use in practice. I show potentials, which I calculate ex post (with all the price developments of a delivery year known). Based on the results of my research, Aldel is able to decide whether the current hedge strategy or hedge conditions should be altered to improve the EBIT, and if alternative products should be considered in this decision.
In this research I use prices of aluminium and electric power futures contracts for the delivery years 2004 until 2008. Depending on the delivery year, up to three years of daily price quotes are available of aluminium and electric power (e.g., for the delivery year 2004 the aluminium prices are available from the beginning of 2002). To have more variation in the price developments of aluminium and electric power I run two different Monte Carlo simulations, each creating 100 different price developments of aluminium and electric power of three years. The first simulation follows a Geometric Brownian Motion (GBM), while the second follows an Ornstein–Uhlenbeck process, which is an one-factor mean reverting simulation model. The reason to include a mean-reverting model is that Aldel has the presumption that both prices return to a long-term mean.
2 ALDEL
In the first paragraph I briefly describe the primary process of Aldel and the aluminium and electric power exchanges, which is necessary to understand the hedge strategy of Aldel. Paragraph 2.2 discusses the hedge strategy of Aldel.
2.1 Primary Process 2.1.1 Primary process
The production chain of aluminium starts at mining bauxite, the most important aluminium ore. The next step is refining bauxite to alumina. The alumina smelts during the next process into aluminium. The last step involves mixing the pure (primary) aluminium with alloys during the foundry process to give the end-product certain properties. Different sectors use aluminium, e.g. in the transportation, packaging, and construction sector.
Aldel does not mine bauxite, nor it refines the bauxite to alumina. Aldel imports the alumina, which is transported every month to the Netherlands from, among others, Suriname and Ireland. Aldel stores the ore and feeds the ore into the furnaces later. The furnaces contain electrolyte, a salt solution in which the aluminium ore dissolves. At a temperature of 960 degrees centigrade a direct current exceeding 120,000 amperes passes through the liquid. By electrolysis the dissolved aluminium ore in the electrolyte splits and liquid aluminium results. This liquid aluminium sinks to the bottom of the furnace, a machine sucks the liquid out and takes it to the foundry. The foundry involves cleaning the pure aluminium and mixing it with other substances, like recycled aluminium and other alloys, to give the aluminium certain qualities. At the end the liquid pours into the shape of a Rolling Ingots or Extrusion Billets. Aldel sells approximately 160,000 ton of Rolling Ingots and Extrusion on a yearly base. The firm produces approximately 120,000 ton of pure (primary) aluminium during the electrolyse process and recycles approximately 40,000 ton of old metal / aluminium during the foundry process. It is not possible to shutdown a furnace without damaging the furnace, so Aldel produces 24 hours a day, seven days a week. The foundry process cannot be halted because the liquid aluminium is not storable. The end-products however are easily storable.
2.1.2 The aluminium and electric power exchanges
aluminium, with a certain quality and shape which is described in the contract specification. All price quotes are in US dollars per tonne. The broker of Aldel automatically converts the price from dollars to euros using a dollar to euro forward rate. Trading is possible the whole day. The LME settles profit or loss on the futures contracts in cash at maturity.
Aldel uses the price quotes of electric power of the Endex, a Dutch power exchange. The Endex offers various products, but Aldel only uses base load calendar products. This product concerns the physical supply of electric power for a whole year, 24 hours per day for the same price. Price quotes are in euros.
It is possible to sell futures contracts up to five years on the LME, and Endex calendar price quotes are available up to three years. Due to margining costs and liquidity constraints Aldel can hedge up to two years.
2.1.3 Business plan
The management team of Aldel formulates a business plan for each year which includes, among others, a projection of the sales and production. Based on the plan, the needed amount and costs of anodes, alloys, labour, material and miscellaneous are known. The production of 1 tonne of aluminium requires on average 1.9 tonne of alumina. The total electric power consumption is 230Mw each hour. In normal circumstances Aldel has several customers with a stable demand for certain aluminium products1. Based on the product wishes of the customers, Aldel estimates the needed scrap and alloys. The overhead costs are constant over a year.
Aldel bases the price of the end-products on the price per tonne of a LME aluminium futures contract of the delivery month plus a premium. The management team fixes the premium in a contract with the customer. The exact price the customer has to pay depends on the futures price at the moment he decides to fix the price. A customer is able to fix (the LME part of) the price up to a year before the delivery month, depending on what he wishes.
The price of alumina and scrap depend on the LME aluminium price. A common method to price alumina is an agreed percentage of the average spot LME aluminium price during the whole month prior the month of physical delivery of the alumina; on average 15%. Aldel and the supplier sign a contract that includes agreements regarding the quality of the alumina, the delivery volume, the delivery days, and the percentage for a whole year. The price of scrap is the LME aluminium price of the delivery month plus a (low) premium or discount.
Aldel buys electric power on the Endex or directly from an electric power supplier. The futures price quote on the Endex is the reference price of the negotiations with suppliers to set up bilateral contracts. If a supplier does not offer a better price than the market, Aldel uses the Endex to buy electric power.
