Narrow Results

This study provides a comparative analysis of hedging determination for four international equity index futures, namely S&P 500, FTSE 100, Nikkei 225, and TAIEX futures contracts. Three alternative estimations are used to determine the hedge ratio for sizing hedge positions: a conventional OLS model, a conventional OLS model with an AR(2)-GARCH(1,1) error structure and an error correction model. Additionally, we evaluate the hedging effectiveness of these alternative models in different stock markets. First, three alternative methods of conducting optimal hedging in different markets are not identical. Moreover, comparisons of in-sample hedging performance reveal that the conventional OLS model outperforms two alternative models for these four stock markets. However, our out-of-sample hedging performance reveals that all hedge ratios which considering heteroscedastic error or cointegration relationship are superior to that of hedge ratio estimated by conventional OLS model. Overall, it is found that considering the existence of heteroscedastic error structure or cointegration relationship cannot be ignored when sizing hedge positions.

In this paper, we undertake a study of occupation time derivatives that is derivatives for which the pay-off is contingent on both the terminal asset's price and one of its occupation times. To this end we use a formula of M. Kac to compute the joint law of Brownian motion and one of its occupation times. General pricing formulas for occupation time derivatives are established and it is shown that any occupation time derivative can be continuously hedged by a controlled portfolio of the basic securities. We further study some examples of interest including cumulative barrier options and discuss some numerical implementations.

The main purpose of this paper is to investigate hedge ratios in terms of the international index futures markets. Instead of looking at hedging in a single market, we construct a simultaneous equations system to study the index hedging in the light of the cross-country linkage and interaction. The three-stage least squares (3SLS) estimating procedure is then applied to CAC40 and FTSE100 indices over the period 1990–2008. The empirical results indicate that the cross-country hedging strategy in both markets is feasible and the investors can bring down the holding position in own futures market. Moreover, the hedging effectiveness of cross-country hedging strategy performs better than the traditional single market hedging strategy in terms of the percentage reduction in variance.

This study provides a comparative analysis of hedging determination for three alternative international equity index futures, namely FTSE 100, NIKKEI 225 and S&P 500 futures contracts. Both the conventional regression and the error correction modeling approaches are used to estimate the minimum-variance hedge ratios and to evaluate the hedging effectiveness. Comparisons of out-of-sample hedging performance reveal that the error correction model outperforms the conventional model, suggesting that the error correction model serves as a better hedging model than conventional model in a hedge using stock index. In addition, the effects of temporal aggregation on hedge ratio estimates and hedging effectiveness are evaluated. It is found that temporal aggregation plays an important role on sizing hedging positions and measuring hedge effectiveness.

In this paper, we analytically derive the adjustments needed for the conventional hedge ratio due to the presence of short-run and long-run dynamics. We also analytically show the performance impact of these dynamics. We apply the method discussed in the paper to eight different stock index futures contracts from seven different countries. It is found that the short-run dynamics has no effect whereas the long-run dynamics may produce significant effects on the optimal hedge ratio and the hedging performance.

This chapter discusses both static and dynamic hedge ratio in detail. In static analysis, we discuss minimum-variance hedge ratio, Sharpe hedge ratio, and optimum mean-variance hedge ratio. In addition, several time series analysis methods such as the multivariate skew-normal distribution method, the autoregressive conditional heteroskedasticity (ARCH) and generalized autoregressive conditional heteroskedasticity (GARCH) methods, the regime-switching GARCH model, and the random coefficient method are used to show how hedge ratio can be estimated.

It is well known that the optimal hedge ratios derived based on the mean-variance approach, the expected utility-maximizing approach, the mean extended-Gini approach, and the generalized semivariance approach will all converge to the minimum-variance hedge ratio if the futures price follows a pure martingale process and if the spot and futures returns are jointly normal. In this chapter, we perform empirical tests to see if the pure martingale and joint normality hypotheses hold using 25 different futures contracts and five different hedging horizons. Our results indicate that the pure martingale hypothesis holds for all commodities and all hedging horizons except for three stock index futures contracts. As for joint normality, we propose two new tests based on the generalized method of moments, which allow for calculating multivariate test statistics that take account of the contemporaneous correlation across spot and futures returns. Our findings show that the joint normality hypothesis generally does not hold except for a few contracts and relatively long hedging horizons.

This chapter first presents a review of various theoretical models and six estimation methods to the optimal futures hedge ratios. Then we use data to show how some of the hedge ratios can be applied to estimate hedge ratio in terms of S&P 500 future. We also show the estimation procedure on how to apply OLS, GARCH, and CECM models to estimate optimal hedge ratios through R language. These approaches are theoretically derived in terms of minimum variance, mean-variance, expected utility, and Value-at-Risk. Various ways of estimating these hedge ratios are also discussed, ranging from simple ordinary least squares to complicated heteroskedastic cointegration methods. Under martingale, joint-normality conditions, and some other conditions, different hedge ratios can be shown that this different ratio can be converted to the minimum variance hedge ratio. Otherwise, the optimal hedge ratios based on the different approaches are in general different. Finally, our empirical findings suggest the importance of capturing the heteroskedastic error structures including the long-run equilibrium error term in conventional regression model.

This chapter estimates and compares the hedge ratios of the conventional and the error correction models using three advanced international stock markets with different time intervals. Comparisons of out-of-sample hedging performance reveal that the error correction model outperforms the conventional model, suggesting that the hedge ratios obtained by using the error correction model do a better job in reducing the risk of the cash position than those from the conventional model. In addition, this chapter evaluates the effects of temporal aggregation on hedge ratios. It is found that temporal aggregation has important effects on the hedge ratio estimates.

The main purpose of this chapter is to investigate hedge ratios in terms of the international index futures markets. Instead of looking at hedging in a single market, we here construct a simultaneous equations system to study the index hedging in the light of the cross-country linkage and interaction. The three-stage least squares (3SLS) estimating procedure is then applied to S&P500, FTSE100, and NIKKEI225 indices over the period 1990–2020. The empirical results indicate that the cross-country hedging strategy in both markets is feasible and the investors can bring down the holding position in own futures market. Moreover, the hedging effectiveness of cross-country hedging strategy performs better than the traditional single market hedging strategy in terms of the percentage reduction in variance.

The following sections are included:

• INTRODUCTION

• PRICE INDEXES
  • Simple Aggregative Price Index
  • Simple Average of Price Relatives
  • Weighted Relative Price Index
  • Weighted Aggregative Price Index

• QUANTITY INDEXES
  • Laspeyres Quantity Index
  • Paasche Quantity Index
  • Fisher’s Ideal Quantity Index
  • FRB Index of Industrial Production

• VALUE INDEX

• STOCK MARKET INDEXES³
  • Market-Value-Weighted Index
  • Price-Weighted Index
  • Equally Weighted Index
  • Wilshire 5000 Equity Index

• BUSINESS AND ECONOMIC APPLICATIONS
  • Deflation of Value Series by Price Indexes
  • Using Business and Economic Index Numbers to Predict Business Cycles
  • CPI, Inflation Rate and Interest Rate

• Summary

• Appendix 19A Options on Stock Indices and Currencies⁶
  • I. Index Options
  • II. Currency Option

• Appendix 19B Index Futures and Hedge Ratio

• Questions and Problems

In this chapter, we shall proceed one step further to investigate how a conditional mean as mentioned in Chap. 2 could be estimated using linear statistical relationship between the two variables. The two-variable linear regression is studied and an application on financial futures hedging will be investigated later in the chapter.