chrilly's toolbox of energy futures trading. chrilly donninger chief...

Chrilly's Toolbox of Energy Futures Trading.Chrilly Donninger

Chief Scientist, Sibyl-ProjectSibyl-Working-Paper, August 2015

Come writers and criticsWho prophesize with your pen

And keep your eyes wideThe chance won't come again

And don't speak too soonFor the wheel's still in spinAnd there's no tellin' who

That it's namin'.For the loser now

Will be later the winFor the times they are a-changin'

(Bob Dylan: The Times They are A-Changin')

Abstract:

In a previous working paper I analyzed the performance of several rolling strategies for the 5 most important Energy Futures in the last 10 years. It was assumed that one is always long the Futures. The task was to minimize the harm of rolling. Due to the weak performance of this sector there was in absolute terms (almost) nothing to gain. This working paper analyzes several strategies which try to exploit all aspects - rolling, the term structure, mean reversion, seasonal-patterns and trends - of the Energy Futures market. Anything goes as long as it is profitable. Some of the strategies perform considerable better then the long-only portfolios. But the times they are A Changin' in the Energy-Futures market. It is difficult to find a consistent strategy which handles the different market-regimes successfully. Some of the winners proposed in the literature performed fine once upon a time. But they are the losers now.

1) The General Setting:

This investigation is a follow-up of a study [1] about optimal Energy Futures rolling. The previous paper focused on the question how one can minimize the roll-losses of long Futures positions. The market has changed in recent years from “natural backwardation” to contango. This market regime had a devastating effect on the performance of simple-minded long-only portfolios. The spot is considerable outperforming the Futures. This effect is especially pronounced for the WTI (see Figure 2 below from [2]).

This investigation uses the same data set as [1]. Daily Futures data for WTI- (ticker CL) and Brent-Crude Oil (LCO), Heating-Oil (HO), Unleaded Gasoline (RB) and Natural Gas (NG) from 2005 to July2016. The historical simulation is run for the last 10 years, from 2005-06-01 till 2015-06-01. The initial index-value was set to 2.000.000$. It is assumed that one trades the individual Futures and not a market defined spread in a single transaction. I do not have spread data and there are no (liquid) spreads for several general strategies available. It is a question of implementing a strategy if one shouldtrade in bundles or the Futures individually.

The trade cost per Future and trade is given in the table to the left. It is assumed that each trade costs per Future a fixed amount of 5$ plus the bid-ask spread. The 1st and 2nd CL and LCO Futures have a spreadof 0.01, the 3rd to 5th of 0.02 and longer maturities of 0.03. The 1st HOand RB Futures have a spread of 0.0005, the 2nd to 4th of 0.0008 and longer maturities of 0.001. CL and LCO are traded in barrels. The $-

multiplier is 1000. HO and RB in gallons. The $-multiplier is 42.000. The 1st NG Future has a spread of0.001, the 2nd to 4th of 0.002 and longer maturities of 0.003. NG is traded in million British thermal units. The $-multiplier is 10.000. These numbers are current market-conditions. The results are relative robust to different/higher trading costs assumptions.

Graphic-1 shows the price of the most nearby CL and LCO Future from 2005-06-01 till 2015-06-01. No rolling effects are considered. One just draws the current prices. This can be considered as a first approximation to the spot price. Graphic-2 is the same for HO and RB. Graphic-3 shows the (devastating) performance of NG.

The table on the left shows the start- and the end-priceand the overall performance. A remarkable and puzzling effect is the different performance of CL andLCO. WTI has slightly better chemical characteristics.It traded in 2005 (and before) at a premium to Brent. But the relation has reversed in recent years. WTI

now trades at a significant discount. The usual explanations are market and logistic frictions.

2005-06-01 2015-06-01 P&LCL 54.6000 60.2000 10.26LCO 53.2700 64.8800 21.79HO 1.5400 1.9264 25.09RB 1.5442 2.0422 32.25NG 6.7890 2.6490 -60.98

Short Middle LongCL 15.0 25.0 35.0LCO 15.0 25.0 35.0HO 26.0 38.6 47.0RB 26.0 38.6 47.0NG 15.0 25.0 35.0

Graphic-1: 1st Future 2005-06-01 till 2015-06-01. CL (red), LCO (yellow)

Graphic-2: 1st Future 2005-06-01 till 2015-06-01. HO (red), RB (yellow)

Graphic-3: 1st Future 2005-06-01 till 2015-06-01. NG (red)

2) Front-Running the Goldman-Roll:

Commodity index investment experienced dramatic growth over the last decade and now constitutes a significant fraction of investment in commodity futures markets ([3]).

The most popular index is the Standard and Poor's-Goldman Sachs Commodity Index (SP-GSCI). The SP-GSCI rolls futures forward from the 6th to the 9th business day of each month, and its rolling activityis usually called the Goldman roll. The involved futures are specified in the Roll-Tables in Appendix A.The first-generation index rolls from column 0 to 1. The second generation dynamic indexes roll between the columns which optimize the roll yield. One tries to exploit this effect by front-running the basic Goldman-role. One shorts before the role-period the Futures the SP-GSCI is currently holding and longs the deferred contracts it will roll into. During the role period one unwinds the position. According to [3] one builds up the position from the 10th to 6th trading day before the Goldman-roll. During the Goldman-roll one sells each day 20%. As an alternative I have tried a strategy where one enters the whole position 10-trading days before the roll and sells the total position at the 5th business day. This is besides for RB better than the approach proposed in [3]. One can experiment with different dates. The results are similar. One starts with an initial account of 2.000.000$ and buys/sells 30 Futures.

The table on the left shows in the left part the result for the enter- and close-days from [3]. The right part is for alternative described above. The first column P&L is the Profit&Loss in percent,The second Sharpe is the monthly Sharpe-Ratio and the third Rel.DD is the maximum relative Drawdown. The full performance of CL is shownin Graphic-4. The red line corresponds to the left

part of the table, the yellow to the right.Generally the method works fine till 2009, but then levels off. The strategy is still profitable before trading costs. There is also little risk involved and one could increase the leverage considerably.But the trading costs start to “eat up” the gain. For LCO the trading costs drag down the performance below break even (Graphic-5). The same holds for the other Futures.The results are in accordance with Figure 6 from [4].

The regime-change can be explained by the bad performance of first-generation index products. A part of the investors has switched to 2nd generation indexes. Some have closed their commodity portfolio at all. One could try to Front-Run the second generation Indexes, too. But there are several of them. According the results in [1] the effects are too small to be – after trading costs – exploitable. Additionally one has a considerable higher calendar-spread risk. The difference in maturity is usually (much) larger than 1 month. I have therefore not investigated this idea further.

