1 Intro and summary

This document shows how we think about the sizing of all the relative trades. The table below summarizes the sizing for each strategy. Here the different size columns represent the number of contracts we trade to create the different spreads.

2 BO vs IJ

• The oil content of rapeseed is around 43%.
• The processing is usually made in two steps: pre-pressing plus solvent extraction.
• Sometimes only deep-pressing is applied.

\[ 1 \text{contract IJ} = 50 \text{ t IJ} \rightarrow 50 \times 0.43 = 21.5 \text{ t BO} = 21.5 \times 2204.62 = 47399.33 \text{ lb BO} = 0.79 \text{ contracts BO} \] For every 1 contract of IJ we need 0.79 contracts of BO.

3 BO vs SH

\[ 1 \text{contract SH} = 10 \text{ Mt SH} = 10 \times 2204.62 = 22046.2 \text{ lb SH} \rightarrow \frac{10 \times 2204.62}{60 000} = 0.3674 \text{ contracts BO} \]

\[ SH:BO = 1:0.3674 = 2.7:1 \]

4 BO vs SH

\[ 1 \text{contract SH} = 10 \text{ Mt SH} = 10 \times 2204.62 = 22046.2 \text{ lb SB} \rightarrow \frac{10 \times 2204.62}{60 000} = 0.3674 \text{ contracts BO} \]

\[ SH:BO = 1:0.3674 = 2.7:1 \]

5 C vs CRD

US vs Brazillian corn.

\[ 1 \text{contract C} = 5000 \text{ bu} \]

\[ 1 \text{contract CRD} = 450 \text{ bags of }60 \text{kg each} = 450 \times 60 \text{kg} = \frac{450 \times 60 \times 2.20462}{56} = 1062.94 \text{bu} \]

For every 1 contract of C we need 4.7 contracts of CRD.

6 C vs CT

\[ 5000 \text{ bu C} = 5000 \times 56 = 280000 \text{ lb C} \]

\[ \frac{[\text{C}]}{[\text{CT}]} = \frac{280000}{50000} = 5.6 \]

For every 1 contract of C we need 5.6 contracts of CT.

7 C vs CUA

source: CME trading the corn ethanol crush

\[ \begin{align} 1 \text{ bu Corn } &\rightarrow 2.8 \text{ gal Ethanol} + 17 \text{ lb DDG} \\ 56 \text{ lb Corn } &\rightarrow 2.8 \text{ gal Ethanol} + 17 \text{ lb DDG} \\ 56 - 17 = 39 \text{ lb Corn } &\rightarrow 2.8 \text{ gal Ethanol}\\ 1 \text{ lb Corn } &\rightarrow \frac{2.8}{39} \text{ gal Ethanol}\\ 1 \text{ bu Corn } &\rightarrow \frac{2.8 \times 56}{39} \text{ gal Ethanol}\\ 5000 \text{ bu Corn } &\rightarrow 5000 \times \frac{2.8 \times 56}{39} = 20102.56 \text{ gal Ethanlol} \end{align} \]

\[ \frac{[\text{CUA}]}{[\text{C}]} = \frac{42000}{20102.56} = 2.09 \] For every 1 contract of CUA we need 2.09 contracts of C.

A Note on how the spread is calculated in Shiny:

From the above calculation we have

\[ \frac{39}{56} \text{ lb Corn} = 2.8 \text{ gal Ethanol} \] We then define the spread (in USd/gal) as

\[ S = 100 \times \text{CUA} - \frac{39}{56 \times 2.8} \text{C} \]

8 C vs DL

source: CME trading the corn ethanol crush

\[ \begin{align} 1 \text{ bu Corn } &\rightarrow 2.8 \text{ gal Ethanol} + 17 \text{ lb DDG} \\ 56 \text{ lb Corn } &\rightarrow 2.8 \text{ gal Ethanol} + 17 \text{ lb DDG} \\ 56 - 17 = 39 \text{ lb Corn } &\rightarrow 2.8 \text{ gal Ethanol}\\ 1 \text{ lb Corn } &\rightarrow \frac{2.8}{39} \text{ gal Ethanol}\\ 1 \text{ bu Corn } &\rightarrow \frac{2.8 \times 56}{39} \text{ gal Ethanol}\\ 5000 \text{ bu Corn } &\rightarrow 5000 \times \frac{2.8 \times 56}{39} = 20102.56 \text{ gal Ethanlol} \end{align} \]

\[ \frac{[\text{DL}]}{[\text{C}]} = \frac{29000}{20102.56} = 1.44 \] For every 1 contract of DL we need 1.44 contracts of C.

