The forward pricing function of industrial metal futures – evidence from cointegration and smooth transition regression analysis

Abstract

The prices of internationally traded metals have experienced wild swings and increased volatility in recent years. The relationship between spot and futures prices is an important topic in this context, as the current period’s price of a futures contract should be an unbiased estimator of next period’s spot price under the joint assumption of risk neutrality and rationality. Taking as a basis data from the Dow Jones UBS Commodity Index, which uses metals traded on the London Metal Exchange and US exchanges, this study adopts nonlinear smooth transition models to analyze whether the forward spread is a leading indicator of future spot price movements. Our findings suggest that such a price discovery function can in most cases only be identified in periods of low volatility or small previous spreads. Moreover, the underlying dynamics are captured best by the use of a logistic transition function.

Keywords:

• cointegration
• commodities
• metal
• spot and futures markets
• smooth transition regression

JEL Classifications:

• G13
• G14
• Q43

Acknowledgements

We thank Jan Wagemester and an anonymous referee for useful comments.

Notes

1. Using panel data for different commodities, Czudaj and Beckmann (2012) also provide evidence for nonlinearity in the spot and futures price relation based on an evaluation of different sample periods before and after 2000.

2. The threshold could be characterized by ‘carrying costs’, which consist of costs of transportation and storage of commodities and make an investor indifferent to buying a spot commodity or a futures contract.

3. Furthermore, Cunado and Perez de Garcia (2003) as well as Maslyuk and Smyth (2009) used the Gregory and Hansen (1996) framework to account for the presence of structural breaks in the relationship between spot and futures prices. Recently, Lee and Zeng (2011) used quantile cointegration regression to describe the connection between oil spot and futures prices.

4. The Fama (1984) approach, which is based on the theory of uncovered interest rate parity (UIP), has been used by Sarno, Valente, and Leon (2006), Baillie and Kilic (2006), Hochradl and Wagner (2010), Olmo and Pilbeam (2011) as well as Pilbeam and Olmo (2011) to analyze the relationship between the spot return and the forward premium for different exchange rates. The theory of UIP also implies and .

5. Our framework could also be extended to allow for the possibility of asymmetric autoregressive conditional heteroscedasticity, which is considered by Lundbergh and Teräsvirta (1998). However, this topic is left for further research.

6. Values above unity would indicate an overshooting while values below zero signify that the dynamic pattern is explosive.

7. We have also considered gold and silver, however the cointegration analysis conducted in the next section revealed that there is apparently no long-run relation between prices for spot and futures of these precious metals. We therefore dropped both from the analysis in the following, since the basis cannot be adequately used as the transition variable in those cases.

8. See Tang and Xiong (2010) and Gilbert (2010) for details regarding the DJ-UBSCI and its subindices. Following Tang and Xiong (2010), the correlation between the GS and the DJ-UBS commodity indices is over 0.9. As a result, using GSCI would not significantly change our findings. Among others, Irwin and Sanders (2012) have applied the DJ-UBSCI dataset for a similar purpose. In a comparable study, Figuerola-Ferretti and Gonzalo (2010) also used spot and futures prices for aluminum, copper, nickel, and zinc from the LME.

9. We have also applied the more powerful Ng and Perron (2001) MZa test to ascertain the robustness of our findings. These statistics are reported in Table 1 as well. To account for the possibility of structural breaks in our series, which in general reduce the power of conventional unit root tests to reject the null, we have conducted the Perron (1989) test in the fashion described by Perron and Vogelsang (1992). To save space, the findings are not presented; however, they do support our results as given in Table 1.

10. We do not report the coefficients and test statistics, but they are available upon request. Among others, Crowder and Hamed (1993), Peroni and McNown (1998), McKenzie and Holt (2002), Switzer and El-Khoury (2007) and especially Figuerola-Ferretti and Gonzalo (2010) support our finding of a cointegration relationship between spot and futures prices for commodities.

11. Adopting the particular estimated cointegrated relationships instead of the proportional relations provides qualitatively unchanged results. Hence, we only report the results for the latter since these are more feasible in terms of interpretability.

12. In the case of small samples in combination with a large number of explanatory variables, F versions of the LM test statistics are preferable, as they have better size properties (Granger and Teräsvirta 1993; Teräsvirta 1998; van Dijk, Teräsvirta, and Franses 2002).

13. The number of degrees of freedom 3p refers to the number of regressors p, which in our case is one. Furthermore, the test assumes that all regressors, as well as the transition variable z_t , should be stationary and uncorrelated with the error in equation (4) u_t+k (Teräsvirta 1998). As shown in Section 3.2.1, our only regressor and transition variable is a stationary linear combination of non-stationary I(1) variables.

14. Longer delays have turned out to be less suitable in previous estimations carried out by the authors. The results are available upon request.

15. See Granger and Teräsvirta (1993), Teräsvirta (1994) or van Dijk, Teräsvirta, and Franses (2002) for details. Escribano and Jordá (1999) propose an alternative selection procedure, which augments Equation (8) by the term and tests the hypotheses and . If the rejection of is the strongest in terms of the largest test statistic, the LSTR (ESTR) model should be selected.

16. Several modified estimations have been carried out to test for the robustness of the overall results. In particular, we have modified our estimations with respect to the choice of the transition variable by introducing different lags for the lagged spread. For instance, the results remain qualitatively unchanged if the lag order is chosen to be one for each commodity. Estimations of all models with exponential or logistic transition functions suggest that the established results continue to hold. Overall, the results indicate that our findings are robust with respect to different configurations. To save space, the corresponding results are not presented here, but are available upon request.