Multiperiod hedging with futures contracts

Abstract

The hedging problem is examined where futures prices obey the cost-ofcarry model. The resultant hedging model explicitly incorporates maturity effects in the futures basis. Formulas for the optimal static and dynamic hedges are derived. Although these formulas are developed for the case of direct hedging, the framework used is sufficiently flexible so that these formulas can be applied to many cross-hedging situations. The performance of the model is compared with that of several other models for two hedging scenarios: one involving a financial asset and the other involving a commodity. In both cases, significant maturity effects were found in the first and second moments of the futures basis. Our hedging formulas outperformed other hedging strategies on an ex-ante basis.

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).…”

Forecasting oil price movements: Exploiting the information in the futures market

“…Taking logs, Equation (1) can be rewritten as: (2) where the left side of the equation is the log-basis. Following Low et al (2002) and Sarno and Valente (2005), it can be assumed that market expectations about the cost of carry c for each period are drawn from independent and identical normal distributions, with mean c -and variance :…”

“…Since both spot and futures prices series are non-stationary (as shown in the next section), the stationarity of their relationship implies cointegration between futures and spot prices with a cointegrating relationship given by: (5) where the cointegrating vector z t is the log-basis adjusted for the time-tomaturity effect and can be seen as the stationary deviation from the cost of carry model. 5 In turn, the Granger representation theorem (Engle & Granger, 1987) implies that futures and spot prices can be represented by a VECM, where the log-basis adjusted for the expected cost of carry (z t ) works as the error correction term (Low et al, 2002;.…”

“…This work contributes to the literature in that it provides a forecasting model built on the dynamic relationship between spot and futures prices. The empirical methodology that is followed relies on a particular version of the cost of carry model, as described by Low, Muthuswamy, Sakar and Terry (2002) and applied by Sarno and Valente (2005) in a similar forecasting approach. The cost of carry model implies the existence of a long-run equilibrium between the spot and the futures prices.…”

Structurally sound dynamic index futures hedging

“…This predictable component in the level (but not necessarily the variance) of futures/spot returns was captured by error-correction hedging models, based on the notion of cointegration. Examples include Kroner and Sultan (1993); Brenner and Kroner (1995);and Low, Muthuswamy, Sakar, & Terry (2002).…”