A Note on how the spread is calculated in Shiny:

From the above calculation we have

\[ \frac{39}{56} \text{ lb Corn} = 2.8 \text{ gal Ethanol} \] We then define the spread (in USd/gal) as

\[ S = 100 \times \text{DL} - \frac{39}{56 \times 2.8} \text{C} \]

9 C vs EP

\[ 5000 \text{ bu C} = \frac{5000 \times 56}{2204.62} = 127.006 \text{ t C} \]

\[ \frac{[\text{C}]}{[\text{EP}]} = \frac{127.006}{50} = 2.54 \]

For every 1 contract of C we need 2.54 contracts of EP.

10 C vs FC

• LC average animal weight = 1250 lb
• FC average animal weight = 750 lb
• 1 lb C produces 6 lb weight gain in feedlot
• Feedlot rations consist of 60% to 85% corn (we assume 75%)

\[ 1250 \text{ lb LC} \rightarrow 750 \text{ lb FC} + (1250 - 750) \times 6 \times 0.75 \text{ lb C} = 750 \text{ lb FC} + 2250 \text{ lb C} \]

\[ \begin{align} 1 \text{ animal FC} &\rightarrow 2250 \text{ lb C} = \frac{2250}{56} \text{ bu C} \\ 1 \text{ contract FC} = 66.67 \text{ animal FC} \rightarrow \frac{2250}{56} \times 66.67 &= 2678.705 \text{ bu C} \rightarrow \frac{2678.705}{5000} = 0.53 \text{ contracts C} \end{align} \]

For every 1 contract of FC we need 0.53 contracts of C.

11 C vs KW

For every 1 contract of C we need 1 contract of KW.

12 C vs LC

• LC average animal weight = 1250 lb
• FC average animal weight = 750 lb
• 1 lb C produces 6 lb weight gain in feedlot
• Feedlot rations consist of 60% to 85% corn (we assume 75%)

\[ 1250 \text{ lb LC} \rightarrow 750 \text{ lb FC} + (1250 - 750) \times 6 \times 0.75 \text{ lb C} = 750 \text{ lb FC} + 2250 \text{ lb C} \]

\[ \begin{align} \frac{[\text{FC}]}{[\text{LC}]} &= \frac{50000}{750} \times \frac{1250}{40000} = 2.08 \\ 1 \text{ animal FC} &\rightarrow 2250 \text{ lb C} = \frac{2250}{56} \text{ bu C} \\ 1 \text{ contract FC} = 66.67 \text{ animal FC} \rightarrow \frac{2250}{56} \times 66.67 &= 2678.705 \text{ bu C} \rightarrow \frac{2678.705}{5000} = 0.53 \text{ contracts C} \end{align} \]

For every 2.08 contracts of LC we need 0.53 contracts of C.

Or stated differently, for every 1 contract of C we need 3.93 contracts of LC.

13 C vs LH

Similar to C vs LC, because of one-to-one sizing ratio in LH vs LC. For every 1 contract of C we need 3.93 contracts LH.

14 C vs MW

For every 1 contract of C we need 1 contract of MW.

15 C vs RR

\[ \begin{align} 2000 \text{ cwt RR} = 2000 \times 112 = 224000 \text{ lb RR} \\ 5000 \text{ bu C} = 5000 \times 56 = 280000 \text{ lb C} \end{align} \]

\[ \frac{[\text{C}]}{[\text{RR}]} = \frac{280000}{224000} = 1.25 \]

For every 1 contract of C we need 1.25 contracts of RR.

16 C vs S

For every 1 contract of C we need 1 contract of S.