Goldman Front-Running [10,6] – [5,9] [10,10] – [5,5]

P&L Sharpe Rel.DD P&L Sharpe Rel.DDCL 23.21 0.75 2.36 25.71 0.84 2.94LCO 4.26 0.30 6.48 5.34 0.37 5.64HO 0.78 0.04 9.40 7.40 0.34 5.82RB 12.86 0.19 19.66 7.92 0.11 24.55NG 7.06 0.18 13.62 19.73 0.45 7.87

Graphic-4: CL Front-Running 2005-06-01 till 2015-06-01.

Graphic-5: LCO Front-Running 2005-06-01 till 2015-06-01.

3) Momentum in Carry:

Andreas Neuhierl and Andrew Thomson argue in [4] that the Front-Running strategy does not properly work any more (see Figure 6 from this paper above). Their alternative is the momentum of the spread/term-structure. One calculates the 50-days average of the spread between the 1st and 2nd Future and compares it with the current spread. This forms the signal.

Signal(t) = ln(F1,t)-ln(F2,t) >= 1/50 * SUM(ln(F1,t-i)-ln(F2,t-i)) i=0,..,49

If the signal is true (the current spread is above the moving average) one goes the next trading day the spread between the 1st Future and a Future with longer maturity (far out the term structure) long. If the signal is false, one goes the spread short. It is argued by the authors that any implementable strategy must have this kind of delay. The dynamic roll-indexes use for the same reason this mechanism.But one could argue that the spread moves only slowly. One could determine in real-time the signal and

trade a second later. This is more a problem of historic simulation with daily data. The result improvessignificantly if one uses the current instead of the delayed signal. The table shows the performance of the strategy. As in [4] a one day delay is used.

1/10 means the traded spread is between the Future in the 1st and 10th column in the Roll-Table of Appendix A. This Roll-Table is from the SP-Dynamic Roll Index (see [1] for a detailed discussion).The Roll-Table takes liquidity into account. E.g. for CL and LCO the long maturities are traded only with the December Futures. Long/Short means one goes – like in [4] – the Spread long and short. But according to the simulation most of the profit is made with the long Spread. In the Long-Only columns one trades only the long-spread. If the signal is false one stays out of the market. Besides a momentum in carry the strategy assumes that the term-structure moves in sync. The spread trend between the 1st and 2nd Future is the same as between the 1st and the far-out Future which is actually traded. This is not necessarily the case. E.g. RB and NG have a strong seasonal component. Additionally one assumes that the 1st Future moves faster than the far-out.

Graphic-6 shows the performance of the strategy for CL. The red-line is the 1/10, Long/Short parameter setting. The yellow line is 1/10, Long-Only. The green line 1,8 Long/Short, light-blue 1,8, Long-Only. The dark-blue line is the performance of the red-line if one uses the current trading signal and not the delayed one. The strategy works fine till 2012, but is less spectacular in the recent 2-3 years. The data in [4] ends in 2013. The reported performance is hence considerably higher. The performance of LCO is worse. The strategy ifor RB and HO is a disaster. Graphic-7 shows the performance of NG. The colors have the same meaning as in Graphic-6. There is till 2009 a lot of fun and risk (see also the Amaranth strategy below). The performance is since then – after trading costs – almost flat. The NG market has fundamentally changed due to fracking.

Graphic-6: CL Carry Momentum 2005-06-01 till 2015-06-01.

Carry Momentum with Roll-Table, Daily1,10, Long/Short 1,10,Long-Only 1,8,Long/Short 1,8,Long-Only

P&L Sharpe Rel.DD P&L Sharpe Rel.DD P&L Sharpe Rel.DD P&L Sharpe Rel.DDCL 123.26 0.64 20.44 116.15 0.71 15.21 81.00 0.63 15.45 89.06 0.78 9.99

LCO 89.81 0.46 21.50 73.52 0.51 21.64 39.50 0.30 21.85 48.24 0.49 15.74HO -76.00 -0.73 81.26 -8.06 -0.13 31.70 -76.00 -0.73 81.26 -8.06 -0.13 31.70RB -36.73 -0.37 58.25 -45.51 -0.59 54.33 -36.73 -0.37 58.25 45.51 -0.59 54.33NG 208.83 0.59 43.20 227.31 0.72 36.74 199.71 0.60 43.27 215.67 0.73 37.51

Graphic-7: NG Carry Momentum 2005-06-01 till 2015-06-01.

The method can generate high trading costs. If the signal does not change one has to roll the spread each month according the Roll-Table. If the signal flips around within a month the spread has to be reversed. One can reduce the trading costs by determining the side of the spread at the roll-date and ignoring the signal in between. The downside is of course that one will usually lose extra money by reacting later to a change in the term-structure.

The 1,8, Long-Only parameter setting has the highest Sharpe Ratio. Graphic-8 compares the daily (red) with the monthly adjustment. The final win is slightly larger for the daily-adjustment, but the monthly adjustment has a slightly higher Sharpe-Ratio. But it should be noted that for the other parameter settings (and Futures) the daily-adjustment has a clear edge. I have tried other rules like adjusting the position every Wednesday. This did not improve the performance.

Carry Momentum with Roll-Table, Monthly1,10, Long/Short 1,10,Long-Only 1,8,Long/Short 1,8,Long-Only


LCO 69.38 0.39 34.42 63.18 0.45 30.31 43.85 0.38 25.21 51.15 0.55 17.78HO 11.29 0.12 24.99 35.44 0.42 14.86 11.29 0.12 24.99 35.44 0.42 14.86RB -54.40 -0.45 70.03 -51.33 -0.66 57.83 -54.40 -0.45 70.03 -51.33 -0.66 57.83NG 149.34 0.43 50.66 195.30 0.63 41.16 142.46 0.44 49.32 186.02 0.63 40.75

Graphic-8: CL Carry Momentum Daily/Monthly 2005-06-01 till 2015-06-01.

4) Extending the S&P GSCI Dynamic Roll to Long/Short:

This strategy is based on the S&P GSCI Dynamic Roll Methodology (see [1] and [5]). One calculates the spread to the next-nearer Future for each Future. This can also be interpreted as the slope of the term-structure. One sorts the Futures according to the spread. The Future with the smallest spread is gone short, with the largest spread gone long. The signal/selection is done on the 1st business day of the month. The position is changed accordingly at the 2nd business day. One has the same separation between signal and trade like for the Momentum-Carry strategy and all the Index-methodologies. The S&P GSCI Dynamic Roll is a long-only strategy. The purpose is to optimize the roll. One just selects the long-leg. This strategy tries to exploit the difference in carry along the term-structure.

