Connecting VIX and Stock Index ETF with VAR and Diagonal BEKK

Chia-Lin Chang,Tai-Lin Hsieh,Michael Mcaleer

doi:10.3390/jrfm11040058

Abstract

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 (named after Baba, Engle, Kraft and Kroner) 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.

Highlights

One of the major reasons why great importance is attached to risk management in financial markets is that the growth in derivative financial products, including the Volatility Index (VIX) and Exchange-Traded Funds (ETFs), has increased market risk
Vector autoregressive (VAR) models were used to determine whether daily VIX returns with different moving average processes affect ETF returns
The autoregressive conditional heteroskedasticity (ARCH)-LM test shows that there is conditional heteroskedasticity in the ETF returns, so the Diagonal BEKK model was estimated to accommodate the conditional heteroskedasticity in the vector autoregressive (VAR) estimates of ETF returns

Summary

Introduction

One of the major reasons why great importance is attached to risk management in financial markets is that the growth in derivative financial products, including the Volatility Index (VIX) and Exchange-Traded Funds (ETFs), has increased market risk. The risk associated with the returns on future investments is referred to as investment risk which, together with the rise in hedging theory, indicates that market participants are increasingly aware of the information implied in markets. Regardless of whether risk management relies on two standard measures of risk, namely the Volatility Index (VIX), compiled by the Chicago Board Options Exchange (CBOE), or the autoregressive conditional heteroskedasticity (ARCH) model (see Engle 1982), such analysis is intended to provide accurate methods of estimating risk to lead to optimal risk management and dynamic hedging strategies

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Conclusion