Commodity Forward Curves : The Old and the New

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1 Commodity Forward Curves : The Old and the New Helyette Geman Birkbeck, University of London & ESCP Europe Member of the Board of the UBS- Bloomberg Commodity Index To be presented at the Workshop on New Commodity Markets Oxford Man Institute - June 13 to 15, 2011

2 Commodities and Shipping They have existed as long as humankind, and will continue to be there for a long time In the last 100 years, there have been a number of cycles of boom. The end of the 1970s boom can be identified with the crash in 1980 of precious commodities and the failure of the famous Hunt brothers squeeze of the silver market. Then followed nearly 20 years of stagnation in commodity prices. The 2000s decade started with gigantic rises in all commodity prices (at different points in time across the years 2001 to 2005), witnessed the effect of the financial crisis on commodities and a rebound afterwards. As far as theory is concerned, commodities have been up to the late 1980s essentially part of economic theory, with no major results coming from finance, and contributions by economists called Keynes (1936), Kaldor (1939), Working (1949)

3 The Outlook of Commodity Markets in 2010 Increasing wealth invested in commodity indexes (DJ UBS, GSCI, DB, RICI ) Financial investors were usually positioned on the first nearby as the best to the spot and avoid the hurdles of physical delivery and warehousing. Given the «noise» on the first nearby and the frequent contango shape of the forward curve, they now go to more and more distant maturities which used to be the domain of action of the specific industry. Hence, correlations and co- movements of the forward curve need to be taken into account Banks and private equity are buying physical assets, such as power plants, aluminium smelters, which give them direct exposure to the spot price in particular for hedging activities. At the same time, we witness a flurry of M&As, sometimes hostile, in the mining industry worlwide, with some major actors being partly or fully state- owned (Chinalco, Petrobras..)

4 mai-91 oct-91 mars-92 août-92 janv-93 juin-93 nov-93 avr-94 sept-94 févr-95 juil-95 déc-95 mai-96 oct-96 mars-97 août-97 janv-98 juin-98 nov-98 avr-99 sept-99 GSCI TR DJ-AIGCITR Growth of $100 invested in two major indexes during the period : Mean Reversion in prices

5 mars-00 juin-00 sept-00 déc-00 mars-01 juin-01 sept-01 déc-01 mars-02 juin-02 sept-02 déc-02 mars-03 juin-03 sept-03 déc-03 mars GSCI TR DJ-AIGCITR Commodities as a Valuable Asset Class as of 2000

6 DJ AIG Petroleum Index Dec June DJ-AIG Petroleum Sub-index Is Mean-Reversion Dead? ( Geman - Sept 2005, J of Alternative Investments )

7 CRB Commodity Index 1990 to 2011

8 Commodity Prices: Back to Fundamentals The price of a commodity is firstly driven by supply and demand Quantity Supply Demand Supply Q P Demand Price Short-term inelastic supply and demand

9 Another key quantity is the available inventory at the date of analysis, worldwide or in a given region. This inventory has in impact on prices hence, is carefully watched by many CTAs (Commodity Trading Advisers) and on price volatility (see G - Nguyen, Management Science, 2005). For exhaustible commodities like crude oil, copper, gold.. reserves are the fourth key quantity ultimately important In contrast to financial markets, volume risk in commodity markets is as important as price risk. Commodity markets (electricity, natural gas) have been used to handling volume risk (Operational research, dynamic programming); financial markets are used to price risk. The mathematical challenge today is to address both simultaneously; the financial economics one is the market incompleteness, of various degrees of profoundity.

10 Playing the WTI/ Brent spread while being crude oil price neutral

11 Theory of Storage Keynes (1936), Kaldor (1939), Working (1949), Brennan (1958) Four fundamentals results: The convenience yield accounts for the benefit that accrues to the holder of the physical commodity but not to the holder of the futures contract. It is represented as an implicit dividend The volatility of the commodity spot price is high when inventory is low The volatility of Futures contracts decreases with the maturity: "Samuelson effect Moreover, forward curves used to be viewed as being mostly in backwardation, the so- called normal backwardation, due both to the convenience yield and an assumption of mean- reversion in prices

