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It is well recognized that for the producing companies hedging the commodity price using financial products like forwards or futures has become an important part of the company's production process. But apart from the direct impacts of hedging on the production and hedging costs the use of financial products affects the financing of the company: hedging the volatile commodity prices leads to a reduction of the risk premium the company has to pay for its debt capital, since hedging contributes to more confidence of the investors in the redemption of the debt. In this paper we therefore analyze this dependency of hedging and financing and derive optimal hedging extents for companies in different market situations based on a long-term model. By hedging the commodity price, companies can realize a surplus in profits. Thereby, the optimal hedging extent for a monopolist is often up to 100%, whereas for companies in a polypolistic market the optimum is always less than 100%. These results are illustrated by examples for a producing company.

Motivation Undergoing a financial crisis to an extent, which had never even been imagined, crude oil prices were one of the first commodity prices to be strongly affected in 2008 leading to a high volatility. In the beginning of May 2008 Goldman & Sachs Corp. had predicted a crude oil price increase up to $200 for the time period of the following six month to two years as growth in supply apparently failed to keep pace with the increased demand from the developing nations (Subrahmaniyan, 2010). Still according to this prediction the West Texas Intermediate hit an all-time high of $145.31 per barrel on July, 3 2008. However, not even six month later on December, 23 2008 it had fallen to only $30.28 per barrel (U.S. Energy Information Administration, 2010). On the other hand, companies such as airlines depending on commodities like oil are being endangered by these volatile prices. For instance, the Lufthansa Group, Germany's biggest airline, states according to its annual report in 2008 that 21% of the group's operating expenses was owed to its fuel consumption. It is especially industries like the aircraft industry that strongly depend on commodities and their price evolution. But the occurrence of extreme volatile price evolutions are not only restricted to crude oil prices. To name just a few among many, prices of wheat, steel and copper have not been lagging behind regarding their price volatility in the last years (see e.g. Chen, 2010). Inevitably, companies competing in these and similar industries have to hedge their commodity demand since this provides a basic degree of security in the ever more competitive and volatile commodity markets of today. But hedging also influences the financing of a company: hedging the volatile commodity prices leads to a reduction of the risk premium a company has to pay for its debt capital, since hedging contributes to more confidence of the investors in the redemption of the debt. To reduce the risk of volatile commodity prices, only few companies decide to hedge their idiosyncratic commodity risk by backward vertical integration, the majority prefers to use financial products like future or forward contracts for this purpose. The importance that economies and companies attach to commodities, their exploitation, and along with that their prices and hedging against them can be found widely. Hedging not only reduces risks for the company buying the commodity e.g. the Lufthansa Group, as hedging is done with counterparties: either directly with the provider of the commodity or indirectly with an intermediary or speculator who then hedge themselves with the providers. In both the cases, the market risk for all market participants taken together, intermediaries, speculators, buyers and sellers of the commodity may be reduced if allocated properly (see e.g. Rafiq et al., 2009). Then, the long-term commodity price may become more stable and predictable for the companies depending on the resources, both as producers and consumers. This eventually contributes to lower volatilities in markets and economies, and in the end to a world that is less risky, and hence more desirable for all market participants in the long run. Consequently, the probability of a possible resource price crisis can be reduced, or – on a microeconomic level – industries and companies can predict their commodity expenses more accurately. Literature overview While many have dealt with the various reasons for hedging (e.g. Smith and Stulz, 1985), first studies were conducted into deriving the optimal hedging extent as far back as 1960, starting off with Johnson (1960) who was the first to derive the number of future or forward contracts necessary to hedge a certain spot position based on the attempt to minimize the variance of a hedged portfolio followed by Cecchetti et al. (1988). Since then many others have analyzed similar aspects varying the techniques and assumptions of previous studies, and for instance examined the history of future markets and forward pricing of commodities (e.g. Goss, 1981) or the role and significance of futures trading of commodities (e.g. Weston and Silverii, 1985). However, many of them thereby focused on the risk reduction of the commodity prices as a result of hedging (e.g. Lien and Tse, 