To be presented at the Workshop on New Commodity Markets Oxford Man Institute - June 13 to 15, 2011

Helyette GemanBirkbeck, University of London & ESCP Europe

Member of the Board of the UBS- Bloomberg Commodity Index

Commodity Forward Curves :The Old and the New

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. Thenfollowed nearly 20 years of stagnation in commodity prices.

The 2000s decade started with gigantic rises in all commodity prices (at differentpoints in time across the years 2001 to 2005), witnessed the effect of the financialcrisis 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)

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 needto 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 miningindustry worlwide, with some major actors being partly or fully state- owned(Chinalco, Petrobras..)

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Growth of $100 invested in two major indexes during the period 1991-1999 : Mean – Reversion in prices

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Commodities as a Valuable Asset Class as of 2000

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DJ-AIG Petroleum Sub-index

Is Mean-Reversion Dead ? ( Geman - Sept 2005, J of Alternative Investments )

DJ – AIG Petroleum Index Dec 2001 - June 2006

CRB Commodity Index – 1990 to 2011

Commodity Prices: Back to Fundamentals

→ The price of a commodity is firstly driven by supply and demand

Short-term inelastic supply and demand

P°

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Price

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DemandQ°

Demand Supply

→ 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.

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

Theory of StorageKeynes (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

Spot-Forward Relationship for a Storable Commodity

Under no arbitrage

( ) ( ) ( ) ( ) ( )⎥⎥⎥

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tTytTctTr1tStf 1T

If we define a convenience yield net of cost of storage

( ) ( ) ( )( )[ ]tTyr1tStf T −−+=

Or in continuous time, at a fixed date t for a given maturity T

( ) ( ) ( )( )tTyrT etStf −−=

Correlation Spot- Prompt month (Nordpool):The standard convenience yield does not apply to electricity

(Eydeland- G, RISK, 1998)

The Forward Curve

→ The set {FT (t) , T > t} is the forward curve prevailing at date t for a givencommodity in a given location

→ It is the fundamental tool when trading commodities, as spot prices may beunabservable 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

A typically backwardated commodity forward Curve - 27 May 2008

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Copper COMEX

Copper Forward Curve, Oct 2009

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 32.15 Troy ounces in a kilo)

COMEX Gold 28/2/2007

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Gold Forward Curve - 27 May 2008

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Gold Forward Curve, October 26, 2009

Gold Forward Curve – Feb 2010

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

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 severalagricultural 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

→ 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 1986-1992 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

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

→We used a price database consisting of daily NYMEX Futures pricesfor the oil from January 1990 to August 2006for natural gas from January 1993 to August 2006

→We use for inventory data the EIA websitefor crude oil, we collect the volume of all stored petroleum products in OECD countries at the end of each month from the end of December1989 to the end of July 2006. This volume is expressed in billion barrels for oilfor 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 1992 - end of July 2006

This inventory is expressed in Trillion cubic feet

→ Using detrended inventory, it becomesRel-spread = 0.046 – 0.691 Inv

withResidual standard error = 0.092R² = 26%

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Crude Oil Adjusted Spread vs Detrended Inventory

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

WTI Oil Prices Jan 2002 - Oct 2007

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Spread of the Oil Forward Curve - Dec 1995 / Dec 2005

Forward Curve

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WTI Forward Bid WTI Forward Offer

Oil Forward Curve - March 2006 (Bid and Ask)

Back to Backwardation in September 2007

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Crude Oil Future curve (17/11/2008)

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Crude Oil Forward Curve – Feb 2010

References

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

hgeman@hotmail.com