Post on 22-Oct-2014
Section 1: Energy Commodities Basics
Glen Swindle
20 March 2012
c© Glen Swindle: All rights reserved
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Outline
What makes energy commodities different?
Pricing and Delivery
Forward Yields
Macro Perspective
Hedging and Common Structures
Themes
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What makes energy commodities different?High Volatility
Realized volatility for a price series p(n) is defined as:[250
∑n
R2(n)
] 12
where R(n) = log[
p(n)p(n−1)
]For commodities we have used the first traded contract (defined shortly)
GT10 volatility was proxied by the product of duration and change in yield.
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 20100
0.1
0.2
0.3
0.4
0.5
0.6
0.7Historical Vols
SPXEURGC1GT10WTI
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 20100
0.2
0.4
0.6
0.8
1Historical Vols Normalized by WTI Vol
SPXEURGC1GT10
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What makes energy commodities different?
High Volatility
Does this really matter?
Options markets exist for energy commodities that can be used to hedge
vol exposures.
Returns statistics for NYMEX crude oil (WTI) and natural gas(NG):
First contract and the rolling 12 month (”cal”) strip
1 and 10 day intervals
Statistic WTI 1st Month WTI 1Y NG 1st Month NG 1Y
Std Dev (1 Day) 0.024 0.020 0.035 0.022p1,99 (1 Day) 0.067 0.053 0.093 0.059
Std Dev (10 Day) 0.073 0.059 0.107 0.069p1,99 (10 Day) 0.228 0.172 0.272 0.180
Table: Returns Statistics (2000-2010)
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What makes energy commodities different?
High Volatility: Deal Pricing
Suppose you are purchasing an energy asset, for example:
A set of oil or natural gas production fields.
An efficient power generation asset.
In these (and many other cases) the value is approximatelylinear in the price of the underlying commodity.
During the course of two weeks one can expect:
A 6-7% change in value
p1,99 of nearly 20%
For the acquirer paying say a billion dollars, as well as for thelenders supporting such an activity, a 20% change in valuewould be highly problematic.
Simply converging on an acquisition price with suchunderlying volatility can be challenging.
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What makes energy commodities different?
High Volatility: Colateral
Whether exchange traded or OTC, hedging activities areusually accompanied by colateral posting requirements.
High volatility in the underlying requires significant availabilityof cash and/or letters of credit (LCs) .
High volatility amplifies mismatches in colateral posting terms.
Example: Retail energy companies
Provide commodities to retail end-users (who typically are not margined)
Hedge this native short position via standard futures or OTC swaps
markets (which are margined)
This mismatch in credit support can result in lethal colateral calls in
highly volatile times.
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What makes energy commodities different?High Volatility: Colateral
The following plots shows the rolling cal strip for NYMEX WTI, NGand PJM power prices.
PJM is a power market in the eastern U.S. and the largest power market
in North America
The colateral calls against entities with long energy hedges put on
in mid-2008 were onerous.
2007 2008 2009 2010 20110
50
100
150
$/Ba
rrel
WTI
2007 2008 2009 2010 20110
5
10
15
$/M
MBt
u
NYMEX NG
2007 2008 2009 2010 20110
50
100
150
$/M
Wh
PJM Peak
Figure: Rolling Calendar Strips
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What makes energy commodities different?”Specialness”
Another relevant feature is that energy commodities arealways going ”special.”
”Special” is a term borrowed from bond markets in whichparticular bonds that are ”cheapest to deliver” (CTD) into afutures contract trade at a premium due to limited supply
0 5 10 15 20 250
0.005
0.01
0.015
0.02
0.025
0.03
0.035
Duration(Y)
Yield
Yield Versus Duration: 15Jan2009
10Y Futures CTD
Long Bond Futures CTD
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What makes energy commodities different?
”Specialness”
For commodities supply/demand variations are far moreextreme than in other markets resulting in breakdowns of”typical” relationships—i.e. specialness.
Specialness in commodities is either temporal or locational.
A single commodity delivered at two different times orlocations can behave functionally as two entirelydifferent assets.
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What makes energy commodities different?Temporal Specialness
The following figure shows a sample NYMEX NG forwardcurve.The periodicity (and non-monotone) prices are due toseasonal variations in demand.The winter months trade special to the summer months.This increases the dimensionality of risk management;
Limited effectiveness using front month contracts to hedge winter
exposures.
2010 2011 2012 2013 2014 2015 20165.5
6
6.5
7
7.5
8
Forw
ard
Price
($/M
MBt
u)
NYMEX NG Forward curve: 25−Jan−2010
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What makes energy commodities different?Temporal Specialness
Spot price behavior shows short time-scale ”specialness.”The term ”spot price” refers to the price for delivery of the commodity for
delivery ”now.”
