As stock market indexes are not tradeable, the importance and trading volume of Exchange Traded Funds (ETFs) cannot be understated. ETFs track and attempt to replicate the performance of a specific index. Numerous studies have demonstrated a strong relationship between the S&P500 Composite Index and the Volatility Index (VIX), but few empirical studies have focused on the relationship between VIX and ETF returns. The purpose of the paper is to investigate whether VIX returns affect ETF returns by using vector autoregressive (VAR) models to determine whether daily VIX returns with different moving average processes affect ETF returns. The ARCH-LM test shows conditional heteroskedasticity in the estimation of ETF returns, so that the diagonal BEKK model is used to accommodate multivariate conditional heteroskedasticity in the VAR estimates of ETF returns. Daily data on ETF returns that follow different stock indexes in the USA and Europe are used in the empirical analysis, which is presented for the full data set, as well as for the three sub-periods Before, During, and After the Global Financial Crisis. The estimates show that daily VIX returns have: (1) significant negative effects on European ETF returns in the short run; (2) stronger significant effects on single market ETF returns than on European ETF returns; and (3) lower impacts on the European ETF returns than on S&P500 returns. For the European Markets, the estimates of the mean equations tend to differ between the whole sample period and the sub-periods, but the estimates of the matrices A and B in the Diagonal BEKK model are quite similar for the whole sample period and at least two of the three sub-periods. For the US Markets, the estimates of the mean equations also tend to differ between the whole sample period and the sub-periods, but the estimates of the matrices A and B in the Diagonal BEKK model are very similar for the whole sample period and the three sub-periods.

Additional Metadata
Keywords Stock market indexes, Exchange Traded Funds, Volatility Index (VIX), Global Financial Crisis, Vector autoregressions, moving average processes, conditional heteroskedasticity, diagonal BEKK
JEL Time-Series Models; Dynamic Quantile Regressions (jel C32), Financial Econometrics (jel C58), Asset Pricing (jel G12), International Financial Markets (jel G15)
Persistent URL hdl.handle.net/1765/111552
Series Econometric Institute Research Papers
Citation
Chang, C-L, Hsieh, T-L, & McAleer, M.J. (2018). Connecting VIX and Stock Index ETF with VAR and Diagonal BEKK (No. EI2018-37). Econometric Institute Research Papers. Retrieved from http://hdl.handle.net/1765/111552