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Heterogeneous interconnections between precious metals: Evidence from asymmetric and frequency-domain spillover analysis
Resources Policy 64 (2019) 101509
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Heterogeneous interconnections between precious metals: Evidence from asymmetric and frequency-domain spillover analysis Gazi Salah Uddin a, Syed Jawad Hussain Shahzad b, c, *, Gideon Boako d, Jose Areola Hernandez e, Brian M. Lucey f a
Department of Management and Engineering, Link€ oping University, Link€ oping, Sweden Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Viet Nam Faculty of Finance and Banking, Ton Duc Thang University, Ho Chi Minh City, Viet Nam d Office of the Vice President, Ghana e ESC Rennes School of Business, Rennes, Brittany, France f Trinity Business School, Trinity College, Dublin, Ireland b c
A R T I C L E I N F O
A B S T R A C T
JEL classification: C12 C58 Q02 L61
We examine the spillover characteristics of returns and volatilities of precious metals: gold, silver, platinum and palladium. We find evidence of homogenous and time varying asymmetric spillovers between the returns and volatilities of the precious metals suggesting similarities in their cyclical relationship with global and local fundamentals. Negative and positive shocks cause the asymmetric spillovers and are more pronounced in times of financial turmoil. The largest transmission of net spillovers is exerted by gold and silver. Silver in the short and long runs and in good and bad market conditions leads the spillover transmission. The pairs silver-gold and palladium-platinum display the largest directional spillovers. Lastly, while palladium and platinum act mainly as spillover receivers, gold and silver act mainly as transmitters of spillovers. Implications of the results are discussed.
Keywords: Precious metals Risk spillovers Asymmetries Frequency dynamics
1. Introduction Precious metals may serve as a store of value, barometer of risk, diversifier of asset portfolios and for economic development of countries depending heavily on precious metal exports (Batten et al., 2015). Accordingly, price changes in commodity markets do affect the income perception of multiple stakeholders (e.g. commodity-consuming and commodity-producing nations), while serving as indicators and pre dictors of economic performance (Hamilton, 2011; Jacks and Stuermer, 2018; Shahzad et al., 2019a). The relationship between price swings of commodities across various time periods and the economic performance of resource-based (i.e., precious metal-based) economies raises in policy makers, and in security portfolio and risk managers, a concern about the spillover effects of those commodities’ return and volatilities. This is
particularly so when determining economy sector resource allocation, fiscal and monetary policy and portfolio rebalancing (Uchezuba, 2010).1 This concern of policy makers and risk managers is difficult to address under different periods of uncertainty and crisis, and if the nature of the spillovers is asymmetric. Asymmetric spillovers, in specific, accentuate the transmission and reception of variation between precious metal commodities and their underlying sectors, making the determination of future prices more complex (Nguyen et al., 2015; Uchezuba, 2010). In the last two decades, diversification using precious metals has become an important approach for risk management and portfolio allocation due primarily to increasing contagion risk emanating from higher integration and interdependence among financial markets worldwide.2 The increasing financialization of commodity markets has opened possibilities for risk hedging that accounts for dynamics of
* Corresponding author. E-mail addresses: [email protected] (G.S. Uddin), [email protected] (S.J.H. Shahzad), [email protected] (G. Boako), [email protected] (J.A. Hernandez), [email protected] (B.M. Lucey). 1 See Jacks and Stuermer (2018). 2 Embracing a diversified portfolio might raise total earnings, decrease risk and enhance the sharp ratio (Batten et al., 2010). The risk-reducing attributes of commodities in a diversified portfolio of stocks and bonds have been well documented by Abanomey and Mathur (2001), Georgiev (2001), and Chan and Young (2006). https://doi.org/10.1016/j.resourpol.2019.101509 Received 29 May 2019; Received in revised form 27 September 2019; Accepted 30 September 2019 Available online 7 October 2019 0301-4207/© 2019 Elsevier Ltd. All rights reserved.
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Fig. 1. Time trend of precious metal prices. Notes: The figure displays the behavior of the selected precious metal price series across time (July 16, 1999–July 17, 2019).
returns and volatilities of precious metals such as gold, silver, platinum and palladium, making asymmetries in bidirectional (transmission and reception) spillovers an important subject of investigation (Bekiros et al., 2015). Our research study in this regard investigates the asym metric spillover dynamics between the returns and conditional volatil ities of four largely traded precious metal commodities, namely gold, silver, platinum and palladium. In doing so, we use an asymmetric version of the spillover index approach of Diebold and Yilmaz (2012) that is based on a generalized forecast error variance decomposition (FEVD) of vector autoregressions (VARs). We also use the frequency domain spillover measures of Barunik and Krehlik (2018). By combining the aforementioned spillover index frameworks with the asymmetries in returns and volatilities, we are able to simultaneously examine the time and frequency based spillovers among the selected precious metals. Our research study broadly links to those conducted by Hammoudeh et al. (2010), Sensoy (2013) and Batten et al. (2015). Hammoudeh et al. (2010) use a nonlinear version of a GARCH model to investigate the dependence and conditional volatility of precious metals (gold, silver, platinum, palladium) and find that platinum and palladium have the largest positive correlations, while gold and palladium have the weak est. Focusing on the same commodities, Sensoy (2013) identifies gold as the only commodity exerting contagion effects on all the others. Silver exerts contagion effects only on palladium and platinum. The study by
Batten et al. (2015) investigates the degree of interconnectedness be tween precious metals’ returns and volatilities across time. Their find ings indicate that silver acts as a source of spillovers during the 2008 global financial crisis (GFC) while platinum and palladium are spillover receivers in similar market conditions. Chen and Wu (2016), by applying an index methodology and dynamic conditional correlations (DCC) on energy, agricultural and livestock commodities, reveal stronger vola tility shocks (spillovers) between commodities of the same category or sector. The energy commodities are observed to exert the strongest in fluence on the rest. Apergis et al. (2017), using nonlinear cointegration tests and a threshold error correction model on biofuel and agricultural commodities (corn and sugar), identify long-term bidirectional asym metric spillovers between the volatilities and returns of those com modities. Other studies that broadly relate to ours in the measurement and analysis of spillover effects between various types of commodities have been conducted by Balli et al. (2019), Mensi et al. (2013), Abder ladi and Serra (2015), Antonakakis and Kizys (2015), Shahzad et al. (2019b) and Yaya et al. (2016). Compared to those studies ours has the comparative advantage of modelling asymmetric return and volatility behaviour under frequency domains. We, for the first time, study the time and frequency domain asym metric return and volatility spillovers among precious metals because these precious metals are often considered as alternative investment 2
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diversification, short-term investors (such as day traders or hedge funds) are concerned about the association at higher frequencies whereas the long-term investors (such as big institutional investors) focus on the lower frequency. These difference in investment time horizons and resulting time objectives help them formulate and manage their in vestments strategies. It is therefore important to not only cater for the asymmetries but also the investment horizons while analyzing the spillovers among precious metals. This study contributes to the relevant literature in different ways. Firstly, our study is the first to investigate the frequency domain asymmetric spillovers among the precious metal commodities consid ered. Secondly, we employ the cutting-edge methodologies of Diebold and Yilmaz (2012) and Barunik and Krehlik (2018) which are capable of accounting for asymmetric nonlinearities in the return distribution of the precious metal commodities under investigation. Thirdly, the data sample considered is large and as such provides a clear picture of changes in spillovers during different market conditions. Time varying asymmetric spillovers suggest similarities in response of precious metals to global and local fundamentals.3 Based on our empirical setting, we find that silver and gold display the largest transmission of net spill overs. Silver leads the spillover transmission at different trading hori zons, including the short-, medium- and long-run, and under different states of the economy (market downturns and upturns). The “silver- gold” and “palladium-platinum” pairs display the strongest directional connectedness. Silver and gold are mainly transmitters of spillovers, while palladium and platinum are mainly spillover receivers. Portfolio managers should take the asymmetric characteristics of the spillovers between the precious metal commodities considered when forecasting their future prices. Particular attention should be paid to
Table 1 Statistical properties of time series and correlation matrix. Gold
Silver
Platinum
Palladium
0.0218 19.518 12.358 1.8673 0.9116 11.506 16456.30*** 74.089*** 74.086*** 0.1523 5218
0.0169 14.417 18.678 1.4718 0.3769 18.459 52087.35*** 71.878*** 71.888*** 0.4493 5218
0.0291 26.689 15.253 2.0371 0.6878 12.498 20027.27*** 67.730*** 67.713*** 0.1427 5218
(a). Descriptive statistics Mean Minimum Maximum Std. Dev. Skewness Kurtosis J-B ADF PP KPSS No. of obs.
0.0330 9.8206 8.8872 1.0987 0.0903 9.7529 9921.54*** 72.561*** 72.562*** 0.2170 5218
(b). Correlation matrix Gold
1.0000
Silver
0.7685*** (86.738) 0.5299*** (45.126) 0.3890*** (30.494)
Platinum Palladium
1.0000 0.5424*** (46.628) 0.4583*** (37.237)
1.0000 0.5390*** (46.214)
1.0000
Notes: The abbreviations “Std. Dev.” and “J-B” stand for standard deviation and Jarque-Bera test of normality, respectively. The acronyms ADF, PP and KPSS refer to the empirical statistics of the augmented Dickey-Fuller (1979) test, the Phillips-Perron (1988) unit root test, and the Kwiatkowski et al. (1992) statio narity test, respectively. The symbols *** indicate rejection of the null hypoth esis of normality and unit root at 1% level of significance. The numbers in parenthesis refer to the t-statistics of the correlation significance. Table 2 The model estimates for conditional volatilities. Gold Silver Platinum Palladium
ω
α
β
γ
0.007*** (0.003) 0.015*** (0.002) 0.010** (0.004) 0.052* (0.028)
0.018 (0.015) 0.017 (0.011) 0.027*** (0.003) 0.063*** (0.016)
0.990*** (0.000) 0.994*** (0.000) 0.969*** (0.001) 0.927*** (0.021)
0.079*** (0.007) 0.099*** (0.011)
LogLik
AIC
BIC
7509.82
2.88
2.885
9968.79
3.8225
3.8275
9050.48
3.4701
3.4739
10710.6
4.1064
4.1102
Notes: This table reports the parameter estimates of the GARCH/EGARCH models to estimate the conditional volatilities. The standard errors are in brackets. The acronyms Loglik, AIC and BIC stand for log likelihood and the Akaike and Bayesian information criteria. The symbols ***, ** and * indicate significance at 1%, 5% and 10% level, respectively.
price movements of gold and silver as those most strongly spillover to others especially during stressed market scenarios. For policy makers, information about asymmetric spillovers among precious metals can provide an early warning sign of contagion for economies that heavily depend on exports of precious metal commodities.4 Specifically, in those types of economies pre-emptive measures could be taken to better deal with layoffs in the commodities’ underlying sectors during market downturns and due to strong sector asymmetric spillovers. The remainder of the paper is arranged as follows. Section 2 explains
vehicles to hedge traditional asset portfolios. In particular, gold and silver tend to perform well under uncertainty and during financial crisis periods, thus adding value through their inflation hedging property (Shahzad et al., 2019c). Indeed, it is during financial crisis periods where the risk hedging capacity of precious metals and their asymmetric spillover behaviour are more visible. These precious metals are impacted by economic and business cycles, financial crisis, central bank monetary policy and geo-political conflicts. In specific, these events have the potential of causing asymmetries, through uncertainty, in the connectedness between precious metals. Financial crises for instance are well-known sources of uncertainty that can lead to asymmetric spill overs between precious metal commodities. Monetary policy changes, through increases and decreases of interest rates, can instill in the financial and commodity markets the uncertainty that can lead to asymmetric spillovers between precious metals. The impact of economic and business cycles on asymmetric spillovers is usually evident in the downside, or at the end of the business cycles, which is commonly fol lowed by a recession. It is also interesting to note that the impact of economic and business cycles or market shocks produces heterogeneous frequency responses. From the perspective of hedging and
3 Our motivation for considering returns and volatilities of the precious metal commodities under consideration is that while returns define the ultimate reward of investors, volatility quantifies the risk of investors, thus being rele vant to investors when rebalancing their portfolios from one market to another (Garham and Nikkinen, 2011). 4 Some of these economies are, for instance, the largest exporters of gold (China, Canada, USA, Russia, Australia, South Africa), silver (Mexico, Peru, Russia, Poland), platinum (South Africa, UK, Russia, USA, Germany, Italy, Switzerland, Hong Kong, Japan), and palladium (South Africa, Russia, Zimbabwe, Canada, USA).
3
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Fig. 2. Conditional volatilities of precious metal returns. Notes: The figure displays the behavior of the conditional volatilities of the selected precious metal return series across time (July 17, 1999–July 17, 2019).
the methodology frameworks implemented. Section 3 justifies the selected precious metal commodities and the length of the sample. Section 4 explains and discusses the empirical results, and Section 5 concludes the analysis.