The following shows daily spot prices and spot returns forHenry Hub natural gas.
Henry Hub is the location underpinning the NYMEX NG.
Note that daily returns in excess of 500% are not uncommon.
2000 2002 2004 2006 2008 20100
5
10
15
20
$/M
MBt
u
Henry Hub Spot Prices
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011−3
−2
−1
0
1
2
3x 10
4
%
Annualized Returns (%)
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What makes energy commodities different?
Locational Specialness
The figure shows historical daily spot prices for Henry Huband for TETM3, a delivery location in the northeast.
The middle figure shows the spot basis price, which is thedifference between TETM3 and the benchmark Henry Hubprices.
The bottom figure is the price ratio.
While TETM3 is typically premium to Henry Hub due totransportation costs, of particular note are the substantialpremia in spot prices that can arise due to high demand andlow supply on occasional days in the winter.
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What makes energy commodities different?
Locational Specialness
1998 2000 2002 2004 2006 2008 20100
20
40
60
$/M
MBt
uSpot Prices
Henry HubTETM3
1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 20110
10
20
30
$/M
MBt
u
Spot Basis
1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 20110
2
4
6
TETM
3 / H
H
Spot Ratio
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What makes energy commodities different?
Specialness
These phenomena described apply at even shorter time scalesin power: daily, hourly and even sub-hourly.
A commodity for delivery at a particular time and location canexhibit dramatically different price dynamics from the samecommodity deliverable at a different time and location, evenwhen the times and locations are seemingly ”close.”
The set of tradables (swaps and options) available to aportfolio manager is often far smaller than the number ofways that a commodities portfolio can go special.
A major theme of this course is to elaborate on gap betweenrisks that can be hedged and risks that are often embedded incommodities businesses.
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Pricing and Delivery
Basic Terms
The pricing of a commodities trade requires specification of:
The underlying commodity
When and where will the commodity delivered/referenced
The price to be paid for the commodity
The notional quantity
The mechanics of delivery/settlement
Credit / Margining:
OTC contracts: specific margining provisions in ISDAs or related energy
specific credit docs.
Futures: Exchange traded with daily margining / mark-to-market.
For futures settlement has occurred implicitly through daily
margining.
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Pricing and Delivery
Examples
WTI Crude CME/NYMEX (Futures)
Notional 1000 barrels delivered anytime in the contract month
Specific grades of crude (adjusted for value) delivered at Cushing, OK
Natural Gas CME/NYMEX (Futures)
Notional 10,000 MMBtus delivered ratably over the contract month
Delivery location: Henry Hub, LA
Gas Daily Swap (OTC)
Buyer will pay seller $5.20 per MMBtu for 10,000 MMBtu’s per day of
natural gas in Dec 2011
Seller will pay buyer the average Gas Daily Index at Henry Hub for the
delivery month.
Settlement is 10 business days after the last flow date.
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Pricing and Delivery
Physical Versus Financial
Physical transactions (forwards and some futures) involvedelivery of the commodity at a specified location.
Financial transactions (swaps) involve cash settlement basedupon a benchmark price index prevailing at the time ofanalogous physical delivery.
In a physical transaction no reference to an underlying price index is
required.
Delivery is often assumed to be ratable (uniform volume) over a specified
interval.
The third example is a financial transaction.
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Pricing and Delivery
Notional
The notional quantity of a transaction is often defined interms of flow rate (per day or per hour) as opposed to a totalnotional.
A market standard for delivery quantity is often referred to asa ”lot”.
For natural gas a lot is 10,000 MMBtus.
For crude oil a lot is 1000 barrels.
In the third example:
The total notional would be 310,000 MMBtus.
This would be articulated as ”one lot a day” or more succinctly as
”one-a-day” on a trading desk.
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Pricing and Delivery
Notation
We will denote the forward price observed at time t fordelivery at time T by F (t,T ).
In the case of a delivery interval, this will be replaced byF (t,T ,T + S) where [T ,T + S ] defines delivery interval overwhich ratable (uniform) delivery of the commodity is assumed.
In cases where the delivery interval is a contract month m wewill abbreviate notation along the lines of Fm(t) or F (t,Tm).In the third example F (0,Tm) = $5.20 .
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Pricing and Delivery
Notation
In practice the delivery interval is treated as a discrete set ofdelivery days for the purpose of pricing and operations.
Note that:
Fm(t) =1
Tm+1 − Tm
∫ Tm+1
Tm
F (t,T )dT (1)
There is no discounting here as settlement usually occurs onthe same date in the following month.
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Pricing and Delivery
Spot Prices
The floating price in the third example is often referred to a”spot price”, which is the price for ”immediate” delivery.
