Futures Basis Profit/Loss (PnL) Analysis

Futures Basis PnL

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Cetin Karakus
cetin.karakus@gmail.com

Table of Contents

• 1. Introduction
• 2. Long and Short
• 3. Generalized PnL for Long/Short Positions
• 4. Basis Position
• 5. Basis PnL Profile
  • 5.1. Bull Market Basis Scenarios for Long Basis Position
  • 5.2. Bear Market Basis Scenarios for Long Basis Position
• 6. Conclusion

1. Introduction

Basis trading is an important trading activity in the futures markets for hedging and speculative proprietary trading. It is therefore important to understand its basics.

Basis is defined as the difference between the spot price(a.k.a. cash price) and futures price. We will consider a single time period with two points T₁ and T₂ for the following discussion. T₁ is the time we open a position (long or short) and T₂ is the when that position is closed.

2. Long and Short

Let’s consider an asset whose price is A₁ at T₁ and A₂ at T₂. Going long means buying the asset at T₁ and selling it at T₂. Going short, on the other hand, is selling it at T₁ and buying it back at T₂. Let’s also assume that we just trade one unit of the asset and there is no transaction costs (broker fees, bid/ask spreads, etc.) for the sake emphasizing main ideas.

Profit/loss (PnL for short) profile of going long and short are then:

• Long PnL = A₂ - A₁

• Short PnL = A₁ - A₂

Most of the assets we encounter have positive prices. However, there are some synthetic assets such as spreads which are linear combinations of other assets and therefore can have both positive as well as negative prices. This might have some unexpected implications in terms of PnL calculation as discussed below

3. Generalized PnL for Long/Short Positions

PnL for a long position is positive if the prices are increasing whether those prices are negative or positive. Similarly, PnL for a short position is positive if the prices are decreasing irrespective of whether they are positive or negative. In other words, prices are considered in an algebraic sense in PnL calculations. Market with increasing prices are referred as "bull" markets and those with decreasing prices are referred as "bear" markets, so we will use those terms as well in the discussions that will follow.

Given two prices A₁ and A₂ corresponding to the asset price at T₁ and T₂ respectively, there are 4 different cases to consider:

1. Negative Increasing Prices: A₁ < A₂ < 0
   Long PnL = A₂ - A₁ > 0 (i.e. positive/profit)
   Short PnL = A₁ - A₂ < 0 (i.e. negative/loss)
   

2. Positive Increasing Prices: 0 < A₁ < A₂
   Long PnL = A₂ - A₁ > 0 (i.e. positive/profit)
   Short PnL = A₁ - A₂ < 0 (i.e. negative/loss)
   

3. Negative Decreasing Prices: A₂ < A₁ < 0
   Long PnL = A₂ - A₁ < 0 (i.e. negative/loss)
   Short PnL = A₁ - A₂ > 0 (i.e. positive/profit)
   

4. Positive Decreasing Prices: 0 < A₂ < A₁
   Long PnL = A₂ - A₁ < 0 (i.e. negative/loss)
   Short PnL = A₁ - A₂ > 0 (i.e. positive/profit)
   

A geometric representation of the above formulas with some illustrative concerete values can be seen in Long/Short PnL Diagram.

Figure 1. Long/Short PnL Diagram

4. Basis Position

In futures trading basis is defined as the difference between spot(cash) price and futures price. Let’s again consider a single period with the beginning and end points of T₁ and T₂ respectively. We will designate the cash price, future price and basis with letters C, F and B respectively. Their values at the beginning and end of the period is referred with relevant subscripts as in that C₁ is the cash price at T₁ and C₂ is the cash price at T₂.

Basis is then defined as follows:

• At T₁ : B₁ = C₁ - F₁

• At T₂ : B₂ = C₂ - F₂

Basis can be positive or negative depending on whether cash/spot prices are higher or lower than the futures prices. A market where futures prices are higher than spot/cash prices is said to be in "contango". Basis, by definition, will be negative in a contango market. A market where futures prices are lower than spot/cash prices is said to be in "backwardation". Basis in such market will be positive.

Markets are normally expected to be in contango (negative basis) as prices generally increase with time (think of inflation). However, short and long term supply/demand dynamics can easily change this and turn a market into backwardation. For example, if there is currently some supply shortages in the market due to some temporary conditions (i.e. they will disappear in next several months), spot prices will be higher than usual due to supply shortages. Futures prices however might stay normal if the market perceives this to be a transionary situation. This will make the spot prices being higher than the futures prices put the market into backwardation.

As basis can be positive as well as negative, terms of "expanding" and "narrowing" are used by basis traders to refer to the absolute value(size) of the basis irrespective of the mathematical sign of the basis. So, when basis changes from -0.50 to -0.25 it is said to be narrowing(contracting) as it’s size(absolute value) has decreased from 0.50 to 0.25. Similary, when it changes from -0.25 to -0.50 it is said to have expanded.

Using the above basis definition, we can calculate PnL for long and short basis positions:

• Long Basis(LB): LB PnL = B₂ - B₁
  = (C₂ - F₂) - (C₁ - F₁)
  = (C₂ - C₁) + (F₁ - F₂)
  This is just Long Cash(LC), Short Futures (SF):
  LB = LC + SF

• Short Basis(SB): SB PnL = B₁ - B₂
  = (C₁ - F₁) - (C₂ - F₂)
  = (C₁ - C₂) + (F₂ - F₁)
  This is just Short Cash(SC), Long Futures (LF).
  SB = SC + LF

If the primary purpose of our trading activity is hedging, long basis position can be referred as "short hedger" as we will be hedging cash position with short futures position. Short basis position is called "long hedger" for a similar reason.

