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Co-movements in commodity markets and implications in diversification benefits

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Abstract

This study examines the co-movement and causality relationship between prices of crude oil, precious metals, and agricultural commodities. We use a novel approach called wavelet coherence analysis, which allows the measurement of co-movements in the time–frequency space based on the daily prices of commodities. We decompose data from September 1986 to September 2017 into 12 levels and 5 subperiods to find more generalized and convincing results. We confirm that commodity prices are in-phase and co-move. Particularly, the coherence is the largest in the long term and rises sharply in the mid-term during the crisis period. The heterogeneous directions of arrows provide strong evidence that the causality relationship between commodity prices varies over time for different frequencies. We find that the mixed commodities portfolio can provide diversification benefits in the mid-term horizons. The findings of this study can guide investors who want to benefit from diversification while investing in commodity markets.

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Notes

  1. The various decomposition levels we obtain correspond to the following time scales: Level 1 (1–2 days); Level 2 (2–4 days); Level 3 (4–8 days); Level 4 (8–16 days); Level 5 (16–32 days); Level 6 (32–64 days); Level 7 (64–128 days [half a year]); Level 8 (128–256 days [1 year]); Level 9 (256–512 days [2 years]); Level 10 (512–1024 days [4 years]); Level 11 (1024–2048 days [8 years]); Level 12 (2048–4096 days [16 years]).

  2. See Percival and Walden (2000) and Addison (2002) for more details.

  3. For \( \omega_{0} = 6 \), we obtain the approximate equation \( f = \frac{{\omega_{0} }}{2\pi s} = \frac{6}{2\pi s} \approx 1/s \), suggesting that broad scale s corresponds to low Fourier frequency \( f \) and fine scale s corresponds to high Fourier frequency \( f \).

  4. As noted by Daubechies (1992), the admissibility condition is defined as \( 0 < C_{\psi } = \mathop \smallint \limits_{0}^{\infty } \frac{{|\varPsi (f)|^{2} }}{f}{\text{d}}f < \infty \).

  5. The Fourier power spectrum of an AR(1) process with lag-1 autocorrelation \( \alpha \) is given by \( P_{f} = \frac{{1 - \alpha^{2} }}{{|1 - \alpha e^{ - 2i\pi k} |^{2} }} \) (estimated from the observed time series; see, for example, Allen and Smith 1996).

  6. For example, in our analysis, the 5% significance level is calculated using \( Z_{2} \left( {0.95} \right) = 3.999 \).

  7. Coherence is identically one at all scales and times without smoothing (see Grinsted et al. 2004 and Cazelles et al. 2007 for details).

  8. See Grinsted et al. (2004) for more details.

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Acknowledgements

We are grateful to three anonymous referees for many helpful comments and suggestions. This work is supported by JSPS KAKENHI Grant Number (A) 17H00983.

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Authors and Affiliations

  1. Graduate School of Economics, Kobe University, Kobe, Japan

    Xiao Jing Cai & Shigeyuki Hamori

  2. Singapore University of Social Sciences, Singapore, Singapore

    Zheng Fang & Youngho Chang

  3. Research Center of Finance, Shanghai Business School, Shanghai, China

    Shuairu Tian

Authors
  1. Xiao Jing Cai
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  2. Zheng Fang
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  3. Youngho Chang
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  4. Shuairu Tian
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  5. Shigeyuki Hamori
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Correspondence to Shigeyuki Hamori.

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Appendix

Appendix

In Appendix, we plot the cross-wavelet transform to analyze the covariance between the six commodity pairs in the time–frequency domain in Fig. 4. As in the WPS plots shown in Fig. 1 and 2, the 5% significance level is shown as the black contour, and the color code reflects the degree of covariance, ranging from high (red) to low (blue) power of covariance. The relative phase relationship is presented via arrows. We can draw the following conclusions from this figure. The most significant common power between pairs of commodity returns occurred in the 256–512-day scales from 2007 to 2008, when significant volatilities in returns were recorded for these scales, as shown in Fig. 1. The information on the phases shows that the relationship among commodities is in-phase and co-move, since most arrows point right, while the other arrows point up and down constantly, implying that their relationships are not homogeneous across scales and over time. More importantly, we find that most arrows in the cross-wavelet plots of oil and other commodities point right and up in the 256–512-day scale during the crisis period from 2007 to 2008, indicating that the covariance that was in phase increased in the crisis period and that oil was leading. Similarly, we find that the covariance among the remaining commodity returns increased in the crisis period and was in phase in the significant regions.

Fig. 4
figure 4figure 4figure 4

Cross-wavelet transform of price returns of pairs of crude oil, precious metals (gold and silver), and agricultural commodities (wheat, corn, and soybean)

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Cai, X.J., Fang, Z., Chang, Y. et al. Co-movements in commodity markets and implications in diversification benefits. Empir Econ 58, 393–425 (2020). https://doi.org/10.1007/s00181-018-1551-3

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