Suppose we have a certain number of assets N and a corresponding
vector of returns rt ¼ ðrt1 ; …; rtN Þ’ . Estimation of asymmetric spillovers firstly involves the decomposition of returns into positive and negative so that each subset can be used as a proxy for market scenarios on the upside and downside. Accordingly, a joint vector that accounts for
2. Methodological framework
þ positive and negative returns is rt ¼ ðrþ 1t ; …rNt ; r1t ; …rNt Þ . For the case of volatility spillovers the latter vector would consist of volatilities. A multidimensional weak stationary VAR(p) process for the forecast error variance decomposition is: ’
2.1. Standard generalized spillover approach In estimating the standard (i.e., non-asymmetric) spillovers we employ the spillover index of Diebold and Yilmaz (2012), which relies on forecast error variance decomposition (FEVD) of vector autore gressions (VARs). The FEVD enables the estimation of volatility and return spillovers by measuring the effect a certain variable j, subject to market innovations, has on the H-step-ahead FEV of another variable i.5
p X
rt ¼
(1)
Φi rt i þ εt ;
i¼1
Eq. (1) shows that forecasted returns are dependent on past returns Φi rt i and on values of the error term matrix εt eð0;Σε Þ. An expression of Eq. (1) that accounts for the invertible VAR process is: ∞ X
rt ¼
5
It should be pointed out that one of the limitations of the Diebold and Yilmaz (2012) spillover index model is that it only provides estimates of total spillovers between pairs of variables and does not provide estimates of direc tional spillovers between pairs. The generalized VAR of Koop et al. (1996) solves this problem by enabling a forecast error variance decomposition and correlated shocks the shocks to each variable are not orthogonalized.
(2)
Ai ε t i :
i¼0
Here Ai is a square matrix of coefficients estimated as Ai ¼
p P j¼1
Ai j Φj , for
Ao ¼ IN , for Ai ¼ 0 if i < 0. When calculating the total spillover index the 4
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variables’ cross-variance (cross-spillovers) is understood as the fraction of the H-step-ahead error variance in forecasting ith ðri ) according to shocks stemming from the jth variable, for i; j ¼ 1; 2; …; N. Hence, i 6¼ j must hold. An expression of the H-step-ahead generalized FEVD matrix θ is: �2 P σjj 1 Hh¼01 e’i Ah Σε ej ωHij ¼ P (3) � ; i; j; ¼ 1; :::; N; H 1 ’ ’ h¼0 ei Ah Σε Ah ei
PN PN ~g ~g i; j ¼ 1 θij ðHÞ i; j ¼ 1 θij ðHÞ i 6¼ j i 6¼ j ¼ Sg ðHÞ ¼ PN g ~ N i;j¼1 θij ðHÞ
(5)
Eq. (5) shows how shocks to returns or volatilities of a certain precious metal commodity spillover on those of all others. The direc tional spillovers between commodity pairs are computed according to the following expressions:
PN PN PN PN ~g ~g ~g ~g i; j ¼ 1 θij ðHÞ i; j ¼ 1 θij ðHÞ i; j ¼ 1 θji ðHÞ i; j ¼ 1 θji ðHÞ i 6¼ j i 6¼ j i¼ 6 j i 6¼ j and Sgi→j ðHÞ ¼ PN g Sgj→i ðHÞ ¼ PN g ¼ ¼ ~θ ðHÞ ~θ ðHÞ N N i;j¼1 ij i;j¼1 ji
The matrix Ah is defined as in Eq. (2), while Σε is a variance matrix of the error term εt from Eq. (1). The pamamter σjj accounts for the jth diagonal components of Σε , and ei and ej are selection vectors. Given that shocks for the processes of Eq. (1) are rarely orthogonal, the variance decomposition rows do not add up to 1 and normalization of all variance decomposition matrix components is required as follows:
ωHij
~ Hij
ω ¼ PN
j¼1
where,
N P j¼1
The above expressions measure the directional return or volatile spillovers transmitted or received by variables i (j) from j ðiÞ. Total net spillovers are obtained according to: Sgi ðHÞ ¼ Sgi→j
~H ω ij ¼ 1 and.
N P i;j¼1
~H ω ij ¼ N:
Sgij ðHÞ ¼
The total spillovers between variables are estimated as follows:
From (j) Silver
Platinum
Palladium
Contribution from others
Gold 49.32 Silver 28.22 Platinum 15.1 Palladium 9.19 Contribution to 52.51 others NET 1.82 (b). Volatility spillover From (j) To (i) Gold
29.24 47.59 15.87 12.94 58.05
13.92 14.09 53.38 17.72 45.73
7.53 10.1 15.65 60.14 33.28
0.89
6.57
50.69 52.41 46.62 39.85 Total spillover index: 47.39
Silver
Platinum
Palladium
Gold Silver Platinum Palladium Contribution to others NET
68.1 26.53 4.48 2.36 33.37
27 66.82 4.34 4.6 35.94
3.11 3.23 86.87 5.8 12.14
1.8 3.42 4.31 87.25 9.53
1.46
2.76
0.99
3.23
5.64
~θg ðHÞ ij
(8)
N
2.2. Frequency domain spillover approach
(a). Returns spillover Gold
g ~ θji ðHÞ
Eq. (8) accounts for the net return or volatility spillover effects of each variable on the returns and volatilities of other variables.
Table 3 Spillover table for N-dimensional VAR model.
To (i)
(7)
Sgj→i ðHÞ
Eq. (7) accounts for net volatility and return spillovers from com modity i to all other commodities j. The net pairwise spillovers result from the following rational matrix relationship:
(4)
ωHij
(6)
Frequency domain spillovers are estimated according to the method of Barunik and Krehlik (2018). This method can be seen as an extension of the spillover index method of Diebold and Yilmaz (2012) in the sense that spectral specifications of variance decompositions are incorporated in line with the approaches of Dew-becker and Giglio (2016) and Stiassny (1996). The frequency response function is a function of a pffiffiffiffiffiffi Fourier transform for the coefficients Ψ and for i ¼ 1 is: Ψ e
ihω
�
∞ X
e
¼
ihω
(9)
Ψh
h¼0
Contribution from others 31.91 33.18 13.13 12.76 Total spillover index: 22.75
where the term ω accounts for the frequency. The power spectrum of the variance distribution of Xt and GFEVD as a function of ω are respectively: SX ðωÞ ¼
∞ X
EðXt Xt h Þe
ihω
¼Ψ e
ihω
�
ΣΨ eihω
�
(10)
h¼0
P∞
2 ihω ÞΣÞij h¼0 ðΨðe ihω ÞΣΨ ðeihω ÞÞ ii h¼0 ðΨðe
σjj 1
Notes: These tables show the percentage of contribution to the forecast error variance of variable i coming from shocks to variable j using all the sample period. The column named “Contribution from others” are the sum of the per centage of contribution of each variable except the own variable. Similarly, the row named “Contribution to others” are the sum of the percentage of contri bution of each variable except the own variable. The total spillover index (expressed as a percentage) appears in the lower right corner of the table. This index is calculated as the sum of all the contributions in the “Contribution to others” column (or the sum of all the “Contribution to others” row) divided by the number of variables included in the model. The net directional spillover index is computed as the difference between the “Contribution from others” and the “Contribution to others” for each variable.
ðθðωÞÞij ¼ P∞
(11)
The parameter ðθðωÞÞij accounts for the frequency dependent varia tion effects on commodity i stemming from the shocks commodity j experiences. Eq. (11) can be standardized as follows: ðθðωÞÞij ð~ θðωÞÞij ¼ Pn h¼1 ðθðωÞÞij
(12)
And an estimate of the connectedness for a certain frequency interval d ¼ ða; bÞ is obtained as follows: 5
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Fig. 3. Total spillover of four precious metalsNotes: This figure displays the time-varying total return spillover index (Panel A) and the total volatility spillover index (Panel B) for the four precious metals (gold, silver, platinum and palladium) considered. They are computed using the approach of Diebold and Yilmaz (2012). These dynamic total spillover indices are calculated from the forecast error variance decompositions using a rolling window size of 500 days and a forecast horizon of H ¼ 100 days. The horizontal axis accounts for the time factor and the vertical axis for the total spillover levels. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
Z ð~θd Þij ¼
b
a
The net spillovers (i.e., within net connectedness) are calculated as the difference between transmission and reception of variance between pairs of commodities:
(13)
ð~ θðωÞÞij dω
The whole connectedness for a certain frequency interval d is esti mated as: Pn Pn ~ ~ ðθd Þii i¼1; i6¼j ðθd Þij d C ¼ P ¼1 (14) Pi¼1 ðθ~d Þ ðθ~d Þ ij
ij
ij
Cdi;net ¼ Cdi→⋅
Cdi;net
In Eq. (17) positive values of indicate greater variation or spillover transmission from commodity i to others than reception from them. The pairwise net spillovers for commodities i and j are obtained as:
ij
The closer C is to 1 the stronger the connectedness and spillovers between the returns (or volatilities) of commodities for a certain fre quency interval d. The spillovers received by a certain commodity i from all other j commodities (i.e., within from connectedness), for i 6¼ j and for a certain frequency interval d are calculated as: d
Cdi←⋅ ¼
n X
ð~ θd Þij
(17)
Cdi←⋅
Cdij ¼ ð~ θd Þji
(18)
ð~θd Þij
The spillover influence of a certain frequency interval d on the overall aggregate system of interdependence, in line with Krehlik and Barunik (2017) is calculated as:
(15)
(19)
~ d ¼ Cd ⋅ΓðdÞ C
j¼1; i6¼j
where ΓðdÞ represent the spectral weight and accounts for the spillover influence of a certain frequency interval d to the whole VAR system and is defined as:
On the other hand, the variation contribution or spillover effect of commodity i on all other j commodities (i.e., within to connectedness), for i 6¼ j and for a certain interval d is computed as: Cdi→⋅ ¼
n X
ð~ θd Þji
n X
(16)
ΓðdÞ ¼ ij¼1
j¼1; i6¼j
6
ð~ θd Þij
n .X ij¼1
ð~ θÞij ¼
n X ij¼1
ð~θd Þij
. n
(20)
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Fig. 4. Net directional spillover. Notes: This figure displays the time-varying net directional return and volatility spillovers for each of the four precious metal commodities across time. The dynamic net spillover indices are calculated by subtracting directional “to” spillovers from directional “from” spillovers. Positive (negative) values of spillovers indicate that the corresponding variable is a net transmitter (receiver) of spillover effects to all the other variables. The horizontal axis accounts for the time parameter and the vertical axis for the net directional spillover index.
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Table 4 Spillover table for 2N-dimensional VAR model with positive and negative components. (a). Returns spillover Rþ
Contribution from others
R
Gold
Silver
Palladium
Gold
Silver
Platinum
Palladium
Rþ
Gold Silver Platinum Palladium
47.23 23.5 11.15 4.99
24.44 45.41 10.5 8.35
9.2 8.48 55.07 10.08
3.88 6.22 8.82 59.83
5.84 4.82 2.98 2.14
4.45 5.83 2.79 2.75
3.12 3.37 5.86 4.18
1.83 2.36 2.83 7.68
46.92 48.75 39.07 32.49
R
Gold Silver Platinum Palladium Contribution to others
5.47 3.91 2.84 1.95 48.34
4.59 5.45 3.31 2.67 53.86
2.41 2.22 5.01 2.87 35.26
1.5 1.96 3.17 6.48 25.55
44.14 23.6 11.64 7.78 52.96
24.47 43.18 12.92 10.24 57.62
10.89 11.67 46.65 15.96 49.19
6.54 8.02 14.46 52.04 36.04
50.4 51.38 48.34 41.47 Total spillover index: 44.85
b). Volatility spillover Vþ
Contribution from others
V
Gold
Silver
Platinum
Palladium
Gold
Silver
Platinum
Palladium
Vþ
Gold Silver Platinum Palladium
57.11 20.53 2.72 1.42
21.03 55.84 2.93 2.8
2.04 1.96 83.01 3.1
1.01 1.91 2.77 79.48
9.89 6.07 0.91 1.14
5.44 9.5 0.92 1.01
2.85 2.66 5.64 2.03
0.63 1.53 1.09 9.03
33.00 34.66 11.34 11.5
V
Gold Silver Platinum Palladium Contribution to others
10.76 5.64 3.2 0.9 34.41
6.51 10.57 2.92 1.92 38.11
0.54 0.65 4.85 1.08 9.37
0.58 0.76 2.27 9.04 9.3
59.87 14.87 4.83 2.2 30.02
15.1 59.71 4.32 3.63 30.42
4.71 4.26 68.43 8.23 24.74
1.93 3.55 9.19 72.99 17.92
29.37 29.73 26.73 17.96 Total spillover index: 24.29
Notes: These tables display the spillover in relation to positive and negative return and volatility shocks. The abbreviations Rþ , R , V þ and V stand for positive and negative return and volatility shocks, respectively. See Table 3 for details.