5. Basis PnL Profile

How will the PnL of basis positions will change over a single period in different market conditions? More specifically we will consider rising(bull)/declining(bear) markets, contango/backwardation, long/short position, expanding/narrowing basis. This is equivalent to 2x2x2x2 = 16 different cases

PnL for short positions are the opposite of the that of long one as seen the previous discussion. Therefore we will focus on the long basis positions and infer the results for the short position as the opposite of the long ones e.g. if long PnL is positive/profit, short one will be negative/loss.

Recall that PnL for long basis position is B₂ - B₁ and basis values can be both positive and negative. As discussed in Generalized PnL for Long/Short Positions, there are two cases where long position PnL can be positive for an asset with both positive and negative prices (as is the case for the basis). Positive prices mean spot/cash prices being higher than futures and therefore backwardation; negative prices mean the opposite i.e. contango.

In Long/Short PnL Diagram we used the terms "incrasing" and "decreasing" to describe the prices. These terms were used in their mathematical sense. A more market practioner-oriented description would relate the meaning of those terms to the contango (negative prices) and backwardation (positive prices) markets. In contanto markets(negative basis), long position PnL is positive when the basis is contracting/narrowing (i.e. its absolute value decreasing). This can be seen in the top left corner of Long/Short PnL Diagram. In backwardation markets (positive basis), In contanto markets(negative basis), long position PnL is positive when the basis is widenign/expanding (i.e. its absolute value increasing). This can be seen in the top right corner of Long/Short PnL Diagram.

Basis Position Market Direction Neutrality A given basis position PnL does not specifically depend the market direction (whether it is increasing/bull or decreasing/bear). In other words, basis trading is market direction neutral. It primarily depends on the mathematical increase or decrease of the basis. This then translates to: The state of the market: contango or backwardation The state of the basis: narrowing or widening

To see the validity of the above assertion first notice the following:

1. Long basis PnL only depends on the mathematical change in the basis (i.e. B₂ - B₁ )

2. Same mathematical basis changes could take place both in rising/bull and falling/bear markets.

Second point above can best be illustrated geometrically through some hypotetical market scenario diagrams.

5.1. Bull Market Basis Scenarios for Long Basis Position

Consider the bull market scenarios as illustrated in the following diagram:

Figure 2. Bull Market Basis Scenarios

We will consider each cases in that diagram separately and analyze the PnL of a long basis position. Recall that long basis position is equivalent to a combination of long cash and short futures positions as described in "Long Basis PnL Formula". Short basis position PnL will immediately follow as the opposite of the long basis PnL, so we won’t explicity state it here.

1. Widening Basis in Contango Market: This is illustrated in the bottom left corner of the diagram. While we make positive PnL from the long cash position, we lose money from short futures position. The loss from the short futures position is higher than the profit from long cash position, resulting in a net negative PnL. To see it notice the following:

   1. Futures prices start and stay higher than the spot prices (Contango market)

   2. The gap between the futures price and the spot price widens at the end of priod, implying that the future price has increased more than the spot price.

2. Narrowing Basis in Contango Market: This is illustrated in the top left corner of the diagram. While we make positive PnL from the long cash position, we lose money from short futures position. The loss from short futures position is lower than the profit from long cash position, resulting in an overall positive PnL. To see it notice the following:

   1. Futures prices start and stay higher than the spot prices (Contango market)

   2. The gap between the future price and spot price narrows at the end of priod, implying that the spot price has increased more than the futures price.

3. Widening Basis in Backwardation Market: This is illustrated in the bottom right corner of the diagram. While we make positive PnL from the long cash position, we lose money from the short futures position. The loss from short futures position is lower than the profit from long cash position, resulting in an overall positive PnL. To see it notice the following:

   1. Spot price starts and stays above than the futures price (backwardation market)

   2. The gap between the spot price and futures price widens at the end of priod, implying that the spot price has increased more than the futures price.

4. Narrowing Basis in Backwardation Market: This is illustrated in the top left corner of the diagram. While we make positive PnL from the long cash position, we lose money from the short futures position. The loss from short futures position is higher than the profit from long cash position, resulting in an overall negative PnL. To see it notice the following:

   1. Spot price starts and stays above than the futures price (backwardation market)

   2. The gap between the spot price and futures price narrows at the end of priod, implying that the futures price has increased more than the spot price.

5.2. Bear Market Basis Scenarios for Long Basis Position

Consider the bear market scenarios as illustrated in the following diagram:

Figure 3. Bull Market Basis Scenarios

As in Bear Market Basis Scenarios for Long Basis Position, we will consider four different scenarios for a long basis position. Short basis position PnL will be the numerical opposite of the respective long position PnL and will be not stated explicitly.

1. Widening Basis in Contango Market: This is illustrated in the bottom left of the diagram. While we make positive PnL from short futures position, we lose money from long cash position. The profit from short futures position is lower than the loss from long cash position becasue the futures price drops less than the spot price. To see this, notice the following:

   1. The futures price starts and stays above the spot price (contango market)

   2. The gap between the futures price and the spot price widens at the end of priod, implying that the spot price has dropped more than the futures price.

