EFFICIENCY IN THE CRUDE OIL FUTURES MARKET: … · Efﬁciency in crude oil markets •there is...

Chair for Management Science and Energy EconomicsProf. Dr. Christoph Weber

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EFFICIENCY IN THE CRUDE OIL FUTURES MARKET:BACKTESTING RECENT DEVELOPMENTS WITH

MULTIFACTOR MODELS

IAEE European ConferenceSeptember 9th, Vienna

Andreas FritzChristoph Weber

University Duisburg-Essen


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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


Jan2002 Jan2004 Jan2006 Jan2008 Jan20100

50

100

150

trading days

Spot Prices in US-$

Price development of the spot price for Brent crude oilJan 2002 – Dec 2008

Oil prices peaked inSummer 2008 ondifferent oil markets.

The graph does notshow the boom fromthe beginning of 2009.


Term structure Brent crude oil futures in 2008


Objectives

• study aims at a deeper understanding of speculationin commodity markets

• backtesting recent price developments

Can the hypothesis of informational efficiency be maintained?


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Agenda

1. Introduction




5. Conclusion


Informational efficiency

• Samuelson (1965) is the beginning of the discussion about efficientmarkets in modern economics

• Fama (1970) uses the taxonomy weak-form, semistrong-form andstrong-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 marketis said to be efficient with respect to some information set”

link between the flow of information and the reaction on the movementof spot and futures prices

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Stylized facts of price movements in crude oil markets

• lot of studies investigated the nature of price movements incommodity markets in general

– e. g. Irwin et al. (1996) showed that futures prices are not well describedby a pure mean-reversion process but by a random walk

– otherwise Samuelson’s maturity effect is justified by a mean-reversionSamuelson (1965); volatility of futures prices increases as expiry nears

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

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Efficiency in crude oil markets

• there is autocorrelation in Brent crude oil returns but theautocorrelation 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 behaviorin energy futures prices is still an unresolved matter of research– there is some evidence that the market exhibits inefficiencies in the short-

term and becomes efficient in the long term

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Agenda

1. Introduction




5. Conclusion


State-space model for oil prices (I)

• generally, spot and futures prices can be described as a function ofseveral latent (unobservable) factors or state-variables multifactor model

• here, log futures prices are described as an affine function of latentstate-variables in the style of Cortazar, Naranjo (2006)

the multifactor model is applied to explain the stochastic behaviour ofspot prices using all information available from futures prices

in line with the assumption of weak informational efficiency ofobservable spot and futures prices

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State-space model for oil prices (II)

• in this model, the spot price process of the commodity can bedescribed as:

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

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log____= 1'xt + ____!

__x__= __Kx___ ______+ ___w__!


State-space model for oil prices (III)

• Cox et al. (1981) showed that the price of a futures contract at time twith a maturity at time T can be determined by taking expectations ofthe spot price under the risk-neutral measure

• the solution to futures prices match:

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___x__,__,___= ____

________!

___x__,__,___= exp___1____+ _ ______________________

__

__=2

+ ____+ ____ __1 +1

2__1_____ ___

_ _1_ ______________

____

__

__=2

____+1

2_ ______________

1_ ________+____________

____+ _________!1

_!


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 otherrelevant economic variables

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

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Agenda

1. Introduction




5. Conclusion


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

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Method

• actual price developments are compared to the ex-ante distributionusing the Rosenblatt transform

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

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( )!! ++ = !! "#$ " "

( ) ( )!!

##!

+

!"

+== #

+

!

"

!"#%&&'$

!

" "

"


Challenge: Testing the hypothesis of informationalefficiency

• 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 breaksEither identifying departures from informational efficiency whencontinuous information flow assumedOr identifying changes in information flow under assumption ofcontinued informational efficiency

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Tests for structural breaks vs. Distribution tests

• Both can be used to test joint hypothesis of informational efficiencyand continous information arrival

But focus is different:• Test for structural breaks aims at identifying single changes in

information characteristics of marketsAt best a few structural breaks might be simultaneously tested for

• Distribution tests aim at assessing the frequency of deviations frompre-specified information characteristics of marketsWhether 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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Histograms for subsamples Jan 02–Dec 2005 andJan 06-Dec 08

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

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!

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14

16

Histogram till 01-Jan-2006104 observations

y

Frequency

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

30

35

40

Histogram from 01-Jan-2006150 observations

y

Frequency


Example for deviation between ex-ante multifactormodel predictions and ex-post price developments

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Jan2006 Jan2007 Jan2008 Jan200920

40

60

80

100

120

140

160

trading days

Spot Prices in US-$

Confidence Intervals for Crude Oil Spot Price Estimationout of sample test, simulation day: 20-Sep-2006

observed spotprice

3-factor-model mean spot price

CI (90%)


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Agenda

1. Introduction




5. Conclusion


Conclusions

• method allows to test the joint hypothesis of efficient and structurallyinvariant markets

• structure of the information flow would have been alteredfundamentally 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 inrecent years prices have been more driven by “animal spirits” orspeculation than by rational information processing

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Thank you very much for your attention.


References (I)

Alvarez-Ramirez, J.; Cisneros, M.; Ibarra-Valdez, C.; Soriano, A. (2002):Multifractal Hurst analysis of crude oil prices. In: Physica A-StatisticalMechanics And Its Applications, Jg. 313, H. 3-4, S. 651–670.

Alvarez-Ramirez, Jose; Alvarez, Jesus; Rodriguez, Eduardo (2008): Short-TermPredictability of Crude Oil Markets: A Detrended Fluctuation AnalysisApproach. In: Energy Economics, Jg. 30, S. 2645–2656.

Cortazar, Gonzalo; Naranjo, Lorenzo (2006): An N-Factor Gaussian Model of OilFutures Prices. In: The Journal of Futures Markets, Jg. 26, H. 3, S. 243–268.

Fama, Eugene F. (1970): Efficient Capital Markets - Review Of Theory AndEmpirical Work. In: Journal Of Finance, Jg. 25, H. 2, S. 383–423.

Irwin, Scott H.; Zulauf, Carl R.; Jackson, Thomas E. (1996): Monte Carlo Analysisof Mean Reversion in Commodity Futures Prices. In: American Journal ofAgricultural Economics , S. 387-399.


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 fluctuaterandomly. In: Industrial Management Review, Jg. 6, H. 2, S. 41–49.

Tabak, Benjamin M.; Cajueiro, Daniel O. (2007): Are the Crude Oil MarketsBecoming Weakly Efficient Over time? A Test for Time-Varying Long-RangeDependence in Prices and Volatility. In: Energy Economics, Jg. 29, H. 1, S.28–36.

Pindyck, Robert S. (2001): The Dynamics of Commodity Spot and FuturesMarkets. In: The Energy Journal, S. 1-30.

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