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Top1. Introduction
Financial markets are characterized by high volatility. Since then, fluctuations in foreign exchange rates, commodities prices, interest rates, and stock prices have been extreme and unpredictable. It increased the pressure on stock market investors to efficiently manage risk. Price changes make predicting future returns difficult for investors. Derivative instruments are quite useful for hedging in this situation. Index futures are one type of derivatives instrument that is typically utilized for hedging. Index futures contracts allow market players to easily reduce their exposure of adverse price changes. This requires investors to assess the relationship between futures and the underlying stock. Regulators, financial institutions, and investors, on the other hand, make choices on a separate time scale. They operate minute-by-minute, hour-by-hour, day-by-day, month-by-month or year-by year. Due to the different decision-making time horizons among investors, the dynamic structure of stock futures and its underlying stock varies over different time scales. Typically, only the short-run and long-run time frames are illustrated by economists and financial analysts. The inability to divide the data into more than two time periods is caused by the lack of mathematical or statistical techniques.
The time-varying nature of the covariance in many financial markets, as in Lee,1999's study, makes the traditional assumption of the time-invariant optimal hedge ratio unsuitable. Early research merely used the slope of an ordinary least squares regression of stock prices on futures prices to estimate such a ratio. Adopting the stochastic volatility (SV) model (see Anderson and Sorensen 1996; Lien and Wilson 2001) or the bivariate generalized autoregressive conditional heteroskedasticity (GARCH) framework has improved the situation (see Kroner and Sultan 1993; Lien and Luo 1994; Moschini and Myers 2002). The time-varying covariance/correlation aspects are successfully captured in this research, however a lot of them concentrate on the myopic hedging issue. Lien and Luo's (1993, 1994), Howard and D'Antonio's (1991), Geppert (1995), and Lien and Wilson (2001) are not subject to this criticism.
Determining the optimal hedge ratio (OHR) in futures hedging is a critical challenge. Chang et al. (2011) investigated minimum variance hedge ratios for Brent and WTI crude oil using various multivariate conditional volatility models like constant conditional correlation (CCC), dynamic conditional correlation (DCC), vector autoregressive moving average (VARMA-GARCH), and VARMA-asymmetric GARCH models. Their findings highlighted the dependence of the hedge ratio on the specific model employed. In a similar vein, Cotter and Hanly (2012) utilized quadratic, logarithmic, and exponential utility functions to derive optimum hedge ratios. They incorporated GARCH-M to estimate time-varying risk aversion coefficients in analyzing crude oil and natural gas futures at different frequencies (5-day and 20-day). Notably, they observed substantial disparities between utility-based OHRs, particularly in datasets exhibiting skewness and kurtosis. Conlon and Cotter (2013) employed hedge ratios based on minimum variance, Value-at-Risk (VaR), and conditional VaR (CVaR) at varying confidence levels. They also applied wavelet transform to assess hedging effectiveness across different horizons, discovering an increased effectiveness in hedging at longer horizons, particularly using heating oil futures. Moreover, Alexander et al. (2013) considered hedge ratios based on minimum variance and quadratic utility functions for crude oil, gasoline, and heating crack spreads. Their analysis revealed that the variance reduction achieved by all models was statistically and economically indistinguishable from a simple one-to-one “naïve” hedge.