2. Narrowing Basis in Contango Market: This is illustrated in the top left of the diagram. While we make positive PnL from short futures position, we lose money from long cash position. The profit from short futures position is higher than the loss from long cash position becasue the futures price drops more than the spot price. To see this, notice the following:

   1. The futures price starts and stays above the spot price (contango market)

   2. The gap between the futures price and the spot price narrows at the end of priod, implying that the futures price has dropped more than the spot price.

3. Widening Basis in Backwardation Market: This is illustrated in the bottom right of the diagram. While we make positive PnL from short futures position, we lose money from long cash position. The profit from short futures position is higher than the loss from long cash position becasue the futures price drops more than the spot price. To see this, notice the following:

   1. The spot price starts and stays above the futures price (backwardation market)

   2. The gap between the futures price and the spot price widens at the end of priod, implying that the spot price has dropped less than the futures price.

4. Narrowing Basis in Backwardation Market: This is illustrated in the top right of the diagram. While we make positive PnL from short futures position, we lose money from long cash position. The profit from short futures position is lower than the loss from long cash position becasue the futures price drops less than the spot price. To see this, notice the following:

   1. The spot price starts and stays above the futures price (backwardation market)

   2. The gap between the futures price and the spot price narrows at the end of priod, implying that the spot price has dropped more than the futures price.

6. Conclusion

We have established the following in this paper:

• Long basis position is equivalent to a combination of long cash and short futures positions

• Short basis PnL is just numerical opposite of the long basis positions i.e. a combination of short cash and long futures positions

• Long basis PnL depends on the market (whether it is in contango or backwardation) and the dynamics of the basis (whether it is narrowing or widening). It does not, however, depends on whether it is a bull/rising or bear market!

• Long basis position PnL is positive when either the increase in the spot price is higher than the increase in the futures price or the decrease in the spot price is lower than the decrease int the futures prices. The former happens when the basis narrows in a contango market and the latter happens when the basis widends in a backwardation market.

We now summarize the PnL implication of 16 cases mentioned earlier in the paper in the following table:

Table 1. Basis PnL Summary

Position	Mkt Dir.	Market	Basis	PnL
Long	Bull	Contango	Widening	Negative
Long	Bear	Contango	Widening	Negative
Long	Bull	Contango	Narrowing	Positive
Long	Bear	Contango	Narrowing	Positive
Long	Bull	Backwardation	Widening	Positive
Long	Bear	Backwardation	Widening	Positive
Long	Bull	Backwardation	Narrowing	Negative
Long	Bear	Backwardation	Narrowing	Negative
Short	Bull	Contango	Widening	Positive
Short	Bear	Contango	Widening	Positive
Short	Bull	Contango	Narrowing	Negative
Short	Bear	Contango	Narrowing	Negative
Short	Bull	Backwardation	Widening	Negative
Short	Bear	Backwardation	Widening	Negative
Short	Bull	Backwardation	Narrowing	Positive
Short	Bear	Backwardation	Narrowing	Positive

Last updated 2019-10-15 01:08:21 Central Daylight Time

Oil Exchange For Physical (EFP) Instrument Analysis

PDF Version

Cetin Karakus
cetin.karakus@gmail.com

Table of Contents

• 1. Introduction
• 2. EFP Basics
  • 2.1. Delivery Location and Differential
  • 2.2. Posted and Invoice Price
• 3. EFP Mechanics
  • 3.1. Long EFP Transaction
  • 3.2. Short EFP Transaction
• 4. Synthetic EFP Instruments
  • 4.1. Synthetic Physical Floating-price(Indexed) Oil
  • 4.2. Synthetic Physical Fixed-price Oil
  • 4.3. Synthetic Basis Swap
  • 4.4. Synthetic Futures Swap
  • 4.5. Synthetic Index (Fixed-Floating) Swap
• Appendix A: Terminology and Formalism
  • Simple Physical Deal Example
• Appendix B: Basic Instruments
  • Futures
  • Physical Floating-price(Index) Oil
  • Physical Fixed-price Oil
  • Futures Swap
  • Basis Swap
  • Index Swap (Fixed-Floating Swap)
• Appendix C: Abbreviations
• Glossary

1. Introduction

Exchange For Futures(EFP) is a very widely used financial instruments in commodity markets in general and energy markets in particular. It links the financial trading to the physical trading world, letting market participants to take advantage of the price discovery and market liquity of the financial energy markets while still be able to do the actual physical trading as required for their line of business.

EFP might look like a simple contract but the apparent simplicity is quite deceptive. It is in fact a bundling of three trading instruments (one physical, two financial derivatives) and as such provides great flexibility in terms of creating other synthetic instruments through unbundling(stripping out) of the constituent parts as appropriate.

There is not much documentation on the actual mechanics of how EFPs work in the literature. Even the futures exchanges, where EFPs are traded, do not provide detailed description of how this instrument works. Their documentation give a very superficial overview of how it might be used by market participants without giving sufficient details about the inner workings of the instrument. That is why the author has taken up on himself to provide a detailed, under-the-hood description of the mechanics of this instrument in the context of the oil trading world.

2. EFP Basics

An exchange of futures for physical (EFP) contract is a trading arrangement between two parties, under which one party will give futures contracts to the other and receive physical oil from the other party in return. Parties to an EFP transaction agrees on the following terms:

• Posted Price: The price at which the futures contracts are transferred from one account to the other.

• Differential: The adjustment to be made over the posted price to arrive at the price to be used in the physical asset transaction. This normally reflects the value difference between the futures price and the price of the physical asset at the point of delivery.