The table below shows the performance for different ranges of the Roll-Table. Range-10 means the strategy can select any pair from the 1st to the 10th column. For Range-6 the selection is restricted to the 6th column. Usually the selected Futures are on the borders of the range. For Range-10 one trades the Futures in the 1st and 10th column of the Roll-Table. This has some additional profit potential, but the linkage/correlation between the prices gets weaker. The risk of severe losses increases. Range-6 has thesmallest fun but also by far the smallest risk. It is the best risk-adjusted choice. Range-8 is an interesting alternative. The numbers are in agreement with the main results in [6].

“We find large variations over time in the amount of information shared by contracts with different maturities. Although on average short-dated contracts (up to 6 months) emit more information than backdated ones, a dynamic analysis reveals that, after 2012, similar amounts of information flow backward and forward along the futures maturity curve. The mutual information share increased substantially starting in 2004 but fell back sharply in 2012-2014. In the crude oil space, our findings point to a puzzling re-segmentation of the futures market by maturity in 2012-2014”.

The re-segmentation and the backwards flow of information has also serious impacts on the previous Momentum in Carry Strategy.

Graphic-9 shows the performance of the Futures for Range-6. The red-line is CL, yellow LCO, green HO, light-blue RB and dark-blue NG. The strategy works reasonably for CL and LCO. Like before it does not work for HO, it is a disaster for RB. NG is extremely volatile till 2009. It is smooth but also uninspired in the last years.

Graphic-9: S&P-Dynamic Long-Short for Range-6 2005-06-01 till 2015-06-01.

5) Extending the DBLCI Optimum Yield Index to Long/Short:

The idea of this strategy is similar to the previous one. But instead of the S&P GSCI Dynamic Roll one extends the The Deutsche Bank Liquid Commodities Indexes Optimum Yield to Long/Short (see [1]). The index methodology determines on the 1st business day the Future with the maximum implied yield and rolls on business day 2 to 6. Like before the signal is determined on the 1st and the new position is completely traded on the 2nd business day.. The DBLCI selects consecutive Futures. I have instead used the Roll-Tables like in the previous strategy. The strategies differ in the calculation of the implied yield.The S&P-GSCI calculates the local-slope of the term-structure. The DBLCI uses essentially the mean-slope between the nearby and more distant Futures.The implied roll yield is defined as:

Y(t,i) = ((PC(t,b)/PC(t,i))^(365/F(t,i,b))) – 1 (1)

Y(t,i) = Implied Roll Yield for Future i on day t.PC(t,b) = Closing price of base (most nearby) Future b. PC(t,i) = Closing price of Future i.F(t,i,b) = Fraction of a year between expiry of the base Future and i.

S&P-Dynamic-Long-ShortRange-10 Range-9 Range-8 Range-6


LCO 87.83 0.57 26.69 86.20 0.60 23.18 70.84 0.67 14.78 42.31 0.71 8.69HO 3.78 0.06 30.32 3.78 0.06 30.32 3.78 0.06 30.32 16.00 0.26 20.01RB -48.44 -0.41 62.28 -48.44 -0.41 62.28 -48.44 -0.41 62.28 -48.44 -0.41 62.28NG 51.63 0.17 47.30 21.61 0.06 70.10 13.10 0.03 84.71 81.42 0.42 30.24

The table shows the results for different ranges. There is one noticeable difference to the previous method: Brent-oil (LCO) performs better than WTI (CL). The last row shows a simple portfolio of 15 Futures CL and 15 Futures LCO. The performance of this portfolio is smoother.

Graphic-10 shows the performance of the Futures for the best range 8. The red-line is CL, yellow LCO,green HO, light-blue RB, dark-blue NG and magenta the combination of CL and LCO.

Graphic-10: DBLCI Optimum Yield Long-Short for Range-8 2005-06-01 till 2015-06-01.

6) Crude-Oil Dynamic Yield:

So far the strategies were based on calendar spreads. But one can combine this with pairs-trading. The by far most appropriate pair is CL and LCO. From their physical properties WTI and Brent are similar. WTI traded for a long time above Brent. The relation has reversed in recent years. The usual explanations are market and logistic frictions (see also [1]). Graphic-11 shows the prices of the 1st Future for CL (red) and LCO (yellow) in the last 10 years.

OptYield-SPTable-Long-ShortRange-10 Range-8 Range-7 Range-6


LCO 99.92 0.60 24.23 90.64 0.80 13.31 61.47 0.78 10.84 47.48 0.77 9.33HO 34.97 0.40 18.24 34.97 0.40 18.24 34.97 0.40 18.24 32.54 0.43 15.31RB -35.02 -0.31 48.52 -35.02 -0.31 48.52 -35.02 -0.31 48.52 -35.02 -0.31 48.52NG 92.64 0.31 44.78 90.65 0.31 44.78 74.21 0.29 42.22 75.09 0.40 25.15

CL+LCO 88.48 0.62 12.47 76.47 0.80 9.57 55.76 0.78 9.23 44.42 0.79 7.38

Graphic-11: 1st Future 2005-06-01 till 2015-06-01. CL (red), LCO (yellow)

The strategy calculates for both Futures the implied roll-yield of equation (1). One goes the minimumroll-yield short. Let's assume this is a CL Future. Then one goes the LCO Future with the largest yield long. The maximum roll yield of CL could be larger than max. LCO. In this case one could trade a plain calendar spread like above. I did not encounter such a situation and the strategy always trades CL against LCO. The strategy increases the profit potential by considering a wider yield-differential. Thereis of course also an additional risk involved. The short-long position is not as well cointegrated as a plain calendar spread. For this reason I tried also a Stop-Loss rule. If one loses more than 2% since the last roll the position is closed. One enters the market again at the next roll.

The table on the left shows the performance of the strategy. 6-6 means, one selects for CL and for LCO from the first 6 entries of the Roll-Table. One could think about other combinations like 6-4, but restricting both Futures to the same range is clearly preferable.The left side of the table shows the results without any Stop-Loss. The right side uses a Stop-Loss of 2.0%. The 2.0% threshold was not optimized. I just took the first reasonable percentage which came to my mind. As before a range of 6 or 7 seems to be the best compromise between profit potential and risk.

With the Stop-Loss one can extend the range to 9. Graphic-12 shows the performance. The red-line is for range-6 and no Stop-Loss. Yellow is the performance with Stop-Loss. Green is for range-9 without Stop-Loss, light-blue with Stop-Loss.

