An empirical investigation of optimal Energy Futures rolling.Chrilly Donninger

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

Cleaned a lot of plates in memphisPumped a lot of tane down in new orleansBut I never saw the good side of the cityTill I hitched a ride on a riverboat queen

Big wheel keep on turningProud mary keep on burning

And we're rolling, rollingRolling on the river

(John Fogerty, Proud Mary)

Abstract:When the first Commodity Futures Indexes were constructed not much thought was spent on the rollover strategies. The Futures were in backwardation and one cashed in the roll-yield by simply rolling over from the most nearby Future to the next one. The only consideration was liquidity. Market conditions have changed in recent years. Contango is now the more frequent case. The roll strategy is more sophisticated in the second index generation. This investigation analyzes the performance of several rolling strategies for the 5 most important Energy Futures in the last 10 years. It is shown that one should avoid the crowd if one has to roll nearby Futures. The second generation indexes have - besides for RB - a clear edge. The performance of the different indexes is similar, with the S&P Dynamic Roll Strategy having a slight edge. Optimal rolling is most important for the CL- and NG-Futures.Note: This is a major rework of a previous working paper [1] which considered only WTI and Brent Futures

The times they are changing:

Figure 1 from [2] shows the performance of a broad commodity portfolio over the last 55 years.Up to 2005 the gap between the spot- and the Futures performance was widening each year. The roll-yield was the major profit factor. This has reversed in the last years. The spot is considerable outperforming the Futures. This effect is especially pronounced for the WTI (see Figure 2 from [2]).

A lot of papers have been published about the reasons for the inversion of the Futures term structure. But this is not the topic of this paper. Contango is considered as a fact of trading-life. The paper answers the question how to deal best with this situation. The best strategies are general enough to deal also with backwardation. But as the results for RB indicate they are at it's best on par with the simple roll.

The General Setting:

This investigation uses 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 July 2016. The historic simulation is run for the last 10 years, from 2005-06-01 till 2015-06-01. In each period a total of 30 Futures is held long. The numbers were chosen to get an integral number of Futures for all the considered strategies at each rollover step. The initial index-value was set to 10.000.000$. This choice

represents a realistic leverage. 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 spread of 0.01, the 3rd to 5th of 0.02 and longer maturities of 0.03. The 1st HO and RB Futures have a spread of 0.0005, the 2nd to 4th of 0.0008 and longer maturities of 0.001. CL

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

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 of 0.001, 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 is 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

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

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)

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

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

The Base Strategy:

The most important first generation index is the S&P GSCI ([3],[4],[5]). The iShares ETF GSG tracks this index. The roll is done from the 5th to the 9th business day of each month. On each day a fifth of the position is rolled over. The contract is specified for each Future by a roll-table. The tables 1 to 5 in Appendix A define the rolls for the energy Futures. The S&P-GSCI rolls from column 0 to 1. Columns 2 to 11 are used in the Dynamic Roll Strategy. The tables differ due to the different expiry rules and seasonal liquidity patterns. CL expires 3 business days before the 25th of the preceding month. The June2015 contract expires at May 19th. The LCO Futures expire 15 calendar days before the end of the preceding month. The expiry for the June 2015 contract is May 14th. For this reason the contracts differ for the base strategy by one month. HO and RB expire at the last business day of the previous contract month. NG 3 business days before the 1 calendar day of the contract month. The S&P GSCI roll contracts (column 0 and 1 in the roll tables) are therefore the same as for CL. The dynamic roll is due to the seasonal liquidity patterns more involved. Long term crude-oil Futures are traded with the December contract. The quarter contracts H, M, U have also a higher liquidity and are therefore favored in the CL and LCO roll tables. The other energy Futures have different seasonal effects. There are no long term contracts in their roll table due to a lack of liquidity. The quarter months have also no priority.The second popular index is the Dow Jones-UBS Commodity Index (DJ-UBSCI). The DJ-UBSCI rolls from the 6 to the 10 business day. Rolling is done every second month.Graphic-4 shows the performance for the basis strategy for CL (red), LCO (yellow), HO (green) and RB (blue). Graphic-5 for NG (red). The time range is always the ten years from 2005-06-01 till 2015-06-01.

