Chair for Management Science and Energy Economics Prof. Dr. Christoph Weber

EFFICIENCY IN THE CRUDE OIL FUTURES MARKET: BACKTESTING RECENT DEVELOPMENTS WITH MULTIFACTOR MODELS IAEE European Conference September 9th, Vienna

Andreas Fritz Christoph Weber University Duisburg-Essen

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Chair for Management Science and Energy Economics Prof. Dr. Christoph Weber

Agenda 1. Introduction 2. Price formation in the crude oil market: theory and related literature 3. Modeling the price dynamics of crude oil 4. (Preliminary) Empirical Results 5. Conclusion

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Chair for Management Science and Energy Economics Prof. Dr. Christoph Weber

Price development of the spot price for Brent crude oil Jan 2002 – Dec 2008 $ S U

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Oil prices peaked in Summer 2008 on different oil markets.

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The graph does not show the boom from the beginning of 2009. 50

0 Jan2002

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Chair for Management Science and Energy Economics Prof. Dr. Christoph Weber

Term structure Brent crude oil futures in 2008

Chair for Management Science and Energy Economics Prof. Dr. Christoph Weber

Objectives • study aims at a deeper understanding of speculation in commodity markets • backtesting recent price developments  Can the hypothesis of informational efficiency be maintained?

Chair for Management Science and Energy Economics Prof. Dr. Christoph Weber

Agenda 1. Introduction 2. Price formation in the crude oil market: theory and related literature 3. Modeling the price dynamics of crude oil 4. (Preliminary) Empirical Results 5. Conclusion

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Chair for Management Science and Energy Economics Prof. Dr. Christoph Weber

Informational efficiency • Samuelson (1965) is the beginning of the discussion about efficient markets in modern economics • Fama (1970) uses the taxonomy weak-form, semistrong-form and strong-form informational efficiency – weak-form efficiency means that all past information is incorporated in the prices of assets – the market is informationally efficient in weak-form

• more accurate definition provided by Malkiel who noted “…the market is said to be efficient with respect to some information set”  link between the flow of information and the reaction on the movement of spot and futures prices 7

Chair for Management Science and Energy Economics Prof. Dr. Christoph Weber

Stylized facts of price movements in crude oil markets • lot of studies investigated the nature of price movements in commodity markets in general – e. g. Irwin et al. (1996) showed that futures prices are not well described by a pure mean-reversion process but by a random walk – otherwise Samuelson’s maturity effect is justified by a mean-reversion Samuelson (1965); volatility of futures prices increases as expiry nears

• from a theoretical point of view Pindyck (2001) investigates the relationship between spot and futures markets – mean-reversion and random walk is justified

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Chair for Management Science and Energy Economics Prof. Dr. Christoph Weber

Efficiency in crude oil markets • there is autocorrelation in Brent crude oil returns but the autocorrelation is diminishing over time Alvarez-Ramirez et al. (2002), Tabak, Cajueiro (2007) – market for Brent crude oil is becoming more efficient over time and was in the eighties highly inefficient

• Alvarez-Ramirez et al. (2008) find that the random walk type behavior in energy futures prices is still an unresolved matter of research – there is some evidence that the market exhibits inefficiencies in the shortterm and becomes efficient in the long term

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Chair for Management Science and Energy Economics Prof. Dr. Christoph Weber

Agenda 1. Introduction 2. Price formation in the crude oil market: theory and related literature 3. Modeling the price dynamics of crude oil 4. (Preliminary) Empirical Results 5. Conclusion

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Chair for Management Science and Energy Economics Prof. Dr. Christoph Weber

State-space model for oil prices (I) • generally, spot and futures prices can be described as a function of several latent (unobservable) factors or state-variables  multifactor model

• here, log futures prices are described as an affine function of latent state-variables in the style of Cortazar, Naranjo (2006)  the multifactor model is applied to explain the stochastic behaviour of spot prices using all information available from futures prices  in line with the assumption of weak informational efficiency of observable spot and futures prices

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Chair for Management Science and Energy Economics Prof. Dr. Christoph Weber

State-space model for oil prices (II) • in this model, the spot price process of the commodity can be described as: ' log__ ! _ _= 1 xt + ____

• under the so-called equivalent martingale measure Q the dynamics of the state variables can be described as:

__ x_ _= __ Kx_ __ ______ + ___ w_!_

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Chair for Management Science and Energy Economics Prof. Dr. Christoph Weber

State-space model for oil prices (III) • Cox et al. (1981) showed that the price of a futures contract at time t with a maturity at time T can be determined by taking expectations of the spot price under the risk-neutral measure __ _ _ _! __x_,__ _ ,__= __ __ _ ____

• the solution to futures prices match: __ _ ___ ____ ____ __ _x _,__ _ = exp___ _+ _ __ __ _+ ____ + ___ _ __ _ ,__ 1___ __ ___ 1+ _=2 _ __

__ ______ ____ 1_ __ 1 __ __ + _ __ __ 2 __ _=_2

___!_1

1 2

__ _ __ _ 1 ____ _

_

_____ _+ ___ __ __ __ _ 1 _ __ __ _! ___ ____ _____ __ + __ __ __

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Chair for Management Science and Energy Economics Prof. Dr. Christoph Weber

Estimation methodology • Kalman filter in an error decomposition of the log-likelihood function  in the finance literature, the Kalman filter is a well known procedure to estimate stochastic models of commodities, interest rates and other relevant economic variables

• the estimation of model parameters Ψ is obtained by maximizing the log‑likelihoodfunction of innovations:

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Chair for Management Science and Energy Economics Prof. Dr. Christoph Weber

Agenda 1. Introduction 2. Price formation in the crude oil market: theory and related literature 3. Modeling the price dynamics of crude oil 4. (Preliminary) Empirical Results 5. Conclusion

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Chair for Management Science and Energy Economics Prof. Dr. Christoph Weber

Data • Brent crude oil futures contracts from Jan 2000 to Dec 2008 • contracts for crude oil are traded with maturities up to 36 months in the future (maturities larger than 36 months are omitted) • two subperiods – January 2002 till December 2005 – January 2006 till December 2008

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Chair for Management Science and Energy Economics Prof. Dr. Christoph Weber

Price spread between the far month (36 month) contract for Brent and the nextmonth contract for Brent

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Chair for Management Science and Energy Economics Prof. Dr. Christoph Weber

Method • actual price developments are compared to the ex-ante distribution using the Rosenblatt transform

$ ! +! = #"! +(!" ! +! ) " $ !+ ! = # '# (& )%& = ## (" ! + ! ) "!