• Invoice Price: This is derived as the sum of the posted price and differential and indicates the price to be paid by one party to another for the physical asset transaction. The grade/quality of the physical oil in the physical transaction is assumed to be same as the one that underlies the futures contract (e.g. BFOE). A price escalator scheme that accounts for grade/quality differences have to be agreed by the counterparties if that is not the case.

• Delivery Location: The location where one party will deliver and the other will receive the physical oil. This is likely to be different than the delivery location of futures contracts (when the futures are physically settled) and hence is also known as alternative delivery location (ADP).

• Size: The size of the physical oil to be bought/sold either in terms of volumentric terms (e.g. 600,000 barrels) or equivalent futures contracts (e.g. 600 ICE Brent Futures)

2.1. Delivery Location and Differential

Of the above terms, the most important one is the delivery location. It is the location where physical oil transaction is going to take place and directly influences the differential to be negotiated by the counterparties to an EFP transaction.

EFPs acts like an instrument that links the financial futures markets to the physical commodity markets such as the physical oil markets. As each physical oil trading location(market) has different supply/demand dynamics and price structure at any given time, a different diffential will exist that links the price of the physical at that location to the price of oil futures which reference a standard delivery location (if the futures are physically settled). Therefore the differential has to be negotiated between counterparies to reflect value differences between the physical oil at the given location versus price underlying the futures contracts.

Following are some of the main drivers that influence the setting of this differential:

• Location Spread: Transporation cost related differences

• Physical Premium: Physical being in demand

• Location Premium: Particular supply/demand dynamics in a given location.

2.2. Posted and Invoice Price

3. EFP Mechanics

There are two parties to an EFP transaction: buyer and seller. EFP buyer is said to be long EFP and EFP seller is said to be short EFP.

In order the see the underlying mechanics of an EFP transaction, we will first look at and EFP transaction from the perspective of an EFP buyer (i.e. long EFP position). We will then examine the same transaction from the seller’s (short position) perspective.

We will use a terminology and formalism we describe in Terminology and Formalism in the subsequent discussions.

3.1. Long EFP Transaction

In a nutshell, buyer of an EFP delivers futures contracts in return to receive physical oil from the seller. More specifically, EFP buyer does the following:

1. Deliver Futures Contracts: Transfers futures contracts from its futures account into the seller’s account. This is likely to be done through the intermediation of the buyer’s and the seller’s brokers.
   This transfer registers as a futures sale at the posted price in buyer’s account. Positions for the futures contracts to be delivered could have been opened long before, just before or after the EFP transaction is agreed. There are legitimate business cases for each one of these transaction timing differences. The important thing to notice is that EFP transaction itself does not preimpose any such particular arrangement so long as the buyer is able to deliver the futures contracts to the seller, how and when they are acquired is of no consequence to the other parties to the transaction (the seller and the exchange as the intermediary)

2. Pay Invoice Price: Pays the invoice price (the posted price plus the differential) to the seller for the physical oil

3. Receive Physical Oil: Receives the physical oil at the agreed upon delivery point (a location likely to be different than the futures contract delivery point) from the seller

The above flows associated with a long EFP position can best be understood when shown in a asset flow diagram:

Figure 1. Long EFP Asset Flow Diagram

This diagram clearly illustrates the essential elements of a long EFP transaction:

1. Long Physical Oil: Long EFP allows receiving physical oil at the delivery location

2. Short Futures: As futures contracts has to be delivered in return for the physical oil, it creates short futures position.

3. Long Basis: While physical oil delivered can be sold at the delivery location index price, it is financed at the cost of the futures. In other words, EFP buyer receives physical index oil price while paying futures contract price. This is a long basis exposure.

A more detailed understanding of the long EFP position can be attained by examining its trade position report (see Terminology and Formalism for the notation):

Table 1. Long EFP Trade Position Statement(TPS)

TX#	Sign	Flow	Transaction	Description
T01	-	FuturesContracts	Futures Transfer	Deliver futures contracts
T02	+	PostedPrice$	Futures Transfer	Receive the posted price for the delivered futures
T03	-	PostedPrice$ + Differential$	Physical Oil Transaction	Pay the invoice price (posted price + differential) for the physical oil transaction
T04	+	PhysicalOil	Physical Oil Transaction	Receive the physical oil at the delivery location
S01	=	+PhysicalOil - FuturesContracts -Differential$	Tally	Net equivalent long EFP position

The algebraic expression in the final tally above is of great importance to fully understand the mechanics of EFP and to prove the assertion we have made in Introduction, namely that an EFP is a bundling of other basic (physical and derivatives) trading instruments.

3.1.1. Long EFP Unbundling

We start with long EFP equivalent position expression we have derived in Long EFP Trade Position Statement(TPS) and do a bit of algebraic manipulation as follows:

Dissection of Long EFP Position

Long EFP = +PhysicalOil -FuturesContracts -Differential$   (1)
Long EFP = (+PhysicalOil -OilIndexPrice$) + OilIndexPrice$ - FuturesContracts -Differential$   (2)
Long EFP = (+PhysicalOil -OilIndexPrice$) + OilIndexPrice$ -FuturesPrice$ +FuturesPrice$- FuturesContracts -Differential$   (3)
Long EFP = (+PhysicalOil -OilIndexPrice$) + OilIndexPrice$ -(FuturesPrice$ + Differential$) + (FuturesPrice$- FuturesContracts)    (4)
Long EFP = (+PhysicalOil -OilIndexPrice$) + OilIndexPrice$ -(FuturesPrice$ +BasisSpread$ + (-BasisSpread$ +Differential$)) + (FuturesPrice$- FuturesContracts)    (5)
Long EFP = (+PhysicalOil -OilIndexPrice$) + (OilIndexPrice$ -(FuturesPrice$ +BasisSpread$)) + (BasisSpread$ -Differential$) + (FuturesPrice$- FuturesContracts)    (6)
Long EFP = PhysicalOilIndex + BasisSwap + SpreadDiff +  Short Futures  (7)
Long EFP = PhysicalOilIndex + BasisSwap + Short Futures  (8)

