VIX指數、美元指數及石油期貨價格對黃豆期貨價格及對咖啡期貨價格之影響

黃冠甄

doi:10.6840/cycu201600624

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VIX指數、美元指數及石油期貨價格對黃豆期貨價格及對咖啡期貨價格之影響

Examining The Impact of Volatility Index, US Dollar Index and Oil Futures Price on Soybeans Futures Price and on Coffee Futures Price

黃冠甄 , Masters　　Advisor：胡為善　　

繁體中文 DOI： 10.6840/cycu201600624

油期貨價格、向量自我迴歸模型、向量自我修正模型、咖啡期貨價格、波動率指數、美元指數、黃豆期貨價格、衝擊反應函數、變異數分解； Coffee Futures Price、Impulse Response Function ； Oil Futures Price ； Soybeans Futures Price ； US Dollar Index ； VAR ； Variance Decomposition ； VECM ； Volatility Index

Abstract │ Reference (16) │ Altmetrics

Abstract 〈TOP〉

近二十年來全球之黃豆、小麥、玉米(簡稱黃小玉)等農產品期貨的交易活動越趨頻繁及飲用咖啡之習慣更加普遍之下，咖啡及黃小玉已成為全球貿易量相當高的大宗物資商品。其中咖啡期貨，一般係以在美國洲際期貨交易所交易的阿拉卡比咖啡為主。此外，由於黃豆、小麥、玉米彼此間的相關係數超過80%以上，且小麥和玉米的期貨價格之波動率走勢過於類似，因此本研究選擇以黃豆代表黃小玉。由於近來黃豆與咖啡受到氣候急遽變化之影響，使得黃豆期貨與咖啡期貨價格呈現大幅波動。本研究主要採用Granger因果檢定、向量自我迴歸 (VAR)、向量誤差修正 (VECM)、衝擊反應函數及預測誤差變異數等模型，以探討黃豆期貨價格與咖啡期貨價格分別對VIX (恐慌)指數、石油期貨價格及美元指數之影響。並探討各變數間是否具有因果關係及長期均衡關係。本研究樣本期間共分兩段，其中第一段期間係自2007年1月1日至2011年12月31日止。由於該段期間受到美國次級房貸及美、歐金融海嘯之影響，使得VIX指數呈現大幅震盪。第二段期間則自2012年1月1日至2015年12月31日止。該段期間則受到氣候異常變化的影響，導致黃豆與咖啡產量下降，因而引起黃豆期貨與咖啡期貨的價格暴漲。本研究比較不同期間內黃豆期貨價格與咖啡期貨價格，分別與VIX指數、石油期貨價格及美元指數間之互動關係。實證結果彙總如下： 
1.根據ADF單根檢定之結果，發現各期間內所有變數之原始序列，除了VIX指數之外，其他皆無法拒絕非定態之虛無假設，表示存在單根現象，但經由一階差分後，所有變數皆呈定態。
