期貨指數交易型債券（ETNs）報酬率之動態波動

Volatility Dynamics in the Returns of Commodity Exchange-Traded Notes (ETNs)

本文利用Granger因果關係測試與三種MGARCH模型，並進行穩定性檢測，分析7種期貨指數交易型債（ETNs）和對應的期貨報酬率之關聯。研究結果顯示大部分的落後期ETNs可作為當期商品期貨報酬率的領先指標，此支持MGARCH模型的結果，表示兩者存有長期持續性的關係。以長期而言，ETNs報酬率衝擊的確會影響商品期貨報酬率之變動。另發現ETNs與商品期貨的報酬率存有固定條件相關性。而測試結果顯示兩者存在顯著的時間－變動相關性，表示動態模式較優於固定條件假設的模式。研究指出ETNs與商品期貨報酬率之條件共變異數分別為其落後期的條件共變異數與落後期的市場衝擊的函數，此證明ETNs報酬率波動會影響商品期貨報酬率。

This study uses the Granger Causality test, three Multivariate General Autoregressive Conditional Heteroskedasticity (MGARCH) models and a robustness check to analyze seven commodity ETNs with their corresponding futures contract returns. The study found that a majority of lagged ETNs is a leading indicator to the present values of futures contract, which supports the MGARCH model results indicating the presence of long-run persistence, wherein shocks in ETNs may have an effect on the futures contracts over a long time horizon. Constant conditional correlations between the volatilities of ETN and future contract returns are also discovered. However, additional testing shows the strong presence of time-varying correlations suggest that dynamic models are more appropriate than constant correlation assumptions. This research also finds conditional covariances of the ETNs and futures contracts to be a function of their lagged covariances and lagged cross-products of the shocks, which proves that the volatilities of ETN returns have an impact on their futures contracts.