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2.2 Hedge Strategy Aldel 2.2.1 Hedge strategy
Aldel uses a part of the aluminium sales to cover the costs of alumina and scrap2. The selling price of the aluminium is the same as the LME aluminium price used to fix the price of alumina. Remember the average price for alumina is on average 15% of the LME aluminium price. An example: if Aldel buys 228 kilo tonne of alumina in a year for 1,800 euro per tonne, Aldel sells (228 x 0.15 = ) 34.2 kilo tonne of aluminium for that same price (plus a premium). The firm also sells a part of the aluminium for the exact same price (excluding premium) used to buy scrap (excluding premium). The premium of the scrap aluminium is lower than the premium of the aluminium Aldel sells. The delivery month of the aluminium is the same as the delivery month of alumina and scrap. This ensures the costs of alumina are 15% of the earnings of aluminium (excluding premium), and the costs of scrap (excluding discount/premium) the same as the earnings of aluminium (excluding premium).
The total aluminium sales minus sales used to cover the costs of alumina and scrap is part of the other hedge strategy; the “long term hedge strategy”. The fixed costs (related to anodes, labour, material, premium of scrap, and miscellaneous costs), fixed earnings (related to premium and miscellaneous earnings), and costs of electric power are also part of the “long term hedge strategy”.
The long term hedge strategy involves hedging the price risk of aluminium and electric power to fix a profit. Aldel sells aluminium futures for all months in the year because Aldel buys electric power also for a whole year. E.g.: the price for aluminium for 2008 is actually the average of the aluminium futures price for January 2008 until December 2008 at that specific moment. The traders of Aldel try to sell aluminium contracts on the LME and buy electric power on the Endex or via bilateral contracts with the same or better price at the moment the combination of the both prices is above the predetermined profit.
The trader closes the LME aluminium futures short position at the moment a customer desires to fix the price of physical delivery of aluminium. The trader closes the position by taking a long position in LME aluminium futures contracts with the same delivery date as the physical delivery (and the open short position). If the trader does not take a long position Aldel there is an “open position”. In that case, any adverse price movement of aluminium between this moment and the delivery date would have a negative impact on the EBIT.
2 In this case selling aluminium refers to either selling a futures contract at the moment Aldel fixes the price of
2.2.2 Reason to focus on the long term hedges
This research focuses only on the “long term hedge strategy”, because a price increase of electric power or aluminium affects the net result the most. For example, a 10% increase in the price of aluminium contracts (long term hedge strategy) results in a 123% increase of the EBIT, and a 10% increase in the price of electric power a decrease of 66% of the EBIT. In contrast, a 10% increase in the premium of scrap will negatively affect the yearly result with 2%. A 10% increase of the alumina price, so that the alumina price is 16.5% instead of 15% of the LME aluminium price, results in a 49% decrease of the net result. See the table below for an overview of all costs and their effect on the EBIT.
Table 2.1: Change in EBIT by price increase of various products
The prices in a normal situation give a EBIT of 10 million euro. A 10% increase in the aluminium price means the EBIT raises by 123% to 22.3 million.
Product Change of EBIT
3 LITERATURE
3.1 Motives for corporate hedging
Under the assumptions of the work by Modigliani and Miller (1958) financial decisions by the firm have no influence on the value of a firm. They argue a firm creates value by making profitable investments and the way a firm finances these investments is completely irrelevant. Individual investors are in the idealized world of Modigliani-Miller able to perfectly replicate the financial decisions a firm makes; the so-called home-made leverage. Their work can be extended to all financing decisions, like the firm’s dividend policy (Miller and Modigliani, 1961) and the firm’s risk management policy. The idealized world of Modigliani-Miller assumes perfect capital markets, which means there are no information asymmetries, no taxes (or no discriminatory corporate and personal taxes), and no transaction costs.
Several possible motives of hedging at a corporate level arise, because the assumptions of the framework of Modigliana-Miller are not met in practice. Because of market imperfections, firms are able to create value by hedging in ways shareholders cannot achieve on their own. I discuss the hedging motives to maximize shareholder value in the sub-paragraphs below. Other hedging motives, e.g. managerial utility maximization3, are not relevant to this research as Aldel tries to maximize shareholder value.
3.1.1 Hedging lowers the probability of incurring financial distress costs
The theory of Mayers and Smith Jr. (1982) and Smith and Stulz (1985) suggest that the possibility of costly financial distress can induce firms to hedge. According to Rawls and Smithson (1990) the expected costs of financial distress are driven by the probability of encountering financial distress and the costs imposed by a possible bankruptcy. Both direct costs, e.g. legal costs of lawyers, and indirect costs, e.g. loss of reputation, can be substantial. By reducing cash flow variability, hedging could lower the probability of incurring financial distress costs. By using leverage as a proxy for the possibility of encountering financial distress, empirical research finds a positive relation between hedging and leverage (e.g. Graham and Rogers, 2002; Haushalter, 2000). For other data and control variables empirical research does not find support (e.g. Geczy, Minton, and Schrand, 1997; Nance, Smith, and Smithson, 1993).