2.3. Measuring asymmetric spillovers
is that it accounts for various economic and financial events of large scale among them most notably the global financial crisis of 2008 and the European sovereign debt crisis which cause uncertainty in the financial markets and a flight to safety for investors who sought for precious metals to hedge their financial positions. Fig. 1 depicts the time trend of precious metal prices from 1999 to 2019. As shown the prices of precious metals are generally in a trend of escalation from 2001 until the 2008. The effects of the 2008 global financial crisis and the Eurozone debt crisis are observed in all precious metal commodities. Gold prices show resilience in the wake of the 2008 global financial crisis, most likely due to its safe-haven attributes (see for example, Baur and Lucey (2010), Baur and McDermot (2010) and Omane-Adjepong and Boako (2017)), while platinum prices sharply plummet during that crisis event. This shows the positive response characteristic of gold to financial and economic shocks, as well as uncertainty. Between 2009 and 2011, the prices of all four precious metals sharply increase and, with the exception of palladium, undergo there after a trend of decline until 2016, when prices pick up slightly. Com modity prices may exhibit such tendencies of ‘all-rising’ or ‘all-falling’ if there is a relationship between them as complements or substitutes in production or consumption. Commodities showing such price de velopments may also transmit idiosyncratic demand or supply shocks to one another. Despite this, commodity-specific shocks may not adequately explain broad co-movements across unrelated commodities (Pradhananga, 2016) that have been attributed to rises in their demand and supply (Kilian, 2009), financialization (see e.g., Jacks and Stuermer, 2018; Tang and Xiong, 2012), and price dynamics (Akram, 2009).6
The negative and positive returns of the time series are defined as: rþ t ¼ maxðrt ; 0Þ and rt ¼ minðrt ; 0Þ. The H-step-ahead GFEVD matrix Ω for a 2N-dimensional VAR is: �2 P σjj 1 Hh¼01 e’i Ah Σε ej ωHij ¼ P � ; i; j; ¼ 1; :::; 2N; (21) H 1 ’ ’ h¼0 ei Ah Σε Ah ei The asymmetric spillovers in the directional influence are expressed by the term “TO” which refers to transmission, as opposed to “FROM” which refers to reception or absorption of spillovers. The “TO” asym metric spillovers are obtained as the sum of values in the 2N � 2N spillover matrix, with the exception of the values in the diagonal matrix for i 6¼ j, and two diagonals in the N � N block sub-matrices (lower left and upper right), for ji jj 6¼ N. The directional asymmetric spillover from a certain commodity i to all others is obtained as: S
H 2N;i→�
¼ 100 �
2N 1 X ~ Hj;i ; i; j; ¼ 1; :::; 2N ω 2N
(22)
i¼1;i6¼j
ji jj6¼N
3. Data The data on which the spillover frameworks are implemented con sists of prices for daily tradable futures of silver, gold, platinum and palladium. The data sample spans from July 16, 1999 to July 17, 2019. The data is extracted from Thomson Reuters Datastream International. We select precious metals for the analysis of asymmetric spillovers because they have historically displayed, in the long run most notice ably, positive trends of appreciation relative to other commodities that have undergone more pronounced trends of appreciation and depreci ation. These precious metal commodities in particular have frequently been used to preserve wealth from inflation increases, and for hedging in market downturns. Our motivation for the length of the selected sample
6 Financialization implies that commodity prices are driven not only by fundamental factors, but by the rising importance of financial elements, in stitutions and the speculative behaviour of investors in commodity markets (Falkowski, 2011). Periods of turmoil in financial markets decrease the risk appetite of financial investors, leading them to close-out long positions in € € commodity markets (Oztek and Ocal, 2017).
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Fig. 5. Spillover asymmetry measure - S A M Notes: The figure displays the asymmetric spillovers for return and volatilities of the four precious metal commodities across time. The horizontal axis accounts for the time parameter, and the vertical axis for percentages of spillovers.
Table 1 reports the statistical properties and correlation matrix of the precious metals’ returns. Gold, palladium and silver respectively have the highest average returns whereas platinum has the lowest. Palladium and silver have the highest standard deviations, respectively. Except for platinum, precious metal returns show negative skewness indicating a higher frequency of negative returns. All the series exhibit excess kur tosis indicating frequent extreme observations. The Jarque-Bera test indicates that the returns are not normally distributed. Both the augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) tests (Phillips and Perron, 1988) show that the returns series are stationarity. The precious metals display a significant positive correlation with each other. The significant positive association among commodities could be attributed to the financialization of commodities. The prices of commodities are likely to co-jump if commodity futures are traded based on herd-behaviour but not based on respective market fundamentals. The herding behaviour could usher asset prices not to show substantial deviation from the overall market (Demirer et al., 2015). Table 2 indicates that the volatility dynamics of the commodity se ries are captured best by the EGARCH model with normal distribution. Model parameters are chosen by minimizing the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) values. The results show that average returns of the series record highly persistent volatilities as depicted by the ARCH and GARCH parameters. Evidence of leverage effects is found for gold and silver, positing that their re sponses to informational shocks during the sample period are
asymmetric. Fig. 2 shows the conditional volatilities of the precious metal returns and also highlights the significant impact of the global financial crisis on their price developments. 4. Empirical findings 4.1. Full sample returns and volatility spillover Table 3 displays the full sample symmetric return and volatility spillovers among precious metals. In this spillover table, the percentages of contribution coming from shocks to variable j to the forecast error variance of variable i are reported. The sum of contribution percentages, except own, are shown under the column and row name “Contribution from others” and “Contribution to others”, respectively. The lowest right corner of the table reports the total spillover index (expressed as a percentage). The difference between the “Contribution from others” and “Contribution to others”, for each variable, are named as net directional spillover. The results indicate that silver exerts the largest return spillovers (58.1%) to other precious metals, followed by gold (52.5%). The smallest return spillovers are exerted by platinum (45.7%) and palla dium (33.3%). The largest bidirectional spillovers occur between silvergold and palladium-platinum, implying a stronger interdependence between those pairs. Overall, the spillovers of the volatilities are similar to those of the returns, although smaller in size. These results are similar 9
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Table 5 Frequency domain return spillover table for 2N-dimensional VAR model with positive and negative components. (a). Short-run spillover (1–5 days) Rþ
Contribution from others
R
Gold
Silver
Platinum
Palladium
Gold
Silver
Platinum
Palladium
Rþ
Gold Silver Platinum Palladium
38.89 19.38 8.9 4
20.64 37.53 8.68 6.69
7.81 7.27 44.84 7.7
3.4 5.28 7.13 48.64
4.35 3.75 2.27 1.5
3.11 4.39 2 1.89
2.23 2.6 4.69 2.93
1.33 1.77 2.13 5.63
38.52 40.05 31.11 24.71
R
Gold Silver Platinum Palladium Contribution to others
3.72 2.67 1.93 1.29 38.17
3.34 3.85 2.38 1.81 43.54
1.69 1.61 3.9 1.94 28.02
1.07 1.29 2.11 4.72 20.28
35.75 19.11 9.25 6.26 42.14
19.11 34.42 9.77 7.39 43.27
8.85 9.35 36.85 12.36 38.32
5.27 6.28 11.12 40.62 27.9
39.33 40.31 36.56 31.05 Total spillover index: 35.21
(b). Medium-run spillover (6–90 days) Rþ
Contribution from others
R
Gold
Platinum
Palladium
Gold
Silver
Platinum
Palladium
Rþ
Gold Silver Platinum Palladium
9.03 4.56 2.43 1.25
4.3 8.51 2.08 1.75
1.95 1.68 10.49 2.07
0.65 1.07 1.69 12.59
0.54 0.39 0.27 0.24
0.36 0.34 0.35 0.41
0.27 0.3 0.62 0.54
0.18 0.24 0.39 1.05
7.71 8.24 7.21 6.26
R
Gold Silver Platinum Palladium Contribution to others
0.67 0.4 0.4 0.3 9.34
0.48 0.42 0.43 0.4 9.44
0.29 0.26 0.56 0.42 6.67
0.2 0.36 0.53 0.96 4.50
8.89 4.85 2.6 1.63 9.98
5.56 9.47 3.29 2.59 12.56
2.45 2.58 10.09 4.07 10.21
1.55 1.93 3.59 11.98 7.88
10.53 10.38 10.84 9.41 Total spillover index: 8.82
c). Long-run spillover (more than 90 days) Rþ
Contribution from others
R
Gold
Silver
Palladium
Gold
Silver
Platinum
Palladium
Rþ
Gold Silver Platinum Palladium
0.5 0.26 0.14 0.07
0.24 0.48 0.12 0.1
0.11 0.09 0.59 0.12
0.04 0.06 0.09 0.71
0.03 0.02 0.01 0.01
0.02 0.02 0.02 0.02
0.01 0.02 0.03 0.03
0.01 0.01 0.02 0.06
0.43 0.46 0.4 0.35
R
Gold Silver Platinum Palladium Contribution to others
0.04 0.02 0.02 0.02 0.53
0.03 0.02 0.02 0.02 0.53
0.02 0.01 0.03 0.02 0.37
0.01 0.02 0.03 0.05 0.25
0.5 0.27 0.15 0.09 0.55
0.32 0.54 0.19 0.15 0.72
0.14 0.15 0.57 0.23 0.58
0.09 0.11 0.21 0.68 0.45
0.61 0.58 0.62 0.53 Total spillover index: 0.50
Notes: These tables display the spillover in relation to positive and negative return and volatility shocks. The abbreviations Rþ , R , V þ and V stand for positive and negative return and volatility shocks, respectively. See Table 3 for details.
to those found in Batten et al. (2015). The net return and volatility spillover values are positive for gold and silver, whereas those for palladium and platinum are negative. The total return and volatility spillovers among all four metals are 47.39 and 22.75, respectively. We also observe that silver and gold share the strongest relationship as gold accounts for 28.2% of forecast error variations of silver returns, and silver accounts for 29.2% of forecast error variations in gold returns. This strength of interdependence between gold and silver is also found in Batten et al. (2015).
undergoes a relatively even path and do not show any significant trend of increase (decrease) up until 2007. Spillovers after the sharp decline in 2007 sharply increase in the short-term moving from around 48%–52% towards the end of 2012. This period of fluctuations underlies the effects the 2008 global financial crisis and the Eurozone sovereign debt crisis had on the prices of all precious metal commodities. From 2013 to the end of the first quarter of 2015 the total spillover index sharply declines. This high degree of integration between the precious metal commod ities’ returns could be attributed to an overall global drop in commodity prices due to a strengthening of the US dollar and concerns over China’s faltering growth. Specifically, by September 2014 the global oil market fell 1.7% to $96.6 a barrel, and the excess commodity index fell to a five year low of 118.2 points. The total volatility spillover index, as shown in panel (b) of the figure, displays similar behaviour. In Fig. 4, gold and silver are net return spillover transmitters, while palladium is a net spillover receiver. For volatilities silver appears as net spillover transmitter, whereas palladium is a spillover receiver. Gold and platinum generally remain balanced in terms of net volatility spillover transmission and reception.
4.2. Rolling window based returns and volatilities spillover Fig. 3a and b displays the total volatility and return spillovers7 estimated according to the spillover index of Diebold and Yilmaz (2012). The horizontal axis accounts for the time factor and the vertical axis for the total spillover levels. The total return spillover index oscillates be tween 20% and 28% from 2001 to mid-2004, with the peak occurring at late 2002. From late 2003 total return spillovers undergo a steady in crease to reach a peak error variance of 57% in mid-2005 after which it
4.3. Asymmetric returns and volatility spillover analysis
7
Total spillover indices are calculated using a rolling window size of 500 days and a forecast horizon of H ¼ 100 days.
