Static Hedge

Static hedging consists of choosing a fixed hedge ratio, h₀, at the beginning of the hedging horizon, and keeping it fixed until the period is over. In our case the static hedge is chosen at time t = 0 and held fixed up until the time the company has agreed to buy German gasoil in the spot market, at time t= 6.

A static hedging strategy enables a company to lock in the price and reducing the price risk to just the basis risk, resulting in a certain cash flow. If the maturity of the futures contract matches the hedging horizon the basis risk might also be eliminated (Ritchken, 1999). In our analysis we thus considered a futures contract with a 6-months maturity, which matches the hedging horizon. However, as mentioned in Chapter 3, holding a futures contract close to maturity may be risky, as the company runs the risk of having to take physical delivery of the commodity. Thus the company must be vigilant to cash settle it some time before the settlement date, meaning it will have to sell the futures before, and then buy the commodity in the spot market as agreed upon.

In many cases it might be wiser for the company to hold futures contracts that have longer maturities than the hedging horizon. This way it will not be exposed to the risk of taking delivery, but there will remain basis risk. For this reason, we also considered hedging with different futures of different maturities, specifically maturities from 7 months up until 12 months. The company now holds the futures contracts until month 6 and then settles prematurely. However, as discussed in Chapter 3, liquidity should be taken into account when choosing which contract to hedge with. As we saw, liquidity decreases with increased maturities. Thus, even though it could in some cases seem more attractive to hedge with a 12-months futures contract, it will most likely be less liquidly traded than, for instance, a 7-months contract. Consequently, in practice a company can incur higher transaction costs when choosing a more illiquid futures contract, and the overall hedging result may not be as beneficial as assumed.

The results for the static hedging strategy, hedging with 6 to 12-months futures contracts, using both a MV, mean-variance and na¨ıve hedge are shown in Tables 6.3 and 6.4.

When looking at the results in Table 6.3, some general remarks are noticed. First, the hedge ratios are in every case larger than one. The reason for this, as is nicely explained in one footnote in the article by Cecchetti, Cumby, and Figlewski (1988), might be that if the futures price used for hedging has equal or higher volatility than the spot price, the hedge ratio cannot exceed the correlation coefficient between them, and is thus less than one. Nevertheless, if the futures price has a lower volatility than that of the spot price, which in this case is the German gasoil, then the hedge ratio can be more than one. From our summary statistics in Table 5.2, we notice that this is the case.

Second, as the maturity of the Brent crude oil futures contract increases, the HR and the effectiveness increase across the different hedging strategies. The SD of the HPRs and the VaR is decreasing, although not consistently. The effectiveness is higher for the parameter strategy (PAR) than for the regression strategy (REG), which is a good result as it shows that the 3-factor model is better than a simple OLS regression when estimating the MV hedge ratio. This is also in line with what Bertus, Godbey, and Hilliard (2009) find in their article. The hedging effectiveness ranges from 64% to 77% over the different strategies.

Moreover, the na¨ıve strategy, where a hedge ratio of 1 is pursued, is better than the other strategies for the shorter maturities up to a maturity of 7 months. From 8 months maturities and upwards, the other strategies are better with respect to effectiveness. One reason for this result could be that it can be wiser to follow a

“simple” strategy such as the na¨ıve one for shorter maturities since the volatility is higher for these contracts than for longer maturities. Yet as the volatility decreases with higher maturities, it will become more reasonable to go for another strategy.

One explanation for the decrease in volatility as the maturity of the futures contract increases, could be the Samuelson Effect. Information in the markets will most likely not be reflected as heavily in the futures prices of more distanced contracts. If the market for example experiences positive news of some sort, it is more likely that the prices of a front-month futures contract will be affected than those of a 12-months futures contract, since this contract is meant to be closed farther into the future when this information might be less important.

In Table 5.3, the correlation coefficients between German gasoil and the differ-ent futures were presdiffer-ented. The correlation between GGO and a 12-months Brdiffer-ent futures is lower than that between GGO and a front-month Brent futures contract.

It is therefore natural to assume that it would be better to hedge with a nearby futures contract. It seems as though we are witnessing a trade-off in this case be-tween correlation and volatility, as the effectiveness is higher the longer the time to maturity (TTM) of the futures contract.

In addition, what is striking is the equivalence between the MV and the mean-variance hedge ratios. As Ankirchner and Heyne (2010) write, it is plausible that futures prices are in fact martingales, and that the expected return is close to or equal to zero. When this is the case, the mean-variance hedges will be reduced to the MV hedge.

In the case of ARA gasoil, we see some similar trends in the results. As maturity increases, the effectiveness tend to increase for the REG and mean-variance hedges, whilst they decrease for the PAR and na¨ıve hedges. The effectiveness is clearly highest for PAR, and lowest for Na¨ıve. The effectiveness is as high as 95.9% for the PAR hedge using 6-months futures, which is very good. Comparing Brent Crude and ARA gasoil, we know that ARA in general has a higher volatility in prices than Brent. Also, the correlation between ARA and German gasoil is higher than the correlation between Brent and GGO. Furthermore, although there are some similar trends between hedging with both commodities, we see an overall higher effectiveness and VaR when hedging with ARA gasoil futures, than with Brent crude oil futures.

This can possibly be explained by that the market for ARA gasoil futures is a more closely related to market of the German gasoil market, than what the Brent crude oil futures market is. However, as already discussed, the ARA gasoil market may run the risk of being a less liquidly traded market than the Brent crude oil market, thus essentially incurring higher transaction costs.

We have also done an out-of-sample analysis, and the results, which can be found in Tables A.2 and A.3 in Appendix A.2, demonstrates the significance of our results, as the trends are rather similar out of sample as for the full sample. If using Brent crude oil futures, the out of sample results can be summarized as follows from Table A.2. The SD of the HPRs decreases with the time to maturity for each strategy.

The effectiveness increases with TTM across the strategies, and the VaR decreases.

These results are good, as a higher effectiveness combined with a lower SD of the HPRs and a lower VaR would make profitable strategies.

Regarding the out of sample results for ARA gasoil, which can be found in Table A.3 in Appendix A.2, we see that as maturity increases the effectiveness decreases

for REG and Mean-Variance as opposed to the results from full sample. Similar to the full sample results, the effectiveness decreases for PAR and Na¨ıve. The VaR decreases across all strategies overall, even though it is at its lowest for the maturities in the middle for the strategies other than PAR. Worth to mention is that the changes in the HR, effectiveness and VaR are minimal, so they do not tell us much or are of little consequence as to which of the futures contracts is the best to use.