Dynamic hedge ratio for stock index futures: application of threshold VECM

Abstract

This study represents one of the first papers in stock-index-futures arbitrage literature to investigate the effects of arbitrage threshold on stock index futures hedging effectiveness by using threshold vector error correction model (hereafter threshold VECM). Moreover, in contrast to prior studies focusing on examining case studies involving mature stock markets, this study not only adopts US S&P 500 stock market as the sample but also adds an analysis of one emerging stock market, Hungarian BSI and examines the differences between them. Finally, this investigation employs a rolling estimation process to examine the impact of arbitrage threshold behaviours on the setting of futures hedging ratio. The empirical findings of this study are consistent with the following notions. First, arbitrage behaviour reduces co-movement between futures and spot markets and increases the volatility of both futures and spot markets. Second, this article denotes the outer regime of futures-spot market for the case of Hungarian BSI (US S&P 500) as a crisis (an unusual) condition. Moreover, arbitrage threshold behaviours make remarkable (unremarkable) shift on optimal hedge ratio between two different market regimes for the case of Hungarian BSI (US S&P 500). Finally, the framework involving regime-varying hedge ratio designed in this study provides a more efficient futures hedge ratio design for Hungarian BSI stock market, but not for US S&P 500 stock market.

Acknowledgement

The author is thankful to the suggestion from an anonymous referee.

Notes

¹This study uses the criterion of BIC for selecting the lag lengths for the ADF test (the author is thankful to the suggestion from an anonymous referee). Specifically, the setting with minimum BIC values is used for the ADF test with intercept. Taking the error correction term, namely z_t as an example, the setting with lag length numbers of 4 (2) is for the case of the US S&P 500 (Hungary BSI). Last but not the least, the conclusion from unit root and cointegration tests is robust for the setting with various lag length numbers.

²The value of kurtosis coefficient is one measure of the fatness of the tails of distribution.

³Regarding the determination of lag number, the two most widely used criteria are AIC and BIC. However, in the rolling-estimation used here, each estimation work corresponds to different data periods. To our knowledge, the results of AIC and BIC are time-sensitive, and thus it is impossible to obtain a consistent conclusion regarding the lag number. Furthermore, the parameter numbers increase with the lag number. In detail, consider the threshold VECM with two states, there are additional 12(=2 × 2 × 3) parameters in the setting with p = 2 and q = 2 relative to the setting with p = 1 and q = 1. Therefore, for convenience and to avoid over-parameter problems, this study adopts the simple case with a lag of one, namely p = 1 and q = 1.

⁴See Li and Lin (2004) for the related discussions.

⁵Undeniably, a smidge of inconsistent results occurs in the rolling estimation process. However, it is much less than average. In detail, for the 1109 out-sample results, there is the proportion of 80-in-1109 or 7.2% (105-in-1109 or 9.5%) for the situation of HR ^{k =2}exceeding HR ^{k =1}in the case of US S&P 500 (Hungarian BSI).

⁶See Li (2005) for the related discussions.