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This study examines the conditional volatility and correlation dependency and interdependency for the four major precious metals (i.e., gold, silver, platinum and palladium), while accounting for geopolitics within a multivariate system. The implications of the estimated results for portfolio designs and hedging strategies are also analyzed. The results for the four metals system show significant short-run and long-run dependencies and interdependencies to news and past volatility. Furthermore, these results become more pervasive when the exchange rate and federal funds rate are included. Monetary policy also has a differential impact on the precious metals and the exchange rate volatilities. Finally, the applications of the results show the optimal weights in a two-asset portfolio and the hedging ratios for long positions.

The literature on commodities has concentrated on price co-movements and their roles in transmitting information about the macroeconomy. The research covers a wide scope of commodities including agricultural commodities, base metals, industrial metals and energy. The existing research on precious metals focuses mainly on gold and silver. Much of the past research on industrial metals is less generous when it comes to examining the volatility of returns of the precious metals. It mainly employs univariate models of the GARCH family to analyze volatility. Previous studies focused on own shock and volatility dependencies, while ignoring volatility and correlation interdependencies over time. Thus, they do not examine precious metals' shock and volatility cross effects. This could be a major shortcoming when one considers such applications as hedging, optimal portfolio diversification, inter-metal predictions and regulations. In this regard, we are interested in ascertaining to what extent precious metal interdependencies exist and the roles of hedging and diversification among them. In addition to policy makers, traders and portfolio managers, manufacturers would be interested in this information because the metals have important and diversified industrial uses in jewelry, medicine, and electronic and autocatalytic industries, as well as being investment assets. The broad objective of this study is to examine conditional volatility and correlation dependency and interdependency for the four major precious metals: gold, silver, platinum and palladium, using multivariate GARCH models with alternative assumptions regarding the conditional means, conditional variances, conditional covariances and conditional correlations. We include the vector autoregressive, moving average GARCH (VARMA-GARCH) model and the dynamic conditional correlation (DCC) model. We use the DCC-GARCH model as a diagnostic test of the results of the VARMA-GARCH model. This method enables us to examine the conditional volatility and correlations cross effects with meaningful estimated parameters and less computational complications that characterize these models. A second objective is to examine the volatility feedback effects between the four precious metals and the US dollar/euro exchange.1 Almost all metals are sensitive to changes in the dollar exchange rates, particularly the dollar/euro rate, which is followed closely by currency and commodity practitioners and policy makers. We expect to have metals' volatility heighten when the dollar is weak and volatile because investors move to the safety of the dollar-priced precious metals. But we are also keen on knowing whether some precious metals volatility contributes to heightened volatility for the US dollar since both types of assets may be included in international foreign reserves. A third objective is to derive the implications of the estimated results on variances and covariances for effectuating optimal portfolio designs and hedging strategies.2 This paper is organized as follows. After the introduction, we present a review of the literature on precious metal volatility in Section 2. Section 3 provides the data and their descriptive statistics. Section 4 illustrates the VARMA-GARCH and DCC-GARCH methodologies. The empirical results are discussed in Section 5, while Section 6 provides implications of the estimates of the models. Section 7 concludes.

This paper investigates conditional own and spillover volatilities and correlations for gold, silver, platinum and palladium and also with the exchange rate in simultaneous multivariate settings using the VARMA-GARCH and the more restrictive VARMA-DCC models. The results of these models are used to calculate the optimal two-asset portfolio weights and the hedging ratios. The models have varying-levels of restrictions relative to the BEKK model, which did not converge when exogenous variables were included. Even when the exogenous variables were removed, BEKK gave less reasonable estimates.18 On the other hand, VARMA-GARCH and VARMA-DCC gave more interpretable parameters and have less computational and convergence complications. Thus, our broad objective in this study is to examine the volatility and correlation interdependence among those seemingly close metals and with the US dollar/euro exchange rate in the presence of monetary policy and geopolitics. Our consequential objective is to apply the results to derive optimal portfolio weights and hedging ratios. The results show that almost all the precious metals are moderately sensitive to own news and weakly responsive to news spilled over from other metals in the short run. This underscores the importance of hedging in the short run, but it also shows that hedging precious metals against each other has its limitation. There is however strong volatility sensitivity to own past shocks in the long run, with the strongest sensitivity bestowed on silver and the weakest on gold. The saying goes “if you like gold, buy silver and if you want to sell gold sell silver.” The spillover volatilities are also stronger than the spillover shocks or news, which implies that these volatilities are predictable. The CCC matrix shows that gold and silver have the highest conditional correlations (0.42) among any pairs of the precious metals after platinum and palladium (0.48). Examining the volatility sensitivity of precious metals to the exchange rate volatility in the presence of monetary policy in Model II, the estimates show this sensitivity is strong, particularly for silver. The results reflect the fact that gold is the safest haven in the flight from the dollar to the safety of the precious metals. There are also weak reverse volatility spillovers from the precious metals to the exchange rate. The above results reflect on the strategies that aim at designing optimal portfolio holdings and effective hedging. Among the pairs of metals that are highly correlated like gold and silver, the optimal two-asset holding tilts strongly for one asset at the expense of the other ones. The results show we do not have well balanced two-asset portfolios for the precious metals. These findings also manifest themselves in the size of the hedging ratios between pairs of metals and metals/exchange rate. These results point out to the specificity of hedging gold against exchange rate risk.