17 C vs SB

Here we use the results from

• XB vs SB
• XB vs DL
• C vs DL

assuming C and SB compete on a energy basis.

\[ \begin{align} &\text{XB} : \text{SB} = 1:9.04 \\ &\text{XB} : \text{DL} = 1:2.15 \\ &\text{DL} : \text{C} = 1:1.44 \\ \\ \implies& \text{XB:C} = 1:2.15 \times 1.44 = 1:3.096 \\ \implies& \text{C} : \text{SB} = 3.1 : 9.04 = 1:2.92 \end{align} \]

For every 1 contract of C we need 2.92 contracts of SB.

18 C vs W

For every 1 contract of C we need 1 contract of W.

19 C vs XB

Here we use results from

• C vs DL
• XB vs DL

\[ \begin{align} &\text{C} : \text{DL} = 1.44 : 1 \\ &\text{XB} : \text{DL} = 1 : 2.15 \\ \\ \implies& \text{XB:C} = 1:2.15 \times 1.44 = 1:3.096 \approx 3.1 \end{align} \]

A note on how the spread is calculated in Shiny:

Recall the C vs DL spread is calculated using the corn crush spread where we had

\[ S' = 100 \times \text{DL} - \frac{39}{56 \times 2.8} \text{C} \]

From the XB vs DL spread we have

\[ \text{DL} = \frac{84400}{125000} \text{XB} \] to make the two equivalent in terms of BTU. From the above we then define the spread (in USd/gal) as

\[ S = \frac{84400}{125000} \text{XB} - \frac{39}{56 \times 2.8} \text{C} \]

20 C vs YW

\[ 5000 \text{ bu C} = \frac{5000 \times 56}{2204.62} = 127.006 \text{ t C} \]

\[ \frac{[\text{C}]}{[\text{YW}]} = \frac{127.006}{100} = 1.27 \]

For every 1 contract of C we need 1.27 contracts of YW.

21 CRD vs YW

US vs Brazillian corn.

\[ 1 \text{contract YW} = 100 \text{ Mt} \]

\[ 1 \text{contract CRD} = 450 \text{ bags of }60 \text{kg each} = 450 \times 60 \text{kg} = 27000 \text{kg} = 27 \text{Mt} \]

For every 1 contract of YW we need 3.7 contracts of CRD.

22 cattle roi

• LC average animal weight = 1250 lb
• FC average animal weight = 750 lb
• 1 lb C produces 6 lb weight gain in feedlot
• Feedlot rations consist of 60% to 85% corn (we assume 75%)

\[ 1250 \text{ lb LC} \rightarrow 750 \text{ lb FC} + (1250 - 750) \times 6 \times 0.75 \text{ lb C} = 750 \text{ lb FC} + 2250 \text{ lb C} \]

\[ \begin{align} 40000 \text{ lb LC} \rightarrow \frac{40000}{1250} = 32 \text{ animals LC} \\ 50000 \text{ lb LC} \rightarrow \frac{50000}{750} = 66.67 \text{ animals FC} \end{align} \]

\[ \begin{align} \frac{[\text{FC}]}{[\text{LC}]} &= \frac{50000}{750} \times \frac{1250}{40000} = 2.08 \\ 1 \text{ animal FC} &\rightarrow 2250 \text{ lb C} = \frac{2250}{56} \text{ bu C} \\ 66.67 \text{ animal FC} \rightarrow \frac{2250}{56} \times 66.67 &= 2678.705 \text{ bu C} \rightarrow \frac{2678.705}{5000} = 0.53 \text{ contracts C} \end{align} \] For every 1 contract of FC we need 2.09 contracts of LC and 0.53 of C.

23 China S crush

\[ \text{crush margin} = \left(\text{AE} \times 0.8 + \text{SH} \times 0.183 \right) - \text{AK} \]

\[ 1 \text{contract AK} = 10 \text{ Mt AK} \rightarrow 8 \text{ Mt AE} = 0.8 \text{ contract AE} \]

\[ 1 \text{contract AK} = 10 \text{ Mt AK} \rightarrow 0.183 \times 10 = 1.82 \text{ Mt SH} = 0.183 \text{ contract SH} \]

\[ AK:AE:SH = 1:0.8:0.183 \]

24 CC vs QC

For every 1 contract fo CC we need 1 contract of QC

25 CO vs CL

For every 1 contract of CL we need 1 contract of CO.