Table 4 displays the spillovers that account for the cumulative sum of 10
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Table 6 Frequency domain volatility spillover table for 2N-dimensional VAR model with positive and negative components. (a). Short-run spillover (1–5 days) Vþ
Contribution from others
V
Vþ
Gold Silver Platinum Palladium
Gold 45.09 15.93 1.77 1.09
Silver 16.47 43.23 2.02 2.1
1.16 1.36 65.71 1.85
Palladium 0.79 1.5 1.96 62.76
Gold 8.77 5.48 0.85 1.04
Silver 4.91 8.32 0.7 0.81
Platinum 2.4 2.18 4.7 1.67
Palladium 0.55 1.36 0.87 7.35
26.28 27.81 8.17 8.56
V
Gold Silver Platinum Palladium Contribution to others
9.82 5.07 2.77 0.73 27.36
5.86 9.55 2.48 1.69 30.62
0.45 0.53 4.23 0.82 6.17
0.51 0.62 1.79 8.02 7.17
46.6 11.15 3.44 1.13 23.09
11.14 44.02 3.37 2.36 23.29
3.42 3.14 40.04 3.83 16.64
1.08 2.1 3.46 43.01 9.42
22.46 22.61 17.31 10.56 Total spillover index: 17.97
(b). Medium-run spillover (6–90 days) Vþ
Contribution from others
V
Gold
Silver
Palladium
Gold
Silver
Platinum
Palladium
Vþ
Gold Silver Platinum Palladium
11.35 4.34 0.89 0.31
4.29 11.9 0.85 0.66
0.83 0.56 16.35 1.17
0.21 0.38 0.76 15.8
1.08 0.57 0.07 0.09
0.52 1.13 0.21 0.19
0.43 0.46 0.91 0.35
0.09 0.17 0.22 1.61
6.37 6.48 3 2.77
V
Gold Silver Platinum Palladium Contribution to others
0.92 0.56 0.43 0.17 6.7
0.64 1.0 0.43 0.24 7.11
0.09 0.11 0.61 0.26 3.02
0.07 0.14 0.46 1.02 2.02
12.45 3.47 1.25 0.96 6.41
3.7 14.72 0.88 1.17 6.67
1.18 1.04 26.07 3.96 7.42
0.77 1.32 5.14 27.53 7.71
6.45 6.64 8.59 6.76 Total spillover index: 5.88
c). Long-run spillover (more than 90 days) Vþ
Contribution from others
V
Gold
Silver
Palladium
Gold
Silver
Platinum
Palladium
Vþ
Gold Silver Platinum Palladium
0.68 0.27 0.06 0.02
0.27 0.71 0.05 0.04
0.05 0.04 0.95 0.08
0.02 0.03 0.05 0.92
0.04 0.02 0 0
0.02 0.05 0.01 0.01
0.02 0.02 0.03 0.01
0 0 0.01 0.07
0.38 0.38 0.18 0.16
V
Gold Silver Platinum Palladium Contribution to others
0.02 0.01 0 0 0.36
0.01 0.02 0.01 0 0.38
0 0 0 0 0.17
0 0 0.02 0.01 0.12
0.81 0.25 0.14 0.11 0.52
0.26 0.97 0.07 0.1 0.47
0.1 0.08 2.32 0.45 0.68
0.08 0.13 0.6 2.45 0.82
0.45 0.47 0.84 0.66 Total spillover index: 0.44
Notes: These tables display the spillover in relation to positive and negative return and volatility shocks. The abbreviations Rþ , R , V þ and V stand for positive and negative return and volatility shocks, respectively. See Table 3 for details.
negative and positive shocks. Cumulative positive and negative shocks are estimated according to Hatemi-j (2012). In simple terms, positive returns shocks (Rþ) or positive volatility shocks (Vþ) capture spillovers due to positive changes in the markets. The reverse is true for R- and V-. Accordingly, gold and silver are the largest transmitters and receivers of negative and positive volatility and return spillovers. Larger negative shocks (bad news) on the precious metals markets are observed to cause larger return and volatility spillover effects, as opposed to large positive shocks (good news). All commodities spillover positively and negatively on each other. Silver and palladium display noticeable spillover transmission and reception. Their spillovers, moreover, are time varying and nonhomogenous. The spillovers between each individual commodity and their aggregates are characterized by extreme net positions. This phe nomenon is more pronounced in the volatility spillovers than the return spillovers. Fig. 5 displays the aggregate asymmetric volatility and return spill overs of the four precious metals under consideration. They are esti mated as the variance between the spillover indices of the metal pairs with cumulative positive and negative shocks. Returns and volatilities with positive (negative) innovations are termed as good (bad), along with Barunik et al. (2017), Patton and Sheppard (2015), and Segal et al. (2015).
Negative values of the asymmetric return spillovers suggest that total spillovers among precious metals are higher for negative returns compared to positive returns. The asymmetric return spillovers reach their highest values during the last two quarters of 2007 and the second quarter of 2008. This asymmetric effect between commodity returns during that period may be traced to the beginning of the turmoil phase of the 2008 global financial crisis.8 Another trend of increasing asymmetric return spillovers is observed from 2010 to the end of the fourth quarter of 2014, where the largest values are reached. This asymmetric influ ence between precious metal commodity returns is coherent with the increasing uncertainty caused by the Eurozone sovereign debt crisis, as investors relied on precious metals to hedge against economic and geopolitical uncertainty within the region. The total asymmetric volatility spillovers (assuming positive in novations) react differently relative to the return spillovers (having negative innovations). The index’s positive values imply that the
8 The large asymmetric spillovers during late 2007 and the first two quarters of 2008 are partially due to the stock market volatility caused by the turmoil of the GFC. From a macroeconomic perspective this reflects the monetary policy responses of the US Fed during the crisis. This also corroborates the conclusion of Hammoudeh et al. (2010) that monetary shocks are sensitive to metals such as gold and silver.
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Fig. 6. Frequency domain asymmetric spillovers - S A M . Notes: This figure depicts the time-frequency dynamics of the total return connectedness (Panel A) and the total volatility connectedness (Panel B) among the four precious metals considered. They are computed using the method of Barunik and Krehlik (2018). The figures in the top show the connectedness at the higher frequency band, which corresponds to movements up to five days (one week). The figures in the middle display the connectedness at the medium frequency band, which corresponds to movements from six to ninety days (approximately three months). The figures in the lower part show the connectedness for the low frequency band, which corresponds to more than ninety days. These dynamic total connectedness measures are computed using a rolling window size of 500 days and a forecast horizon of H ¼ 100 days, although the time-frequency connectedness method of Barunik and Krehlik (2018) is not influenced by the particular forecast horizon.
spillovers among precious metals are higher for increases in volatility. The largest trend of increasing asymmetric volatility spillover occurs during 2008-09, 2010–11 and 2014, being highest in 2010. This specific asymmetric effect could be linked to negative shocks. All in all, we conclude that negative return (Fig. 5a) and bad volatility (Fig. 5b) spillovers between precious metals dominate positive return and good volatility spillovers.
aggregate asymmetric return and volatility spillovers for the short-term (1–5 days), medium-term (5–90 days) and long-term (more than 90 days). In the short-term gold and silver exert and receive the largest net return spillovers to and from platinum and palladium most noticeably. Silver overall, followed by gold, exerts the strongest asymmetric influ ence in the short and medium terms, for both positive and negative shocks. We also observe that asymmetric spillovers for positive returns (positive components) are stronger than those for negative returns (negative components), indicating a stronger effect on the upside than on the downside, from leading metal commodities such as silver and gold. Also, as in the previously discussed spillover measures, gold and
4.4. Frequency domain asymmetric spillover analysis Tables 5 and 6 show the values corresponding to individual and 12
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silver most strongly influence each other for both positive and negative components and for the short-term and medium-term. The short- and medium-term asymmetric spillovers for both positive and negative components are clearly bigger than those in the long-term. The asymmetric spillovers based on volatilities for positive and negative components are consistent with those based on returns in general. Silver appears to lead the asymmetric spillovers for negative and positive return scenarios and in short and medium run, followed by gold. Gold and silver are net transmitters of spillovers, while platinum and palladium are spillover receivers. Lastly, Fig. 6 displays the frequency domain asymmetric spillover indexes. It is clear from those figures that spillovers from negative return shocks (also bad volatility) are more profound compared to positive return (good volatility) shocks. Also, these spillovers are higher in the short- to medium-term. Collectively, we can conclude that precious metals are no different than traditional asset classes in terms of risk and return spillovers and that panic drives the contagion effect.
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Jumping hedges: an examination of movements in copper spot and futures markets. J. Futures Mark. 26 (2), 169–188. Chen, S., Wu, X., 2016. Comovements and Volatility Spillover in Commodity Market. Agricultural & Applied Economics Association Annual Meeting, Boston, Massachusetts. July 31-August 2. Demirer, R., Lee, H.T., Lien, D., 2015. Does the stock market drive herd behavior in commodity futures markets? Int. Rev. Financ. Anal. 39, 32–44. Dew-becker, I., Giglio, S., 2016. Asset pricing in the frequency domain: theory and empirics. Rev. Financ. Stud. 29 (8), 2029–2068. Dickey, D.A., Fuller, W.A., 1979. Distribution of the estimators for autoregressive time series with a unit root. J. Am. Stat. Assoc. 74 (366a), 427–431. Diebold, F.X., Yilmaz, K., 2012. Better to give than to receive: predictive directional measurement of volatility spillovers. Int. J. Forecast. 28 (1), 57–66. Falkowski, M., 2011. Financialization of commodities. Contemp. Econ. 5 (4), 4–17. Graham, M., Nikkinen, J., 2011. Co-movement of the Finnish and international stock markets: a wavelet analysis. Eur. J. Financ. 17 (5-6), 409–425. Georgiev, G., 2001. Benefits of commodity investment. J. Altern. Investments 4 (1), 40–48. Hamilton, J.D., 2011. Nonlinearities and the macroeconomic effects of oil prices. Macroecon. Dyn. 15 (S3), 364–378. Hammoudeh, S.M., Yuan, Y., McAleer, M., Thompson, M.A., 2010. Precious metals–exchange rate volatility transmissions and hedging strategies. Int. Rev. Econ. Financ. 19 (4), 633–647. Hatemi-j, A., 2012. Asymmetric causality tests with an application. Empir. Econ. 43 (1), 447–456. Jacks, D.S., Stuermer, M., 2018. What drives commodity price booms and busts? Energy Econ. https://doi.org/10.1016/j.eneco.2018.05.023. Kilian, L., 2009. Not all oil price shocks are alike: disentangling demand and supply shocks in the crude oil market. Am. Econ. Rev. 99 (3), 1053–1069. Koop, G., Pesaran, M.H., Potter, S.M., 1996. Impulse response analysis in nonlinear multivariate models. J. Econom. 74 (1), 119–147. K�rehlík, T., Baruník, J., 2017. Cyclical properties of supply-side and demand-side shocks in oil-based commodity markets. Energy Econ. 65, 208–218. Kwiatkowski, D., Phillips, P.C., Schmidt, P., Shin, Y., 1992. Testing the null hypothesis of stationarity against the alternative of a unit root: how sure are we that economic time series have a unit root? J. Econom. 54 (1-3), 159–178. Mensi, W., Beljid, M., Boubaker, A., Managi, S., 2013. Correlations and volatility spillovers across commodity and stock markets: linking energies, food, and gold. Econ. Modell. 32, 15–22. Nguyen, D.K., Sousa, R.M., Uddin, G.S., 2015. Testing for asymmetric causality between US equity returns and commodity futures returns. Financ. Res. Lett. 12, 38–47. Omane-Adjepong, M., Boako, G., 2017. Long-range dependence in returns and volatility of global gold market amid financial crises. Phys. A Stat. Mech. 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5. Conclusion Asymmetric spillovers among return and volatilities of commodities and financial markets are a problem for portfolio and risk managers. Policy makers should also be concerned because of the risk asymmetric spillovers pose to public sector resource allocation. In this study, aware of the peculiar risks that asymmetric spillovers entail, we measure and examine the time and frequency domain spillovers among four precious metals, namely, silver, gold, palladium and platinum. We draw our empirical results by implementing the spillover index of Diebold and Yilmaz (2012) and the frequency domain spillover measures of Barunik and Krehlik (2018). Our results indicate that the asymmetric spillovers between the volatilities and returns of the precious metals considered are time varying. Negative and positive shocks cause the asymmetric spillovers and are more pronounced in times of financial turmoil. The largest transmission of net spillovers is exerted by gold and silver. Silver in the short and long runs and in good and bad market conditions leads the spillover transmission. The pairs silver-gold and palladium-platinum display the largest directional spillovers. Also, while palladium and platinum act mainly as spillover receivers, gold and silver act mainly as transmitters of spillovers. Portfolio and investment managers should bear in mind the char acteristics of asymmetric spillovers among the precious metals when rebalancing their portfolios and forecasting future prices of commod ities. Policy makers’ understanding of asymmetric spillovers between precious metal commodities would enable them to adequately allocate the resources, particularly during market downturns and for economies that heavily depend on exports of these metal commodities. Resourcebased economies, specifically, could consider preemptive measures to better deal with layoffs in the commodities’ underlying sectors due to strong and asymmetric spillover influence between sectors during market downturns. Furthermore, policy makers, through stronger in vestment concentration in negatively correlated sectors, or by gradually reshaping the structure of the economy, can increase the diversification of the economy and reduce the impact of distressed resources sectors on the overall economy. Acknowledgements: Earlier version of this paper was presented at the 2018 African Re view of Economics and Finance Conference under the “Modelling Asset Prices and Returns” session, South Africa. Gazi S. Uddin is thankful for the financial support provided by the Jan Wallander and Tom Hedelius Foundations (Ref. W2016:0364:1), Sweden.
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Shahzad, S.J.H., Bouri, E., Roubaud, D., Kristoufek, L., 2019. Safe haven, hedge and diversification for G7 stock markets: gold versus bitcoin. Econ. Modell. https://doi. org/10.1016/j.econmod.2019.07.023. Shahzad, S.J.H., Rehman, M.U., Jammazi, R., 2019. Spillovers from oil to precious metals: quantile approaches. Resour. Policy 61, 508–521. Shahzad, S.J.H., Mensi, W., Hammoudeh, S., Sohail, A., Al-Yahyaee, K.H., 2019. Does gold act as a hedge against different nuances of inflation? Evidence from Quantileon-Quantile and causality-in-quantiles approaches. Resour. Policy 62, 602–615. Stiassny, A., 1996. A spectral decomposition for structural VAR models. Empir. Econ. 21, 535–555.
Tang, K., Xiong, W., 2012. Index investment and the financialization of commodities. Financ. Anal. J. 68 (6), 54–74. Uchezuba, I.D., Jooste, A., Willemse, J., 2010. Measuring asymmetric price and volatility spillover in the South African broiler market. In: AAAE Third Conference/AEASA 48th Conference. Yaya, O.S., Tumala, M.M., Udomboso, C.G., 2016. Volatility persistence and returns spillovers between oil and gold prices: analysis before and after the global financial crisis. Resour. Policy 49, 273–281.