Crude-Oil Roll-Yield-DynamicNo-Stop-Loss Stop-Loss 2.0

P&L Sharpe Rel.DD P&L Sharpe Rel.DD1-1 45.38 0.35 21.68 56.70 0.45 16.562-2 78.80 0.63 15.43 80.20 0.63 10.703-3 85.19 0.66 13.86 93.08 0.72 11.064-4 98.93 0.75 12.70 106.49 0.79 9.955-5 98.04 0.77 12.12 105.66 0.82 9.586-6 105.23 0.79 11.65 108.38 0.82 9.697-7 109.27 0.79 11.71 113.96 0.83 9.638-8 117.52 0.72 18.26 127.19 0.82 11.009-9 127.50 0.72 14.73 146.06 0.85 9.14

10-10 111.83 0.63 18.33 137.53 0.81 11.7611-11 118.79 0.66 14.81 136.91 0.79 10.84

Graphic-12: Crude-Oil Dynamic Yield for Range 6 and 9 2005-06-01 till 2015-06-01.

7) Crude Oil Momentum:

The two sources of commodity-trading profits are the carry and momentum (see see [8] and the references herein). The Momentum strategy goes the Crude Oil Future with the higher return in the last k-months long and the other short. The selection is restricted to the 1st column of the roll-table. I tried also fixed longer maturities. The performance for the nearest Futures is clearly superior. A dynamic approach which takes also the full-term structure into account is analyzed in the next paragraph.

The table on the left shows the performance for different window lengths. A look back window of 1 month is clearly the best choice. This is in full agreement with the results in [8]. Another popular choice are 12 months. But this does not work in this context. Interestingly the second best result is a window length of 21 months. The results in the left part of the table are without a Stop-Loss. The right part uses the Stop-Rule of the previous paragraph. The red line in Graphic-13 shows the performance for the best window length of 1 month, the yellow line is for a window length

of 12 months. The performance is similar till 2012, but the 1 year window generates heavy losses in thelast 3 years. This can be reduced somewhat with the Stop-Loss rule. The 1 month window is nevertheless the by far better choice.

Crude-Oil Trend-1-1-FixedNo-Stop-Loss Stop-Loss 2.0

P&L Sharpe Rel.DD P&L Sharpe Rel.DD1 91.41 0.65 19.28 80.69 0.61 15.983 29.10 0.23 22.24 32.24 0.28 18.386 -23.52 -0.21 45.27 10.50 0.10 23.069 28.92 0.24 23.94 55.88 0.46 14.5312 11.70 0.11 38.39 38.48 0.36 26.2315 48.96 0.37 27.74 64.28 0.51 20.4218 57.81 0.43 23.88 65.66 0.50 20.0521 78.81 0.58 15.51 81.45 0.59 17.9124 16.71 0.13 33.85 43.34 0.35 31.25

Graphic-13: Crude-Oil Trend for 1 and 12 months window-length 2005-06-01 till 2015-06-01.

8) Combining Crude Oil Momentum and the Dynamic Yield:

An obvious extension is to combine the trend and the dynamic yield strategy. One determines first with the 1-month trend the long and short side. In the next step one selects for the short side the Future with the smallest yield and on the long side the Future with the largest yield. One tries to exploit both sources of profit. As before the term-structure is restricted a range of the roll-table.

The table on the left shows the performance for different ranges. The 1-1 setting is the same than the simple trend strategy above. This corresponds with the red-line in Graphic-14. The yellow line is the performance of range-5, the green line of range-6 and the light-blue line of range-7. Range-6 is the best choice. Combining the trend with the term-structure boosts the performance. Range-6 and 7 have the best risk-adjusted performance of all the strategies considered so far. The Stop-Loss improves the performance only for the far-end. For shorter maturities it is preferable to be all the time in the market.

Crude-Oil Trend-DynamicNo-Stop-Loss Stop-Loss 2.0

P&L Sharpe Rel.DD P&L Sharpe Rel.DD1-1 91.41 0.64 19.28 78.90 0.60 16.142-2 99.01 0.72 16.66 91.98 0.69 14.753-3 100.79 0.74 16.35 89.00 0.67 15.744-4 107.78 0.79 15.22 101.15 0.75 13.845-5 116.66 0.83 14.64 105.38 0.77 12.916-6 124.13 0.86 14.70 108.46 0.78 13.147-7 126.36 0.86 15.32 106.07 0.74 15.988-8 119.36 0.73 25.77 108.02 0.73 15.889-9 128.36 0.73 19.63 125.55 0.76 11.84

10-10 126.80 0.67 23.98 133.55 0.77 12.28

Graphic-14: Crude-Oil Trend Dynamic 2005-06-01 till 2015-06-01.

9) Slaying the Natural Gas Contango Dragon:

Graphic-15 shows the performance of the United States Natural Gas ETF UNG. UNG was introduced at 2007-04-18. This was a reaction to the strong increase in Natural Gas prices. The ETF tracks the performance of the most nearby Future. It rolls every month a few days before expiry (the details are not revealed) to the next contract. The ETF suffers since 2008 not only from the falling gas prices but also from contango. UNL, launched at 2009-11-18, was an attempt by the same issuer to minimize the effect of contango by holding twelve months of natural gas futures contracts. Contango is likely to be steepest at the front end of the futures curve and flatter in the more distant months. Graphic-16 compares the performance of UNG and UNL. The time-series are scaled to 100.0 at the beginning. UNL did somewhat better, but the difference is not dramatic. UNG is still by far more popular. The net assets at this writing are 562.06 M$ to 11.91 M$.

Graphic-15: United States Natural Gas 2007-05-01 till 2015-06-01.

Graphic-16: UNG (red) and UNL (yellow) Gas 2010-01-04 till 2015-06-01.

Just spreading contango over the term-structure is obviously no real solution. A more radical approach was the introduction of UBS Natural Gas Futures Contango ETN GASZ. GASZ goes the first Future short and the 12th Future long.

“The ISE Natural Gas Futures Spread™ Index, through a series of investments in natural gas sub-indices, effectively provides short exposure in front month natural gas futures contracts and long exposure in mid-term natural gas futures contracts. This is achieved by taking a 100% long position in the components of the ISE Short Front Month Natural Gas Futures™ Index, which provides short (or inverse) exposure to the ISE Long Front Month Natural Gas Futures™ Index and an aggregate 100% long position in the components of the ISE Twelfth Month Natural Gas Futures™ Index, ISE ThirteenthMonth Natural Gas Futures™ Index and ISE Fourteenth Natural Gas Futures™ Index (33.33% per index), which provides long exposure to the mid-term Henry Hub Natural Gas Futures (NG) futures contracts. The index is rebalanced monthly before the Sub-Indices’ roll process to maintain the 1:1 ratio.” (from [9]).