2.本研究發現，黃豆期貨價格與VIX指數、石油期貨價格及美元指數在各個階段中皆具備有共整合關係；但咖啡期貨價格只在全樣本期間及第二段期間內，與VIX指數、石油期貨價格及美元指數存在共整合關係。
3.由向量誤差修正結果得知，在全樣本期間及第一段期間內，黃豆期貨價格與VIX指數、石油期貨價格及美元指數之最適落後期均為一期。但修正誤差項對VIX指數及油價均呈顯著正向關係，意即VIX指數與油價須經長時間之修正才能調整至均衡。而在第二段期間內，黃豆期貨價格與VIX指數、石油期貨價格及美元指數之最適落後期數均為1期，且修正誤差項對黃豆期貨價格呈現顯著正向關係，表示黃豆期貨價格也須經長時間修正才能調整至均衡；但修正誤差項對VIX指數卻呈顯著負向關係，表示VIX指數可迅速調整至均衡；至於在第二段期間內，咖啡期貨價格與VIX指數、石油期貨價格及美元指數之最適落後期數亦均為1期，但其修正誤差項對VIX指數呈顯著正向關係，顯示VIX指數須經長時間之修正才能調整至均衡；但其對石油期貨價格卻呈顯著負向關係，表示石油期貨價格可迅速調整至均衡。
4.本研究由共整合結果可知，在第一段期間內，咖啡期貨價格與VIX指數、油價及美元指數間並無共整合之情形，因此，本研究將各相關變數取一階差分後之定態序列，以向量自我迴歸模型 (	VAR)，來探討各變數間之短期互動分析，其結果顯示，最適落後期數亦為1期。本研究透過向量自我迴歸模型得知，咖啡期貨價格受到VIX指數落後2期，油價落後1期及美元指數落後1期之負向影響。而VIX指數則受到咖啡期貨價格落後1期，其自身落後1期及油價落後1期之影響，石油期貨價格受到其自身、咖啡期貨價格及VIX指數落後1期之負向影響，但受美元指數落後二期之正向影響。而美元指數則受到VIX指數落後一期之影響。
5.本研究根據Granger因果關係測試結果發現，在全樣本期間內，VIX指數及石油期貨價格皆對黃豆期貨價格呈現單向因果關係，而VIX指數對咖啡期貨價格及石油期貨價格亦呈單向因果關係；但咖啡期貨價格對美元指數又呈單向因果關係。至於在第一段期間內，VIX指數及石油期貨價格對黃豆期貨價格呈單向因果關係。而VIX指數對石油期貨價格及美元指數亦呈單向因果關係。另外，VIX指數與咖啡期貨價格則呈現互相回饋之關係；而石油期貨價格對咖啡期貨價格則呈現單向因果關係；至於VIX指數與美元指數對石油期貨價格則呈現單向因果關係；且VIX指數及咖啡期貨價格對美元指數，亦呈單向因果關係。此外，在第二段期間內，本研究發現石油期貨價格對VIX指數，呈單向因果關係。而VIX指數對咖啡期貨價格與美元指亦呈單向因果關係。
6.本研究由衝擊反應函數結果發現，五個變數均受其本身之衝擊效果最為明顯，且當該五個變數受到衝擊後，均會在短期間內迅速收斂，表示該金融市場為有效率的市場。
7.在預測誤差變異數分解方面，本研究發現在全樣本期間及在第二段期間中，五個變數除石油期貨價格、咖啡期貨價格及美元指數外，其自身解釋之程度都相當高，較不易由外在因素加以解釋。但石油期貨價格在第一段期間內，除受自身之影響降至75%左右，且受到黃豆期貨價格之影響達16%。而美元指數在第一段期間內，除受其自身之影響易降至79%左右，其受到黃豆期貨價格及石油期貨價格之影響共超過15%。

