The impact of the lengths of estimation periods and hedging horizons on the effectiveness of a Hedge: Evidence from foreign currency futures

Abstract

INTRODUCTIONohnson (1960), Stein (1961), and more recently, Ederington (1979), McEnally and J Rice (1979), Franckle (1980), and Hill and Schneeweis (1982) apply the principles of portfolio theory to show that the optimal or minimum-risk hedge ratio of a futures contract is given by the ratio of the covariance between the changes in the spot and futures prices and the variance of the changes in the futures prices. The hedger's objective is to minimize the variance of price changes:Min Var(AH,) = Var(AS,) + N;Var(AF,) + 2Nf Cov(AS,, AF,) (1) s.t. AH, = E(AS,) + NfE(AF,)where: AS,, AFt = price changes during period t of the spot currency and the futures contract, respectively; and AH, = target change in value (or target profit from the hedged portfolio) during period t of a portfolio composed of one unit of the spot currency and Nf units of the futures contract.We are thankful to the Columbia Futures Center for supplying us with some data used in this study and to Wichai Saenghirunwattana for computational assistance. Two anonymous referees and Mark Powers of thisJournal provided us with excellent comments which helped us greatly in improving our paper. Any errors are our responsibility. The minimum-risk hedge ratio is determined by setting the derivative of the hedged portfolio variance with respect to Nf equal to zero and solving for Nf*: A. G. Malliaris is theThe optimal or minimum-risk hedge ratio is equivalent to the negative of the slope coefficient of a regression of spot price changes on futures price changes.That is, Nf* can be estimated by running an OLS regression with A S as the dependent variable and A F as the independent variable:where b = NT = beta or optimal hedge ratio.The above regression gives the optimal or correct hedge ratio for a particular dataset. The effectiveness of the minimum-variance hedge can be determined by examining the percentage of risk reduced by the hedge. The measure of hedging effectiveness is defined as the ratio of the variance of the unhedged position, Var(U), minus the variance of the hedged position, Var(H), over the variance of the unhedged position:where Ef denotes the measure of hedging effectiveness. Ederington (1979) shows also that Ef is equal to R2, the coefficient of determination of the OLS regression of eq. (3). That is, Nf' Var(AF,)Var(AS,)Given that R2 is the square of the correlation coefficient, the higher the correlation between spot and futures price changes, the more effective the futures contract is as a hedging instrument, provided the R2 is correctly interpreted as suggested by Lindahl (1989). Minimum-risk hedge ratios and measures of hedging effectiveness are estimated for GNMA futures by Ederington (1979), Hill, Liro, and Schneeweis (1983), and Hill and Schneeweis (1984; for foreign currency futures by Schneeweis (1981, 1984), Grammatikos and Saunders (1983), and Grammatikos (1986); for CD futures by Overdahl and Starleaf (1986); for T-bill futures, by Ederington (1979), Franckle (1980), and Howard and DAntonio (1984; and for stock market index f...

Dynamic hedging of paper with T bill futures

“…The standard assumption of the regression approach is that the moments of the joint distribution of cash and futures prices are constant over time. This assumption, however, runs contrary to the findings of several studies, for instance, Anderson (1985), Malliaris and Urrutia (1991), Kroner and Sultan (1993), and Park and Bera (1987) among others. Consequently the use of constant regression-based hedge ratios may lead to inferior hedging decisions.…”

An empirical analysis of the relationship between the hedge ratio and hedging horizon: A simultaneous estimation of the short‐ and long‐run hedge ratios

“…1 A few studies that consider the effect of the length of hedging horizon include Ederington (1979), Hill and Schneeweis (1982), Malliaris and Urrutia (1991), Benet (1992), and Geppert (1995). These studies find that in-sample hedging effectiveness tends to increase as the investment horizon lengthens.…”

“…For example, some of the studies use such a simple method as the ordinary least-squares (OLS) technique (e.g., see Benet, 1992;Ederington, 1979;Malliaris & Urrutia, 1991). However, others use more complex methods such as the conditional heteroscedastic (ARCH or GARCH) method (e.g., see Baillie & Myers, 1991;Cecchetti, Cumby, & Figlewski, 1988;Sephton, 1993), the random coefficient method (e.g., see Grammatikos & Saunders, 1983), the co-integration method (e.g., see Chou, Fan, & Lee, 1996;Geppert, 1995;Ghosh, 1993;Lien & Luo, 1993), and the co-integration-heteroscedastic method (e.g., see Kroner & Sultan, 1993).…”

An empirical analysis of the relationship between hedge ratio and hedging horizon using wavelet analysis

“…For example, some of the studies use a simple method such as the ordinary least-squares (OLS) technique (e.g., see Benet, 1992;Ederington, 1979;Malliaris & Urrutia, 1991). Others use more complex methods such as the conditional heteroscadestic (ARCH or GARCH) method (e.g., see Baillie & Myers, 1991;Cecchetti, Cumby, & Figlewski, 1988;Sephton, 1993), the random coefficient method (e.g., see Grammatikos & Saunders, 1983), the cointegration method (e.g., see Chou, Fan, & Lee, 1996;Geppert, 1995;Ghosh, 1993;Lien & Luo, 1993), and the cointegration-heteroscadestic method (e.g., see Kroner & Sultan, 1993).…”