1	EFP equivalent position we have have derived in the long EFP TPS from the flows seen in the asset flow diagram.
2	Simulatenously substract and add "OilIndexPrice$" to the expression and group the first two terms as physical oil index instrument payoff
3	Simulatenously substract and add "FuturesPrice$"
4	Group the related terms; the last one is the short futures position payoff
5	Simulatenously add and substract "BasisSpread" and group basis spread and differential together
6	Group oil index price, futures price and spread together to form basis swap payoff. Factor out basis spread and differential difference as a separate group.
7	Designate each group with the instrument whose payoff they are representing
8	Remove the basis spread vs differential difference based on the assumption that differential is usually set as being equal to the basis spread (We will expand on this if that is not the case)

There you have it!. Through a set of algebraic manipulations we have dissected the long EFP position to its constituent parts:

1. Physical Oil Index: Buying physical oil at a floating price(indexed) price. See Physical Floating-price(Index) Oil for more details.

2. Basis Swap: Receiving of index price of physical oil at the delivery location while paying futures prices plus a spread. See Basis Swap for more details.

3. Short Futures: Short positions on the futures contracts. See Futures for more details.

4. Spread Difference: Difference between the basis swap spread and the EFP differential. EFP differential is usually set to be equal to the basis swap spread and likely to remain same throughout the lifetime of the EFP. When those assumptions are correct, the differential and the spread cancel each other and they disappear from the overall equation. When, however, they are not, we have to include the difference as a separate element. In practice,those assumptions are mostly valid for two main reasons:

   • Fair Rate:EFPs are structured such that EFP differential is equal to the basis swap spread.

   • Recency: The time between an EFP position being setup and the underlying physical oil transaction taking place is short enough not to witness any dislocations in the basis spread market. Therefore, we will mostly ignore this difference in most of the discussions in the rest of this document. There are, of course, cases where this differene is material and we will examine them separately.

3.2. Short EFP Transaction

Short EFP position is the reverse of the long EFP position. More specifically, EFP seller does the following:

1. Receive Futures Contracts: Receive futures contracts from the EFP buyer. This is likely to be done through the intermediation of the buyer’s and the seller’s brokers.
   This transfer registers as a futures purchase at the posted price in the seller’s futures account.

2. Receive Invoice Price: Receive the invoice price (the posted price plus the differential) from the buyer in return for the physical oil to be delivered

3. Deliver Physical Oil: Deliver the physical oil at the agreed upon delivery point (a location likely to be different than the futures contract delivery point) to the buyer.

The above flows associated with a short EFP position can best be understood when shown in a asset flow diagram:

Figure 2. Short EFP Asset Flow Diagram

This diagram clearly illustrates the essential elements of a short EFP transaction:

1. Short Physical Oil: Short EFP allows selling physical oil at the delivery location

2. Long Futures: As futures contracts are received in return for the physical oil to be sold, it creates long futures position.

3. Short Basis: Oil to be delivered to the buyer can be sourced at the prevaling index price at the delivery location and long futures position can be closed at the prevaling futures prices, resulting in EFP seller receiving the futures prices while paying the index price i.e. short basis exposure.

A more detailed understanding of the short EFP position can be attained by examining its trade position report (see Terminology and Formalism for the notation):

Table 2. Short EFP Trade Position Statement(TPS)

TX#	Sign	Flow	Transaction	Description
T01	+	FuturesContracts	Futures Transfer	Receive futures contracts
T02	-	PostedPrice$	Futures Transfer	Pay the posted price for the delivered futures
T03	+	PostedPrice$ + Differential$	Physical Oil Transaction	Receive the invoice price (posted price + differential) for the physical oil transaction
T04	-	PhysicalOil	Physical Oil Transaction	Deliver the physical oil at the delivery location
S01	=	-PhysicalOil + FuturesContracts +Differential$	Tally	Net equivalent short EFP position

Just as we did for the long EFP position in section Long EFP Unbundling, we will now show that the short EFP position is actually bundling of 3 major trading instruments:

3.2.1. Short EFP Unbundling

We start with short EFP equivalent position expression we have derived in Short EFP Trade Position Statement(TPS) and do a bit of algebraic manipulation as follows:

Disection of Short EFP Position

Short EFP = -PhysicalOil +FuturesContracts +Differential$   (1)
Short EFP = (-PhysicalOil +OilIndexPrice$) - OilIndexPrice$ + FuturesContracts +Differential$   (2)
Short EFP = (-PhysicalOil +OilIndexPrice$) - OilIndexPrice$ +FuturesPrice$ -FuturesPrice$ + FuturesContracts +Differential$   (3)
Short EFP = (-PhysicalOil +OilIndexPrice$) - OilIndexPrice$ +(FuturesPrice$ + Differential$) + (-FuturesPrice$ + FuturesContracts)    (4)
Short EFP = (-PhysicalOil +OilIndexPrice$) + (-OilIndexPrice$ +(FuturesPrice$ +BasisSpread$)) + (Differential$-BasisSpread$) + (-FuturesPrice$ + FuturesContracts)    (5)
Short EFP = -PhysicalOilIndex - BasisSwap - SpreadDiff +  FuturesContracts  (6)
Short EFP = Short PhysicalOilIndex + Short BasisSwap +  Short SpreadFiff + Long Futures  (7)
Short EFP = Short PhysicalOilIndex + Short BasisSwap +  Long Futures  (8)

