Commodities and Energy Markets Supplementary Notes: Energy Commodities Basics

Transcription

1 Commodities and Energy Markets Supplementary Notes: Energy Commodities Basics Princeton RTG summer school in Financial Mathematics Presenters: Michael Coulon and Glen Swindle 17 April 2013 c Glen Swindle: All rights reserved 1 / 45

2 Outline What makes energy commodities different? Pricing and Delivery Forward Yields and the Carry Formalism 2 / 45

3 What makes energy commodities different? High Volatility Realized volatility for a price series p(n) is defined as: [ ] R 2 (n) n [ ] where R(n) = log p(n) p(n 1) - For commodities we have used the first traded futures contract. - GT10 volatility proxied by duration change in yield. (1) Annualized Volatility SPY EUR GT10 GC1 WTI Volatility Ratio Versus WTI SPY EUR GT10 GC1 Historical Vols Normalized by WTI Vol / 45

4 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) p 1,99 (1 Day) Std Dev (10 Day) p 1,99 (10 Day) Table: Returns Statistics ( ) 4 / 45

5 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 approximately linear in the price of the underlying commodity. During the course of two weeks one can expect: - A 6-7% change in value - p 1,99 of over 15% For the acquirer paying say a billion dollars, as well as for the lenders supporting such an activity, a 15% change in value would be highly problematic. Simply converging on an acquisition price with such underlying volatility can be challenging. 5 / 45

6 What makes energy commodities different? High Volatility: Colateral Whether exchange traded or OTC, hedging activities are usually accompanied by colateral posting requirements. High volatility in the underlying requires significant availability of 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. 6 / 45

7 What makes energy commodities different? High Volatility: Colateral The following plots shows the rolling cal strip for NYMEX WTI, NG and 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. $/Barrel $/MMBtu $/MWh WTI NYMEX NG PJM Peak / 45

8 What makes energy commodities different? Specialness Another relevant feature is that energy commodities are always going special. Special is a term borrowed from bond markets in which particular bonds that are cheapest to deliver (CTD) into a futures contract trade at a premium due to limited supply Yield Versus Duration: 15Jan Long Bond Futures CTD 0.02 Yield Y Futures CTD Duration(Y) 8 / 45

9 What makes energy commodities different? Specialness For commodities supply/demand variations are far more extreme 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 or locations can behave functionally as two entirely different assets. 9 / 45

10 What makes energy commodities different? Temporal Specialness The following figure shows a sample NYMEX NG forward curve. The periodicity (and non-monotone) prices are due to seasonal variations in demand. The winter months trade special to the summer months. This increases the dimensionality of risk management; - Limited effectiveness of front-month contracts to hedge winter exposures. 8 NYMEX NG Forward curve: 25 Jan 2010 Forward Price ($/MMBtu) / 45

11 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 for Henry Hub natural gas. - Henry Hub is the location underpinning the NYMEX NG. - Note that daily returns in excess of 500% are not uncommon. 20 Henry Hub Spot Prices $/MMBtu x 104 Annualized Returns (%) 2 1 % / 45

12 What makes energy commodities different? Locational Specialness The figure shows historical daily spot prices for Henry Hub and for TETM3, a delivery location in the northeast. The middle figure shows the spot basis price, which is the difference between TETM3 and the benchmark Henry Hub prices. The bottom figure is the price ratio. While TETM3 is typically premium to Henry Hub due to transportation costs, of particular note are the substantial premia in spot prices that can arise due to high demand and low supply on occasional days in the winter. 12 / 45

13 What makes energy commodities different? Locational Specialness $/MMBtu Spot Prices Henry Hub TETM3 Spot Basis $/MMBtu TETM3 / HH Spot Ratio / 45

14 What makes energy commodities different? Specialness These phenomena described apply at even shorter time scales in power: daily, hourly and even sub-hourly. A commodity for delivery at a particular time and location can exhibit dramatically different price dynamics from the same commodity deliverable at a different time and location, even when the times and locations are seemingly close. The set of tradables (swaps and options) available to a portfolio manager is often far smaller than the number of ways that a commodities portfolio can go special. A major theme of this course is to elaborate on gap between risks that can be hedged and risks that are often embedded in commodities businesses. 14 / 45

15 Pricing and Delivery Forward Pricing and Delivery We have already made reference to forward curves. This figure shows the forward curve for WTI on 15Jan2009. Each point represents the price for WTI delivered in subsequent months as of this pricing date. 75 WTI Forward curve: 15 Jan Forward Price ($/Barrel) / 45

