The Impact of Delivery Risk on Optimal Production and Futures Hedging

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractMultiple delivery specications exist on nearly all commodity futures contracts. Sellers are typically allowed to choose among several grades of the underlying commodity. On the delivery day, the futures price converges to the spot price of the cheapest-to-deliver grade rather than to that of the par-delivery grade of the commodity. This imposes an additional delivery risk on hedgers. This paper derives the optimal production and futures hedging strategy for a risk-averse competitive rm in the presence of delivery risk. We show that, depending on its relative valuation, the delivery option may induce the rm to produce more than in the absence of delivery risk. If delivery risk is additively related to commodity price risk, the rm will under-hedge its exposure to commodity price risk. If delivery risk is multiplicatively related to commodity price risk, the rm will under-or over-hedge this exposure. For constant relative risk aversion, this is illustrated by a numerical example. JEL classication: G11, D81Keywords: delivery risk, futures, risk management, production * We gratefully acknowledge nancial support from the Germany/Hong Kong Joint Research Scheme provided by the German Academic Exchange Service (DAAD) and the Hong Kong Research Grants Council (RGC). We would like to thank Günter Franke and Donald Lien for very helpful comments and Harald Lohre for valuable research assistance. Remaining errors are our responsibility. 1The impact of delivery risk on optimal production and futures hedgingMultiple delivery specications exist on nearly all commodity futures contracts. Sellers are typically allowed to choose among several grades of the underlying commodity. On the delivery day, the futures price converges to the spot price of the cheapest-to-deliver grade rather than to that of the pardelivery grade of the commodity. This imposes an additional delivery risk on hedgers. This paper derives the optimal production and futures hedging strategy for a risk-averse competitive rm in the presence of delivery risk. We show that, depending on its relative valuation, the delivery option may induce the rm to produce more than in the absence of delivery risk. If delivery risk is additively related to commodity price risk, the rm will under-hedge its exposure to commodity price risk. If delivery risk is multiplicatively related to commodity price risk, the rm will under-or over-hedge this exposure. For constant relative risk aversio...

Futures hedging with basis risk and expectation dependence

“…On the delivery date, the futures price as such converges to the spot price of the cheapestto-deliver grade and not to that of the par-delivery grade of the commodity (Adam-Müller and Wong, 2003;Kamara and Siegel, 1987;Lien, 1988Lien, , 1991Lien and Wong, 2002;Wong, 2014).…”

Production and hedging implications of executive compensation schemes

“…8 However, according the later empirical analysis conducted by Chang (1985), the pro unbiased future pricings neither convincingly confirm nor deny the normal backwardation 1 Other extensions appear in Holthausen (1979) and Danthine (1980, 1981). 2 For example, Stulz (1984), Benninga et al (1985), Adam-Muller (1997), Adam-Muller and Wong (2003), Machnes (2005), Smith and Stulz (1985), Froot et al (1993), Nance et al (1993), DeMarzo and Duffie (1995), Mian (1996), Graham and Smith (1999), Graham and Rogers (2002), Tufano (1996), Battermann et al (2000), Bartram (2006), Bartram et al (2009) Adam et al (2007), Mackay and Moeller (2007) and Campello et al (2011). We rarely see a model that simultaneously integrates all the following: managers-owners distinction of risk aversion and incentives, equity-linked compensation as an incentive mechanism, i.e., Grossman and Hart (1983), the determination of output, and the conduction of risk management activities.…”