CL looses -22.24% without and -23.39% with trading costs. The roll accounts for -32.49 %, another -1.15% are the trading costs. For LCOthe values are -6.32% and -7.47%. The roll loss is -28.11% and the trading costs are -1.15%. The other value can be seen in the

table. Besides NG the negative roll yield turns a profitable spot performance into a loosing game.

No Tr.Cost Incl. Tr.Cost Roll-Yield Tr.CostCL -22.24 -23.39 -32.49 -1.15LCO -6.32 -7.47 -28.11 -1.15HO -13.45 -14.94 -38.54 -1.50RB 11.29 9.79 -20.96 -1.50NG -68.79 -69.65 -7.81 -0.86

Graphic-4: S&P-GSCI Roll for CL (red), LCO (yellow), HO (green) and RB (blue)

Graphic-5: S&P-GSCI Roll for NG (red)

I have analyzed if the choice of the business days has an influence. The Roll is done on the 5th to the 10th business day. The 10th was included to capture also the roll-effect of the DJ-UBSCI. Alternatively one rolls already the complete position on the 1st or on the 11th business day. Graphic-6 shows the resultfor CL. There is obviously a significant effect.

The table shows the result for all energyFutures. The CL performs better more than 4% if one rolls ahead of the crowd at the 1th business day. The same holds for LCO and RB. For HO and NG it is better to roll later at the 11th. A very

detailed analysis can be found for CL and LCO in my previous paper [1]. The effect almost disappears if one rolls from column 4 to 5 (instead of 0 to 1) of the dynamic roll table. Yiqun Mou claims in [6] that one can exploit this effect with a profitable low-risk trading strategy. This point will be analyzed ina forthcoming working paper.

Roll 5-10 Roll 1-1 Diff Roll 11-11 DiffCL -23.33 -19.26 4.08 -19.40 3.93LCO -7.42 -4.62 2.80 -5.75 1.68HO -14.12 -13.24 0.88 -10.68 3.44RB 10.43 16.48 6.06 14.29 3.87NG -69.50 -71.16 -1.66 -64.58 4.93

Graphic-6: S&P-GSCI Roll for CL with different roll dates

Constant Maturity Rolling:

Constant Maturity Rolling belongs according the classification in [7] to the second generation indexes. The methodology is the same as for the VIX-Short-Term Indexes and the corresponding ETFs VXX and VXZ. One rolls daily a fraction of the portfolio to maintain a fixed mean maturity (see [8]). Graphic-7 shows the performance for CL with a constant maturity of 93 (yellow), 186 (green) and 279 (blue) calendar days in comparison with the base strategy (red). Graphic-8 is the same for RB and Graphic-9 for NG.

The table lists the performance for all energy Futures. CL, LCO and HO have a similar pattern. The effect is most pronounced for CL.RB performs completely different. Longer maturities are a disaster. The difference is dramatic for NG.

Graphic-7: Constant Maturity Roll in Comparison to Base for CL

CM-93 Diff CM-186 Diff CM-279 DiffCL -10.15 13.24 -3.07 20.32 -0.14 23.25LCO -4.85 2.62 -0.97 6.50 1.69 9.16HO -11.35 3.59 -5.36 9.58 -0.55 14.40RB 10.63 0.84 4.45 -5.34 2.68 -7.11NG -51.57 18.09 -37.84 31.82 -23.51 46.14

Graphic-8: Constant Maturity Roll in Comparison to Base for RB

Graphic-9: Constant Maturity Roll in Comparison to Base for NG

In [8] also longer maturities are defined. But it should be difficult to find adequate contracts. The S&P Dynamic Roll approach handles the long maturities in a more market specific way (see below). The constant maturity roll avoids any bad and good days problems by rolling daily. But the trading costs aresomewhat higher than for the other second generation indexes.