Parallel Abstract 〈TOP〉

Over the past two decades, the global agricultural futures such as soybeans, corns and wheats trading activities became more frequent than before, and the habit of drinking coffee was also more prevalent than before. Today coffee and soybeans, corns as well as wheats become the large trading volumes of bulk commodities. Of which, Acarbian coffee futures contracts have been traded at the Continental Trading Exchange in the United States. As the correlation coefficients among soybeans, corns and wheats are higher than 80%, and the trend of the volatility of corns and wheats are very similar, this study determines to use soybeans and coffee as the studying target. Additionally, the prices of soybean futures and coffee futures fluctuated dramatically recently by the impact of heavy change in weather. This investigation employs the Granger causality test, vector autoregression (VAR) test, vector error-correction model (VECM), the impulse response function (IRF) and the forecasting error variance decomposition (FEVD) models to examine the long-term equilibrium relationship among soybean futures price or coffee futures price with the VIX index, oil futures price and US dollar index, respectively. This study divides the full sample period into two sub-periods: the first sub-period runs from 2007/1/1 to 2011/12/31 as the VIX index fluctuated dramatically due to US surprime loan crisis and five european counties crisis; the second sub-period runs from 2012/1/1 to 2015/12/31, as the prices of soybeans and coffee dramatically fluctuated due to the heavy change in weather conditions. Empirical results are summarized below:
1.ADF results show that, during the full sample period of the original sequence of all variables except the VIX index can not reject the assumptions of non-stationary, suggesting that the existence of an unit root. A first-order difference is taken, then all the variables become stationary.
2.This study finds that, during all the periods, the soybean futures prices have co-integration with the VIX index, oil futures price and US dollar index. Meanwhile, during the full sample period and the second sub-period, the coffee futures prices have co-integration with the VIX index, oil futures price and US dollar index.
3.The vector error correction results show that, during the full sample period and the first sub-period, the optimum lag periods for the soybean futures prices, the VIX index, oil futures prices are 1-lag term behind. However, the VIX index and oil futures price have significantly positive correlations with soybeans futures price, suggesting that it will take a long time to adjust the error correction into equilibrium. Whereas, during the second sub-period, the optimum lag period for the soybeans futures price, VIX index, the oil futures price and US dollar index is also 1-lag term behind, and the correction of the error terms for the soybeans futures price is significantly positive, while that for the VIX index is significantly negative, suggesting that the soybeans futures prices can be adjusted for a long time to obtain the equilibrium, but the VIX index is easily adjusted into equilibrium. During the second sub-period, this study finds that the optimum lag period of the coffee futures prices with that of the VIX index, oil futures prices and US dollar index is also 1-lag term behind and the correction of the error terms for the VIX index is significantly positive, but that for the oil price is significantly negative, implying that the VIX can be adjusted for a long time into equilibrium. However, the oil futures price is easily adjusted into equilibrium.
4.The co-integration results indicate that, during the first sub-period, the coffee futures price does not have co-integration with the VIX index, oil futures prices and US dollar index. Therefore, a first-order difference is then taken and a vector auto-regression (VAR) model is employed to examine the short-term interaction among the above variables. This investigation finds that the optimal lag term behind is still one-lag term behind. The VAR test results show that the coffee futures price is negatively affected by the 2-lag term of the VIX index and the 1-lag term of oil price and US dollar index; while the VIX index is negatively affected by the one-lag term of the coffee futures price and the VIX index itself, and is positively affected by the one-lag term of the oil futures price; while oil futures price is positively affected by the one-lag term of the coffee futures price and US dollar index, while the oil futures price is negatively affected by the one-lag term of the VIX index and oil futures price itself, and the two-lag term of the US dollar index. The US dollar index is positively affected by the one-lag term of the VIX index.
5.The Granger causality test results show that, during the full sample period, the VIX index, and oil futures price unilaterally affects the soybean futures prices, while the VIX index unilaterally affects the oil futures prices. Additionally, the VIX index unilaterally affects the coffee futures prices, and the coffee futures price unilaterally affects the US dollar index. During the first sub-period, the VIX index and oil futures price unilaterally affect the soybeans futures price. While the VIX index and US dollar index unilaterally affects the oil futures price, and the VIX index unilaterally affects the US dollar index. Furthermore, the VIX index and the coffee futures price have mutually causal effect. The oil futures price unilaterally affects the coffee futures price, and the VIX index and the US dollar index unilaterally affect the oil futures price. Meanwhile, the coffee futures price and the VIX index unilaterally affect the US dollar index. During the second sub-period, the oil futures price unilaterally affects the VIX index and the VIX index unilaterally affects the coffee futures price and the US dollar index. 
6.The impulse response function results show that every parameter is most significantly affected by the shock arising from itself, and it converges quickly during a short period, suggesting that the financial market is efficient.
7.Empirical findings from the forecast error variance decomposition indicate that the explanatory power arising from each variable itself is very high during the full sample period and the second sub-period. However, during the first sub-period, oil futures price is affected by itself for only 75%, and is also affected by soybeans futures price for about 16%; meanwhile, the US dollar index is affected by itself for only 79%, and is also affected by soybeans futures price and oil futures price.

Reference ( 16 ) 〈TOP〉

劉苑伶 (2000) ，「三個能源期貨價格預測模型比較分析及匯率關聯性之研究－以NYMEX與ICE為例」，中原大學企業管理研究所碩士論文。
連結：
翁靖迪 (2008) ，「美國大宗穀物期貨價格時間序列分析—短期預測模型比較」，國立台灣大學農業經濟研究所碩士論文。
連結：
張欣怡 (2012) ，「波動率指數、美元指數與石油期貨價格關聯性之研究」，中原大學企業管理研究所碩士論文。
連結：
簡慈盈 (2013) ，「碳權價、油價與歐洲股價關聯性之研究」，中原大學企業管理研究所碩士論文。
連結：
Copeland, Maggie M. & Copeland, Thomas E. (1999). “Market Timing: Style and Size Rotation Using the VIX.” Financial Analysts Journal, 55, 73-81.
連結：

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