The introduction of GASZ was not a success story. One can find the symbol on finance.yahoo.com. Butthere is no data available. I could not find GASZ on the UBS ETRACS website. But it is straightforward to simulate (and trade) GASZ from the NG Futures data.

The table on the left shows the performance for different long maturities. The selection does not use the Roll-Table. 1-12 means, one goes the 1st Future short and the 12th Future long. The quantity was set to 10 (and not 30) Futures. NG is – at least till 2009 – much more volatile than the other Energy Futures. The different maturities behave similar on a risk adjusted basis. Graphic-17 shows the performance for the 12th (red), 10th (yellow), 6th (green) and 4th (light-blue) long Future.

NG Short-LongP&L Sharpe Rel.DD

1-13 77.42 0.58 20.08 1-12 79.51 0.60 20.37 1-11 79.82 0.60 20.32 1-10 80.79 0.61 20.28 1-9 78.12 0.61 20.13 1-8 72.11 0.59 19.89 1-7 61.80 0.58 17.59 1-6 58.92 0.69 12.39 1-5 50.46 0.69 11.941-4 43.73 0.72 12.32

Graphic-17: NG Short/Long. 2005-06-01 till 2015-06-01.

I tried the same simple idea also for the other Energy Futures. The performance is generally on par or even superior with more sophisticated approaches. It works best for WTI.

The table on the left shows the performance for CL. The quantity is 30.Otherwise the setting is the same as for NG. Graphic-18 shows the performance for the 12th (red), 10th (yellow), 6th (green) and 4th (light-blue) long Future. The performance is on a risk adjusted basis similar. The more nearby maturities 4th to 6th have have a somewhat higher Sharpe Ratio. This is in agreement with the findings in [6] already quoted above.

Graphic-18: CL Short/Long. 2005-06-01 till 2015-06-01.

CL Short-LongP&L Sharpe Rel.DD

1-13 103.89 0.73 17.56 1-12 101.40 0.74 16.92 1-11 98.01 0.75 16.23 1-10 93.99 0.76 15.47 1-9 90.99 0.78 14.61 1-8 87.78 0.80 13.70 1-7 82.67 0.82 12.64 1-6 76.43 0.83 11.39 1-5 67.32 0.84 9.991-4 59.88 0.87 8.15

10) The (Inverse) Amaranth Strategy:

Amaranth Advisors LLC was a hedge fund operating in Greenwich, CT. The fund was the darling of the fund-of-funds industry. There was at that time a lot of fun in Energy and especially Natural Gas trading. There was of course also a lot of risk, but nobody cared about risk.In May 2006, the fund suffered losses of $974M. In June the fund made $548M, in July it lost $44M, and in August it made $550M. By the end of the summer, the Amaranth Advisors LLC fund was up $2.094B for the year. On September 21 the fund capsized. On 14 September 2006, the fund experienced it’s worst day withlosses of around $560M ([10]).End of August 2006 the positions for the next 12 months was for the winter (November till March) contracts long and the summer (April to October) contracts short. Short to long was balanced 1:1. The trades were leveraged 5-6 times. For the October 2006 contract Amaranth’s positions equaled 79.6% of the open interest on NYMEX ([10]).

Even if one knows the static position for a given date, it is not clear how the position was build up. For simulating the Amaranth strategy I assumed that one initially buys the next 12 months according the winter/summer scheme. One rolls over on the 1st business day of an expiring month to the next years contract.On April 1st 2015 one rolls over the May 2015 contract to May 2016 (the May contract already expires in April). Graphic-19 shows the performance of this strategy if one trades 30 Futures long and short. The performance is during 2006 in good agreement with the Amaranth figures. There is also the crash in the3rd week of September 2006. The strategy is also after wards a losing game. Going the winter months long sounds logical. The price of Natural Gas has a pronounced seasonal pattern. With higher prices in winter and lower prices in summer. But this is a well known pattern and already priced in the Futures.

Graphic-19: Amaranth Strategy 2005-06-01 till 2015-06-01.

One can flip the strategy around. Going the winter months short and the summer long. The table below shows the performance for different ranges of winter/summer months. The first row is the initial Amaranth approach. The last two rows trade the Feb contract short and the March or April contract long. The red line in Graphic-20 shows the performance for the Nov-Mar/Apr-Oct scheme. Yellow Jan-Feb, March-Oct and green is the Feb (short)/Mar (long) scheme. The strategy is at the beginning extremely risky, but behaves acceptable from 2007 on.

I have tried in vain to find better ideas to exploit the seasonal pattern. I have done also an intensive literature research. There are zillions of papers about the economics of natural gas storage and the spot to Futures relation. But I have not found anything reasonable how to exploit the seasonal pattern directly with the Futures market. Maybe it is indeed the case that one can only successfully play the seasonal game if one has additionally a storage facility at hand.

Graphic-20: Invers Amaranth Strategy 2005-06-01 till 2015-06-01.

11) The Crude-Oil Crack Spread:

The Crude-Oil Crack Spread is the relation between the Crude-Oil price on one side and unleaded gasoline and heating oil on the other. The term derives from the refining process which “cracks” crude oil into its constituent products ([11]). The standard crack has the relation 3:2:1. Actually one goes the crude-oil Future short and the cracked products long. So the exact notation is -3:2:1. The standard NYMEX spread is based on WTI. But by trading the individual futures – and not the spread itself – onecan of course also trade a Brent-based spread. The Brent-spread behaves somewhat more “regular”.The current analysis is based on the trading individual Futures. Another popular spread is 5:3:2. The idea is not restricted to Crude-Oil. The Frac spread is the relation between Natural Gas and Propane. The Sparc spread between Natural Gas and Electricity ([12]). There are similar spreads in the agricultural sector. I considered only the Crack, because I had no data for Propane and Electricity Futures. According to [12] the Frac spread can be profitable traded. But the investigation ends in 2010. The behavior of Natural Gas has fundamentally changed in the meantime.

Amaranth-InversP&L Sharpe Rel.DD

Nov-Mar/Apr-Oct 31.19 0.19 27.31Dec-Feb/Apr-Oct 52.92 0.24 34.97Dec-Feb/Mar-Oct 56.39 0.25 36.79Dec-Feb/Mar-Nov 54.52 0.27 31.95Jan-Feb/Mar-Oct 71.40 0.30 37.62

Feb/Mar-Oct 67.86 0.32 37.77Feb/Apr-Oct 64.39 0.31 37.52

Feb/Apr 79.79 0.29 48.21Feb/Mar 76.68 0.32 43.46

Graphic-21: Crack-Spread 2005-06-01 till 2015-06-01.