26 crack 321

\[ \begin{align} \text{CL} : \text{XB} : \text{HO} = 3:2:1 \end{align} \]

27 crack 532

\[ \begin{align} \text{CL} : \text{XB} : \text{HO} = 5:3:2 \end{align} \]

28 crush

\[ \text{crush margin} = \left(\text{SM} \times 0.8 + \text{BO} \times 0.183 \right) - \text{S} \]

\[ 1 \text{contract S} = 5000 \text{ bu S} = 5000 \times 60 = 300000 \text{ lb S} \rightarrow 5000 \times 60 \times 0.8 = 240000 \text{ lb SM} = \frac{240000}{2000} \text{ short ton SM} = 120 \text{ short ton SM} = 1.2 \text{ contract SM} \]

\[ 1 \text{contract S} = 5000 \text{ bu S} = 5000 \times 60 = 300000 \text{ lb S} \rightarrow 5000 \times 60 \times 0.183 = 54900 \text{ lb BO} = 0.915 \text{ contract BO} \]

\[ S:SM:BO = 1:1.2:0.915 \]

29 DAE vs XB

30 DF vs KC

\[ 37500 \text{ lb KC} = \frac{37500}{2204.62} = 17.00973 \text{ t KC} \] \[ \frac{[\text{KC}]}{[\text{DF}]} = \frac{17.00973}{10} \approx 1.7 \] For every 1 contract of KC we need 1.7 contrats of DF.

31 EP vs CA

For every 1 contract of CA we need 1 contract of EP.

32 HO vs BO

\[ \begin{align} 1 \text{ t BO} \approx 292.5 \pm 7.5 \text{ gal Biodiesel} = 300 \text{ gal Biodiesel} \\ 1 \text{ lb BO} \rightarrow \frac{300}{2204.62} \times 0.92 \text{ gal Biodiesel} \\ 60000 \text{ lb BO} \rightarrow \frac{60000 \times 300}{2204.62} \times 0.92 = 7511.499 \text{ gal Biodiesel} \end{align} \] For HO equivalent we use 92% BO and 8% Methanol. Source: Casper and RJO conversion tables and formulas.

\[ \frac{[\text{HO}]}{[\text{BO}]} = \frac{42000}{7511.499} = 5.59 \]

For every 1 contract of HO we need 5.59 contracts of BO.

33 HO vs XB

Gasoline gallon equivalent table. Source: RJO conversion tables and forulas

\[ \begin{align} 1 \text{ gal HO} \rightarrow 139000 \text{ Btu} \\ 1 \text{ gal XB} \rightarrow 125000 \text{ Btu} \\ \end{align} \]

\[ \frac{[\text{XB}]}{[\text{HO}]} = \frac{139}{125} = 1.112 \]

For every 1 contract of XB we need 1.112 contracts of HO.

34 IJ vs RS

\[ \frac{[\text{IJ}]}{[\text{RS}]} = \frac{5}{2} = 2.5 \]

For every 1 contract of Ij we need 2.5 contracts of RS.

35 RS vs S

\[ \text{1 contract S} = 136.08 \text{ tons} = \frac{136.08 \text{ tons}}{20 \text{ tons}} = 6.8 \text{ contracts RS} \]

For every 1 contract of S we need 6.8 contracts of RS.

36 KO vs BO

\[ 60000 \text{ lb BO} = \frac{60000}{2204.62} = 27.22 \text{ t BO} \]

\[ \frac{[\text{BO}]}{[\text{KO}]} = \frac{27.22}{25} = 1.09 \] For every 1 contract of Bo we need 1.09 contracts of KO.

37 KW vs EB

\[ 5000 \text{ bu KW} = \frac{5000 \times 60}{2204.62} = 136.08 \text{ t KW} \]

\[ \frac{[\text{KW}]}{[\text{EB}]} = \frac{136.08}{50} = 2.72 \]

For every 1 conract of KW we need 2.72 contracts of EB.