The DBLCI Optimum Yield Index:

The Deutsche Bank Liquid Commodities Indexes Optimum Yield (DBLCI-OY) employs a rule-based approach when it rolls from one futures contract to another for each commodity in the index. Rather than select the new future base on a predefined schedule (e.g. monthly) the index rolls to that future (from the list of tradeable futures which expire in the next thirteen months) which generates the maximum implied roll yield. The index aims to maximize the potential roll benefits in backwardated markets and minimize the loss from rolling down the curve in contago markets. (from [9]).

The PowerShares DBC ETF is tracking this index. The DBC has currently 3.17 Billion $ Net Assets. The index methodology determines on the 1st business day the Future with the maximum implied yield.The position is rolled from the 2nd to the 6th business day. The roll-volume is determined by:

N(t,i) = N(t-1,i)*6-db(t)/(7-db(t)) (1)

N(t-1,i) = Notational holding of Future i on calculation day t-1N(t,i) = Notational holding of Future i on calculation day tdb(t) = Number of business days up to and including t.

The implied roll yield is defined as:

Y(t,i) = ((PC(t,b)/PC(t,i))^(365/F(t,i,b))) – 1 (2)

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

The contract with the maximum roll yield is selected. If the current index holding no longer meets the inclusion criteria the monthly index roll unwinds the old contract holding and enters a position in the new contract. Graphic-10 shows the performance of the CL Optimum Yield where only the first 3 (yellow), the first 6(green), the first 9 (blue) and the full range of 12 Futures (dark blue) are tradeable. The overall picture is similar to the constant maturity roll. The performance of the more dynamic optimal yield is somewhat higher. This holds also for LCO and HO. Graphic-11 shows the RB. The Optimum-Yield handles the varying term structure better than the constant maturity approach. But the simple roll or restricting the range to the 3rd Future is a superior choice. There is again a dramatic difference for NG. But the more rigid constant maturity method has an edge. As noted already above liquidity drops considerable for the longer maturity HO, RB and NG Futures.

The table on the left lists all results for the Optimum Yield in detail.

Range 3 Diff Range 6 Diff Range 9 Diff Range 12 DiffCL -14.51 8.89 -9.02 14.37 -1.08 22.31 3.67 27.06LCO -5.00 2.47 -4.77 2.70 1.24 8.71 5.73 13.21HO -13.48 1.47 -6.53 8.42 -2.49 12.45 0.98 15.93RB 10.19 0.40 5.91 -3.88 4.08 -5.71 3.28 -6.52NG -55.90 13.76 -43.87 25.78 -35.02 34.64 -30.39 39.27

Graphic-10: Optimum Yield Roll in Comparison to Base for CL

Graphic-11: Optimum Yield Roll in Comparison to Base for RB

Graphic-12: Optimum Yield Roll in Comparison to Base for NB

The S&P GSCI Dynamic Roll Index:

The S&P GSIC Dynamic Roll index determines the tradeable Futures with the roll-tables 1 to 5 from Appendix A. The tradeable Futures are not just the next 11 ones. Liquidity is taken into account. For both crude oil futures long dated Futures are only traded with the December contract. But also for shorter maturities the quarter-months H, M and U have priority. The other energy Futures have a more irregular seasonal pattern. The roll-table approach is from the practical point of view probably superior to the Optimum-Yield scheme. The implied roll-yield is calculated differently to equation (2). The roll-yield is not calculated in relation to the base-Future, but locally along the full term-structure. It is the relative difference to the previous Future.

Y(t,i) = (PC(t,i-1)-PC(t,i))/(PC(t,i)*d) (3)

d = Difference of maturity in months.

