magnitude, and we therefore cannot conclude that our results are unreliable. The most optimal hedging strategies from our full sample results are also the ones that are most optimal in the out of sample results - for both Brent crude oil and ARA gasoil futures.
We also performed a static rolling hedging strategy, where the hedge ratio is kept fixed, but the futures contracts have shorter maturities than the hedging horizon, so that they are rolled-over. Also here, the results were a bit inconclusive. Using Brent crude oil futures, the Na¨ıve strategy is the one with the lowest potential loss, while the PAR strategy stands to loose the most. The REG and mean-variance strategies are the runner-ups if using front-month contracts. If the hedger chooses to acquire ARA gasoil futures, then the PAR strategy is the definite winner with respect to effectiveness. However, compared with the static strategy, the static rolling strategy is not entirely as effective as the static one. The out of sample results in the static rolling hedging strategy also showed overall good reliability, where both effectiveness and VaR moved in the same direction with respect to TTM using Brent crude oil futures, even though the SD varied a bit inconsistently. That being said, the inconsistency is not remarkable in size. When using ARA gasoil futures, both the SD and the effectiveness move in the same direction with respect to TTM as the full sample results show. The most promising strategies from the full sample results are also the ones that are the most promising out of sample.
Lastly, we tested a semi-dynamic hedging strategy, where the hedge ratio is updated at discrete points in time as new information about prices is revealed.
Transaction costs, as for example a bid-ask spread, are not taken into account here, but will be applied in the next chapter. If using Brent crude oil futures, the futures contracts with shorter maturities perform better - this while going for the MV and Quadratic Utility strategies. The Log Utility strategy is the poorest performing one.
But also here, the na¨ıve strategy from the static and rolling hedge performs better overall. If using ARA gasoil futures in this semi-dynamic approach, we see that the Log Utility actually performs rather well for shorter maturities. In general, shorter maturities up to 3 months are showing better results than the longer maturities.
Here we had two different out of sample strategies, where one was to update the hedge ratio based on historical data and the other on simulated data. Let us first look at the Brent futures case first. The effectiveness goes down with the TTM and the SD and the VaR increases as the TTM increases for both categories of
out of sample results. We also see that the MV and Quadratic Utility strategies perform better than the Log Utility strategy, and that the shorter maturities are more effective. For ARA gasoil futures, the way the different estimates move are in line with the full sample results, and it also seems like all strategies perform well for rather short maturities. What can be taken away from these results, are that our results from using the entire sample are rather good, and that our simulated data also provides good results compared to the historical data.
This was a recap of our results from the previous section. We have tested our results by doing out of sample tests, which conveys information about the reliability of our results overall. If accepting a couple of exceptions, our results are rather sta-ble and we see an overall trend. Furthermore, the static case demonstrates higher effectiveness and seems to be less risky, and outperforms the other strategies. Over-all, hedging using ARA gasoil futures also seems more effective than using Brent crude oil futures, even though there might be more risks involved when looking at the VaR.
One could ask what we could have done differently, even though our results are rather good. First of all, we could have looked at different hedging strategies. We could have developed a utility-based hedge ratio based on parameters from our 3-factor model. This would be an interesting next step within this area of research, also given the rather good results we get from applying the PAR hedge. This is also in line with the results that Bertus, Godbey, and Hilliard (2009) find. We chose to focus on the results presented in this thesis, and will now move forward with a practical example of an energy company, more specifically DONG Energy, trying to hedge risk exposures in the spot market.
Case: DONG Energy buying Gas
Up until now this paper has discussed and investigated different ways of hedging against price risks by going to other markets and countries to invest in futures contracts. In this chapter we try to apply our model and findings to a real case, where an actual firm exposed to the very same problems with non-existent futures markets when wishing to hedge energy prices. DONG Energy, one of Denmark’s largest Energy companies, has agreed to buy natural gas in the spot market. However the price of natural gas is indexed to German gasoil, for which there exists no liquid futures market. Thus DONG Energy has to consider other markets when mitigating price risks.
First we give an introduction to pricing natural gas in Europe, then we present the relevant contract price for DONG Energy when buying gas and finally we test our findings to this specific situation.
7.1 Continental European Term Contracts
Chapter 2 gave an introduction to energy markets and while there exists a highly liquid market for oil worldwide, this is not the case for natural gas. UK is the only liquidly traded market in Europe, where the spot price is determined by supply and demand. However, continental Europe is characterized by natural gas prices being indexed to the oil and oil product prices (Geman, 2005). The reason for this type of pricing is that while the oil market has become a global market, the natural gas market is fragmented into different regional markets. Geman (2005) explains that within given market segments, such as for European energy companies, gas
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prices compete with alternative fuels, such as crude oil and gasoil. Thus, there are usually two ways of pricing natural gas in Europe; spot markets and indexed to other fuels. For the indexed price Frisch (2010) introduces the pricing arrangement of Continental European Gas Pricing Formula. This pricing system is based on long term supply contracts, which is the most frequently used when buying gas in Continental Europe and can last for periods of twenty years.
The Continental European term contracts are often based on a base price P0, which can be the agreed upon-price or the price in the beginning of the period.
Geman (2005) defines the price,P, of the contract as
P =P0+a(X−X0) +b(Y −Y0), (7.1.1) where X and Y are commodity prices that are computed as averages of the last certain number months and whereaand bare constants. The priceP will only vary with the averages X and Y for a period and then be readjusted.