2002 and Chen et al., 2003) neglecting further impacts of hedging on the company. But since hedging also influences for example the company's financing, other authors turned their attention towards this field: Froot et al. (1993) developed a model for corporate risk management in which they linked the activity of hedging to a company's overall financial situation. Another approach was introduced by Rogers (2002) who scrutinized the dependency between the hedging extent of a certain company and its CEO's risk taking incentives while others analyzed the impact of hedging on tax payments (see Smith and Stulz, 1985 and Leland, 1998). Furthermore, Franke (2003) showed how the hedging policy of a company depends on the characteristics of the exchange rate process, the real investment option and the costs of financial distress, whereas Broll et al. (1999) show that to hedge the exchange rate risk in forward markets, it does not imply standard full hedging. But neither of the above mentioned developed their model with the main focus on commodity price risks and in dependence of the market structure in which the analyzed company interacts. In the last few years, research concentrated mainly on analyzing the various and different time series data of commodities (see e.g. Chen, 2010 and Cortazar and Eterovic, 2010 among many others). These studies try to predict the future development of the commodity prices or the prices of commodity futures and forwards. Due to the findings of these extensive data analysis that, however, often neglects the impact of commodity prices on the commodity buying or selling company, and due to the lessons learnt from the recent financial and economic crisis, we refocus on the methodological aspects between commodity hedging and the company's financial situation, particularly with respect to debt financing. Thus, in this paper we develop a model that derives optimal hedging extents for companies subject to its financial costs in different market situations based on a long-term model. It additionally makes a contribution to help establish a more sustainable environment. To begin with we present the basic model and its key players in Section “The model”. Based on this model we derive the long term optimal hedging extents for risk-neutral companies in different types of markets: first we analyze the model within a monopolistic sales market in Section “Monopoly”, and then we continue within a polypolistic one in Section “Polpoly”. Section “Conclusion and outlook” concludes.

In this paper we analyzed the profit of a risk neutral company with regard to a long term hedging extent, where hedging contributes to less fluctuation and so to better predictable commodity markets. We scrutinized the impact of several different quantifiable factors that influence the decision of the hedging extent: the type of market a company was trading its own products in and the type of market it was satisfying its commodity demand in, the access of the company to financial services, the importance of commodities to the company and the risk aversion towards the public perception of being a speculative company. While the evolved model focuses on these factors, it does not account for currency issues and varying tax systems, which have to be included into a financial analysis as well. Another interesting research area can be the analysis of short term price evolutions in a competitive market where a company faces direct competitors that also use the instrument of hedging. However, in this paper we demonstrated how all the factors listed above led to a long term optimal hedging extent and thus to a surplus in profits depending on particular market situations and a more stable commodity market for all market participants. In the basic model of a monopolist we showed how the expected reduction in the risk premium of the newly issued capital and the way it was reduced could realize a surplus in profits, for instance $129,152 in the illustrated example for the monopolist. While this added to the advantageousness of hedging, the costs involved with hedging resulted in a downside of hedging. Once the risk premium reduction preponderated, we often obtained marginal solutions of 100% as the optimal hedging extent. However, this changed when considering a polypolistic market of the company's product. The volatile demand for the company's product and along with that the volatile demand for the commodity led to the possibility of being overhedged. In order to circumvent this we introduced an upper restriction to the hedging extent. In the given example this restriction evoked a reduction of the optimal hedging extent from 100% to 98.4%. In conclusion we can state that the long term optimal hedging extent evolved in this paper helps the company to plan and organize its current and future expenses for the following business periods. As speculation is reduced, the model helps to contribute to a more stable demand of the underlying commodity in general. Thus, market participants including the provider and the buyer of the commodity as well as the commodity industries and economics profit from hedging the commodity price. This adds in the end to a positive and sustainable influence on the environment, since, for example, the exploitation of non-renewable resources like oil or iron ore can be managed and planned with less risk involved.