3.1.2 Hedging results in tax benefits
The theory of by Stulz (1996), Ross (1996) and Leland (1998) suggest the tax shields associated with debt financing also provide an incentive for hedging. They argue that most of the benefits to
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reduction by hedging for an optimally-levered firm stem not from reduced bankruptcy cost, but from increased debt capacity and the resulting tax benefits. Empirical support is found by Graham and Rogers (2002), but not by Geczy et al. (1997).
Related to the latter motive, Mayers and Smith Jr. (1982), Smith and Stulz (1985), Rawls and Smithson (1990), and Stulz (1996) suggest firms facing progressive effective marginal tax rate can increase the firm value by hedging the pre-tax income. By reducing the fluctuations in taxable income, hedging can lead to lower tax payments since it ensures that the largest possible proportion of corporate income falls in the optimal range of tax rates4.
3.1.3 Hedging reduces agency and borrowing costs
The literature on agency problems, with Jensen and Meckling (1976) as pioneering authors, points out that shareholders of leveraged firms have incentives to pursue selfish strategies at the cost of bondholders. Anticipating on these incentives, bondholders require higher returns on their capital or impose debt covenants resulting in higher cost of debt to the firm. Agency costs of debt can result from adverse selection, which can be underinvestment and the risk-shifting problem.
Underinvestment arises in the case of debt overhang (Myers, 1977). The management, which acts in favour of the shareholders, of a firm in financial distress will give up profitable investment opportunities if too little of the value of the investment goes to the shareholders. The risk-shifting problem is actually the opposite of the first form of adverse selection: the management, still acting in favour of the shareholders, may engage in risky investment opportunities, even with a negative net present value, when the potential gains accrue to the shareholders while potential losses goes to the bondholders (Jensen and Meckling, 1976).
Anticipating on these problems, Bessembinder (1991) argues that since hedging reduces the probability of financial distress it effectively shifts individual future states from default to non-default outcomes. Therefore, the hedging firm can effectively commit to meet obligations in states where it otherwise could not and therefore reduce agency costs and lower borrowing costs. Froot, Scharfstein, and Stein (1993) show hedging enables the firm to avoid unnecessary fluctuations in investment spending or costly external financing, and thus also reducing the underinvestment problem. Empirical research tests the theory by researching the relationship between hedging and growth opportunities. When using R&D as a proxy, Nance et al. (1993), Geczy et al. (1997), and Allayannis and Ofek (2001) find support for the theory.
Investments in the aluminium industry can be quite substantial when they have to be made. These investments relate to, among others, R&D, production expansion, and improving production efficiency to reduce productions costs.
4 However, the corporate tax rate in The Netherlands is flat above the €200,000, so Aldel is not able to profit
3.2 Hedge strategies and products
In this paragraph I discuss literature on hedge strategies and products5. Sub-paragraph 3.2.1 is about a simultaneous hedge strategy that is comparable to the current hedge strategy of Aldel. The next sub-paragraph introduces a hedge strategy that incorporates market views. The last sub-sub-paragraph discusses the value of using options in the hedge strategy.
3.2.1 Hedging simultaneously increases the profits and reduces risk for cattle feeders
As I describe in sub-paragraph 2.2.1 Aldel simultaneously hedges the price risk of aluminium and electric power. Relevant is the evidence from studies on cattle feeding hedging strategies. Shafer, Griffin, and Johnson (1978) propose hedging simultaneously by taking long positions in input commodities (feeder cattle and corn futures) and a short position in the output (live cattle) at the same time. The goal of hedging simultaneously in this research is to lock in a certain margin profit.
Shafer et al. (1978) compare four different (simultaneously) hedging strategies to the cash (spot) market strategy (buying and selling products for the spot price). They evaluate the expected lock-in margin (ELIM) daily to the required lock-in margin (RLIM) during the two month period before the actual cattle feeding starts. The formula to calculate ELIM contains the input and output amounts, related futures prices for the input and output, and other costs. One strategy is the Lock-in or Cash Market (LICM): if hedging is not possible during the two month period, the producer uses cash prices for both input and output instead. It is possible to hedge simultaneously 13 of the 47 pens’ periods using this strategy. Comparing to the cash market strategy, the mean increases from -2.29 to 9.57, and the variance decreases from 5052 to 3348. This means that the profit from the hedge in the 13 periods is higher than the profit of the cash market strategy. The authors claim the prices of the commodities became uncertain due to the increased volatility of the commodity prices after 1972. This hedge strategy removes some of the uncertainty by capturing the moments that all prices give a certain profit margin.
Further research on simultaneously hedging the input and output in the cattle industry moves to finding the optimal hedge ratios to reduce basis risk, by viewing hedging as an application of the basic portfolio theory (e.g. Anderson and Danthine, 1980; Fackler and McNew, 1993), as Johnson (1960) and Stein (1961) proposes.