A spot price is in almost all situations technically a forwardprice with a delivery time very close to the present.
Formally the spot prices is represented by F (t, t)
In practice, the price is usually established slightly before thedelivery time, rendering the distinction between spot andforward somewhat arbitrary.
In the case of natural gas, trading for delivery on day d occurs on day
d − 1 which is when the index print is established.
For power the spot price can be set a day before, hour before or
immediately at delivery.
For coal in which logistics and shipment are an issue, ”spot” can refer to
a time-lag between trade date and delivery measured in weeks or months.
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Pricing and Delivery
Basic Facts about Forwards
The unit value of a long position in a forward contract at timet struck at time t = 0 is given by:
V (t,F (t,T )) = d (t, τ) N [F (t,T )− F (0,T )] (2)
where τ denotes the settlement time, N the notional and d()the discount factor.
Deltas for forwards are discounted notionals:
∆ ≡ ∂V
∂F (t,T )= d (t, τ) N (3)
For a futures contract the unit ∆ is the undiscounted notionalN due to daily margining.
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Pricing and Delivery
Basic Facts about Forwards
Swaps and forwards often trade as strips.
The term strip refers to a set of adjacent months.
Except at short tenors, commodities usually trade as strips.
Seasonal strips are a collection of commodity specific adjacent months.
Calendar strips to the months in a calendar year. ”Cal12”, for example,
refers to the delivery period consisting of the twelve months comprising
the year 2012.
Strips typically trade at a single fixed price, even thoughindividual contract prices can vary significantly.
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Pricing and Delivery
Basic Facts about Forwards
The fair-value of the strip m ∈ {M1, . . . ,M2} must satisfy:
M2∑m=M1
Nm [Fm − K ] d (t, τm) = 0
where:
τm are the settlement times
Nm denotes the monthly notionals (which in general are different due to
day count.
Therefore the fixed price for the strip is:
K =
∑M2m=M1
NmFmd (t, τm)∑M2m=M1
Nmd (t, τm)
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Pricing and Delivery
Options
Mechanics varies by commodity.
Common Themes
Options mechanics tend to mirror conventions for futures andswaps.Expiration can result in either financial settlement or physicalpositions.Expiry is usually ”close” to the contract month.
”MxN” options markets where expiry can be M units of time before
delivery at N are not traded.
Multiple Time Scales
Typically markets support options that exercise into monthly
exposure or into annual (cal strip) exposure.
For power daily options are commonly traded.
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Forward Yields
Backwardation and Contango
Backwardation: Forward price decreases with tenor(associated with supply stress).
Contango: Forward price increases with tenor (associated withsupply excess).
The following figures shows snapshots of forward curves forWTI and NG.
Note the variations in regime, including mixed states ofcontango and backwardation
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Forward YieldsSnapshots
WTI forward curve at a variety of dates:Note the range of prices as well as the changes in the monotonicity
2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 201640
50
60
70
80
90
100
$/BBl
WTI Forward Curves
05−Jan−200605−Jan−200707−Jan−200805−Jan−200905−Jan−201005−Jan−2011
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Forward YieldsSnapshots
NG forward curve at a variety of dates:Note:
The seasonality superimposed on macro trends.
The breakdown from the WTI price levels in recent years.
2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 20214
5
6
7
8
9
10
11
12
$/MMB
tu
NG Forward Curves
05−Jan−200605−Jan−200707−Jan−200805−Jan−200905−Jan−201005−Jan−2011
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Forward Yields
The Carry Formalism
Forward curves can be viewed as yield curves.
Forward yield:
y(t,T ,T + S) =1
Slog
[F (t,T + S)
F (t,T )
]The forward yield annualized rate implied by borrowing to buythe commodity at time T and sell it at time T + S .
Negative forward yields imply that market participants arewilling to pay a premium for earlier delivery
This is effectively lending at negative rates.
This happens when supply is contrained.
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Forward YieldsThe Carry Formalism
Yields often exhibit extreme values.
The following is the WTI forward curve and forward yield forS = one month in early Jan2009.
2009 2010 201135
40
45
50
55
60
65
70
Forw
ard P
rice (
$/Barr
el)
WTI Forward curve: 15−Jan−2009
2009 2010 20110
50
100
150
200
250
Yield
(%)
WTI Forward Yields: 15−Jan−2009
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Forward YieldsThe Carry Formalism
Seasonality yields negative forward yields consistently forseasonal commodities.
2010 2011 2012 20135.5
6
6.5
7
7.5
Forw
ard P
rice (
$/MMB
tu)NYMEX NG Forward curve: 25−Jan−2010
2010 2011 2012 2013−150
−100
−50
0
50
100
Yield
(%)
NYMEX NG Forward Yields: 25−Jan−2010
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Forward Yields
The Carry Formalism
For purely financial assets the presence of decreasing forwardcurves presents an apparent arbitrage opportunity.