"

• resulting distribution is tested against the Null-Hypothesis of a uniform " distribution by means of the Kolmogorov-Smirnov test

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Chair for Management Science and Energy Economics Prof. Dr. Christoph Weber

Challenge: Testing the hypothesis of informational efficiency • Difficulty: Available information set not directly observable • Typical test: Joint test on information efficiency and some assumptions on information arrival and processing • Example: Tests for structural breaks Either identifying departures from informational efficiency when continuous information flow assumed Or identifying changes in information flow under assumption of continued informational efficiency

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Chair for Management Science and Energy Economics Prof. Dr. Christoph Weber

Tests for structural breaks vs. Distribution tests • Both can be used to test joint hypothesis of informational efficiency and continous information arrival But focus is different: • Test for structural breaks aims at identifying single changes in information characteristics of markets At best a few structural breaks might be simultaneously tested for

• Distribution tests aim at assessing the frequency of deviations from pre-specified information characteristics of markets Whether and how often such deviations occur is the primary interest, not the date of occurence

 For the present purpose, the latter type of test is better suited

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Chair for Management Science and Energy Economics Prof. Dr. Christoph Weber

Histograms for subsamples Jan 02–Dec 2005 and Jan 06-Dec 08 Histogram till 01-Jan-2006 104 observations

Histogram from 01-Jan-2006 150 observations

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y c n 10 e u q 8 e r F 6

y c n 25 e u q 20 e r F 15

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 histograms (and Kolmogorov-Smirnov tests) indicate that in the second sample the possible price pathes are to narrow

!

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Chair for Management Science and Energy Economics Prof. Dr. Christoph Weber

Example for deviation between ex-ante multifactor model predictions and ex-post price developments Confidence Intervals for Crude Oil Spot Price Estimation out of sample test, simulation day: 20-Sep-2006 $ S U

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observed spotprice 3-factor-model mean spot price CI (90%)

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Chair for Management Science and Energy Economics Prof. Dr. Christoph Weber

Agenda 1. Introduction 2. Price formation in the crude oil market: theory and related literature 3. Modeling the price dynamics of crude oil 4. (Preliminary) Empirical Results 5. Conclusion

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Chair for Management Science and Energy Economics Prof. Dr. Christoph Weber

Conclusions • method allows to test the joint hypothesis of efficient and structurally invariant markets • structure of the information flow would have been altered fundamentally in the analyzed period – defendable hypothesis for the period after mid 2008 (global financial and economic crisis) – assumption of fundamentally changed information structures for summer 2006 and/or beginning of 2008 seems hardly justifiable

 conclusion seems appropriate, that at least during some periods in recent years prices have been more driven by “animal spirits” or speculation than by rational information processing

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Chair for Management Science and Energy Economics Prof. Dr. Christoph Weber

Thank you very much for your attention.

Chair for Management Science and Energy Economics Prof. Dr. Christoph Weber

References (I) Alvarez-Ramirez, J.; Cisneros, M.; Ibarra-Valdez, C.; Soriano, A. (2002): Multifractal Hurst analysis of crude oil prices. In: Physica A-Statistical Mechanics And Its Applications, Jg. 313, H. 3-4, S. 651–670. Alvarez-Ramirez, Jose; Alvarez, Jesus; Rodriguez, Eduardo (2008): Short-Term Predictability of Crude Oil Markets: A Detrended Fluctuation Analysis Approach. In: Energy Economics, Jg. 30, S. 2645–2656. Cortazar, Gonzalo; Naranjo, Lorenzo (2006): An N-Factor Gaussian Model of Oil Futures Prices. In: The Journal of Futures Markets, Jg. 26, H. 3, S. 243–268. Fama, Eugene F. (1970): Efficient Capital Markets - Review Of Theory And Empirical Work. In: Journal Of Finance, Jg. 25, H. 2, S. 383–423. Irwin, Scott H.; Zulauf, Carl R.; Jackson, Thomas E. (1996): Monte Carlo Analysis of Mean Reversion in Commodity Futures Prices. In: American Journal of Agricultural Economics , S. 387-399.

Chair for Management Science and Energy Economics Prof. Dr. Christoph Weber

References (II) Malkiel, Burton G. (2003): The Efficient Market Hypothesis and Its Critics. In: Journal of Economic Perspectives, Jg. 17, H. 1, S. 59–82. Samuelson, Paul Anthony (1965): Proof that properly anticipated prices fluctuate randomly. In: Industrial Management Review, Jg. 6, H. 2, S. 41–49. Tabak, Benjamin M.; Cajueiro, Daniel O. (2007): Are the Crude Oil Markets Becoming Weakly Efficient Over time? A Test for Time-Varying Long-Range Dependence in Prices and Volatility. In: Energy Economics, Jg. 29, H. 1, S. 28–36. Pindyck, Robert S. (2001): The Dynamics of Commodity Spot and Futures Markets. In: The Energy Journal, S. 1-30.

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