Graphic-21 shows the 3:2:1 spread for Brent (red) and WTI (yellow). The calculation is basedon the most nearby Future. The roll is done – like in all calculations – on the 1st business day. No roll-effects are considered. One just adds and subtracts the current Futures prices. The WTI spread is in recent years above the Brent-spread, because WTI traded on a discount to Brent.

11.1) The Hurst-Exponent of the Crack:

There is a technical relation between crude oil and the products of the cracking process. One can hence assume that the crack has a mean reverting behavior. The Hurst exponent is used as a measure of long-term memory of time series. It relates to the autocorrelations of time series, and the rate at which these decrease as the lag between pairs of values increases. Studies involving the Hurst exponent were originally developed in hydrology for the river Nil ([13]). The Horst Exponent H is the relation between the Rescaled Range RS and the length n of the time-series.

RS = n^H (2)H = log(RS)/log(n) (3)

Note: The right side in (2) is usually written as c*n^H. But it is argued in [14] that c introduces a bias. I used for the following calculations formula (2) If X is the original time-series the Rescaled Range RS is calculated by first normalizing with the mean m.

Y(t) = X(t) – m (4).

The cumulative deviate series Z is

Z(t) = Sum(Y(t)) t=1...n The Range R is

R(n) = max(Z(t)) – min(Z(t))

https://en.wikipedia.org/wiki/Long-range_dependency

https://en.wikipedia.org/wiki/Long-range_dependency

https://en.wikipedia.org/wiki/Autocorrelation

https://en.wikipedia.org/wiki/Time_series

For the Rescaled Range one divides R(n) by the Standard-Deviation S of X (or Y).

RS(n) = R(n)/S(n)

The usual procedure for estimating the Hurst-Exponent of the whole time series is first to calculate RS(n) for the whole time-series. The time-series is then split into 2 halves. One calculates RS for both halves. The Time-Series is split into 3 equal parts. One calculates again for each part RS. This process is repeated. The smallest chunk should have at least size 16. H is estimated with equation (3) by plain OLS. A Random walk has a Hurst-Exponent of 0.5. If the time-series is trending (it does not matter if up or down) the Hurst-Exponent is greater than 0.5. This is related to a positive autocorrelation. But it should be noted that the Hurst-Exponent and Autocorrelation are different concepts. If the time-series ismean-reverting, the Hurst exponent is below 0.5. The autocorrelation should be negative.I have not estimated the Hurst-Exponent for the whole time-series. Instead I have calculated from equation (3) a running window of H. In Graphic-22 the window-Length is 63 business days (3 months),in Graphic-23 126-business days (half a year) and in Graphic-24 252 business days (full year). On the left there are not enough data. I have replaced this part with the overall mean. The mean is 0.52 for 63 days, 0.51 for 126 days and 0.50 for 252 business days. There are strong up- and down-swingsof the Hurst-Exponent from trending to mean-reverting and back to trending again. But the overall mean corresponds to a random walk. Please note that calculating the mean of a running window is NOT the statistical correct approach to estimate H. For the correct estimation the time-series chunks must be disjunctive. The point of this exercise was to show that the Crack is dynamically changing and it is hence difficult to develop a good trading strategy. Sometimes a mean-reverting strategy, sometimestrend following would be appropriate. The Hurst-Exponent is in this respect no real help. It is a backwards looking measure and has no forecast power. But it is popular in academic papers for testing hypotheses about the past.

Graphic-22: Brent-Crack, Running Hurst Exponent 63-days 2005-06-01 till 2015-06-01.



11.2) Trading the Crack with Bollinger-Bands:

The Bollinger-Band is a venerable strategy for trading mean-reversion. One defines a moving average MA of the past prices and calculates the volatility/standard deviation. The Bollinger-Band is usually 2 Standard-Deviations around the MA. Jasper Breebart defines in [12] four different Bollinger variants.

BCISCO: Buy when price moves back into band and sell when it moves out opposite bandBCOSCO: Buy when price moves out of the band and sell when it moves out opposite bandBCISMA: Buy when price moves back into band and sell when it crosses the M.A.BCOSMA: Buy when price moves out of the band and sell when it crosses the M.A.

The Crack-Spread as displayed in Graphics-21 can not be directly traded because it ignores roll-effects (see (15) for a detailed discussion of this point). One has to build a portfolio where the involved Futures are rolled over. This is the real starting point of a Bollinger-Band strategy. Graphic-25 shows the performance of a Brent-Crack-Spread for the 1st Futures. The position is rolled on the 1st business day. The red-line is the daily performance. The yellow line a 21-days MA and the green line an 189

days (9 month) MA.

Graphic-25: Brent-Crack 3:2:1 Portfolio with MA-21, -63 and -189. 2005-06-01 till 2015-06-01.

The table below shows the behavior for the Brent-Crack Bollinger-Band strategy for different MA-Lengths (left column). The steps are in 21-business days or 1 month. The Standard-Deviation is always calculated with a 21-days window. The standard setting of 20 days (the table shows only 21 days, but the results are practically identical) does not work at all. This can also easily be seen from Graphic-25. There are much longer up- and down trends. A MA of 189 (9 months) or 210 (10 months) works generally best. This corresponds to the green line in Graphic-25.

.

If one inspects the table in detail the BCOSCO method (buy when price moves out of the band and sell when it moves out of the opposite band) has a slight edge over BCISCO (buy when price moves back into band and sell when it moves out of the opposite band). BCOSCO and BCISCO are for most MA-Lengths better than BCISMA and BCOSMA which close the position already when the performance of the index has come back to the MA. It is better to wait till one reaches the opposite band.Graphic-26 shows the performance of the different Bollinger variants for MA(189). The red line is BCISCO, yellow BCOSCO, green BCISMA and light-blue BCOSMA.

Bollinger-Band for Brent 3:2:1BCISCO BCOSCO BCISMA BCOSMA

P&L Sharpe Rel.DD P&L Sharpe Rel.DD P&L Sharpe Rel.DD P&L Sharpe Rel.DD21 -31.13 -0.16 65.85 -0.96 0.00 68.28 8.17 0.13 22.48 -13.57 -0.11 38.9942 -9.38 -0.05 47.81 -11.25 -0.06 52.32 0.00 0.00 41.87 -12.11 -0.07 47.4163 34.96 0.22 22.26 36.50 0.25 23.96 5.43 0.04 30.88 15.29 0.11 32.3384 46.04 0.33 21.29 61.60 0.40 21.73 16.97 0.15 20.30 34.75 0.28 21.81105 40.98 0.28 19.56 50.71 0.32 18.95 33.86 0.27 21.77 38.06 0.29 18.02126 45.60 0.37 18.13 36.35 0.30 20.95 53.95 0.45 15.96 46.24 0.38 16.76147 71.34 0.55 14.65 71.12 0.55 13.25 48.91 0.43 15.22 56.71 0.46 13.65168 76.55 0.70 12.73 85.85 0.63 11.91 37.93 0.49 13.87 64.17 0.54 12.32189 97.14 0.74 12.88 101.85 0.75 11.31 58.32 0.55 13.42 80.19 0.68 10.24210 101.00 0.74 12.82 98.91 0.72 11.42 69.69 0.66 11.52 82.99 0.70 10.08231 102.88 0.71 12.86 99.66 0.67 11.61 67.69 0.66 11.85 68.74 0.64 10.74252 66.85 0.52 14.40 52.25 0.41 14.76 40.65 0.44 12.96 37.90 0.40 17.11

Graphic-26: Brent-Crack 3:2:1 Portfolio with MA-189 2005-06-01 till 2015-06-01.