3.2.2 Selective hedging is profitable with informational advantage
Stulz (1996) reviews a practice of corporate risk management he calls ‘selective’ hedging instead of ‘full-cover’ hedging. The goal of this hedge strategy is to eliminate costly lower-tail outcomes, i.e. the
5 The hedge strategy of Aldel is constructed such way that basis risk does not exist. Literature on this topic is
goal is to reduce the expected costs of financial trouble while preserving the ability to make use of any comparative advance in risk-bearing it may have. For example a firm that has to buy copper next year. With no view about future copper prices, the management will hedge 50% of the purchases to protect the firm against the possibility of financial distress. However, if the management believes that the copper prices are more likely to rise than fall in the coming year, they choose to take a 100% long position. Conversely, if the management is convinced that the copper prices are likely to drop sharply (with almost no possibility of a major increase) they might choose to hedge 20% of the exposure of the firm.
Stulz points out that selective hedging will increase shareholder value if managers have a (private) informational advantage relative to other market participants. This suggests semi-strong market efficiency where prices adjust only to publicly available new information very rapidly and in an unbiased fashion, such that traders earn no excess returns by trading on that information (see for example: Haugen, 2001). However, if managers believe they have informational advantages while they do not, selective hedging will merely result in an increase in the variability of cash flows that could potentially reduce shareholder value.
Brown, Crabb, and Haushalter (2006) investigate the time variation in hedge ratios of gold producers. They find gold producers follow a selective hedge strategy and also have (limited) success, e.g. some producers realize gains of $500,000 per quarter during the research period. Shareholders do not seem to benefit from this strategy, for instance the return on assets and market-to-book ratio of the group active hedgers is worse than the group of inactive hedgers. The researchers do not find proof for the assumption that managers actually have informational advantages relative to other market participants. Their recommendation is that corporations must undertake a detailed analysis of whether they have an informational advantage relative to other market participants that justifies incorporating market views into financial decisions.
3.2.3 Add options if profits are not linear in price, or if options are underpriced
price uncertainty. The full hedging theorem states that the firm should completely eliminate its price risk exposure by adopting a full-hedge via the unbiased futures contracts.
Options could be an important addition to a hedging strategy using only futures contracts if profits are not linear in price. Moschini and Lapan (1992; 1995) show that joint production and price risk (with and without basis risk) lead to a hedging role for options in addition to futures contracts if the firm fixes production decisions ex post. If production decisions are fixed ex ante futures contracts are a better choice than options because profit is in this case linear in price. The model of Brown and Toft (2002) shows that the optimal hedge using futures and options depends on the correlation between prices and production, and the volatility of futures sales and the volatility hedgeable price risk. Other studies are in line with these findings (Sakong and Hayes, 1993). The theory of Benninga and Oosterhof (2004) states that there is a hedging role for put options in combination with futures contracts, if both the prices of forward contracts as well as put options are unbiased and a firm is able to alter the production level.
4 DATA
This chapter has three paragraphs. Paragraph 4.1 gives a description of the unmodified data as I collect from the different sources. The subsequent paragraph shows how I convert the aluminium prices to euros, calculate the aluminium option volatility and premium, and calculate the electric power price with the aluminium/power swap formula. The last paragraph presents the descriptive statistics.
4.1 Data description
4.1.1 Aluminium and electric power
I use official daily spot and futures price quotes of aluminium contracts published by the LME. The price quotes are available from Thomson Reuters DataStream and Thomson Reuters One. The price quotes are in US dollars, the average of the bid and ask price, and are end of day. Spot prices are available from the 13th of October 1988 until the end of 2008. Future prices are available from the beginning of 2002 until the end of 2008, depending on the delivery year (see Table 4.1). The maturity date of an aluminium futures contract is each third Wednesday of the month. The LME settles profit or loss on the futures contracts in cash at maturity. Settlement is against the day closing price.
The reference price I use for electric power is the price quote of an electric power futures contract published by the Endex, because Aldel uses the Endex to buy electric power or to price bilateral contracts. Endex distinguishes calendar contracts, quarterly contracts and monthly contracts. The prices concern both the bid and ask price, which are end of day and quoted in euros. Prices are available from February 2003 until the end of 2008. Because only the average of the bid and ask price of aluminium is available I use the average of the bid and ask price of these contracts. The maturity date of the calendar contract is the third last trading day of the year. At maturity the contracts cascades into three month contracts and three quarter contracts, where monthly contract moves into physical delivery and quarterly contract cascades into three individual monthly contracts.
Table 4.1: Availability of daily price quotes for specific delivery year
This first price quote for aluminium futures contracts for the delivery year 2008 is available from the end of 2003, while the first price quote of electric power futures for this delivery year is available from the end of 2004. The last available price quote for the delivery year 2008 is the last trading day in 2007 is. The same explanation applies to the other delivery years.
Delivery year Product
Aluminium Electric Power
2008 4 years 3 years
2007 4 years 2 years 5 months
2006 3 years 2 years
2005 2 years 3 months 2 years
2004 1 year 3 months 11 months
Table 4.1 summarizes the availability of daily price quotes of both futures contracts for each delivery year. The availability of aluminium contracts for the whole year means that for a specific year the prices of a futures contract of January until December are available.