1	Equivalent position we have have derived in the short EFP TPS from the flows seen in the asset flow diagram.
2	Simulatenously add and subtract "OilIndexPrice$" to the expression and group the first two terms as short physical oil index instrument payoff
3	Simulatenously add and subtract "FuturesPrice$"
4	Group the related terms; the last one is the long futures position payoff
5	Simulatenously add and substract "BasisSpread$" and group basis spread and differential together. Group oil price, futures price and basis spread to form short basis group.
6	Designate each group with the instrument whose payoff they are representing
7	Replace negative signs with "Short" designation
8	Remove spread difference group based on the assumption that basis spread will be equal to differential.

Unsurprisingly, the result we have arrived is in alignment with the one we have derived in Long EFP Unbundling. We could have derived the same result a lot more easily by simply making sign adjustments (i.e. positives to negative, longs to shorts and vice versa) in the long EFP expression. This is due to the reverse duality of long and short positions and will be the basis for conversion between long and short position expression in the rest of the document.

4. Synthetic EFP Instruments

We have seen in EFP Mechanics that an EFP contract is actually a bundling of 3 separate trading instruments. We can cancel one or more of these embedded instruments by taking offsetting positions. This way, we can synthesize any of the underlying payoffs that drive the EFP.

4.1. Synthetic Physical Floating-price(Indexed) Oil

We can generate a synthetic physical oil index position by trading out the basis swap and futures parts of a EFP as shown below:

Deriving Physical Index Oil Payoff

Long EFP = PhysicalOilIndex + BasisSwap + Short Futures  (1)
Long EFP + Short BasisSwap = PhysicalOilIndex +   Short Futures  (2)
Long EFP + Short BasisSwap + Long Futures = PhysicalOilIndex (3)

1	We start with the Long EFP equivalent position expression we have derived in Long EFP Unbundling.
2	Remove embedded long basis swap position by shorting it.
3	Remove embedded short futures position by buying futures

The following diagrams show these steps with asset flows:

Figure 3. Physical Oil Floating Price Synthesis

4.2. Synthetic Physical Fixed-price Oil

We have shown in Long EFP Trade Position Statement(TPS) that long EFP is equivalent to PhysicalOil - FuturesContracts -Differential$. If we remove short futures contracts position by buying futures at a fixed cost, we will end up with a long physical position and fixed short cash position that is used to fund the long physical position i.e. Physical fixed-price oil position.

Deriving Physical Fixed-price Oil Payoff

Long EFP = PhysicalOil - FuturesContracts -Differential$ (1)
Long EFP + Long FuturesAtFixedCost  = PhysicalOil + FuturesContract - FuturesContracts -FixedFuturesCost$ -Differential$ (2)
Long EFP + Long FuturesAtFixedCost  = PhysicalOil - (FixedFuturesCost$ +Differential$) (3)
Long EFP + Long FuturesAtFixedCost  = PhysicalOilFixedPrice (4)

1	Long EFP equivalent position
2	Close out embedded short futures position by buying futures at fixed price
3	Remove offsetting terms and group cost elements together
4	Replace the fixed price physical oil expression with the instrument name.

The following diagrams show these steps with asset flows:

Figure 4. Physical Oil Fixed Price Synthesis

4.3. Synthetic Basis Swap

We can generate a synthetic basis swap position by trading out the physical oil and futures parts of an EFP as shown below:

Deriving Basis Swap Payoff

Long EFP = PhysicalOilIndex + BasisSwap + Short Futures  (1)
Long EFP + Short PhysicalOilIndex = BasisSwap + Short Futures  (2)
Long EFP + Short PhysicalOilIndex + Long Futures = BasisSwap (3)

1	We start with the Long EFP equivalent position expression we have derived in Long EFP Unbundling.
2	Remove embedded long physical oil index position by shorting it
3	Remove embedded short futures position by buying futures

The following diagrams show these steps with asset flows:

Figure 5. Basis Swap Synthesis

4.4. Synthetic Futures Swap

Recall that futures swap has the payoff FuturesPrice$ - FixedPrice$. The closest we get to this kind of payoff expression among the constituents of an EFP is the shorts futures position with the payoff FuturesPrice$ - FuturesContracts. If we buy futures contracts at a fixed cost, we can turn this expression into the required futures swap expression: (FuturesPrice$ - FuturesContracts) + (FuturesContracts - FixedPrice$) => FuturesPrice$ - FixedPrice$. Therefore our strategy in this synthesis is first to isolate the short futures position and then add long futures position at a fixed cost to replicate the wanted futures swap payoff. The full derivation is as follows:

Deriving Futures Swap Payoff

Long EFP = PhysicalOilIndex + BasisSwap + Short Futures  (1)
Long EFP + Short PhysicalOilIndex =  BasisSwap + Short Futures  (2)
Long EFP + Short PhysicalOilIndex + Short BasisSwap =   Short Futures  (3)
Long EFP + Short PhysicalOilIndex + Short BasisSwap + Long FuturesAtFixedCost =  ($FuturesPrice - FuturesContracts) + (FuturesContracts - FixedPrice$) (4)
Long EFP + Short PhysicalOilIndex + Short BasisSwap + Long FuturesAtFixedCost =  ($FuturesPrice -  FixedPrice$) (5)
Long EFP + Short PhysicalOilIndex + Short BasisSwap + Long FuturesAtFixedCost =  FuturesSwap (6)

1	We start with the Long EFP equivalent position expression we have derived in Long EFP Unbundling.
2	Remove embedded long physical oil position by shorting it.
3	Remove embedded long basis position by shorting it.
4	Close out the short futures position by buying futures at a fixed cost. This ends up producing the futures swap payoff
5	Remove cancelled out terms
6	Replace futures swap payoff with instrument identifier.

The following diagrams show these steps with asset flows:

Figure 6. Futures Swap Synthesis

4.5. Synthetic Index (Fixed-Floating) Swap

Recall that index swap has the payoff PhysicalOilIndex$ - FixedPrice$. The closest we get to this among EFP constituent payoffs is that of a basis swap: PhysicalOilIndex$ - FuturesPrice$. If we swap out the FuturesPrice$ with FixedPrice$ in that payoff we will end up with the desired index swap payoff expression. This can be done by adding a futures swap position which has a payoff FuturesPrice$ - FixedPrice$ as in : (PhysicalOilIndex$ - FuturesPrice$) + (FuturesPrice$ - FixedPrice$) = PhysicalOilIndex$ - FixedPrice$ = IndexSwap

Full derivation is as follows: .Deriving Index Swap Payoff

Long EFP = PhysicalOilIndex + BasisSwap + Short Futures  (1)
Long EFP + Short PhysicalOilIndex = BasisSwap + Short Futures  (2)
Long EFP + Short PhysicalOilIndex + Long Futures = BasisSwap (3)
Long EFP + Short PhysicalOilIndex + Long Futures + Long FuturesSwap = (PhysicalOilIndex$ - FuturesPrice$) + (FuturesPrice$ - FixedPrice$) (4)
Long EFP + Short PhysicalOilIndex + Long Futures + Long FuturesSwap = IndexSwap (5)

1	We start with the Long EFP equivalent position expression we have derived in Long EFP Unbundling.
2	Remove embedded long physical oil index position by shorting it
3	Remove embedded short futures position by buying futures
4	Add long futures swap position to swap out futures price with a fixed price in the payoff
5	Remove cancelled terms and derive Index swap payoff.

The following diagrams show these steps with asset flows:

Figure 7. Index Swap Synthesis

Appendix A: Terminology and Formalism

The saying "follow the money" could not have been a more suitable principle to adopt to explain the inner workings of trading instruments(both financial and physical). Money of course is just one of the instruments, albeit the most important one, we have to follow through. We also have to follow other assets such as physical commodities(e.g. physical oil), listed derivatives(e.g. futures contract), OTC derivatives, securities (e.g. stocks, bonds, ), etc.

Things could easily get very complicated very soon if we do not a adopt a clear formalism to designate those assets and how they "flow through" a deal transaction.

Just as in mathematical world geometry is used for understanding, intuition and visual explanation of sophisticated mathematical concepts whereas algebra is harnessed for rigorous analytical formulation, abstraction and generalization, we could adopt a dual geometric/algebraic approach to explain the inner workings of complex trading instruments. To this end, we have developed the following three formalisms:

• Asset Flow Diagram (AFD): This is a diagramatic representation of transaction flows in a deal. It helps with quickly showing the asset flows(physical, financial and cash) between counterparties involved in a deal. Aside from being a visual summary of the deal structure, it can help its observer to follow through the flows in the deal transaction easily to get a sense of the deal dynamics.

• Trade Position Statement (TPS): This is a trade-by-trade statement of trading activity and the resulting trading position. It shows both position impact of each trade transaction and the trader’s final overall position. It helps with showing the transaction involved in a deal structure and their positional impact which can help one "seeing" the alternative equivalent(replicating) positions that can produce the same trading exposure.

• Trade Terms Sheet(TTS): This is a document recording the details of trade transaction along the dimensions of significance such as:

  • When: The date (and time if appropriate) when the transaction occured and other dates (when appropriate) that influence the trade (e.g. the date it will be active)

  • Who: Who are the counterparties to the trade. Who is buyer(long) and who is seller (short)

  • What: What is being traded (the name of the product), the acceptable quality/grade/specification of the product and the quantity of to be traded including both numerical size (e.g. 600) and unit of measure (e.g. barrels)

  • How: "Hows" of the trade pricing and settlement process including any formulas to calcuate the final settlement price and provisions to account for quality/grade variations between what is promised(contractual) and what is delivered(actual)

  • Terms: Deal specific details that will be needed by the "hows" of the deal.

We will now explain how above tools can be used within the context of a simple trade transaction.

Simple Physical Deal Example

Let’s consider a simple physical transaction between two parties: Customer and ComputerShop. Unless otherwise specified, we will be looking into the transaction from the perspective of Customer. Its counterpart, ComputerShop, will have the reverse/opposite perspective.

The transaction we will examine is a simple physical purchase of a product, a personal computer called PCModelA, for upfront cash payment.