As the difference is calculated locally it is possible that a Future is rolled to a more nearby one. Under current market conditions the formula favors the Futures at the far end of the term structure. To avoid jumping back and forth the rule for CL Futures is modified. If the current Future is under the best 3 ones, no roll is done. For the other Futures one selects always the best implied yield.

Graphic-13 shows the performance of the CL dynamic roll where only the first 3 (yellow), the first 6 (green), the first 9 (blue) and the full range of 11 (dark blue) Futures are tradeable. Graphic-14 is the same for the RB and Graphic-15 for NG. The overall picture is similar to the other second generation roll approaches. It is interesting to note that for LCO the best strategy is if one restricts the range to 9. One avoids the 2 years maturity Z-Future. This Future has usually the best implied-yield, but it is sometimes better to trade the previous December contract. The Dynamic Roll handles the RB somewhat better. The longer maturities under perform the simple strategy only slightly. The Optimum Yield outperforms the S&P-Dynamic for the HO. But it should be noted that the HO roll-table is much more restricted. The long Optimum Yield ranges operate in thin liquidity air.

The table shows the detailed results.

Range 3 Diff Range 6 Diff Range 9 Diff Range 11 DiffCL -13.98 9.41 -9.17 14.22 -1.16 22.23 1.33 24.72LCO -4.06 3.41 1.50 8.97 10.06 17.53 8.14 15.61HO -10.74 4.21 -7.03 7.92 -6.03 8.91 -6.03 8.91RB 10.52 0.72 5.43 -4.36 7.88 -1.92 8.78 -1.01NG -53.30 16.36 -43.13 26.52 -31.89 37.76 -28.68 40.97

Graphic-13: S&P-GSCI Dynamic Roll in Comparison to Base for CL

Graphic-14: S&P-GSCI Dynamic Roll in Comparison to Base for RB

Graphic-15: S&P-GSCI Dynamic Roll in Comparison to Base for NG

Conclusion:

If one has to roll nearby Futures one should avoid the crowd. For CL, LCO and RB it is preferable to roll already at the beginning of the month. For HO and NG one should roll after the 10th business day.

The second generation indexes have – with the exception of RB Futures - a clear edge. The most practical one seems to be the S&P-GSCI Dynamic Roll. But one can also use the Optimal-Yield strategy. The Constant-Maturity Strategy has a similar performance. On the pro side one avoids any calculation and can roll always in the same way. But one has to trade daily instead of monthly and has also higher overall trading costs. For the Dynamic-Roll and Optimum-Yield one keeps sometimes a position for a year or even longer without any rolling. For the RB it is best to roll the nearby future at the beginning of the month or earlier.

Further Work:

The first and second generation indexes are long-only. The third generation lifts this restriction and trades long/short ([7]). This is a reaction to the low tide in commodity prices. But it should be noted that third generation ETFs have so far not been very attractive. The first generation GSG and the second generation DBC have considerable higher net assets and liquidity. A forthcoming Sibyl-working paper will address this topic. Other interesting ideas are to exploit the crowd-effect (see [6]) or to trade the term-structure.

References:[1] Donninger Chrilly: An empirical investigation of optimal crude oil 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] S&P Down Jones Indices: S&P GSCI Methodology, March 2015[4] S&P Down Jones Indices: S&P GSCI Dynamic Roll Methodology, July 2014[5] Tsui Peter, Srikant Dash: Dynamic Roll of Commodities Futures: An Extended Framework, Feb. 2011[6] Yiqun Mou: Limits to Arbitrage and Commodity Index Investment: Front-Running the Goldman Roll.[7] Joelle Miffre, Comparing First, Second and Third Generation Commodity Indices.[8] UBS Commodities: UBS Bloomberg CMCI, April 2015[9] Daniel J. Arnold: DBIQ Index Guide: DBLCI Optimum Yield Commodity Indices. 6 March 2008.

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