4.1.2 Dollar to euro conversion
In order to have all prices in euros I convert the aluminium prices from dollars to euros using the same dollar to euro forward rate as the broker of Aldel. In Reuters the following forward rates are available: spot, 1 months, 2 months, 3 months, 6 months, 12 months, 24 months, 36 months and 60 months. The bid and ask rates are available for the whole research period, except for the three months rate, and are end of day rate. The one month forward rate matures exactly one month later, e.g. the 1 month forward rate on the first op September 2008 matures on the first of October 2008. If the first of October is not a trading day the forward rate matures the first next trading day, and so further. The RIC code in Reuters is: EURF=EU. I use the average of the bid and ask rate.
4.1.3 Option premiums and volatility
Historical quotes of option premiums and underlying volatilities are not available at Reuters. Also the merchant bank which offers the products is not able to retrieve any historical data. Therefore I calculate the option prices and the underlying volatility using the available data of the underlying asset prices. The aluminium/electric power swap does not require any additional data.
4.2 Calculations related to hedge products 4.2.1 Futures and dollar to euro conversion
Because the aluminium futures contracts matures each third Wednesday of the month I use the forward rate that matures on this same day. For example, a September 2008 aluminium futures contract matures on Wednesday the 17th of September 2008. I convert the price quote of an aluminium futures contract on the 17th of August 2008 using the 1 month forward rate, the price quote of this contract on the 17th of June using the 3 months forward rate, and so further.
it is exactly three months till the maturity of the aluminium contract, and add this to the three month rate of the particular date. For a full overview of the calculations see Table 7.1 in the appendix. 4.2.2 Option volatility and premium
To approximate the option prices of aluminium prices I use the well known Black-Scholes option-pricing formula, and to estimate the volatility I use a GARCH(1,1) model. The Black-Scholes formula is still the only universally accepted formula for option pricing. Although option traders are fully aware that its basic assumptions are flawed, it remains the benchmark model and all other models are usually viewed as its adjustments or corrections (Stoikov, 2006). The GARCH(1,1) model calculates volatility from a long-run average variance rate, the most recent daily volatility estimate, and the most recent daily percentage change of the commodity price. Figuerola-Ferretti and Gilbert (2008) for instance find that the LME copper and aluminium futures prices exhibit long memory processes in volatility, which explains why the GARCH(1,1) model is more appropriate compared to models which does not include a long-term variance in the estimate.
I calculate the option volatility per (monthly) futures contract, so for each delivery year this are 12 different volatilities and option premiums at one date. The maturity date of the option is last trading day of the month. Settlement is against the average spot price of an aluminium contract on the LME during the month.
The equation for the GARCH (1,1) model is:
2 1 2 1 2 − − + + = L n n n
γ
Vα
uβσ
σ
(eq. 4.1) Where: 2 nσ
= daily variance rate on day nL
V
= Long-run average variance rate per day2 1 − n
u = the squared daily return of the commodity price on day n-1
2 1 − n
σ
= estimate of the daily variance on day n-1γ
= the weight assigned toV
Lα
= the weight assigned to un2−1β
= the weight assigned toσ
n2−11
= + +
α
β
γ
To calculate the daily return of the commodity price,un, I use the formula
For calculations I use
ω
, which representsγ
V
L. To calculate the weights I use a maximum likelihoodmethod in Excel, as Hull (2006) describes in his book. The first column contains the date, the second column the aluminium price Sn, the next column un, in the fourth column
2 n
σ
, and in the last column2 2
) ln( n −un
−
σ
. The fourth column starts with un2−1on the third day. I use equation 4.1 on subsequent days. The last column tabulates the likelihood measure. Optimal values ofω
,α
, andβ
maximises the sum of the sixth column. The data starts from the first available data of the futures contract until the maturity of the contract. If a price is missing I use the next available price. The Risk Solver Platform by Frontline Systems6 solves the optimalω
,α
, andβ
.The GARCH (1,1) model calculates the volatility per day on day n. To calculate the expected volatility per annum until the end of the maturity on day n I use the formula:
−
−
+
=
252
1
−[
n2 L]
aT L TV
aT
e
V
σ
σ
(eq. 4.2) where: Tσ
= the volatility per annum until the end of maturityβ
α
+ =ln 1a
T = amount of actual days till maturity of the option
The 252 means there are approximately 252 trading days in a year; 52 multiplied by 5 makes 260, minus 8 special days on which exchanges are closed.
Next is the calculation of the option premium.
Normally the Black-Scholes formula contains an interest variable to discount the premium from maturity date to the date a trader buys the option. But I compare the different strategies at maturity so it is not necessary to discount the premium. I also assume the Aldel and the broker use the same interest rate, otherwise I should include the difference between the interest rates in the formula.
