Static Rolling Hedge

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.

We quickly see that the net gain after the hedging period is 3. If we assume that the initial spot price, in time 0, was 19 and that it increased to 23 at time 6, this loss is partially compensated by the gain from selling the futures.

As seen from the example the company still incurs some loss from an increase in prices. Ritchken (1999) explains this by each time a roll-over is done, the hedging strategy accumulates basis risk. The more roll-overs the less precise the hedging strategy will be. Consequently, although shorter maturities will often be more liquid, rolling the contracts over may have a negative effect on the hedging strategy as a whole. As basis risk is accumulated with more roll-overs, the hedge becomes more and more risky and the company may end up loosing a vast amount of money.

The rationale behind this is the difference between a market being in contango or backwardation (Domanski and Heath, 2007). When the spot price rises above the futures price, e.g. the market moves into contango, the company stands to lose from the hedge, and as more and more contracts are rolled over the losses become greater.

When the spot price is below the futures price, e.g. the market is in backwardation, the company may gain high profits from the hedge, and rolling over more times can be beneficial. Thus, when choosing a rolling hedge strategy, the company should have some idea of as to where the market is heading.

All results from the static rolling hedge are shown in Tables 6.5 and 6.6. We can see from Table 6.5 that the hedging effectiveness is higher for REG and Mean-Variance than for PAR, and that the effectiveness is highest for the na¨ıve hedging strategy with an effectiveness of 73.6% at the most. The effectiveness and the VaR decrease as the time to maturity increases from front-month to 3-months. The REG strategy gives the best results in the static rolling case for Brent crude oil, but one could still wonder why the SD of the HPRs is lowest and the effectiveness highest for the front-month contract, while the VaR is lowest for the 3-months contract.

The HR is higher in the 3-months case than the front-month case, so given that a higher proportion than the risky spot position is actually invested in a less volatile futures position might make the VaR lower. Nevertheless, it seems as though the na¨ıve strategy is the best to follow using front-month futures.

In relation to the static case from Table 6.3, where we found that the hedge results were best for the 12-months contract in the PAR case. In the static rolling case for Brent crude oil futures, we see that the na¨ıve strategy in the front-month futures seem to perform best overall. It looks like the choice is between a na¨ıve

roll-over strategy in a more volatile front-month futures or a more sound static strategy in 12-months futures contracts.

The rolling hedging results using ARA gasoil futures can be seen in Table 6.6.

The effectiveness goes up with the time to maturity of the futures contract for REG, PAR and Mean-Variance, and down for Na¨ıve. It is seen from the results that the PAR hedge outperforms the other strategies for every maturity with an effectiveness being as high as 95.8%, and that the na¨ıve performs the poorest. The VaR increases with the time to maturity for the strategies Mean-Variance and MV, but it decreases for Na¨ıve.

So the VaR is lowest for the REG strategy by using front-month futures, but the effectiveness and the SD seem to convey that the PAR strategy using 3-months futures is better. The differences are not that great, so a uniform conclusion about which maturity to chose is not trivial. The differences between PAR and the other hedging strategies, however, is quite obvious. The VaR is lower for the other strate-gies than it is for PAR, but PAR shows greater effectiveness and lower SD of the HPRs.

We see that the shorter maturities seem to perform better - both in the static and in the static rolling case (here there are only shorter maturities) - when it comes to VaR. However, the effectiveness seems to be better for 3-months futures in the static rolling case, and in 6 or 7-months futures in the static case. PAR does in general have a higher VaR, both in the static and the static rolling case, so there is again this trade-off between risk and return. In order to reach a higher possible effectiveness, then a higher VaR seems to be the only option.

Just as for the static hedge, one sees that for the rolling hedge that effectiveness and VaR are higher when using ARA gasoil futures than for those of Brent crude oil, again giving evidence of a more closely related market.

Again we have performed an out-of-sample analysis for all the static rolling hedges. These results can be found in Appendix A.2, Tables A.4 and A.5. In the case of Brent crude oil, the out-of-sample results are very similar to those from using the full sample. REG and Mean-Variance are more effective than PAR regardless of the time to maturity, but the na¨ıve strategy is even better. The effectiveness, the SD and the VaR decrease with time to maturity for all strategies, but for Na¨ıve the effectiveness sticks around the same level overall.

The out-of-sample results from hedging with ARA gasoil in a static rolling man-ner can similarly be found in Appendix A.2, Table A.5, and shows that the effec-tiveness increases with the time to maturity for every strategy. PAR is the most effective hedging strategy, but also has the highest VaR. The opposite holds for the na¨ıve strategy, which has the lowest effectiveness but also the lowest VaR.