38 KW vs MW

For every 1 contract of KW we need 1 contract of MW.

39 KW vs RR

\[ 2000 \text{ cwt RR} = 2000 \times 112 \text{ lb RR} = \frac{2000 \times 112}{60} \text{ bu RR} = 3733.3 \text{ bu RR]} \]

\[ \frac{[\text{KW}]}{[\text{RR}]} = \frac{5000}{3733.33} = 1.34 \]

For every 1 contract of KW we need 1.34 contracts of RR.

40 LH vs LC

For every 1 contract of LH we need 1 contract of LC.

41 LS vs LC

This spread flook st the difference in price of the Brazillian and US Live Cattle contracts.

\[ 1 \text{contract LC} = 40000 \text{ lb LC} = \frac{40000}{330 \times 33} = 3.67 \text{ contract LS} \]

Where the LS contract is denominated in arroba. Here we take the convention that 1 arroba = 33 pounds.

For every 1 contract of LC we require 3.67 contracts of LS

42 QK vs CA

For every 1 contract of QK we need 2 contracts of CA.

43 RS crush

We assume a 40:60 split between oil and meal with a 75% protein discount on the meal.

\[ \text{RS crush margin} = \left( \text{BO} \times 0.4 + \text{SM} \times 0.6 \times 0.75 \right) - \text{RS} \]

\[ 1 \text{ contract RS} = 20 \text{ t RS} = 20 \times 2204.62 = 44092.4 \text{ lb RS} \rightarrow 44092.4 \times 0.6 \times 0.75 = 19841.58 \text{ lb SM} = \frac{19841.58}{2000} \text{ short ton SM} = 9.92 \text{ short ton SM} = 0.099 \text{ contract SM} \]

\[ 1 \text{ contract RS} = 20 \text{ t RS} = 20 \times 2204.62 = 44092.4 \text{ lb RS} \rightarrow 44092.4 \times 0.4 = 17636.96 \text{ lb BO} = 0.2939 \text{ contracts BO} \]

\[ RS:SM:BO = 10:1:2.9 \approx 10:1:3 \]

44 RS Oil vs BO

• 2.5 tons of Rapeseed produces 1 ton of oil and 1.4 tons of Rapeseed meal.
• Due to lower protein in Rapeseed we can create an equivalent product using $1.40.73 1 $ ton Soybean Meal

\[ 1 \text{ contract RS} = 20 \text{ t RS} = 20 \times \left( \frac{1}{2.5} \text{ t BO} + \frac{1.4 \times 0.73}{2.5} \text{ t SM} \right) \rightarrow 8 \text{ t BO} + 8 \text{ t SM} = \frac{8}{27.22} \text{ contracts BO} + \frac{8}{90.72} \text{ contracts SM} = 0.29 \text{ contracts BO} + 0.09 \text{ contracts SM} \]

For every 1 contract of RS we need 0.29 contracts of BO and 0.09 contracts of SM. Or stated differently, for every 100 contracts of RS we need 29 contracts of BO and 9 contracts of SM.

45 RS vs BO

We use the oil component from RS crush.

\[ 1 \text{ contract RS} = 20 \text{ t RS} = 20 \times 2204.62 = 44092.4 \text{ lb RS} \rightarrow 44092.4 \times 0.4 = 17636.96 \text{ lb BO} = 0.2939 \text{ contracts BO} \]

For every 1 contract of RS we need 0.2939 contracts of BO. Or stated differently, for every 1 contract of BO we need 3.4 contracts of RS.

46 RS vs KO

We use the results from

• KO vs BO
• RS vs BO

\[ \begin{align} &\text{KO}:\text{BO} = 1.09:1 \\ &\text{RS}:\text{BO} = 3.4:1 \\ \implies& RS:KO = 3.4:1.09 \approx 3.12:1 \end{align} \]

For every 1 contract of KO we need 3.12 contracts of RS.

47 S vs SY

\[ 5000 \text{ bu S} = \frac{5000 \times 60}{2204.62} \text{ t S} = 136.08 \text{ t S} \]

\[ \frac{[\text{S}]}{[\text{SY}]} = \frac{136.08}{25} = 5.44 \]

For every 1 contract of S we need 5.44 contracts of SY.

