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Empirical Economics

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01.09.2014

Revealing asymmetries in the loss function of WTI oil futures market

verfasst von: E. C. Mamatzakis

Erschienen in: Empirical Economics | Ausgabe 2/2014

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Abstract

This paper examines behavioural aspects of the West Texas Intermediate (WTI) oil 1-month futures from 1995 to 2012. We consider that oil futures are formed based on an underlying generalised loss function with an unknown shape parameter that provides information regarding preferences. Even without observing fundamentals of WTI oil futures we can assess whether preferences lean towards a symmetric or asymmetric loss function. Our empirical evidence is robust across information sets and shows that overall loss preferences of WTI 1-month oil futures are rather optimistic and thus the underlying loss function is asymmetric. This implies that if one disregards this asymmetry the WTI oil futures should not be viewed as rational. We further provide statistical tests that allow deviations from a symmetric loss function. As part of a sensitivity analysis, and given the long span of our sample, we perform a novel analysis for detecting breakdowns in our series over time. Based on this analysis we re-examine the shape parameters of the loss function for WTI oil month futures for sub-periods. Interestingly, preferences of WTI 1-month oil futures have shifted towards optimism post 2008 period, marking the collapse of Lehman Brothers.

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This paper builds on Elliott et al. (2005) rationality test in WTI oil futures. Their methodology was the first to propose tests of forecast rationality that allow for asymmetric loss. Prior to Elliott et al. (2005) the rationality of forecasts was tested imposing the assumption that a mean squared error loss could map the forecaster’s preferences. The mean squared error loss has been heavily criticised and as a result more general loss functions have been proposed (see Christoffersen and Diebold 1996; Granger and Pesaran 2000; Christodoulakis 2005). Elliott et al. (2005) offer a method to identify the shape parameter of the loss function of the forecaster that would be most consistent with forecast rationality.

Elliott et al. (2005) find that the IMF and OECD systematically over-predict government budget deficits and have asymmetric loss. However, once the existence of an asymmetric loss is taken into account forecast rationality is not rejected. Moreover, Elliott et al. (2005) argue that forecast rationality also requires that the exact same loss function is shared by the producer and the end user of the forecast. To this end, revealing possible asymmetries in the underlying loss function of the WTI oil futures is of high importance for the participants in the oil markets.

Within this framework it is not necessary to know the underlying model of forming oil futures. In line with the literature (Abosedra and Baghestani 2004; Switzer and El-Khour 2006; Sanders et al. 2008), oil futures represent predictions plus a premium. The premium is considered as fixed, and thus exogenous to the loss function.

In the empirical part of the paper three instruments are opted, a constant, the lagged difference between spot and future price, and the lagged difference of spot price.

\(\hat{S}\) depends on \(\alpha _{T}\) and as a result the estimation takes place iteratively, assuming \(\hat{S}=I\) in the first iteration to estimate \(\alpha _{T}\) until convergence.

The U.S. Commodity Futures Trading Commission (CFTC) keeps record of the commercial and non-commercial traders. The classification of traders is based on information on futures positions; a commercial trader uses futures contracts for hedging as defined in CFTC Regulation 1.3(z), 17 CFR 1.3(z), ‘...engaged in business activities hedged by the use of the futures or option markets’. Note that the CFTC keeps record of all big players, whether they are commercial or non-commercial traders, regarding their positions each week. Bloomberg uses this information to classify traders into the two categories in line with the U.S. Commodity Futures Trading Commission. All data used in this paper are from Bloomberg and, therefore, follow the definition of CFTC.

The crude oil price increased 600 % over the period 2002–2008 (DOE 2008)

We opt for weekly frequency because it allows variability in the underlying data-generating process whilst reduces possible excess noise present in daily observations. As a sensitivity analysis, similar testing has been performed also for daily observations without observing significant changes. Results are available under request. Note also that the WTI spot and WTI 1-month futures do not overlap when derived from Bloomberg. This is essential so as to avoid overlapping in the data used and hence correlation in the forecast errors.

‘World Petroleum Consumption, Most Recent Annual Estimates, 1980–2007’(http://www.eia.doe.gov/emeu/international/RecentPetroleumConsumptionBarrelsperDay.xls) and ‘World Production of Crude Oil, NGPL, and Other Liquids, and Refinery Processing Gain, Most RecentAnnualEstimates, 1980–2007’, http://www.eia.doe.gov/emeu/international/RecentTotalOilSupplyBarrelsperDay.xls).

It is noteworthy at this point that commodities pricing literature originates in the theory of storage by Kaldor (1939) and Working (1949). There are two broad categories that have emerged since; the first examines the pricing implications in derivatives (see Schwartz 1997), whilst the second opts for the original theory of storage of Working to search for implications of the price of oil (Routledge et al. 2000). For the purposes of this paper we allow for a specification of the risk premium, though this premium is considered as fixed, and thus exogenous to the loss function. It goes beyond the scope of this study to provide a theoretical explanation of the price of risk in oil futures.

Cointegration between WTI oil spot and future price means that we can proceed with the estimation of shape parameter of the loss function without suffering from spurious results.

For information regarding the construction of the asymptotic variance estimator \(\hat{\sigma }_{m,n}\) see Giacomini and Rossi (2009).

Giacomini and Rossi (2009) have applied their method on the Phillips curve for the economy of US.

Results for all three schemes of providing futures are reported: (i) the fixed scheme; (ii) the rolling scheme and (iii) the recursive scheme.

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Titel: Revealing asymmetries in the loss function of WTI oil futures market
verfasst von: E. C. Mamatzakis
Publikationsdatum: 01.09.2014
Verlag: Springer Berlin Heidelberg
Erschienen in: Empirical Economics / Ausgabe 2/2014
Print ISSN: 0377-7332
Elektronische ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-013-0764-8

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