Note: There is no trading activity the first 189-trading days on the left. I did not have the data do calculate the MA backwards. Stay on the sideline favors slightly the longer MA. But it does not change the overall picture. Jasper Breebart tried in [12] only the usual Bollinger MA(20) and got disappointing results. Nikola Gradojevic and Lento Camillo have investigated in [16] the performance of the standard Bollinger Band for equity indexes. The concept was originally developed for this kind of data. Their conclusion was: The Bollinger-Band is worse than Buy&Hold.

Another variant is the 5:3:2 Crack. This mixture is closer to the technical process than 3:2:1. The performance of 5:3:2 is indeed slightly better than for 3:2:1. For this spread the BCISMA and BCOSMA are on par with BCISCO and BCOSCO. Or with other words one can close the position already when the MA is reached and has not to wait till the other side of the band.

Bollinger-Band for Brent 5:3:2BCISCO BCOSCO BCISMA BCOSMA

P&L Sharpe Rel.DD P&L Sharpe Rel.DD P&L Sharpe Rel.DD P&L Sharpe Rel.DD21 -82.41 -0.21 98.39 -40.23 -10.00 106.79 24.47 0.25 23.56 -33.78 -0.17 65.1142 22.35 0.05 72.16 -0.54 -0.01 78.27 -10.24 -0.03 85.90 -7.33 -0.02 75.2663 44.31 0.16 42.18 42.87 0.18 41.39 -0.82 0.00 51.10 6.13 0.03 49.5284 72.09 0.32 34.36 110.89 0.41 29.76 28.44 0.17 36.02 57.74 0.28 31.73105 60.88 0.27 28.19 98.86 0.36 29.88 44.24 0.22 31.12 80.49 0.34 29.60126 76.43 0.38 28.56 94.92 0.44 27.92 61.78 0.43 18.24 81.49 0.41 23.29147 150.26 0.65 20.28 138.02 0.60 19.69 114.12 0.57 21.41 109.89 0.52 20.76168 95.03 0.53 15.80 130.21 0.60 16.93 62.48 0.50 18.53 109.83 0.55 16.98189 124.97 0.63 16.64 164.79 0.79 13.03 113.95 0.76 13.10 158.88 0.81 10.99210 155.30 0.75 14.57 183.63 0.79 13.55 113.92 0.69 13.09 145.62 0.75 11.42231 161.69 0.80 12.52 187.38 0.82 14.42 109.62 0.69 14.25 128.69 0.69 15.71252 136.69 0.69 14.71 141.10 0.68 16.98 71.66 0.48 16.11 92.97 0.56 17.93

Graphic-27 is besides the different Crack-Ratio identical to Graphic-26.

Graphic-27: Brent-Crack 3:2:1 Portfolio with MA-189 2005-06-01 till 2015-06-01.

The Bollinger-Band strategy does not work reasonably for the WTI-Crack or other mixtures. Jasper Breebart tried in [12] also the Contra-Bollinger-Band. This is a trend following strategy closely related to Moving-Averages Crossover. The Contra-Bollinger Band worked reasonably for the Frac spread. I did not get impressive results for the Crack spread. I also tried term-structure approaches. This only worked for the WTI v. Brent but not for the Crack itself. Trading WTI v. Brent was already considered in paragraphs 6 to 8.

Conclusion:

The energy-futures market went in the considered time range through different regimes. Natural backwardation turned into contango. But there is also a re-segmentation of the Futures market by maturity in 2012-2014 (see Paragraph 6). The performance measures would be quite different if one would consider only the last 5 or 3 years. At the beginning of the time-series the WTI and Brent traded at about the same level. But around 2010 WTI started to trade at a large discount. The gap has closed somewhat in recent time (see Graphic-1). It can also be noted that some of the referred strategies lost most of their edge in the last time (after publication). This is the real out of sample test.

The best risk-adjusted strategy was the combination of crude-oil with the dynamic-yield approach of paragraph 8 with a maturity-range of 6. Besides the plain numbers there is also some intuitive reason for the good performance. If one ignores the wild swings in 2005 and 2006 the simple GASZ strategy of paragraph 9 (short the 1st NG Future and go the 12th long) seems also to be relative reasonable.

The (Contra) Bollinger-Band Crack strategy operates on a very shaky ground. I would not trust these results too much.

I tried for a long time to exploit the seasonality of NG and also of RB. But I could not find anything better than the inverse Amaranth. I stopped these attempts because I had the feeling to go nuts. But there must be something.

Further Work:

I have the feeling that I have sucked out the Energy-Futures Data. There is for the immediate Future no similar work planned. But the NG seasonality question will certainly nag further on my mind.

References:[1] Chrilly Donninger: An empirical investigation of optimal Energy Futures rolling. Sibyl-Working-Paper, July 2015.[2] Geetesh Bhardwaj, Gary Gorton, Geert Rouwenhorst: Facts and Fantasies about Commodity Futures Ten Years Later. Yale ICF Working Paper No. 15-18, May 25, 2015.[3] Yiqun Mou, Limits to Arbitrage and Commodity Index Investment: Front-Running the Goldman Roll. Dec. 2, 2010[4] Andreas Neuhierl, Andrew Thompson: Trend Following Strategies in Commodity Markets and the Impact of Financialization, December 30, 2014[5] S&P Down Jones Indices: S&P GSCI Dynamic Roll Methodology, July 2014[6] Delphine Lautier, Franck Raynaud, Michel Robe: Information Flows across the Futures Term Structure: Evidence from Crude Oil Prices.[7] Daniel J. Arnold: DBIQ Index Guide: DBLCI Optimum Yield Commodity Indices. 6 March 2008.[8] Ana-Maria Fuertes, Joelle Miffre, Georgios Rallis: Tactical Allocation in Commodity Futures Markets: Combining Momentum and Term Structure Signals[9] Bill Luby: Slaying the Natural Gas Contango Dragon. from vixandmore.blogspot.co.at/2012/02/slaying-natural-gas-contango-dragon.html[10] Ludwig Chincarini: The Amaranth Debacle: What Really Happened, August 13, 2007 [11] NYMEX: Crack Spread Handbook.[12] Jasper Breebaart: Analysing Bollinger Bands in Relation to Energy Spreads, Masters Thesis, British Univ. in Dubai, May 2010.[13] en.wikipedia.org/wiki/Hurst_exponent[14] Jamal Munshi: Methods for Estimating the Hurst Exponent of Stock Returns: A Note[15] Chrilly Donninger: The Poverty of Academic Finance Research: Spread trading strategies in the crude oil futures market. Sibyl-Working-Paper, June 2015[16] Nikola Gradojevic, Lento Camillo: Investment information content in Bollinger Bands?