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Heterogeneous interconnections between precious metals: Evidence from asymmetric and frequency-domain spillover analysis Gazi Salah Uddin a, Syed Jawad Hussain Shahzad b, c, *, Gideon Boako d, Jose Areola Hernandez e, Brian M. Lucey f a
Department of Management and Engineering, Link€ oping University, Link€ oping, Sweden Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Viet Nam Faculty of Finance and Banking, Ton Duc Thang University, Ho Chi Minh City, Viet Nam d Office of the Vice President, Ghana e ESC Rennes School of Business, Rennes, Brittany, France f Trinity Business School, Trinity College, Dublin, Ireland b c
A R T I C L E I N F O
A B S T R A C T
JEL classification: C12 C58 Q02 L61
We examine the spillover characteristics of returns and volatilities of precious metals: gold, silver, platinum and palladium. We find evidence of homogenous and time varying asymmetric spillovers between the returns and volatilities of the precious metals suggesting similarities in their cyclical relationship with global and local fundamentals. Negative and positive shocks cause the asymmetric spillovers and are more pronounced in times of financial turmoil. The largest transmission of net spillovers is exerted by gold and silver. Silver in the short and long runs and in good and bad market conditions leads the spillover transmission. The pairs silver-gold and palladium-platinum display the largest directional spillovers. Lastly, while palladium and platinum act mainly as spillover receivers, gold and silver act mainly as transmitters of spillovers. Implications of the results are discussed.
Keywords: Precious metals Risk spillovers Asymmetries Frequency dynamics
1. Introduction Precious metals may serve as a store of value, barometer of risk, diversifier of asset portfolios and for economic development of countries depending heavily on precious metal exports (Batten et al., 2015). Accordingly, price changes in commodity markets do affect the income perception of multiple stakeholders (e.g. commodity-consuming and commodity-producing nations), while serving as indicators and pre dictors of economic performance (Hamilton, 2011; Jacks and Stuermer, 2018; Shahzad et al., 2019a). The relationship between price swings of commodities across various time periods and the economic performance of resource-based (i.e., precious metal-based) economies raises in policy makers, and in security portfolio and risk managers, a concern about the spillover effects of those commodities’ return and volatilities. This is
particularly so when determining economy sector resource allocation, fiscal and monetary policy and portfolio rebalancing (Uchezuba, 2010).1 This concern of policy makers and risk managers is difficult to address under different periods of uncertainty and crisis, and if the nature of the spillovers is asymmetric. Asymmetric spillovers, in specific, accentuate the transmission and reception of variation between precious metal commodities and their underlying sectors, making the determination of future prices more complex (Nguyen et al., 2015; Uchezuba, 2010). In the last two decades, diversification using precious metals has become an important approach for risk management and portfolio allocation due primarily to increasing contagion risk emanating from higher integration and interdependence among financial markets worldwide.2 The increasing financialization of commodity markets has opened possibilities for risk hedging that accounts for dynamics of
* Corresponding author. E-mail addresses: [email protected] (G.S. Uddin), [email protected] (S.J.H. Shahzad), [email protected] (G. Boako), [email protected] (J.A. Hernandez), [email protected] (B.M. Lucey). 1 See Jacks and Stuermer (2018). 2 Embracing a diversified portfolio might raise total earnings, decrease risk and enhance the sharp ratio (Batten et al., 2010). The risk-reducing attributes of commodities in a diversified portfolio of stocks and bonds have been well documented by Abanomey and Mathur (2001), Georgiev (2001), and Chan and Young (2006). https://doi.org/10.1016/j.resourpol.2019.101509 Received 29 May 2019; Received in revised form 27 September 2019; Accepted 30 September 2019 Available online 7 October 2019 0301-4207/© 2019 Elsevier Ltd. All rights reserved.
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Fig. 1. Time trend of precious metal prices. Notes: The figure displays the behavior of the selected precious metal price series across time (July 16, 1999–July 17, 2019).
returns and volatilities of precious metals such as gold, silver, platinum and palladium, making asymmetries in bidirectional (transmission and reception) spillovers an important subject of investigation (Bekiros et al., 2015). Our research study in this regard investigates the asym metric spillover dynamics between the returns and conditional volatil ities of four largely traded precious metal commodities, namely gold, silver, platinum and palladium. In doing so, we use an asymmetric version of the spillover index approach of Diebold and Yilmaz (2012) that is based on a generalized forecast error variance decomposition (FEVD) of vector autoregressions (VARs). We also use the frequency domain spillover measures of Barunik and Krehlik (2018). By combining the aforementioned spillover index frameworks with the asymmetries in returns and volatilities, we are able to simultaneously examine the time and frequency based spillovers among the selected precious metals. Our research study broadly links to those conducted by Hammoudeh et al. (2010), Sensoy (2013) and Batten et al. (2015). Hammoudeh et al. (2010) use a nonlinear version of a GARCH model to investigate the dependence and conditional volatility of precious metals (gold, silver, platinum, palladium) and find that platinum and palladium have the largest positive correlations, while gold and palladium have the weak est. Focusing on the same commodities, Sensoy (2013) identifies gold as the only commodity exerting contagion effects on all the others. Silver exerts contagion effects only on palladium and platinum. The study by
Batten et al. (2015) investigates the degree of interconnectedness be tween precious metals’ returns and volatilities across time. Their find ings indicate that silver acts as a source of spillovers during the 2008 global financial crisis (GFC) while platinum and palladium are spillover receivers in similar market conditions. Chen and Wu (2016), by applying an index methodology and dynamic conditional correlations (DCC) on energy, agricultural and livestock commodities, reveal stronger vola tility shocks (spillovers) between commodities of the same category or sector. The energy commodities are observed to exert the strongest in fluence on the rest. Apergis et al. (2017), using nonlinear cointegration tests and a threshold error correction model on biofuel and agricultural commodities (corn and sugar), identify long-term bidirectional asym metric spillovers between the volatilities and returns of those com modities. Other studies that broadly relate to ours in the measurement and analysis of spillover effects between various types of commodities have been conducted by Balli et al. (2019), Mensi et al. (2013), Abder ladi and Serra (2015), Antonakakis and Kizys (2015), Shahzad et al. (2019b) and Yaya et al. (2016). Compared to those studies ours has the comparative advantage of modelling asymmetric return and volatility behaviour under frequency domains. We, for the first time, study the time and frequency domain asym metric return and volatility spillovers among precious metals because these precious metals are often considered as alternative investment 2
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diversification, short-term investors (such as day traders or hedge funds) are concerned about the association at higher frequencies whereas the long-term investors (such as big institutional investors) focus on the lower frequency. These difference in investment time horizons and resulting time objectives help them formulate and manage their in vestments strategies. It is therefore important to not only cater for the asymmetries but also the investment horizons while analyzing the spillovers among precious metals. This study contributes to the relevant literature in different ways. Firstly, our study is the first to investigate the frequency domain asymmetric spillovers among the precious metal commodities consid ered. Secondly, we employ the cutting-edge methodologies of Diebold and Yilmaz (2012) and Barunik and Krehlik (2018) which are capable of accounting for asymmetric nonlinearities in the return distribution of the precious metal commodities under investigation. Thirdly, the data sample considered is large and as such provides a clear picture of changes in spillovers during different market conditions. Time varying asymmetric spillovers suggest similarities in response of precious metals to global and local fundamentals.3 Based on our empirical setting, we find that silver and gold display the largest transmission of net spill overs. Silver leads the spillover transmission at different trading hori zons, including the short-, medium- and long-run, and under different states of the economy (market downturns and upturns). The “silver- gold” and “palladium-platinum” pairs display the strongest directional connectedness. Silver and gold are mainly transmitters of spillovers, while palladium and platinum are mainly spillover receivers. Portfolio managers should take the asymmetric characteristics of the spillovers between the precious metal commodities considered when forecasting their future prices. Particular attention should be paid to
Table 1 Statistical properties of time series and correlation matrix. Gold
Silver
Platinum
Palladium
0.0218 19.518 12.358 1.8673 0.9116 11.506 16456.30*** 74.089*** 74.086*** 0.1523 5218
0.0169 14.417 18.678 1.4718 0.3769 18.459 52087.35*** 71.878*** 71.888*** 0.4493 5218
0.0291 26.689 15.253 2.0371 0.6878 12.498 20027.27*** 67.730*** 67.713*** 0.1427 5218
(a). Descriptive statistics Mean Minimum Maximum Std. Dev. Skewness Kurtosis J-B ADF PP KPSS No. of obs.
0.0330 9.8206 8.8872 1.0987 0.0903 9.7529 9921.54*** 72.561*** 72.562*** 0.2170 5218
(b). Correlation matrix Gold
1.0000
Silver
0.7685*** (86.738) 0.5299*** (45.126) 0.3890*** (30.494)
Platinum Palladium
1.0000 0.5424*** (46.628) 0.4583*** (37.237)
1.0000 0.5390*** (46.214)
1.0000
Notes: The abbreviations “Std. Dev.” and “J-B” stand for standard deviation and Jarque-Bera test of normality, respectively. The acronyms ADF, PP and KPSS refer to the empirical statistics of the augmented Dickey-Fuller (1979) test, the Phillips-Perron (1988) unit root test, and the Kwiatkowski et al. (1992) statio narity test, respectively. The symbols *** indicate rejection of the null hypoth esis of normality and unit root at 1% level of significance. The numbers in parenthesis refer to the t-statistics of the correlation significance. Table 2 The model estimates for conditional volatilities. Gold Silver Platinum Palladium
ω
α
β
γ
0.007*** (0.003) 0.015*** (0.002) 0.010** (0.004) 0.052* (0.028)
0.018 (0.015) 0.017 (0.011) 0.027*** (0.003) 0.063*** (0.016)
0.990*** (0.000) 0.994*** (0.000) 0.969*** (0.001) 0.927*** (0.021)
0.079*** (0.007) 0.099*** (0.011)
LogLik
AIC
BIC
7509.82
2.88
2.885
9968.79
3.8225
3.8275
9050.48
3.4701
3.4739
10710.6
4.1064
4.1102
Notes: This table reports the parameter estimates of the GARCH/EGARCH models to estimate the conditional volatilities. The standard errors are in brackets. The acronyms Loglik, AIC and BIC stand for log likelihood and the Akaike and Bayesian information criteria. The symbols ***, ** and * indicate significance at 1%, 5% and 10% level, respectively.
price movements of gold and silver as those most strongly spillover to others especially during stressed market scenarios. For policy makers, information about asymmetric spillovers among precious metals can provide an early warning sign of contagion for economies that heavily depend on exports of precious metal commodities.4 Specifically, in those types of economies pre-emptive measures could be taken to better deal with layoffs in the commodities’ underlying sectors during market downturns and due to strong sector asymmetric spillovers. The remainder of the paper is arranged as follows. Section 2 explains
vehicles to hedge traditional asset portfolios. In particular, gold and silver tend to perform well under uncertainty and during financial crisis periods, thus adding value through their inflation hedging property (Shahzad et al., 2019c). Indeed, it is during financial crisis periods where the risk hedging capacity of precious metals and their asymmetric spillover behaviour are more visible. These precious metals are impacted by economic and business cycles, financial crisis, central bank monetary policy and geo-political conflicts. In specific, these events have the potential of causing asymmetries, through uncertainty, in the connectedness between precious metals. Financial crises for instance are well-known sources of uncertainty that can lead to asymmetric spill overs between precious metal commodities. Monetary policy changes, through increases and decreases of interest rates, can instill in the financial and commodity markets the uncertainty that can lead to asymmetric spillovers between precious metals. The impact of economic and business cycles on asymmetric spillovers is usually evident in the downside, or at the end of the business cycles, which is commonly fol lowed by a recession. It is also interesting to note that the impact of economic and business cycles or market shocks produces heterogeneous frequency responses. From the perspective of hedging and
3 Our motivation for considering returns and volatilities of the precious metal commodities under consideration is that while returns define the ultimate reward of investors, volatility quantifies the risk of investors, thus being rele vant to investors when rebalancing their portfolios from one market to another (Garham and Nikkinen, 2011). 4 Some of these economies are, for instance, the largest exporters of gold (China, Canada, USA, Russia, Australia, South Africa), silver (Mexico, Peru, Russia, Poland), platinum (South Africa, UK, Russia, USA, Germany, Italy, Switzerland, Hong Kong, Japan), and palladium (South Africa, Russia, Zimbabwe, Canada, USA).
3
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Fig. 2. Conditional volatilities of precious metal returns. Notes: The figure displays the behavior of the conditional volatilities of the selected precious metal return series across time (July 17, 1999–July 17, 2019).
the methodology frameworks implemented. Section 3 justifies the selected precious metal commodities and the length of the sample. Section 4 explains and discusses the empirical results, and Section 5 concludes the analysis.
