Multiperiod hedging using futures: A risk minimization approach in the presence of autocorrelation

Abstract

he single period model, because of its simplicity and often plausible representa-T tion, is used to describe a wide range of economic and financial decision making. Those who advocate such an approach recognize that the world is truly multiperiod and approximately infinite, but find that a single period model is adequate under certain conditions. Either decisions in one period have little or no effect on future periods or the interperiod dependencies are too complex to be captured in the modeling process. These two reasons are the ones most often cited, explicitly or implicitly, as justification for using a single period model. Leatham (1988), Black (1989), Gagnon et al. (1989), Gardner (1989), Lein (1989), McCabe and Solberg (1989), and Thomas (1989).However, hedgers frequently face a multiperiod situation in which a single period approach simply is not adequate. For example, consider an issuer of commercial paper who is paying off old and offering new commercial paper on a weekly basis. If the issuer finds it attractive to hedge interest costs on next week's issue, then all future weekly issues should be hedged, up to and including the final issue needed to fund the assets supported by the issue . This is because short term interest rates tend to follow a random walk and so higher (lower) interest cost next week will lead to higher (lower) interest costs in all the following weeks. Consequently, the hedge position taken today should take into consideration next week's issue as well as all future weekly issues.Not all series being hedged are autocorrelated. Take, for example, the management of a stock portfolio with negligible cash inflows and outflows and no reinvestment. The series being hedged is the return on the stock portfolio which portrays little or no autocorrelation. Thus, a single period approach is appropriate. Of course, this does not rule out the possibility that the hedger will continuously hold Do not quote without permission. 'See Baesel and Grant (1982) for an example of a multiperiod futures trading model.

A statistical model for the relationship between futures contract hedging effectiveness and investment horizon length

“…Equation (8) avoids the problems associated with the regression methodology and gives the minimum variance hedge ratios for any arbitrary investment horizon. Equation (8) leads to hedge ratio behavior that is consistent with the model found in Howard and D'Antonio (1991), but offers greater detail about the sources of the horizon dependency present in both models. In the Howard and D'Antonio (1991) model, the horizon dependency of the hedge ratio is determined exclusively by the size of the first order autocorrelation coefficient of the spot asset return^.^ Equation (8) demonstrates that several factors influence the behavior of the hedge ratio: the relative size of the variance of the permanent and transitory components, u: and CT:; the degree of persistence of the transitory component, a ; and the extent to which the spot and futures prices react to the underlying components.…”

“…Lastly, this study provides in-sample and outof-sample estimates of hedging effectiveness. Howard and D'Antonio (1991) do not apply their model to actual data and Lien and Luo (1993) do not provide any empirical estimates of the effectiveness of their multiperiod hedge ratios.…”

Multiperiod hedging in the presence of conditional heteroskedasticity

“…The approach is consistent with Baillie and Myers (1991). Alternatively, one could use returns as the operative variables as in Heaney and Poitras (1991), Howard and D'Antonio (1991), and Kolb and Okunev (1993). Witt, Schroeder, and Hayenga (1987) compare simple regression hedge ratios using levels, differences, and percentages of agricultural commodities.…”

“…It is also unclear how the above work applies to the case of a bomfide hedger. To resolve the problem, Howard and D'Antonio (1991) and Mathews and Holthausen (1991) provide a simple characterization of the bona j & hedger by supplanting minimization of the variance of end-of-period wealth as the objective. This approach is a direct extension of the one-period framework.…”

Minimum-variance futures hedging under alternative return specifications

“…No assumptions were made about this process except that it has well-defined conditional first and second moments. The conditional means of the return process could include autoregressive terms (Howard & D'Antonio, 1991), cointegration (Kroner & Sultan, 1993) or fractional cointegration (Lien & Tse, 1999) terms, time to maturity effects (Low, Muthuswamy, Sakar, & Terry, 2002), terms reflecting external information (McNew & Fackler, 1994), or even dependences on other futures prices (Neuberger, 1999). Meanwhile, the conditional second moments could include GARCH (Baillie & Myers, 1991) or stochastic volatility (Lien & Wilson, 2001) effects, terms reflecting external information (McNew & Fackler, 1994), or time to maturity effects (Low, Muthuswamy, Sakar, & Terry, 2002).…”