16 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. 16 / 45

17 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 Seller will pay buyer the average Gas Daily Index at Henry Hub for the delivery month. - Gas Daily Index prices are published by Platts by location. - At each locations the GDI a volumetric weighted average of a survey of trades done for physical delivery. - Survey prices at highly liquid locations are more reliable than at illiquid locations. 17 / 45

18 Pricing and Delivery Examples Natural Gas Penultimate Swaps - Settle on the futures settlement price on the next-to-last trading day of the analogous futures contract. - Options on natural gas futures expire on the same day, rendering this swap particularly useful for options hedging. - Settlement occurring one business day before the futures contract is referred to as penultimate settlement. - The settlement amount is based on the difference between the futures penultimate settlement and the strike at which the trade was done. - Consider an Oct10 swap for one lot per day ( one-a-day ) was entered into on 01Jul2010 at a price of $4.94 /MMBtu. - The penultimate price was settled at $4.79 on 27Sep As there are 31 days in October, the total notional is 310,000 MMBtus, resulting in cash settlement (from the long perspective) of 310, 000 ($4.79 $4.94) = $44, / 45

19 Pricing and Delivery Physical Versus Financial Physical transactions (forwards and some futures) involve delivery of the commodity at a specified location. Financial transactions (swaps) involve cash settlement based upon a benchmark price index prevailing at the time of analogous 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. 19 / 45

20 Pricing and Delivery Notional The notional quantity of a transaction is often defined in terms of flow rate (per day or per hour) as opposed to a total notional. A market standard for delivery quantity is often referred to as a 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. 20 / 45

21 Pricing and Delivery Notation We will denote the forward price observed at time t for delivery at time T by F (t, T ). In the case of a delivery interval, this will be replaced by F (t, T, T + S) where [T, T + S] defines delivery interval over which ratable (uniform) delivery of the commodity is assumed. In cases where the delivery interval is a contract month m we will abbreviate notation along the lines of F m (t) or F (t, T m ). In the third example F (0, T m ) = $ / 45

22 Pricing and Delivery Notation In practice the delivery interval is treated as a discrete set of delivery days for the purpose of pricing and operations. Note that: F m (t) = 1 T m+1 T m Tm+1 T m F (t, T )dt (2) There is no discounting here as settlement usually occurs on the same date in the following month. 22 / 45

23 Pricing and Delivery Spot Prices The floating price in the last 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 forward price 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 the delivery time, rendering the distinction between spot and forward 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. 23 / 45

24 Pricing and Delivery Basic Facts about Forwards The unit value of a long position in a forward contract at time t struck at time t = 0 is given by: V (t, F (t, T )) = d (t, τ) N [F (t, T ) F (0, T )] (3) where τ denotes the settlement time, N the notional and d() the discount factor. Deltas for forwards are discounted notionals: V = d (t, τ) N (4) F (t, T ) For a futures contract the unit is the undiscounted notional N due to daily margining. 24 / 45

25 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 Strips typically trade at a single fixed price, even though individual contract prices can vary significantly. 25 / 45

26 Pricing and Delivery Basic Facts about Forwards The fair-value of the strip m {M 1,..., M 2 } must satisfy: M 2 m=m 1 N m [F m K] d (t, τ m ) = 0 where: - τ m are the settlement times - N m denotes the monthly notionals (which in general are different due to day count. Therefore the fixed price for the strip is: K = M2 m=m 1 N m F m d (t, τ m ) M2 m=m 1 N m d (t, τ m ) 26 / 45

27 Pricing and Delivery Options Mechanics varies by commodity. Common Themes Options mechanics tend to mirror conventions for futures and swaps. Expiration can result in either financial settlement or physical positions. 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. 27 / 45

28 Forward Yields Backwardation and Contango Backwardation: Forward price decreases with tenor (associated with supply stress). Contango: Forward price increases with tenor (associated with supply excess). The following figures shows snapshots of forward curves for WTI and NG. Note the variations in regime, including mixed states of contango and backwardation 28 / 45

29 Forward Yields Snapshots WTI forward curve at a variety of dates: - Note the range of prices as well as the changes in the monotonicity WTI Forward Curves $/BBl Jan Jan Jan Jan Jan Jan / 45