Price of an European call option: c=S0N(d1)−KN(d2) (eq. 4.3) Price of an European put option p=KN(−d2)−S0N(−d1) (eq. 4.4) Where: T T K S d T T
σ
σ
/2) ( ) / ln( 0 2 1 − + = (eq. 4.5 a,b)6 This is an extended version of the Solver add-on of Excel using a more complex algorithm than the standard
T d
d2 = 1−
σ
TS0 = current aluminium futures price
K = exercise price
T
σ
= volatility per annum (see above)N(x) = the cumulative probability distribution function for a standardized normal distribution T = time to maturity of the option
To calculate the option premium I use the DerivaGem software for Excel, supplied with the book of Hull (2006)7. Selling a call option and buying a put option creates a costless collar. If a trader sells a call option which is far out-of-the money, the put option must also be far out of the money. The latter increases the downward potential and thus increases the risk. To minimize the risk, I set the exercise price of the call option €100 higher than the exercise price of an at-the-money option and calculate the premium. Next I calculate the exercise price of the put option, by using the premium of the call-option and the same variables I use to calculate the premium of the call option. This is an iterative process, because the Black-Scholes model is not linear. To solve this automatically (e.g. for the simulations this involves more than 150,000 calculations) I use the solver/goal seeker in Excel in a self-written macro. 4.2.3 Swap: electric power price based on aluminium price
If using the swap the electric power price depends on the aluminium spot price at maturity and “K”. To determine the electric power price (P) in a year the following formula applies:
K A
P= / (eq. 4.6)
where
A = Average aluminium spot price during the delivery year in euros
K = Average aluminium futures price at time of pricing for a whole delivery year in euros divided by the Electric Power price for the whole year in euros
The aluminium prices are the price quotes of contracts on the LME, while the electric power prices are the price quotes of calendar contracts on the Endex.
4.3 Overview
Table 4.2 on the next two pages shows the descriptive statistics of the raw, calculated, and modified data as I explained in the paragraphs above.
7
Table 4.2: Descriptive statistics of the data
Panel A, B and D contain the raw data from the different sources. Panel C contains both raw data and modified data, while the other panels contain calculated or modified data. Panel B, and E until J are the averages of all months for the specific delivery year. Collar lower limit ( panel I), is the difference between the exercise price of an at-the-money option and the exercise price of the out-of-the-money (OTM) put option of the costless collar, and thus shows how far the option is OTM.
Panel A: Electric Power in €
Delivery year Min Max Median Mean SD N
2008 38 69 60 56 8 759
2007 37 74 54 53 12 638
2006 36 61 40 44 7 510
2005 30 43 36 36 4 488
2004 31 45 33 34 3 233
Panel B: Aluminium futures in $
Delivery year Min Max Median Mean SD N
2008 1457 2872 1999 2057 457 1028
2007 1384 2939 1633 1805 432 1087
2006 1375 2392 1600 1621 206 835
2005 1364 1931 1489 1542 142 583
2004 1346 1629 1407 1428 63 351
Panel C: Aluminium cash period 1988-2008
Price or rate Min Max Median Mean SD N
Price in euros 782 2553 1369 1408 330 5275
Price in US dollars 1019 3291 1545 1686 472 5275
Euro/Dollar rate 0.626 1.207 0.820 0.849 0.123 5275
Panel D: Euro/Dollar period 2002 - 2008
Forward rate Min Max Median Mean SD N
Spot 0.860 1.598 1.243 1.238 0.166 1811 1 Month 0.859 1.596 1.243 1.238 0.166 1811 2 Months 0.858 1.594 1.243 1.238 0.166 1811 3 Months 1.080 1.591 1.284 1.306 0.112 1401 6 Months 0.854 1.584 1.245 1.238 0.167 1811 12 Months 0.850 1.571 1.251 1.239 0.167 1811 24 Months 0.851 1.556 1.265 1.244 0.168 1810 36 Months 0.859 1.552 1.277 1.251 0.169 1810 60 Months 0.861 1.545 1.295 1.258 0.171 1810
Panel E: Euro/Dollar rate forward rate
Delivery year Min Max Median Mean SD N
2008 1.20 1.49 1.31 1.31 0.07 1065 2007 1.00 1.40 1.24 1.23 0.08 1063 2006 1.01 1.38 1.22 1.21 0.08 803 2005 0.95 1.37 1.18 1.16 0.10 602 2004 0.92 1.28 1.07 1.07 0.09 431
Table 4.2 continued
Panel F: Aluminium futures in €
Delivery year Min Max Median Mean SD N
2008 1154 2061 1603 1563 309 1028
2007 1173 2242 1309 1475 302 1029
2006 1196 1957 1312 1355 140 776
2005 1192 1479 1330 1329 63 583
2004 1176 1489 1289 1311 72 351
Panel G: Average option volatility
Delivery year Min Max Median Mean SD N
2008 0.16 0.20 0.17 0.17 0.01 1026
2007 0.17 0.22 0.17 0.17 0.01 1027
2006 0.14 0.16 0.14 0.14 0.00 774
2005 0.16 0.17 0.16 0.16 0.00 581
2004 0.15 0.15 0.15 0.15 0.00 349
Panel H: Put option premium
Delivery year Min Max Median Mean SD N
2008 74 224 155 155 28 1026
2007 93 202 148 148 21 1027
2006 73 145 104 104 20 1027
2005 57 154 102 104 24 1027
2004 51 123 80 84 20 1027
Panel I: Collar lower limit
Delivery year Min Max Median Mean SD N
2008 -128 -111 -116 -117 4 1026 2007 -125 -110 -113 -114 3 1027 2006 -121 -113 -116 -116 2 1027 2005 -119 -108 -112 -113 2 1027 2004 -118 -109 -111 -112 3 1027 Panel J: Swap "K"
Delivery year Min Max Median Mean SD N
5 METHODOLOGY
In the first paragraph I present how I calculate the EBIT during a year. This includes the calculation of the profit or loss on a hedging product. The next five paragraphs contain decisions variables and calculations that directly relates to the research questions of this research. Paragraph 5.6 shows how I compare the performance of the strategies and products. The subsequently paragraph presents the formulas and other related variables (like correlation) of the two Monte Carlo simulations, while the last paragraph is about the assumptions I have to make.