Suppose we have a certain number of assets N and a corresponding
vector of returns rt ¼ ðrt1 ; …; rtN Þ’ . Estimation of asymmetric spillovers firstly involves the decomposition of returns into positive and negative so that each subset can be used as a proxy for market scenarios on the upside and downside. Accordingly, a joint vector that accounts for
2. Methodological framework
þ positive and negative returns is rt ¼ ðrþ 1t ; …rNt ; r1t ; …rNt Þ . For the case of volatility spillovers the latter vector would consist of volatilities. A multidimensional weak stationary VAR(p) process for the forecast error variance decomposition is: ’
2.1. Standard generalized spillover approach In estimating the standard (i.e., non-asymmetric) spillovers we employ the spillover index of Diebold and Yilmaz (2012), which relies on forecast error variance decomposition (FEVD) of vector autore gressions (VARs). The FEVD enables the estimation of volatility and return spillovers by measuring the effect a certain variable j, subject to market innovations, has on the H-step-ahead FEV of another variable i.5
p X
rt ¼
(1)
Φi rt i þ εt ;
i¼1
Eq. (1) shows that forecasted returns are dependent on past returns Φi rt i and on values of the error term matrix εt eð0;Σε Þ. An expression of Eq. (1) that accounts for the invertible VAR process is: ∞ X
rt ¼
5
It should be pointed out that one of the limitations of the Diebold and Yilmaz (2012) spillover index model is that it only provides estimates of total spillovers between pairs of variables and does not provide estimates of direc tional spillovers between pairs. The generalized VAR of Koop et al. (1996) solves this problem by enabling a forecast error variance decomposition and correlated shocks the shocks to each variable are not orthogonalized.
(2)
Ai ε t i :
i¼0
Here Ai is a square matrix of coefficients estimated as Ai ¼
p P j¼1
Ai j Φj , for
Ao ¼ IN , for Ai ¼ 0 if i < 0. When calculating the total spillover index the 4
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variables’ cross-variance (cross-spillovers) is understood as the fraction of the H-step-ahead error variance in forecasting ith ðri ) according to shocks stemming from the jth variable, for i; j ¼ 1; 2; …; N. Hence, i 6¼ j must hold. An expression of the H-step-ahead generalized FEVD matrix θ is: �2 P σjj 1 Hh¼01 e’i Ah Σε ej ωHij ¼ P (3) � ; i; j; ¼ 1; :::; N; H 1 ’ ’ h¼0 ei Ah Σε Ah ei
PN PN ~g ~g i; j ¼ 1 θij ðHÞ i; j ¼ 1 θij ðHÞ i 6¼ j i 6¼ j ¼ Sg ðHÞ ¼ PN g ~ N i;j¼1 θij ðHÞ
(5)
Eq. (5) shows how shocks to returns or volatilities of a certain precious metal commodity spillover on those of all others. The direc tional spillovers between commodity pairs are computed according to the following expressions:
PN PN PN PN ~g ~g ~g ~g i; j ¼ 1 θij ðHÞ i; j ¼ 1 θij ðHÞ i; j ¼ 1 θji ðHÞ i; j ¼ 1 θji ðHÞ i 6¼ j i 6¼ j i¼ 6 j i 6¼ j and Sgi→j ðHÞ ¼ PN g Sgj→i ðHÞ ¼ PN g ¼ ¼ ~θ ðHÞ ~θ ðHÞ N N i;j¼1 ij i;j¼1 ji
The matrix Ah is defined as in Eq. (2), while Σε is a variance matrix of the error term εt from Eq. (1). The pamamter σjj accounts for the jth diagonal components of Σε , and ei and ej are selection vectors. Given that shocks for the processes of Eq. (1) are rarely orthogonal, the variance decomposition rows do not add up to 1 and normalization of all variance decomposition matrix components is required as follows:
ωHij
~ Hij
ω ¼ PN
j¼1
where,
N P j¼1
The above expressions measure the directional return or volatile spillovers transmitted or received by variables i (j) from j ðiÞ. Total net spillovers are obtained according to: Sgi ðHÞ ¼ Sgi→j
~H ω ij ¼ 1 and.
N P i;j¼1
~H ω ij ¼ N:
Sgij ðHÞ ¼
The total spillovers between variables are estimated as follows:
From (j) Silver
Platinum
Palladium
Contribution from others
Gold 49.32 Silver 28.22 Platinum 15.1 Palladium 9.19 Contribution to 52.51 others NET 1.82 (b). Volatility spillover From (j) To (i) Gold
29.24 47.59 15.87 12.94 58.05
13.92 14.09 53.38 17.72 45.73
7.53 10.1 15.65 60.14 33.28
0.89
6.57
50.69 52.41 46.62 39.85 Total spillover index: 47.39
Silver
Platinum
Palladium
Gold Silver Platinum Palladium Contribution to others NET
68.1 26.53 4.48 2.36 33.37
27 66.82 4.34 4.6 35.94
3.11 3.23 86.87 5.8 12.14
1.8 3.42 4.31 87.25 9.53
1.46
2.76
0.99
3.23
5.64
~θg ðHÞ ij
(8)
N
2.2. Frequency domain spillover approach
(a). Returns spillover Gold
g ~ θji ðHÞ
Eq. (8) accounts for the net return or volatility spillover effects of each variable on the returns and volatilities of other variables.
Table 3 Spillover table for N-dimensional VAR model.
To (i)
(7)
Sgj→i ðHÞ
Eq. (7) accounts for net volatility and return spillovers from com modity i to all other commodities j. The net pairwise spillovers result from the following rational matrix relationship:
(4)
ωHij
(6)
Frequency domain spillovers are estimated according to the method of Barunik and Krehlik (2018). This method can be seen as an extension of the spillover index method of Diebold and Yilmaz (2012) in the sense that spectral specifications of variance decompositions are incorporated in line with the approaches of Dew-becker and Giglio (2016) and Stiassny (1996). The frequency response function is a function of a pffiffiffiffiffiffi Fourier transform for the coefficients Ψ and for i ¼ 1 is: Ψ e
ihω
�
∞ X
e
¼
ihω
(9)
Ψh
h¼0
Contribution from others 31.91 33.18 13.13 12.76 Total spillover index: 22.75
where the term ω accounts for the frequency. The power spectrum of the variance distribution of Xt and GFEVD as a function of ω are respectively: SX ðωÞ ¼
∞ X
EðXt Xt h Þe
ihω
¼Ψ e
ihω
�
ΣΨ eihω
�
(10)
h¼0
P∞
2 ihω ÞΣÞij h¼0 ðΨðe ihω ÞΣΨ ðeihω ÞÞ ii h¼0 ðΨðe
σjj 1
Notes: These tables show the percentage of contribution to the forecast error variance of variable i coming from shocks to variable j using all the sample period. The column named “Contribution from others” are the sum of the per centage of contribution of each variable except the own variable. Similarly, the row named “Contribution to others” are the sum of the percentage of contri bution of each variable except the own variable. The total spillover index (expressed as a percentage) appears in the lower right corner of the table. This index is calculated as the sum of all the contributions in the “Contribution to others” column (or the sum of all the “Contribution to others” row) divided by the number of variables included in the model. The net directional spillover index is computed as the difference between the “Contribution from others” and the “Contribution to others” for each variable.
ðθðωÞÞij ¼ P∞
(11)
The parameter ðθðωÞÞij accounts for the frequency dependent varia tion effects on commodity i stemming from the shocks commodity j experiences. Eq. (11) can be standardized as follows: ðθðωÞÞij ð~ θðωÞÞij ¼ Pn h¼1 ðθðωÞÞij
(12)
And an estimate of the connectedness for a certain frequency interval d ¼ ða; bÞ is obtained as follows: 5
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Fig. 3. Total spillover of four precious metalsNotes: This figure displays the time-varying total return spillover index (Panel A) and the total volatility spillover index (Panel B) for the four precious metals (gold, silver, platinum and palladium) considered. They are computed using the approach of Diebold and Yilmaz (2012). These dynamic total spillover indices are calculated from the forecast error variance decompositions using a rolling window size of 500 days and a forecast horizon of H ¼ 100 days. The horizontal axis accounts for the time factor and the vertical axis for the total spillover levels. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
Z ð~θd Þij ¼
b
a
The net spillovers (i.e., within net connectedness) are calculated as the difference between transmission and reception of variance between pairs of commodities:
(13)
ð~ θðωÞÞij dω
The whole connectedness for a certain frequency interval d is esti mated as: Pn Pn ~ ~ ðθd Þii i¼1; i6¼j ðθd Þij d C ¼ P ¼1 (14) Pi¼1 ðθ~d Þ ðθ~d Þ ij
ij
ij
Cdi;net ¼ Cdi→⋅
Cdi;net
In Eq. (17) positive values of indicate greater variation or spillover transmission from commodity i to others than reception from them. The pairwise net spillovers for commodities i and j are obtained as:
ij
The closer C is to 1 the stronger the connectedness and spillovers between the returns (or volatilities) of commodities for a certain fre quency interval d. The spillovers received by a certain commodity i from all other j commodities (i.e., within from connectedness), for i 6¼ j and for a certain frequency interval d are calculated as: d
Cdi←⋅ ¼
n X
ð~ θd Þij
(17)
Cdi←⋅
Cdij ¼ ð~ θd Þji
(18)
ð~θd Þij
The spillover influence of a certain frequency interval d on the overall aggregate system of interdependence, in line with Krehlik and Barunik (2017) is calculated as:
(15)
(19)
~ d ¼ Cd ⋅ΓðdÞ C
j¼1; i6¼j
where ΓðdÞ represent the spectral weight and accounts for the spillover influence of a certain frequency interval d to the whole VAR system and is defined as:
On the other hand, the variation contribution or spillover effect of commodity i on all other j commodities (i.e., within to connectedness), for i 6¼ j and for a certain interval d is computed as: Cdi→⋅ ¼
n X
ð~ θd Þji
n X
(16)
ΓðdÞ ¼ ij¼1
j¼1; i6¼j
6
ð~ θd Þij
n .X ij¼1
ð~ θÞij ¼
n X ij¼1
ð~θd Þij
. n
(20)
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Fig. 4. Net directional spillover. Notes: This figure displays the time-varying net directional return and volatility spillovers for each of the four precious metal commodities across time. The dynamic net spillover indices are calculated by subtracting directional “to” spillovers from directional “from” spillovers. Positive (negative) values of spillovers indicate that the corresponding variable is a net transmitter (receiver) of spillover effects to all the other variables. The horizontal axis accounts for the time parameter and the vertical axis for the net directional spillover index.
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Table 4 Spillover table for 2N-dimensional VAR model with positive and negative components. (a). Returns spillover Rþ
Contribution from others
R
Gold
Silver
Palladium
Gold
Silver
Platinum
Palladium
Rþ
Gold Silver Platinum Palladium
47.23 23.5 11.15 4.99
24.44 45.41 10.5 8.35
9.2 8.48 55.07 10.08
3.88 6.22 8.82 59.83
5.84 4.82 2.98 2.14
4.45 5.83 2.79 2.75
3.12 3.37 5.86 4.18
1.83 2.36 2.83 7.68
46.92 48.75 39.07 32.49
R
Gold Silver Platinum Palladium Contribution to others
5.47 3.91 2.84 1.95 48.34
4.59 5.45 3.31 2.67 53.86
2.41 2.22 5.01 2.87 35.26
1.5 1.96 3.17 6.48 25.55
44.14 23.6 11.64 7.78 52.96
24.47 43.18 12.92 10.24 57.62
10.89 11.67 46.65 15.96 49.19
6.54 8.02 14.46 52.04 36.04
50.4 51.38 48.34 41.47 Total spillover index: 44.85
b). Volatility spillover Vþ
Contribution from others
V
Gold
Silver
Platinum
Palladium
Gold
Silver
Platinum
Palladium
Vþ
Gold Silver Platinum Palladium
57.11 20.53 2.72 1.42
21.03 55.84 2.93 2.8
2.04 1.96 83.01 3.1
1.01 1.91 2.77 79.48
9.89 6.07 0.91 1.14
5.44 9.5 0.92 1.01
2.85 2.66 5.64 2.03
0.63 1.53 1.09 9.03
33.00 34.66 11.34 11.5
V
Gold Silver Platinum Palladium Contribution to others
10.76 5.64 3.2 0.9 34.41
6.51 10.57 2.92 1.92 38.11
0.54 0.65 4.85 1.08 9.37
0.58 0.76 2.27 9.04 9.3
59.87 14.87 4.83 2.2 30.02
15.1 59.71 4.32 3.63 30.42
4.71 4.26 68.43 8.23 24.74
1.93 3.55 9.19 72.99 17.92
29.37 29.73 26.73 17.96 Total spillover index: 24.29
Notes: These tables display the spillover in relation to positive and negative return and volatility shocks. The abbreviations Rþ , R , V þ and V stand for positive and negative return and volatility shocks, respectively. See Table 3 for details.