12 Spot-Forward Relationship for a Storable Commodity Under no arbitrage T f 1 () t = S() t 1+ r( T t) + c( T t) y ( T t) cos t of financing cos t of storage implicit dividend If we define a convenience yield net of cost of storage f T [ ] () t = S() t 1+ ( r y)( T t) Or in continuous time, at a fixed date t for a given maturity T f T () () ( r y)( T t = S t e t)

13 Correlation Spot- Prompt month (Nordpool): The standard convenience yield does not apply to electricity (Eydeland- G, RISK, 1998)

14 The Forward Curve The set {F T (t), T > t} is the forward curve prevailing at date t for a given commodity in a given location It is the fundamental tool when trading commodities, as spot prices may be unabservable and options not always liquid It allows to identify possible «carry arbitrage» : buy S, sell a future maturity T and pay the cost of storage and financing as long as the net cashflow is strictly positive The shape of the forward curve is at any date t in a one-to-one mapping with the convenience yield y It will reflect the seasonality in the case of seasonal commodities such as natural gas or Agriculturals

15 A typically backwardated commodity forward Curve - 27 May Copper COMEX M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12 M13 M14 M15 M16 M17 M18 M19 M20 M21 M22 M23 M24

16 Copper Forward Curve, Oct 2009

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18 Gold as a Numéraire Commodity Historically, gold has been held as an international currency, independent of individual countries. At various times in history, domestic currencies have been backed by gold: the gold standard The unit of account of the International Monetary Fund (IMF) used to be denominated in gold; now, a currency basket is used for indexation Over the period following the financial crisis and up to now, gold is viewed in all nations as a currency of intrinsic value and even as an asset class Gold is traded in fine Troy ounces, ounces of actual gold in the ingot (there are Troy ounces in a kilo)

19 COMEX Gold 28/2/2007 mars-07 avr-07 mai-07 juin-07 août-07 oct-07 déc-07 févr-08 avr-08 juin-08 août-08 oct-08 déc-08 juin-09 déc-09 juin-10 déc-10 juin-11 déc-11 Contract months COMEX Gold Price

20 Gold Forward Curve - 27 May Gold M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12 M13 M14 M15 M16 M17 M18

21 Gold Forward Curve, October 26, 2009

22 Gold Forward Curve Feb 2010

23 Number of Ounces of Gold that can buy the Average US House: the Role of the Numéraire in the study of Commodities

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25 Forward Curves and Inventories The importance of inventory in explaining spot price volatility has been widely documented in the economic literature Brennan (1958) and Telser (1958) analyze in the context of several agricultural commodities the spread between a long-term future and the prompt month divided by the prompt month They exhibit a negative correlation between this "relative spread" and the variance of the commodity

26 Fama & French (1987) take as a given the property of the spread being an adequate proxy for inventory. This allows them to analyze 21 commodities, including metals, for which good inventory data were missing in their period of analysis Ng & Pirrong (1994) examine four industrial and one precious metals over the period and use the same proxy for inventory to conclude that fundamentals drive metal price dynamics G. & Nguyen (2005) reconstruct a world database of soybean inventory (with Brazil and Argentina having become more important than the US in the last few years) and establish a quasi perfect affine relationship between scarcity defined as inverse inventory and spot price volatility

27 Inventory and Forward Curve Adjusted Spread in Oil and Natural Gas Markets As said before, crude oil is not a seasonal commodity, natural gas is a very seasonal commodity G- Ohana (Energy Economics, 2009) choose the maturity of the distant Future on criteria of liquidity and ability to filter out the seasonality

28 We used a price database consisting of daily NYMEX Futures prices for the oil from January 1990 to August 2006 for natural gas from January 1993 to August 2006 We use for inventory data the EIA website for crude oil, we collect the volume of all stored petroleum products in OECD countries at the end of each month from the end of December 1989 to the end of July This volume is expressed in billion barrels for oil for natural gas, the website provides the volume of stored natural gas in the United States at the end of each month during the period end of December end of July 2006 This inventory is expressed in Trillion cubic feet

29 Using detrended inventory, it becomes Rel-spread = Inv with Residual standard error = R² = 26% gas relative spread deseasonalized gas inventory