48 SB vs DL

We use results form

• C vs DL
• C vs SB

\[ \begin{align} &C:DL = 1:1.44 \\ &C:SB = 1:2.92 \\ \implies& DL:SB = 1.44 : 2.92 \\ \implies& DL:SB = 1 : 2.03 \end{align} \]

49 SB vs QW

\[ 112000 \text{ lb SB} = \frac{112000}{2204.62} = 50.80241 \text{ t SB} \]

For every 1 contract of SB we need 1 contract of QW.

50 SB vs CB

\[ 1\text{ contract SB} = 50.80241 \text{ t} = 5.08 \text{ contracts CB} \]

For every 1 contract of SB we need 5.08 contract of CB.

51 W vs CA

\[ 1 \text{ contract W} = 5000 \text{ bu W} = \frac{5000 \times 60}{2204.62} \text{ t W} = 136.07 \text{ t W} \rightarrow \frac{136.07}{50} = 2.72 \text{ contract CA} \]

For every 1 contract W we need 2.72 contrats CA.

52 W vs EB

\[ 1 \text{ contract W} = 5000 \text{ bu W} = \frac{5000 \times 60}{2204.62} \text{ t W} = 136.07 \text{ t W} \rightarrow \frac{136.07}{50} = 2.72 \text{ contract EB} \]

For every 1 contract W we need 2.72 contrats EB.

53 W vs KW

For every 1 contract of KW we need 1 contract of W.

54 W vs MW

For every 1 contract of MW we need 1 contract of W.

55 W vs S

For every 1 contract of S we need 1 contract of W.

56 XB vs DL

Gasoline gallon equivalent table. Source: RJO conversion tables and formulas

\[ \begin{align} 1 \text{ gal XB} \rightarrow 125000 \text{ Btu} \\ 1 \text{ gal DL} \rightarrow 84400 \text{ Btu} \end{align} \]

\[ \frac{[\text{XB}]}{[\text{DL}]} = \frac{125000 \times 42000}{84400 \times 29000} \approx 2.15 \]

For every 1 contract of XB we need 2.15 contracts of DL.

57 XB vs SB

From the results of SB vs DL and XB vs DL we have

\[ SB:DL = 1:2.03 \] and

\[ XB:DL = 1:2.15 \] There results in turn give

\[ XB:SB = 1:2.03 \times 2.15 = 1: 4.37 \]

58 YW vs WZ

For every 1 contract of YW we need 1 contract of WZ.

59 SM vs AE

\[ 1 \text{contract AE} = 10 \text{ Mt AE} \rightarrow 11 \text{ short ton} = \frac{11}{100} = 0.11 \text{ contracts SM} \]

\[ AE:SM = 1:0.11 \]

60 S vs AK

\[ 1 \text{contract AK} = 10 \text{ Mt AK} \rightarrow \frac{10 \times 2204.62}{60} = 367.44 \text{ bushels AK} = \frac{367.44}{5000} = 0.0725 \text{contracts S} \] We can rewrite this as \[ 1\text{contract S} \rightarrow 13.6 \text{contracts AK} \]

\[ S:AK = 1:13.6 \]

61 S vs AK

\[ 1 \text{contract AK} = 10 \text{ Mt AK} \rightarrow \frac{10 \times 2204.62}{60} = 367.44 \text{ bushels AK} = \frac{367.44}{5000} = 0.0725 \text{contracts S} \] We can rewrite this as \[ 1\text{contract S} \rightarrow 13.6 \text{contracts AK} \]

\[ S:AK = 1:13.6 \]

62 KO vs PAL

\[ 1 \text{contract KO} = 25 \text{ Mt KO} \rightarrow 2.5 \text{contracts PAL} \]

\[ KO:PAL = 1:2.5 \]

63 KO vs SH

\[ 1 \text{contract KO} = 25 \text{ Mt KO} \rightarrow 2.5 \text{contracts SH} \]

\[ KO:SH = 1:2.5 \]