2.3. Measuring asymmetric spillovers
is that it accounts for various economic and financial events of large scale among them most notably the global financial crisis of 2008 and the European sovereign debt crisis which cause uncertainty in the financial markets and a flight to safety for investors who sought for precious metals to hedge their financial positions. Fig. 1 depicts the time trend of precious metal prices from 1999 to 2019. As shown the prices of precious metals are generally in a trend of escalation from 2001 until the 2008. The effects of the 2008 global financial crisis and the Eurozone debt crisis are observed in all precious metal commodities. Gold prices show resilience in the wake of the 2008 global financial crisis, most likely due to its safe-haven attributes (see for example, Baur and Lucey (2010), Baur and McDermot (2010) and Omane-Adjepong and Boako (2017)), while platinum prices sharply plummet during that crisis event. This shows the positive response characteristic of gold to financial and economic shocks, as well as uncertainty. Between 2009 and 2011, the prices of all four precious metals sharply increase and, with the exception of palladium, undergo there after a trend of decline until 2016, when prices pick up slightly. Com modity prices may exhibit such tendencies of ‘all-rising’ or ‘all-falling’ if there is a relationship between them as complements or substitutes in production or consumption. Commodities showing such price de velopments may also transmit idiosyncratic demand or supply shocks to one another. Despite this, commodity-specific shocks may not adequately explain broad co-movements across unrelated commodities (Pradhananga, 2016) that have been attributed to rises in their demand and supply (Kilian, 2009), financialization (see e.g., Jacks and Stuermer, 2018; Tang and Xiong, 2012), and price dynamics (Akram, 2009).6
The negative and positive returns of the time series are defined as: rþ t ¼ maxðrt ; 0Þ and rt ¼ minðrt ; 0Þ. The H-step-ahead GFEVD matrix Ω for a 2N-dimensional VAR is: �2 P σjj 1 Hh¼01 e’i Ah Σε ej ωHij ¼ P � ; i; j; ¼ 1; :::; 2N; (21) H 1 ’ ’ h¼0 ei Ah Σε Ah ei The asymmetric spillovers in the directional influence are expressed by the term “TO” which refers to transmission, as opposed to “FROM” which refers to reception or absorption of spillovers. The “TO” asym metric spillovers are obtained as the sum of values in the 2N � 2N spillover matrix, with the exception of the values in the diagonal matrix for i 6¼ j, and two diagonals in the N � N block sub-matrices (lower left and upper right), for ji jj 6¼ N. The directional asymmetric spillover from a certain commodity i to all others is obtained as: S
H 2N;i→�
¼ 100 �
2N 1 X ~ Hj;i ; i; j; ¼ 1; :::; 2N ω 2N
(22)
i¼1;i6¼j
ji jj6¼N
3. Data The data on which the spillover frameworks are implemented con sists of prices for daily tradable futures of silver, gold, platinum and palladium. The data sample spans from July 16, 1999 to July 17, 2019. The data is extracted from Thomson Reuters Datastream International. We select precious metals for the analysis of asymmetric spillovers because they have historically displayed, in the long run most notice ably, positive trends of appreciation relative to other commodities that have undergone more pronounced trends of appreciation and depreci ation. These precious metal commodities in particular have frequently been used to preserve wealth from inflation increases, and for hedging in market downturns. Our motivation for the length of the selected sample
6 Financialization implies that commodity prices are driven not only by fundamental factors, but by the rising importance of financial elements, in stitutions and the speculative behaviour of investors in commodity markets (Falkowski, 2011). Periods of turmoil in financial markets decrease the risk appetite of financial investors, leading them to close-out long positions in € € commodity markets (Oztek and Ocal, 2017).
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Fig. 5. Spillover asymmetry measure - S A M Notes: The figure displays the asymmetric spillovers for return and volatilities of the four precious metal commodities across time. The horizontal axis accounts for the time parameter, and the vertical axis for percentages of spillovers.
Table 1 reports the statistical properties and correlation matrix of the precious metals’ returns. Gold, palladium and silver respectively have the highest average returns whereas platinum has the lowest. Palladium and silver have the highest standard deviations, respectively. Except for platinum, precious metal returns show negative skewness indicating a higher frequency of negative returns. All the series exhibit excess kur tosis indicating frequent extreme observations. The Jarque-Bera test indicates that the returns are not normally distributed. Both the augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) tests (Phillips and Perron, 1988) show that the returns series are stationarity. The precious metals display a significant positive correlation with each other. The significant positive association among commodities could be attributed to the financialization of commodities. The prices of commodities are likely to co-jump if commodity futures are traded based on herd-behaviour but not based on respective market fundamentals. The herding behaviour could usher asset prices not to show substantial deviation from the overall market (Demirer et al., 2015). Table 2 indicates that the volatility dynamics of the commodity se ries are captured best by the EGARCH model with normal distribution. Model parameters are chosen by minimizing the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) values. The results show that average returns of the series record highly persistent volatilities as depicted by the ARCH and GARCH parameters. Evidence of leverage effects is found for gold and silver, positing that their re sponses to informational shocks during the sample period are
asymmetric. Fig. 2 shows the conditional volatilities of the precious metal returns and also highlights the significant impact of the global financial crisis on their price developments. 4. Empirical findings 4.1. Full sample returns and volatility spillover Table 3 displays the full sample symmetric return and volatility spillovers among precious metals. In this spillover table, the percentages of contribution coming from shocks to variable j to the forecast error variance of variable i are reported. The sum of contribution percentages, except own, are shown under the column and row name “Contribution from others” and “Contribution to others”, respectively. The lowest right corner of the table reports the total spillover index (expressed as a percentage). The difference between the “Contribution from others” and “Contribution to others”, for each variable, are named as net directional spillover. The results indicate that silver exerts the largest return spillovers (58.1%) to other precious metals, followed by gold (52.5%). The smallest return spillovers are exerted by platinum (45.7%) and palla dium (33.3%). The largest bidirectional spillovers occur between silvergold and palladium-platinum, implying a stronger interdependence between those pairs. Overall, the spillovers of the volatilities are similar to those of the returns, although smaller in size. These results are similar 9
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Table 5 Frequency domain return spillover table for 2N-dimensional VAR model with positive and negative components. (a). Short-run spillover (1–5 days) Rþ
Contribution from others
R
Gold
Silver
Platinum
Palladium
Gold
Silver
Platinum
Palladium
Rþ
Gold Silver Platinum Palladium
38.89 19.38 8.9 4
20.64 37.53 8.68 6.69
7.81 7.27 44.84 7.7
3.4 5.28 7.13 48.64
4.35 3.75 2.27 1.5
3.11 4.39 2 1.89
2.23 2.6 4.69 2.93
1.33 1.77 2.13 5.63
38.52 40.05 31.11 24.71
R
Gold Silver Platinum Palladium Contribution to others
3.72 2.67 1.93 1.29 38.17
3.34 3.85 2.38 1.81 43.54
1.69 1.61 3.9 1.94 28.02
1.07 1.29 2.11 4.72 20.28
35.75 19.11 9.25 6.26 42.14
19.11 34.42 9.77 7.39 43.27
8.85 9.35 36.85 12.36 38.32
5.27 6.28 11.12 40.62 27.9
39.33 40.31 36.56 31.05 Total spillover index: 35.21
(b). Medium-run spillover (6–90 days) Rþ
Contribution from others
R
Gold
Platinum
Palladium
Gold
Silver
Platinum
Palladium
Rþ
Gold Silver Platinum Palladium
9.03 4.56 2.43 1.25
4.3 8.51 2.08 1.75
1.95 1.68 10.49 2.07
0.65 1.07 1.69 12.59
0.54 0.39 0.27 0.24
0.36 0.34 0.35 0.41
0.27 0.3 0.62 0.54
0.18 0.24 0.39 1.05
7.71 8.24 7.21 6.26
R
Gold Silver Platinum Palladium Contribution to others
0.67 0.4 0.4 0.3 9.34
0.48 0.42 0.43 0.4 9.44
0.29 0.26 0.56 0.42 6.67
0.2 0.36 0.53 0.96 4.50
8.89 4.85 2.6 1.63 9.98
5.56 9.47 3.29 2.59 12.56
2.45 2.58 10.09 4.07 10.21
1.55 1.93 3.59 11.98 7.88
10.53 10.38 10.84 9.41 Total spillover index: 8.82
c). Long-run spillover (more than 90 days) Rþ
Contribution from others
R
Gold
Silver
Palladium
Gold
Silver
Platinum
Palladium
Rþ
Gold Silver Platinum Palladium
0.5 0.26 0.14 0.07
0.24 0.48 0.12 0.1
0.11 0.09 0.59 0.12
0.04 0.06 0.09 0.71
0.03 0.02 0.01 0.01
0.02 0.02 0.02 0.02
0.01 0.02 0.03 0.03
0.01 0.01 0.02 0.06
0.43 0.46 0.4 0.35
R
Gold Silver Platinum Palladium Contribution to others
0.04 0.02 0.02 0.02 0.53
0.03 0.02 0.02 0.02 0.53
0.02 0.01 0.03 0.02 0.37
0.01 0.02 0.03 0.05 0.25
0.5 0.27 0.15 0.09 0.55
0.32 0.54 0.19 0.15 0.72
0.14 0.15 0.57 0.23 0.58
0.09 0.11 0.21 0.68 0.45
0.61 0.58 0.62 0.53 Total spillover index: 0.50
Notes: These tables display the spillover in relation to positive and negative return and volatility shocks. The abbreviations Rþ , R , V þ and V stand for positive and negative return and volatility shocks, respectively. See Table 3 for details.
to those found in Batten et al. (2015). The net return and volatility spillover values are positive for gold and silver, whereas those for palladium and platinum are negative. The total return and volatility spillovers among all four metals are 47.39 and 22.75, respectively. We also observe that silver and gold share the strongest relationship as gold accounts for 28.2% of forecast error variations of silver returns, and silver accounts for 29.2% of forecast error variations in gold returns. This strength of interdependence between gold and silver is also found in Batten et al. (2015).
undergoes a relatively even path and do not show any significant trend of increase (decrease) up until 2007. Spillovers after the sharp decline in 2007 sharply increase in the short-term moving from around 48%–52% towards the end of 2012. This period of fluctuations underlies the effects the 2008 global financial crisis and the Eurozone sovereign debt crisis had on the prices of all precious metal commodities. From 2013 to the end of the first quarter of 2015 the total spillover index sharply declines. This high degree of integration between the precious metal commod ities’ returns could be attributed to an overall global drop in commodity prices due to a strengthening of the US dollar and concerns over China’s faltering growth. Specifically, by September 2014 the global oil market fell 1.7% to $96.6 a barrel, and the excess commodity index fell to a five year low of 118.2 points. The total volatility spillover index, as shown in panel (b) of the figure, displays similar behaviour. In Fig. 4, gold and silver are net return spillover transmitters, while palladium is a net spillover receiver. For volatilities silver appears as net spillover transmitter, whereas palladium is a spillover receiver. Gold and platinum generally remain balanced in terms of net volatility spillover transmission and reception.
4.2. Rolling window based returns and volatilities spillover Fig. 3a and b displays the total volatility and return spillovers7 estimated according to the spillover index of Diebold and Yilmaz (2012). The horizontal axis accounts for the time factor and the vertical axis for the total spillover levels. The total return spillover index oscillates be tween 20% and 28% from 2001 to mid-2004, with the peak occurring at late 2002. From late 2003 total return spillovers undergo a steady in crease to reach a peak error variance of 57% in mid-2005 after which it
4.3. Asymmetric returns and volatility spillover analysis
7
Total spillover indices are calculated using a rolling window size of 500 days and a forecast horizon of H ¼ 100 days.