We will first show the trade term sheet corresponding to the transaction:

Table 3. Trade Term Sheet for Computer Purchase

Term	Value
Trade Date:	2018-01-10
Buyer:	Customer
Seller:	ComputerShop
Product:	PCModelA
Quantity:	2
Price:	600 USD/each

Now, let’s see how this transaction represented in an asset flow diagram:

Figure 8. Asset Flow Diagram for Computer Purchase

Things to notice above this diagram:

• Counterparties to the deal are show with rectangular boxes

• Asset flows are shown with arrows. Arrows from a given box(counterpart) indicate outflows, flows leaving(decreasing) the position of the said counterpart, whereas arrows into a box indicate the inflows, flows entering (hence increasing) the position of the said counterpart.

• Each flow has a small round round label attached to it. These labels are used to reference to the given flow later in other contexts such as when desribing the nature of the flow in the following discussions and to referencing it from other documents such as from trade transaction statement

This diagram clearly shows main features of the transaction: cash payment for the physical purchase of a commodity. What it does not show is the resulting position of counterparties to the transaction before, during and after the completion of the flows in the transaction.

To see the positional dynamics of the deal, we have to look into the trade position statement. Since there are two counterparties to every transaction, there are two perspectives e.g. buyer’s and seller’s. To keep things simple, we fix a certain perspective when creating our a TPS. Once a TPS for a given counterpart in a transaction is created, deriving the TPS for the opposing site is mostly a straight-forward process reversing signs of the flows as will be seen in the following example.

Let’s first look at the TPS using customer perspective:

Table 4. Trade Position Statement(TPS) : Customer Perspective

TX#	Sign	Flow	Transaction	Description
T01	-	1200$/GBP	Physical Purchase for Cash	Pay the fixed price for purchase
T02	+	2 PCModelA	Physical Purchase for Cash	Receive 2 PCModelA
S01	=	+2 PCModelA - 1200$/GBP	Tally	Final position

The same deal from ComputerShop’s perspective is:

Table 5. Trade Position Statement(TPS) : ComputerShop Perspective

TX#	Sign	Flow	Transaction	Description
T01	+	1200$/GBP	Physical Sale for Cash	Receive the fixed price for the sale
T02	-	2 PCModelA	Physical Sale for Cash	Deliver 2 PCModelA
S01	=	-2 PCModelA + 1200$/GBP	Tally	Final position

Notice that all asset flows changed sign and we have also change the transaction name and description to better suit the perspective of the ComputerShop (e.g. instead of calling the flow T01 purchase, callign it a sale)

Let’s now describe the elements of TPS and how it is related to the deal transaction dynamics. We will adopt the Customer perspective in the following discussion.

Major elements of a TPS are:

• TX#: This is simple transaction flow reference identifier to let us refence a given flow from other contexs. We adopt a simple naming convention of prefixing asset flows with "T" and any talling/summarizing operations (which are not deal events) with "S" and using a two digit, zero-prefixed numbering scheme to identify each of the flows and tally operations. Numbering does not necassirly have any temporal implications (e.g. T01 takes place before T02) as far as deal timeline dynamics is concerned.

• Sign: We use positive(+) and negative(-) signs to indicate the inflows and the outflows from the perspective of the TPS owner. This helps not only with clearly showing the in and out flows but also allowing us to use postive (absolute value/magnitude) quantities in the flow description. We found this approach to be in very good alignment with the in and out flows in asset flow diagrams (where flows are shown with their magnitude and arrow direction show the sign).

• Flow: Linear formulaic description of the flow. It includes both cash and asset flows. We indicate the cash flows specifically by appending dollar($) sign after a cashflow identifier. Note that dollar sign($) does not mean that the cashflow in question is denominate in US dollar or any other dollar. Dollar sign simply means that the quantity in question is a cash amount. The specific currency of the cash is indicated by what folows after the dollar sign as expalined in the following cases:

  • Position Reporting Currency(PRC): If the quantity is specified with just a dollar sign as in "FixedPrice$", it means that the cash in question is in the currency used for the position reporting. The currency is refered as position reporting currency(PRC). In commodity markets, this is usually the USD but it can be change to any other currency depending on the domicile and preference of the trading entity.

  • Foreign Currency: If a flow is in currency other than the reporting currency, it is said to be in a foreign currency and this is indicated by showing the ISO currency of the said foreign corrency after the dollar sign as in "FixedPrice$/GBP": the quantity "FixedPrice" is a cash amount quoted in GBP i.e. it is FixedPrice units of GBP. "$/GBP" is equivalent to the PRC/GBP (e.g. EUR/GBP rate if reporting currency is EUR) and means the number of reporting unit currency for a single GBP (e.g. if GBP-USD FX rate is 1.5 and reporting currenty is USD, it will be 1.5)

• Transaction: This is a short description to show the type of the transaction generating the flow. A given transaction type might have multiple flows in the deal structure and all of them will have the same transcation field.

• Description: A more flow-specific description of the transaction flow to help an outside observer/reader to understand the meaning of the flow.

Appendix B: Basic Instruments

Futures

Physical Floating-price(Index) Oil

Physical Fixed-price Oil

Futures Swap

Basis Swap

Index Swap (Fixed-Floating Swap)

Appendix C: Abbreviations

Table 6. General Abbreviations

Abbreviation	Description
TPS	Trade Position Statement
AFD	Asset Flow Diagram
CFT	Cash Flow Timeline
PRC	Position Reporting Currency

Glossary

TPS

Trade Position Statement

Last updated 2019-10-14 19:13:14 Central Daylight Time