Appendix A: S&P-GSCI Roll Tables:

CL 0 1 2 3 4 5 6 7 8 9 10 11

Jan G0 H0 J0 K0 M0 N0 U0 Z0 M1 Z1 Z2 Z3

Feb H0 J0 K0 M0 N0 Q0 U0 Z0 M1 Z1 Z2 Z3

Mar J0 K0 M0 N0 Q0 U0 V0 Z0 M1 Z1 Z2 Z3

Apr K0 M0 N0 Q0 U0 V0 Z0 F1 M1 Z1 Z2 Z3

May M0 N0 Q0 U0 V0 X0 Z0 F3 M1 Z1 Z2 Z3

Jun N0 Q0 U0 V0 X0 Z0 F1 M1 N1 Z1 Z2 Z3

Jul Q0 U0 V0 X0 Z0 F1 G1 M1 N1 Z1 Z2 Z3

Aug U0 V0 X0 Z0 F1 G1 H1 M1 N1 Z1 Z2 Z3

Sep V0 X0 Z0 F1 G1 H1 J1 M1 N1 Z1 Z2 Z3

Oct X0 Z0 F1 G1 H1 J1 M1 N1 U1 Z1 Z2 Z3

Nov Z0 F1 G1 H1 J1 M1 N1 U1 Z1 Z2 Z3 Z4

Dec F1 G1 H1 J1 K1 M1 N1 U1 Z1 Z2 Z3 Z4

Table 1: Extended S&P GSCI Roll Table for WTI

LCO 0 1 2 3 4 5 6 7 8 9 10

Jan H0 J0 K0 M0 N0 Q0 U0 V0 Z0 Z1 Z2

Feb J0 K0 M0 N0 Q0 U0 V0 X0 Z0 Z1 Z2

Mar K0 M0 N0 Q0 U0 V0 X0 Z0 F1 Z1 Z2

Apr M0 N0 Q0 U0 V0 X0 Z0 F1 M1 Z1 Z2

May N0 Q0 U0 V0 X0 Z0 F1 M1 Z1 Z2

Jun Q0 U0 V0 X0 Z0 F1 G1 M1 Z1 Z2

Jul U0 V0 X0 Z0 F1 G1 H1 M1 Z1 Z2

Aug V0 X0 Z0 F1 G1 H1 M1 N1 Z1 Z2

Sep X0 Z0 F1 G1 H1 J1 M1 N1 Z1 Z2

Oct Z0 F1 G1 H1 J1 K1 M1 N1 Z1 Z2

Nov F1 G1 H1 J1 K1 M1 N1 Z1 Z2 Z3

Dec G1 H1 J1 K1 M1 N1 U1 Z1 Z2 Z3

Extended S&P GSCI Roll Table for Brent

HO 0 1 2 3 4 5 6 7 8 9 10

Jan G0 H0 J0 K0 M0 N0 U0 Z0

Feb H0 J0 K0 M0 N0 Q0 U0 Z0

Mar J0 K0 M0 N0 Q0 U0 V0 Z0

Apr K0 M0 N0 Q0 U0 V0 X0 Z0

May M0 N0 Q0 U0 V0 X0 Z0 F1

Jun N0 Q0 U0 V0 X0 Z0 F1 G1

Jul Q0 U0 V0 X0 Z0 F1 G1 H1

Aug U0 V0 X0 Z0 F1 G1 H1 M1

Sep V0 X0 Z0 F1 G1 H1 J1 M1

Oct X0 Z0 F1 G1 H1 J1 K1 M1

Nov Z0 F1 G1 H1 J1 K1 M1 Z1

Dec F1 G1 H1 J1 K1 M1 U1 Z1

Table 3: Extended S&P GSCI Roll Table for Heating Oil

RB 0 1 2 3 4 5 6 7 8 9 10

Jan G0 H0 J0 K0 M0 N0 U0

Feb H0 J0 K0 M0 N0 Q0 U0

Mar J0 K0 M0 N0 Q0 U0

Apr K0 M0 N0 Q0 U0 V0

May M0 N0 Q0 U0 V0

Jun N0 Q0 U0 V0 Z0

Jul Q0 U0 V0 X0 Z0

Aug U0 V0 X0 Z0 F1

Sep V0 X0 Z0 F1 H1 J1

Oct X0 Z0 F1 G1 H1 J1

Nov Z0 F1 G1 H1 J1 M1

Dec F1 G1 H1 J1 K1 M1 U1

Table 4: Extended S&P GSCI Roll Table for Unleaded Gasoline

NG 0 1 2 3 4 5 6 7 8 9 10

Jan G0 H0 J0 K0 M0 N0 Q0 V0 Z0 F1 H1

Feb H0 J0 K0 M0 N0 Q0 U0 V0 Z0 F1 H1

Mar J0 K0 M0 N0 Q0 U0 V0 X0 Z0 F1 H1

Apr K0 M0 N0 Q0 U0 V0 X0 Z0 F1 H1 J1

May M0 N0 Q0 U0 V0 X0 Z0 F1 G1 H1 J1

Jun N0 Q0 U0 V0 X0 Z0 F1 G1 H1 J1 V1

Jul Q0 U0 V0 X0 Z0 F1 G1 H1 J1 K1 V1

Aug U0 V0 X0 Z0 F1 G1 H1 J1 K1 V1 Z1

Sep V0 X0 Z0 F1 G1 H1 J1 K1 M1 V1 Z1

Oct X0 Z0 F1 G1 H1 J1 K1 M1 N1 V1 Z1

Nov Z0 F1 G1 H1 J1 K1 M1 N1 V1 Z1 H2

Dec F1 G1 H1 J1 K1 M1 N1 V1 Z1 F2 H2

Table 5: Extended S&P GSCI Roll Table for Natural Gas

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