Why not short the commodity at the high prices andrepurchase at the low prices?
The answer is that you can, but that the lender of thecommodity, being fully aware of the term structure will chargeaccordingly.
In practice this deal structure, referred to as a ”park-and-loan”usually involves repo in the easy direction, namely buying inthe cheaper months and storing to the expensive months.
How does one address this specialness?
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Forward Yields
The Carry Formalism
Case 1: Investment commodity with no storage costs:
F (t,T ) = F (t, t)er(t,T )(T−t)
or more generally:
F (t,T ) = F (t,S)er(t,S ,T )(T−S)
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Forward Yields
The Carry Formalism
Case 2: Investment commodity with storage costs:
F (t,T ) = F (t, t)e [r(t,T )+q(t,T )](T−t)
where q(t,T ) denotes the instantaneous cost of storage.
Given that q(t,T ) ≥ 0 this would result in contango beingobserved almost universally; a statement at odds with thefacts.
The cost of storage is not exogenous.
Storage owners will charge what the market will bear
The cost of storage is in reality a function of forwards and volsas opposed to an input.
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Forward YieldsThe Carry Formalism
Case 3: For a consumption commodity all we can state withcertainty is that:
F (t,T ) ≤ F (t, t)e [r(t,T )+q(t,T )](T−t).
Rationale: One can always buy the commodity at the spotprice and ensure storage to delivery at T .
Convenience Yield: Solely for the comfort of an seeingequality, this is often rewritten as:
F (t,T ) = F (t, t)e [r(t,T )+q(t,T )−η(t,T )](T−t).
All that can be ascertained from market data is q − η, which
makes the above representation more form over substance.
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Forward YieldsThe Carry Formalism
Recall the forward yields for WTI shown shortly afterinception of the credit crisis:
2009 2010 20110
50
100
150
200
250
Yield
(%)
WTI Forward Yields: 15−Jan−2009
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Forward YieldsEffects of Inventory
Inventory levels and forward yields are intimately coupled.High forward yields (contango) incentives owners of storage to
inject—this occurs when there is a surplus.
Negative forward yields (backwardation) encourages withdrawals—during
times of scarcity.
The following figure shows OECD crude oil stocks.
2002 2004 2006 2008 20103700
3800
3900
4000
4100
4200
4300
4400
Millio
ns of
Barr
els
OECD Crude Oil Invetory
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Forward YieldsEffects of Inventory
This figure shows the forward yield between the first two calstrips of the WTI forward curve yield versus inventory levels.
3700 3800 3900 4000 4100 4200 4300 4400−25
−20
−15
−10
−5
0
5
10
15
20
25WTI 1st/2nd Cal Strip Carry Versus Inventory
Millions of Barrels
Annu
alize
d Ca
rry (%
)
Backwardation (Carry<0)
Contango (Carry>0)
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Forward YieldsEffects of Inventory: Forward Yields
Incentives: the huge credit-crisis contango resulted in amassive increase in the use of VLCCs store oil and refinedproducts.The figure shows the result outside of the Port of Singaporeduring Jan2009.
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Forward Yields
Effects of Inventory: Benchmarks
The high dimensional nature of energy commodities requiresbenchmark pricing.
Prices of an array of products are referenced as a spread(basis) to ”liquidity centers.”
For crude oil the dominant global benchmarks are WTI andBrent.
In recent years there has been a massive decoupling of WTIfrom global crudes due to build-up of PADD2 (mid-U.S.)crude oil inventory.
This has resulted in serious concerns about the viability ofWTI as a benchmark.
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Forward YieldsEffects of Inventory: Benchmarks
2005 2006 2007 2008 2009 2010 20115
6
7
8
9
10
11x 10
4
000s
Bbl
PADD2 Inventory
2005 2006 2007 2008 2009 2010 2011−5
0
5
10
15
20
USD/
Bbl
Brent−WTI 2nd Nearby
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Forward YieldsEffects of Inventory: Benchmarks
This figure shows the scatter of the Brent/WTI basis versusPadd2 inventory.
5 6 7 8 9 10 11
x 104
−4
−2
0
2
4
6
8
10
12
14
16
000s Bbl
USD/
Bbl
Brent/WTI 2nd Nearby (Weekly Average) versus PADD2
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Conclusion
Summary
High volatility impacts deal valuation, hedging and creditexposure/capital requirements.
High dimensionality is an inherent feature of energy marketsrequiring benchmark pricing/hedging and often resulting in”residual incompleteness.”
Viewed as yield curves, energy forward curves can exhibit verylarge yields of both signs.
Inventory effects are a significant driver of forward yields (andconversely).
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