5.1 Calculation of the EBIT
The performance measure in this research is the earnings before interest and taxes (EBIT) and is over a whole year. The formula to calculate the EBIT consist of a fixed and a variable part. The fixed part is het net result of fixed income (e.g. premiums, tolling, etc) minus the fixed costs (e.g. alloys, anodes, employment, etc). The variable part are the alumina costs, scrap costs, electric power costs, income from selling all produced aluminium, and income/costs of the hedging instrument. As I mention in paragraph 2.2.1, Aldel hedges the costs of alumina and scrap using the same price as the cost price so I do not have to include these variables in the formula. I replace the amount of sold aluminium by aluminium sold “long-term” (which is the total amount of aluminium Aldel sells minus the amount aluminium the firms sells related to alumina and scrap). The formula below summarizes the description:
H S
i QAL PAL QAL PAL PEP
QEP FC
EBIT= − * + * + * (eq. 5.1)
Where
EBIT: Earnings before interest and taxes in million € FC: Fixed Costs/Profit in million €
QEP: Bought Power in Terawatt/hour
PEPi: Electric Power price, depending on the product “i”, where “i” is the price of an Endex
calendar contract (“futures contract”) or the price based on the aluminium/power swap (“swap”)
QAL: Sold aluminium in mega tonnes (1000 kilo tonne) long term PALS: Aluminium spot price
PALH: Profit/Loss on the hedging product for aluminium, where the product can be a LME
futures contract, a put option, a call option, and a collar
5.1.1 Profit/loss on the hedging products
The variable PALH needs explanation, because the profit or loss calculation differs with each product.
Except for the swap, where the PALH is zero. The option prices are the average of the 12 option prices
of the specific delivery year. The same applies for the futures prices.
The profit or loss on a futures contract is:
Futures contract: PALH =PALF −PALS (eq. 5.2)
Where
PAL
F is the futures price at the moment the hedge is fixed.Because it is not obligatory to exercise an option at maturity, the maximum loss on a put option is the premium and the maximum profit (in theory) is the exercise price:
Put option: PALH =Max(PALK −PALS,0)− premium (eq. 5.3)
PALK is the exercise price of the option. The exercise of the put option is the same as the futures price
at time of pricing. In order to achieve the same EBIT with a put option as with futures (ceteris paribus), the spot price at maturity has to be the exercise price plus the premium. Instead of a normal put option it is possible to create a synthetic put. This a combination of a short position in a futures contract and a long position in a call option. See equation 7-1 in the appendix for the proof.
The maximum profit possible differs between a call option and a put option. In the case of a call option the maximum profit is (in theory) unlimited.
Call option: PALH =Max(PALS −PALK,0)− premium (eq. 5.4)
The collar is a combination of an out-of-the-money short call and long put option. PALK1 is the
exercise price of the call option, and PALK2 is the exercise price of the put option. I calculate the
profit/loss on the collar as follows:
If PALK1 < PALS then PALH =PALK1 −PALS (eq. 5.5 a,b,c)
If PALK2 > PALS then PALH =PALK2 −PALS
If PALK1 > PALS and PALK2 < PALS then
PAL
H=
0
5.2 Conditional and unconditional hedge strategy
The only variable of the unconditional hedge strategy is the fixing moment of the hedge. I distinguish one fixing point: 12 months before the last possible moment available to hedge8. If the last hedge moment is the 23rd of December 2008, I use the aluminium and electric power futures prices of the 23rd of December 2007, or the first trading day before if the specific day is not a trading day. The same applies to other delivery years.
The required profit is the decision variable of the conditional hedge strategy. The three different criteria of required profit are: 0 million, 5 million, and 10 million. If at a certain day, considering the futures price of electric power and aluminium, results in an EBIT that is at least the required profit, I perform the hedge. If I am not able to perform the hedge until the last possible moment to hedge, I use aluminium and electric power spot prices.
Due to the enormous amount of data I use a self-written function in Excel to automatically search for the first profit above 0, 5, or 10 million. For the historical date, each delivery year has an own tab for the EBIT in Excel. The first column of the EBIT tab contains the date. The first row containing data starts at the last day possible to hedge until the first day possible to hedge. The second column contains the EBIT for the delivery year at the specific date using aluminium and electric futures price at that same date. The third column contains the EBIT using the aluminium put option in combination with electric power futures, the fourth column the aluminium collar in combination with electric power futures, and so on. With the simulations, each product has an own tab for each simulation model. In every tab the first column is the date, the second column the first path of the simulation, the third column the second path, until the 100th path.
