Multiscale Hedge Ratio Between the Stock and Futures Markets: A New Approach Using Wavelet Analysis and High Frequency Data

In this chapter, we investigate the multiscale relationship between the stock and futures markets over various time horizons. We propose a new approach — the wavelet multiscaling method — to undertake this investigation. This method enables us to make the first analysis of the multiscale hedge ratio using high frequency data (5 min). Wavelets are treated as a “lens” that enables the researcher to explore the relationships that previously were unobservable. The approach focuses on the relationship in three ways: (1) the lead-lag causal relationship, (2) covariance/correlation, and (3) the hedge ratio and hedging effectiveness. Our empirical results show that the future market Granger causes the stock market. We find that the magnitude of the wavelet correlation between the two markets increases as the time scale increases, indicating that the stock and futures markets are not fundamentally different. We also find that the hedge ratio at the second scale has the lowest value and increases monotonically at a decreasing rate, converging toward the long horizon hedge ratio of one, which suggests that the shared permanent component ties the stock and futures series together, and the effect of the transitory components becomes negligible.