Table 4 displays the spillovers that account for the cumulative sum of 10
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Table 6 Frequency domain volatility spillover table for 2N-dimensional VAR model with positive and negative components. (a). Short-run spillover (1–5 days) Vþ
Contribution from others
V
Vþ
Gold Silver Platinum Palladium
Gold 45.09 15.93 1.77 1.09
Silver 16.47 43.23 2.02 2.1
1.16 1.36 65.71 1.85
Palladium 0.79 1.5 1.96 62.76
Gold 8.77 5.48 0.85 1.04
Silver 4.91 8.32 0.7 0.81
Platinum 2.4 2.18 4.7 1.67
Palladium 0.55 1.36 0.87 7.35
26.28 27.81 8.17 8.56
V
Gold Silver Platinum Palladium Contribution to others
9.82 5.07 2.77 0.73 27.36
5.86 9.55 2.48 1.69 30.62
0.45 0.53 4.23 0.82 6.17
0.51 0.62 1.79 8.02 7.17
46.6 11.15 3.44 1.13 23.09
11.14 44.02 3.37 2.36 23.29
3.42 3.14 40.04 3.83 16.64
1.08 2.1 3.46 43.01 9.42
22.46 22.61 17.31 10.56 Total spillover index: 17.97
(b). Medium-run spillover (6–90 days) Vþ
Contribution from others
V
Gold
Silver
Palladium
Gold
Silver
Platinum
Palladium
Vþ
Gold Silver Platinum Palladium
11.35 4.34 0.89 0.31
4.29 11.9 0.85 0.66
0.83 0.56 16.35 1.17
0.21 0.38 0.76 15.8
1.08 0.57 0.07 0.09
0.52 1.13 0.21 0.19
0.43 0.46 0.91 0.35
0.09 0.17 0.22 1.61
6.37 6.48 3 2.77
V
Gold Silver Platinum Palladium Contribution to others
0.92 0.56 0.43 0.17 6.7
0.64 1.0 0.43 0.24 7.11
0.09 0.11 0.61 0.26 3.02
0.07 0.14 0.46 1.02 2.02
12.45 3.47 1.25 0.96 6.41
3.7 14.72 0.88 1.17 6.67
1.18 1.04 26.07 3.96 7.42
0.77 1.32 5.14 27.53 7.71
6.45 6.64 8.59 6.76 Total spillover index: 5.88
c). Long-run spillover (more than 90 days) Vþ
Contribution from others
V
Gold
Silver
Palladium
Gold
Silver
Platinum
Palladium
Vþ
Gold Silver Platinum Palladium
0.68 0.27 0.06 0.02
0.27 0.71 0.05 0.04
0.05 0.04 0.95 0.08
0.02 0.03 0.05 0.92
0.04 0.02 0 0
0.02 0.05 0.01 0.01
0.02 0.02 0.03 0.01
0 0 0.01 0.07
0.38 0.38 0.18 0.16
V
Gold Silver Platinum Palladium Contribution to others
0.02 0.01 0 0 0.36
0.01 0.02 0.01 0 0.38
0 0 0 0 0.17
0 0 0.02 0.01 0.12
0.81 0.25 0.14 0.11 0.52
0.26 0.97 0.07 0.1 0.47
0.1 0.08 2.32 0.45 0.68
0.08 0.13 0.6 2.45 0.82
0.45 0.47 0.84 0.66 Total spillover index: 0.44
Notes: These tables display the spillover in relation to positive and negative return and volatility shocks. The abbreviations Rþ , R , V þ and V stand for positive and negative return and volatility shocks, respectively. See Table 3 for details.
negative and positive shocks. Cumulative positive and negative shocks are estimated according to Hatemi-j (2012). In simple terms, positive returns shocks (Rþ) or positive volatility shocks (Vþ) capture spillovers due to positive changes in the markets. The reverse is true for R- and V-. Accordingly, gold and silver are the largest transmitters and receivers of negative and positive volatility and return spillovers. Larger negative shocks (bad news) on the precious metals markets are observed to cause larger return and volatility spillover effects, as opposed to large positive shocks (good news). All commodities spillover positively and negatively on each other. Silver and palladium display noticeable spillover transmission and reception. Their spillovers, moreover, are time varying and nonhomogenous. The spillovers between each individual commodity and their aggregates are characterized by extreme net positions. This phe nomenon is more pronounced in the volatility spillovers than the return spillovers. Fig. 5 displays the aggregate asymmetric volatility and return spill overs of the four precious metals under consideration. They are esti mated as the variance between the spillover indices of the metal pairs with cumulative positive and negative shocks. Returns and volatilities with positive (negative) innovations are termed as good (bad), along with Barunik et al. (2017), Patton and Sheppard (2015), and Segal et al. (2015).
Negative values of the asymmetric return spillovers suggest that total spillovers among precious metals are higher for negative returns compared to positive returns. The asymmetric return spillovers reach their highest values during the last two quarters of 2007 and the second quarter of 2008. This asymmetric effect between commodity returns during that period may be traced to the beginning of the turmoil phase of the 2008 global financial crisis.8 Another trend of increasing asymmetric return spillovers is observed from 2010 to the end of the fourth quarter of 2014, where the largest values are reached. This asymmetric influ ence between precious metal commodity returns is coherent with the increasing uncertainty caused by the Eurozone sovereign debt crisis, as investors relied on precious metals to hedge against economic and geopolitical uncertainty within the region. The total asymmetric volatility spillovers (assuming positive in novations) react differently relative to the return spillovers (having negative innovations). The index’s positive values imply that the
8 The large asymmetric spillovers during late 2007 and the first two quarters of 2008 are partially due to the stock market volatility caused by the turmoil of the GFC. From a macroeconomic perspective this reflects the monetary policy responses of the US Fed during the crisis. This also corroborates the conclusion of Hammoudeh et al. (2010) that monetary shocks are sensitive to metals such as gold and silver.
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Fig. 6. Frequency domain asymmetric spillovers - S A M . Notes: This figure depicts the time-frequency dynamics of the total return connectedness (Panel A) and the total volatility connectedness (Panel B) among the four precious metals considered. They are computed using the method of Barunik and Krehlik (2018). The figures in the top show the connectedness at the higher frequency band, which corresponds to movements up to five days (one week). The figures in the middle display the connectedness at the medium frequency band, which corresponds to movements from six to ninety days (approximately three months). The figures in the lower part show the connectedness for the low frequency band, which corresponds to more than ninety days. These dynamic total connectedness measures are computed using a rolling window size of 500 days and a forecast horizon of H ¼ 100 days, although the time-frequency connectedness method of Barunik and Krehlik (2018) is not influenced by the particular forecast horizon.
spillovers among precious metals are higher for increases in volatility. The largest trend of increasing asymmetric volatility spillover occurs during 2008-09, 2010–11 and 2014, being highest in 2010. This specific asymmetric effect could be linked to negative shocks. All in all, we conclude that negative return (Fig. 5a) and bad volatility (Fig. 5b) spillovers between precious metals dominate positive return and good volatility spillovers.
aggregate asymmetric return and volatility spillovers for the short-term (1–5 days), medium-term (5–90 days) and long-term (more than 90 days). In the short-term gold and silver exert and receive the largest net return spillovers to and from platinum and palladium most noticeably. Silver overall, followed by gold, exerts the strongest asymmetric influ ence in the short and medium terms, for both positive and negative shocks. We also observe that asymmetric spillovers for positive returns (positive components) are stronger than those for negative returns (negative components), indicating a stronger effect on the upside than on the downside, from leading metal commodities such as silver and gold. Also, as in the previously discussed spillover measures, gold and
4.4. Frequency domain asymmetric spillover analysis Tables 5 and 6 show the values corresponding to individual and 12
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silver most strongly influence each other for both positive and negative components and for the short-term and medium-term. The short- and medium-term asymmetric spillovers for both positive and negative components are clearly bigger than those in the long-term. The asymmetric spillovers based on volatilities for positive and negative components are consistent with those based on returns in general. Silver appears to lead the asymmetric spillovers for negative and positive return scenarios and in short and medium run, followed by gold. Gold and silver are net transmitters of spillovers, while platinum and palladium are spillover receivers. Lastly, Fig. 6 displays the frequency domain asymmetric spillover indexes. It is clear from those figures that spillovers from negative return shocks (also bad volatility) are more profound compared to positive return (good volatility) shocks. Also, these spillovers are higher in the short- to medium-term. Collectively, we can conclude that precious metals are no different than traditional asset classes in terms of risk and return spillovers and that panic drives the contagion effect.
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Econom. 16 (2), 271–296. Baruník, J., Ko�cenda, E., V� acha, L., 2017. Asymmetric volatility connectedness on the forex market. J. Int. Money Financ. 77, 39–56. Batten, J.A., Ciner, C., Lucey, B.M., 2015. Which precious metals spill over on which, when and why? Some evidence. Appl. Econ. Lett. 22 (6), 466–473. Batten, J.A., Ciner, C., Lucey, B.M., 2010. The macroeconomic determinants of volatility in precious metals markets. Resour. Policy 35 (2), 65–71. Baur, D.G., Lucey, B.M., 2010. Is gold a hedge or a safe haven? An analysis of stocks, bonds and gold. Financ. Rev. 45 (2), 217–229. Baur, D.G., McDermott, T.K., 2010. Is gold a safe haven? International evidence. J. Bank. Financ. 34 (8), 1886–1898. Bekiros, S., Nguyen, D.K., Uddin, G.S., Sj€ o, B., 2015. Business cycle (de) synchronization in the aftermath of the global financial crisis: implications for the Euro area. Stud. Nonlinear Dyn. Econom. 19 (5), 609–624. Chan, W.H., Young, D., 2006. Jumping hedges: an examination of movements in copper spot and futures markets. J. Futures Mark. 26 (2), 169–188. Chen, S., Wu, X., 2016. Comovements and Volatility Spillover in Commodity Market. Agricultural & Applied Economics Association Annual Meeting, Boston, Massachusetts. July 31-August 2. Demirer, R., Lee, H.T., Lien, D., 2015. Does the stock market drive herd behavior in commodity futures markets? Int. Rev. Financ. Anal. 39, 32–44. Dew-becker, I., Giglio, S., 2016. Asset pricing in the frequency domain: theory and empirics. Rev. Financ. Stud. 29 (8), 2029–2068. Dickey, D.A., Fuller, W.A., 1979. Distribution of the estimators for autoregressive time series with a unit root. J. Am. Stat. Assoc. 74 (366a), 427–431. Diebold, F.X., Yilmaz, K., 2012. Better to give than to receive: predictive directional measurement of volatility spillovers. Int. J. Forecast. 28 (1), 57–66. Falkowski, M., 2011. Financialization of commodities. Contemp. Econ. 5 (4), 4–17. Graham, M., Nikkinen, J., 2011. Co-movement of the Finnish and international stock markets: a wavelet analysis. Eur. J. Financ. 17 (5-6), 409–425. Georgiev, G., 2001. Benefits of commodity investment. J. Altern. Investments 4 (1), 40–48. Hamilton, J.D., 2011. Nonlinearities and the macroeconomic effects of oil prices. Macroecon. Dyn. 15 (S3), 364–378. Hammoudeh, S.M., Yuan, Y., McAleer, M., Thompson, M.A., 2010. Precious metals–exchange rate volatility transmissions and hedging strategies. Int. Rev. Econ. Financ. 19 (4), 633–647. Hatemi-j, A., 2012. Asymmetric causality tests with an application. Empir. Econ. 43 (1), 447–456. Jacks, D.S., Stuermer, M., 2018. What drives commodity price booms and busts? Energy Econ. https://doi.org/10.1016/j.eneco.2018.05.023. Kilian, L., 2009. Not all oil price shocks are alike: disentangling demand and supply shocks in the crude oil market. Am. Econ. Rev. 99 (3), 1053–1069. Koop, G., Pesaran, M.H., Potter, S.M., 1996. Impulse response analysis in nonlinear multivariate models. J. Econom. 74 (1), 119–147. K�rehlík, T., Baruník, J., 2017. Cyclical properties of supply-side and demand-side shocks in oil-based commodity markets. Energy Econ. 65, 208–218. Kwiatkowski, D., Phillips, P.C., Schmidt, P., Shin, Y., 1992. Testing the null hypothesis of stationarity against the alternative of a unit root: how sure are we that economic time series have a unit root? J. Econom. 54 (1-3), 159–178. Mensi, W., Beljid, M., Boubaker, A., Managi, S., 2013. Correlations and volatility spillovers across commodity and stock markets: linking energies, food, and gold. Econ. Modell. 32, 15–22. Nguyen, D.K., Sousa, R.M., Uddin, G.S., 2015. Testing for asymmetric causality between US equity returns and commodity futures returns. Financ. Res. Lett. 12, 38–47. Omane-Adjepong, M., Boako, G., 2017. Long-range dependence in returns and volatility of global gold market amid financial crises. Phys. A Stat. Mech. 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5. Conclusion Asymmetric spillovers among return and volatilities of commodities and financial markets are a problem for portfolio and risk managers. Policy makers should also be concerned because of the risk asymmetric spillovers pose to public sector resource allocation. In this study, aware of the peculiar risks that asymmetric spillovers entail, we measure and examine the time and frequency domain spillovers among four precious metals, namely, silver, gold, palladium and platinum. We draw our empirical results by implementing the spillover index of Diebold and Yilmaz (2012) and the frequency domain spillover measures of Barunik and Krehlik (2018). Our results indicate that the asymmetric spillovers between the volatilities and returns of the precious metals considered are time varying. Negative and positive shocks cause the asymmetric spillovers and are more pronounced in times of financial turmoil. The largest transmission of net spillovers is exerted by gold and silver. Silver in the short and long runs and in good and bad market conditions leads the spillover transmission. The pairs silver-gold and palladium-platinum display the largest directional spillovers. Also, while palladium and platinum act mainly as spillover receivers, gold and silver act mainly as transmitters of spillovers. Portfolio and investment managers should bear in mind the char acteristics of asymmetric spillovers among the precious metals when rebalancing their portfolios and forecasting future prices of commod ities. Policy makers’ understanding of asymmetric spillovers between precious metal commodities would enable them to adequately allocate the resources, particularly during market downturns and for economies that heavily depend on exports of these metal commodities. Resourcebased economies, specifically, could consider preemptive measures to better deal with layoffs in the commodities’ underlying sectors due to strong and asymmetric spillover influence between sectors during market downturns. Furthermore, policy makers, through stronger in vestment concentration in negatively correlated sectors, or by gradually reshaping the structure of the economy, can increase the diversification of the economy and reduce the impact of distressed resources sectors on the overall economy. Acknowledgements: Earlier version of this paper was presented at the 2018 African Re view of Economics and Finance Conference under the “Modelling Asset Prices and Returns” session, South Africa. Gazi S. Uddin is thankful for the financial support provided by the Jan Wallander and Tom Hedelius Foundations (Ref. W2016:0364:1), Sweden.
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