The formula starts searching at the first day or step possible to hedge until the last day or step. Next the function stops if it finds a value above 0, 5, or 10, depending on the criteria, and stores the value and the row of this value. If the function does not find a value according to the criteria it shows that the value is not available (N/A).
5.3 Determining the room for improvement of the hedge conditions
This paragraph relates to research question three. When following the conditional and unconditional hedge strategy the hedge decisions are fixed ex ante. To determine the room for improvement of the conditional hedge strategies I search ex post for the maximum EBIT possible with simultaneous hedging using futures. The result of subtracting the EBIT of the conditional simultaneous hedge strategy from this EBIT is the potential or room for improvement. I only use the required profit of 5 million as benchmark of the conditional simultaneous hedge strategy. I find the maximum and minimum EBIT by using the MAX and MIN functions in Excel on the column containing the EBIT.
Besides that, I also compare the performance difference only at the moments the required profit of the conditional hedge strategy is met, and the moments that hedging is not possible. This way it is
8
possible to identify where the biggest potential lies: in capturing higher profits, or in decreasing the loss.
5.4 Determining the potential of the independent hedge
The way to identify the potentials of the independent hedge strategy is central in this paragraph, which relates to research question 4. I determine the potential of the independent hedge strategy by subtracting the maximum and minimum possible EBIT of the independent hedge strategy with respectively the maximum and minimum possible EBIT of the simultaneous hedge strategy.
In Excel the aluminium and electric power prices are similar organized as the EBIT of each delivery year and path. To obtain the highest EBIT with independent hedging I first search for the highest aluminium futures price for the specific delivery year or path using the MAX function in Excel, and I search for the lowest electric power futures price for the same delivery year or path using the MIN function in Excel. The opposite applies to obtain the minimum EBIT.
5.5 Alternative hedge products
The method to calculate the benefits of other hedge products is the main topic in this paragraph, which covers research question 5 and 6. The put option and the collar are in combination with the electric power futures. The swap is different: this product uses the aluminium spot price and the electric power price calculated from the formula, which depends on the “K” and the aluminium spot price.
First I use the three products at the fixing moments of the conditional and unconditional simultaneous hedge strategies, which differs each delivery year or simulation path. Therefore I use the row stored by the Excel function, which represents the date hedging was possible according to the hedge conditions.
Next I have to find the maximum and minimum EBIT possible of each product, for each delivery year or simulation path, if following the simultaneous hedge strategy. I use the MAX and MIN function in excel for this. The fixing date and step differs for each product and delivery year or simulation path.
The way to calculate the maximum EBIT possible following an independent hedge strategy for the put option and collar is by using the highest result on contract, and the lowest electric power price. I also use the MIN and MAX function of Excel in this case. The swap does not involve hedging two products and is excluded from this part.
5.6 Comparing the strategies and products
Central in the comparison is the average EBIT, or the change in EBIT, over the five historical delivery years and the hundred paths of the simulation models. I test the difference between means with a one-sided paired t-test. Furthermore the standard deviation of the mean, and the minimum and maximum EBIT are also shown. Finally, I also present the amount of paths in a certain EBIT category. I distinguish four categories: paths with an EBIT smaller than 15 million, 15 million to 0 million, 0 million to 10 million, and 10 million and higher.
5.7 Monte Carlo Simulation
I use two different models to construct the path of the price of both commodities. The first model follows a geometric Brownian motion, the other model follows an Ornstein–Uhlenbeck process. The difference between the two models is the “drift” term: for the geometric Brownian motion the drift term is constant, whereas for the Ornstein-Uhlenbeck process the drift will be positive if the current value of the process is less than the (long-term) mean, and the drift will be negative if the current value of the process is greater than the (long-term) mean. I discuss the models in detail below.
The path I simulate is the average futures aluminium price for a delivery year and the price of a futures year (calendar) contract of electric power. The models do not simulate spot prices. In this case I use the last step in the path as the “spot” price. Hedging is possible from step number 127 (after a half year), which gives the simulation the possibility to drift away from the starting variables and also represents the liquidity constraints Aldel has.
5.7.1 Geometric Brownian motion
Suppose the process followed by the underlying market variable in a risk-neutral world is:
Pdz Pdt
P
d( )=
µ
+σ
(eq. 5.6)P is the commodity price. According to Hull (2006), it is more accurate to simulate ln(P) instead of P. From Itô’s lemma the process followed by ln(P) is9:
dz dt P d =
µ
−σ
) +σ
2 ( ) ln( 2 (eq. 5.7) The variable P(t) has a normal distribution with the following expressions for the mean, variance, and standard deviation: t t P E ) 2 ( )] ( [ 2σ
µ
−= Var[P(t)]=
σ
2t Sd[P(t)]=σ
t (eq. 5.8 a,b,c)Following Hull (2006), the equation I use to construct a path for P, using discrete time expression:
9
