The energy commodities differ from other trading products in their uniqueness as well as non-renewable nature. Most countries must rely on energy imports owing to the rareness of oil-producing countries. This also leads to that the prices of energy commodities are easily affected by many factors, such as government policy, politics, season, demand, supply, etc. In particular, the US dollar is commonly used as a major currency in the international energy commodity market, and hence the change in US dollar exchange rate will induce the commodity price fluctuation and then affect the economic actions of energy commodity importing and exporting countries.
Over the last few years, energy commodity prices have been experiencing an unprecedented high fluctuation. For example, the crude oil price has risen steadily from $20 per barrel in January 2002 to the tiptop $145 per barrel in July 2008 while fallen sharply and returned to $40 in December 2008 (see, Figure 1). In the meantime, the US dollar index (USDX1) after 2002 exhibits a greatly different tendency to that before 2002 and shows a significantly opposite direction to the crude oil price, that is to say, crude oil prices have been soaring while the US dollar has depreciated to a historical low price meantime and vice versa.
This negative relationship will enable the crude oil commodity and the US dollar currency tool to have diversification and hedging benefits. As a result, modeling and forecasting the volatility and dependence structures of oil and exchange rate returns accurately are of considerable interest to investors and financial institutions.
In recent years, there have been a number of methods proposed to explore the relationship between oil price and US dollar exchange rate. For example, Yousefi and Wirjanto (2004) investigated the impact of US dollar exchange rate fluctuation on the
formation of OPEC2 by using Hansen’s GMM model and verified that the correlation of oil and US dollar exchange rate is negative. Akram (2004) presented evidence of a non-linear negative relationship between oil prices and the Norwegian exchange rate, and pointed out that the nature of the relationship varies with the level and trend in oil prices. Cifarelli and Paladino (2010) used a multivariate CCC GARCH-M model to discover oil price dynamics are associated with exchange rate behavior and found strong evidence that oil price shifts are negatively related to exchange rate changes.
Furthermore, there are other studies focus on the discussion of lead-lag relationship between oil and exchange rate and their interactive influence. Although those studies different from our studies aim but they also support the negative relationship between oil and exchange rate. For Example, Krichene (2005) used the vector error correction model (VECM) and demonstrated the negative impact that falling nominal effective exchange rate could lead to a surge in oil prices, and inversely either long-term effect or short-term effect. Sari et al. (2009) employed the generalized forecast error variance decompositions and generalized impulse response functions to find evidence of weak long-run equilibrium relationship but strong feedback in the short run. Lizardo (2009) used the vector autoregressive (VAR) model and revealed that oil prices significantly explain movements in the value of the US dollar against major currencies. The currencies of oil importers depreciate relative to the USD when the real oil price goes up.
According to the majority of literatures, they point out the negative relationship between oil price and US dollar exchange rate. A number of possible explanations for this negative relationship between the US dollar and crude oil price are summarized as follows. First, oil-exporting countries want to stabilize the purchasing power of their export revenues (US dollar) in terms of their imports (non-US dollar), so they might adopt currencies pegged to the
2 The Organization of the Petroleum Exporting Countries is a cartel of twelve countries. The principal goals are safeguarding the cartel's interests and securing a steady income to the producing countries.
US dollar in order to avoid causing loss. Second, the depreciation of US dollar makes oil cheaper for consumers in non-US dollar regions, thus changing their crude oil demand, which eventually causes adjustments in the oil price, denominated in US dollars. Third, a falling US dollar reduces the returns on US dollar denominated financial assets, increasing the attractiveness of oil and other commodities to foreign investors. Commodity assets are also regarded as a hedge against inflation, since the US dollar’s depreciation raises the risk of inflationary pressures in the United States. Based on above reasons, we must consider the change of exchange rate and oil price at the same time.
The analysis of financial market movements and co-movements are important for effective diversification in portfolio management. Previous researches commonly use multivariate GARCH models to provide one way to estimate time-varying dependence structure, but it is often based on severe restrictions to guarantee a well-defined covariance matrix. The VAR model and multivariate GARCH models assume that the asset returns follows a multivariate normal or student-t distribution with linear dependence. This assumption is at odds with numerous empirical researches, in which it has been shown that crude oil and exchange rate returns are skewed, leptokurtic and fat-tail. And the dependence relationship between oil and exchange rate is non-linear or asymmetrical. To improve the drawbacks, we use the copula-based GARCH models to capture the volatility and dependence structures of crude oil and exchange rate returns. The copula-based GARCH models allow for better flexibility in joint distributions than bivariate normal or student-t distribution. In addition, three types of marginal models are employed to capture a variety of characteristics of oil and exchange rate returns including of volatility clustering, leverage effect, or the long-run effect. Five types of copula functions are also used to provide a more general dependence structures rather than treat it as simple linear correlation.
Furthermore, model performs better statistically does not equivalently imply that the model performs well in practice, and hence we follow Fleming et al. (2001) to evaluate the out-of-sample covariance forecast performance based on the copula-based GARCH models by the use of a strategic asset allocation problem. We also take the transaction cost problem into consideration and compute the break-even transaction cost, discussed in Han (2006).
Based on the break-even cost, an investor would decide to trade or not if the real transaction cost is much higher than the estimated break-even cost.
Our contribution to the literature is twofold. First, we propose the copula-based GARCH models to elastically describe the volatility and dependence structure of oil and US dollar exchange rate returns. The copula-based GARCH model can be used to capture the probable skewness and leptokurtosis in the oil and exchange rate returns as well as the possibly asymmetric and tail dependence between the oil and exchange rate returns. We find that the symmetric copulas seem superior to the asymmetric copulas in the description of dependence structure between the oil and exchange rate returns, The GARCH model with Student-t copula exhibits better explanatory ability of the oil and USDX futures returns. We also observe that the dependence structure between oil and US dollar exchange rate returns is not very significant before 2003 while becomes negative and descends continuously after 2003.
Second, rather than statistical criteria, we examine whether the copula-based GARCH models can benefit an investor by implementing an asset allocation strategy. In terms of out-of-sample results, we find that the dynamic strategies based on the copula-based GARCH models outperform the static strategy and other dynamic strategies based on the CCC GARCH and DCC GARCH models, which demonstrates that skewness and leptokurtosis of crude oil and USDX futures returns are economically significant. Furthermore, a more risk-averse investor would be willing to pay higher fees to switch his strategy from the static strategy to the dynamic strategies based on copula-based GARCH models.
The remainder of this paper is organized as follows. In the next section, we introduce the copula-based GARCH models in detail. Section 3 presents the empirical estimation results.
Section 4 introduces an economic evaluation methodology and investigates the out-of-sample forecasts of the copula-based GARCH models. Finally, Section 5 concludes.