30 Crude Oil Adjusted Spread vs Detrended Inventory

31 Crude Oil Matthew Simmons, Twilight in the Desert "Sooner or later, the worldwide use of oil must peak because oil, like the other two fossils - coal and natural gas - is non renewable Over the past 30 years, daily oil consumption has risen by approximately 33 million barrels, Asia accounting for more than half of this growth in demand Current consumption levels suggest that the world's oil supply should last until around 2045 (without including tar sands) The world's largest producers are Saudi Arabia (13% of world production), Russia (12%), the United States (7%), Iran (6%) and China (5%) The Gulf of Mexico region provides about 29% of the US oil production, hence the disruption created by the long shutdown of many oil rigs after hurricanes Katrina and Rita in summer 2005, and the recent rig accident

32 WTI Oil Prices Jan Oct /1/2002 4/23/2002 8/13/ /3/2002 3/25/2003 7/15/ /4/2003 2/24/2004 6/15/ /5/2004 1/25/2005 5/17/2005 9/6/ /27/2005 4/18/2006 8/8/ /28/2006 3/20/2007 7/10/ /30/2007

33 août-04 déc-04 avr Spread of the Oil Forward Curve - Dec 1995 / Dec 2005 Crude Oil Price Spread 29th Versus 1st août-96 déc-96 avr-97 août-97 déc-97 avr-98 août-98 déc-98 avr-99 août-99 déc-99 avr-00 août-00 déc-00 avr-01 août-01 déc-01 avr-02 août-02 déc-02 avr-03 août-03 déc-03 avr-04 Price Spread 29th Versus 1st avr-96 déc-95

34 68,37 67,37 66,37 65,37 64,37 63,37 62,37 Oil Forward Curve - March 2006 (Bid and Ask) Forward Curve mars-07 juil-07 nov-07 mars-08 juil-08 nov-08 mars-09 juil-09 nov-09 mars-10 juil-10 nov-10 mars-11 juil-11 nov-11 mars-12 juil-12 nov-12 mars-13 juil-13 nov-13 mars-14 juil-14 Maturity WTI Forward Bid WTI Forward Offer nov-06 juil-06 mars-06 Forward Price

35 Back to Backwardation in September M1 M5 M9 M13 M17 M21 M25 M29 M33 M37 M41 M45 M49 M53 M57 M61

36 Crude Oil Future curve (17/11/2008) M1 M4 M7 M10 M13 M16 M19 M22 M25 M28 M31 M34 M37 M40 M43 M46 M49 M52 M55 M58 M61

37 Crude Oil Forward Curve Feb 2010

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43 References H.Geman (2010) Commodities and Numéraire, Encyclopedia of Quantitative Finance H. Geman and Yfong Shi (2009) The CEV model for Commodity Prices, Journal of Alternative Investments H. Geman and S. Kourouvakalis (2008) "A Lattice-Based Method for Pricing Electricity Derivatives under the Geman- Roncoroni Model", Applied Mathematical Finance H. Geman and C. Kharoubi( 2008) Diversification with Crude Oil Futures : the Time-to- Maturity Effect, Journal of Banking and Finance S. Borovkova and H. Geman (2007) "Seasonal and Stochastic Effects in Commodity Forward Curves", Review of Derivatives Research H. Geman and A. Roncoroni (2006) "Understanding the Fine Structure of Electricity Prices", Journal of Business H. Geman (2005) "Energy Commodity Prices: Is Mean Reversion Dead?", Journal of Alternative Investments H. Geman and S. Ohana (2009) "Inventory, Reserves and Price volatility in Oil and Natural Gas Markets,Energy Economics H. Geman (2005) "Commodities and Commodity Prices: Pricing and Modelling for Agriculturals, Metals and Energy", Wiley Finance H. Geman and V. Nguyen (2005) "Soybean inventory and forward curves dynamics", Management Science H.Geman (2004) Water as the Next Commodity, Journal of Alternative Investments H. Geman and M. Yor (1993) "An Exact Valuation for Asian Option", Mathematical Finance A. Eydeland and H. Geman (1999) "Fundamentals of Electricity options" in Energy Price Modelling, Risk Books H. Geman and O. Vasicek (2001) "Forwards and Futures on Non Storable Commodities", RISK H. Geman (2002) "Pure Jump Lévy Processes in Asset Price Modelling", Journal of Banking and Finance H. Geman (2003) "DCF versus Real Option for Pricing Energy Physical Assets" Conference of the International Energy Agency - Paris - March 2003 hgeman@hotmail.com