30 Forward Yields Snapshots 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. NG Forward Curves Jan Jan Jan Jan Jan Jan $/MMBtu / 45

31 Forward Yields The Carry Formalism Forward curves can be viewed as yield curves. Forward yield: y(t, T, T + S) = 1 S log [ F (t, T + S) F (t, T ) The forward yield annualized rate implied by borrowing to buy the commodity at time T and sell it at time T + S. Negative forward yields imply that market participants are willing to pay a premium for earlier delivery - This is effectively lending at negative rates. - This happens when supply is contrained. ] 31 / 45

32 Forward Yields The Carry Formalism Yields often exhibit extreme values. The following is the WTI forward curve and forward yield for S = one month in early Jan2009. Forward Price ($/Barrel) WTI Forward curve: 15 Jan WTI Forward Yields: 15 Jan 2009 Yield (%) / 45

33 Forward Yields The Carry Formalism Seasonality yields negative forward yields consistently for seasonal commodities. Forward Price ($/MMBtu) NYMEX NG Forward curve: 25 Jan NYMEX NG Forward Yields: 25 Jan 2010 Yield (%) / 45

34 Forward Yields The Carry Formalism For purely financial assets the presence of decreasing forward curves presents an apparent arbitrage opportunity. Why not short the commodity at the high prices and repurchase at the low prices? - The answer is that you can, but that the lender of the commodity, being fully aware of the term structure will charge accordingly. - In practice this deal structure, referred to as a park-and-loan usually involves repo in the easy direction, namely buying in the cheaper months and storing to the expensive months. How does one address this specialness? 34 / 45

35 Forward Yields The Carry Formalism Case 1: Investment commodity with no storage costs: or more generally: r(t,t )(T t) F (t, T ) = F (t, t)e r(t,s,t )(T S) F (t, T ) = F (t, S)e 35 / 45

36 Forward Yields The Carry Formalism Case 2: Investment commodity with storage costs: [r(t,t )+q(t,t )](T t) F (t, T ) = F (t, t)e where q(t, T ) denotes the instantaneous cost of storage. Given that q(t, T ) 0 this would result in contango being observed almost universally; a statement at odds with the facts. 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 vols as opposed to an input. 36 / 45

37 Forward Yields The Carry Formalism Case 3: For a consumption commodity all we can state with certainty 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 spot price and ensure storage to delivery at T. Convenience Yield: Solely for the comfort of an seeing equality, 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. 37 / 45

38 Forward Yields The Carry Formalism Recall the forward yields for WTI shown shortly after inception of the credit crisis: 250 WTI Forward Yields: 15 Jan Yield (%) / 45

39 Forward Yields Effects 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 OECD Crude Oil Inventory 4300 Millions of Barrels / 45

40 Forward Yields Effects of Inventory This figure shows the forward yield between the first two cal strips of the WTI forward curve yield versus inventory levels. 25 WTI 1st/2nd Cal Strip Carry Versus Inventory Contango (Carry>0) Annualized Carry (%) Backwardation (Carry<0) Millions of Barrels 40 / 45

41 Forward Yields Effects of Inventory: Forward Yields Incentives: the huge credit-crisis contango resulted in a massive increase in the use of VLCCs store oil and refined products. The figure shows the result outside of the Port of Singapore during Jan / 45

42 Forward Yields Effects of Inventory: Benchmarks The high dimensional nature of energy commodities requires benchmark 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 and Brent. In recent years there has been a massive decoupling of WTI from global crudes due to build-up of PADD2 (mid-u.s.) crude oil inventory. This has resulted in serious concerns about the viability of WTI as a benchmark. 42 / 45

43 Forward Yields Effects of Inventory: Benchmarks 12 x 104 PADD2 Inventory 1000s Barrels Brent WTI 2nd Nearby USD/Barrels / 45

44 Forward Yields Effects of Inventory: Benchmarks This figure shows the scatter of the Brent/WTI basis versus Padd2 inventory. Brent/WTI 2nd Nearby (Weekly Average) versus PADD USD/Barrel s Bbl x / 45

45 Conclusion Summary High volatility impacts deal valuation, hedging and credit exposure/capital requirements. High-dimensionality is an inherent feature of energy markets requiring benchmark pricing/hedging and often resulting in residual incompleteness. Viewed as yield curves, energy forward curves can exhibit very large yields of both signs. Inventory effects are a significant driver of forward yields (and conversely). 45 / 45