Optimal Futures Position Research Articles

Hedging and the regret theory of the firm

This paper examines the production and hedging decisions of the competitive firm under price uncertainty when the firm is not only risk averse but also regret averse. Regret-averse preferences are characterized by a modified utility function that includes disutility from having chosen ex post suboptimal alternatives. The extent of regret depends on the difference between the actual profit and the maximum profit attained by making the optimal production, and hedging decisions had the firm observed the true realization of the random output price. While the separation theorem holds under regret aversion, the prevalence of hedging opportunities may have perverse effect on the firm’s optimal output level, particularly when the firm is sufficiently regret averse. The full-hedging theorem, however, does not hold. We derive sufficient conditions under which the regret-averse firm’s optimal futures position is an under-hedge (over-hedge). We further show that the firm optimally increases (decreases) its futures position when the price risk possesses more positive (negative) skewness.

Futures hedging with basis risk and expectation dependence

This paper examines the behavior of the competitive firm under price uncertainty. The firm has access to a futures market for hedging purposes. Basis risk exists because the random spot and futures prices are not identical at the time when the futures contracts mature. We show that the firm optimally produces less in the presence than in the absence of the basis risk. Furthermore, we demonstrate that the concept of expectation dependence that describes how the basis risk is correlated with either the random spot price or the random futures price plays a pivotal role in determining the firm’s optimal futures position. Specifically, an under-hedge is optimal if either the random spot price or the random futures price is negatively expectation dependent on the basis risk. On the other hand, an over-hedge is optimal if the random futures price is positively expectation dependent on the basis risk. The firm’s optimal futures position becomes indeterminate if the random spot price is positively expectation dependent on the basis risk.

EXPORT AND HEDGING DECISIONS UNDER CORRELATED REVENUE AND EXCHANGE RATE RISK

This paper examines the behaviour of a competitive exporting firm under joint revenue and exchange rate risk. The firm can trade unbiased currency futures contracts for hedging purposes. We show that neither the separation theorem nor the full-hedging theorem holds when the revenue shock prevails. If the correlation between the revenue shock and the random spot exchange rate is non-positive, the firm optimally produces less than the benchmark level when the revenue shock is absent. If, in addition, the firm is prudent, the optimal futures position is an under-hedge. Finally, we derive sufficient conditions under which the firm's optimal output level is higher in the presence than in the absence of the revenue shock. Operational hedging and financial hedging as such interact in a complicated way to better cope with the multiple sources of uncertainty faced by the firm.

Production and hedging in futures markets with multiple delivery specifications

This paper examines the behavior of the competitive firm under price uncertainty. To hedge the price risk, the firm trades unbiased commodity futures contracts with multiple delivery specifications from which delivery risk prevails. We show that the firm optimally produces less in the presence than in the absence of the delivery risk. We show further that the concept of expectation dependence that describes how the delivery risk is correlated with the random spot price plays a pivotal role in determining the firm’s optimal futures position. Specifically, an under-hedge is optimal if the random spot price is positively expectation dependent on the delivery risk. The firm’s optimal futures position becomes indeterminate if the random spot price is negatively expectation dependent on the delivery risk.

Hedging and the competitive firm under correlated price and background risk

This paper examines the behavior of the competitive firm under correlated price and background risk when a futures market exists for hedging purposes. We show that imposing the background risk, be it additive or multiplicative, on the firm has no effect on the separation theorem. The full-hedging theorem, however, holds if the background risk is independent of the price risk. In the general case of the correlated price and background risk, we adopt the concept of expectation dependence to describe the bivariate dependence structure. When the background risk is additive, the firm finds it optimal to opt for an over-hedge or an under-hedge, depending on whether the price risk is positively or negatively expectation dependent on the background risk, respectively. When the background risk is multiplicative, both the concept of expectation dependence and the Arrow–Pratt measure of relative risk aversion are called for to determine the firm’s optimal futures position.

Production and futures hedging with state-dependent background risk

This paper examines the production and futures hedging decisions of the competitive firm under output price uncertainty and with state-dependent background risk. We show that the firm's optimal production decision is independent of the underlying uncertainty and of the firm's risk attitude. We further show that the firm's optimal futures position is a full-hedge that completely eliminates the output price risk if either the background risk is state-independent, or the firm's utility function is quadratic. When the firm's preferences exhibit prudence, an under-hedge or an over-hedge is optimal should the magnitude of the background risk vary in a monotonic manner with changes in the realized state. When the prudent firm has access not only to the unbiased futures contracts but also to fairly priced options, we construct a reasonable example wherein the firm optimally includes the options in its hedge position. Hence, we offer a rationale for the hedging role of options, which is over and above that of futures, in the case of state-dependent background risk.

Production and hedging under state‐dependent preferences

AbstractThis study examines the behavior of the competitive firm under output price uncertainty and state‐dependent preferences. When there is a futures market for hedging purposes, the firm's optimal production decision is independent of the output price uncertainty and of the state‐dependent preferences. If the futures contracts are unbiased, the firm's optimal futures position is an over‐hedge or an under‐hedge, depending on whether the firm is correlation averse or correlation loving, and on whether the output price is positively or negatively expectation dependent on the state variable. When the firm has access not only to the unbiased futures but also to fairly priced options, sufficient conditions are derived under which the firm's optimal hedge position includes both hedging instruments. This study thus establishes a hedging role of options, which is over and above that of futures, in the case of state‐dependent preferences. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 32:945–963, 2012

Optimal futures heading: Quadratic versus exponential utility functions

AbstractAlthough quadratic and exponential utility functions both lead to mean‐variance expected utility analysis, this study demonstrates that the two approaches produce different optimal futures hedging decisions. Specifically, the deviation between the optimal production level and the optimal futures position is always smaller under the exponential utility framework. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28: 208–211, 2008

The effect of liquidity constraints on futures hedging

AbstractThis article assumes that because of liquidity constraints, a hedge program will be terminated if the cumulative loss from a futures position exceeds a certain threshold. The constraint leads to a smaller futures position. If the hedger has a quadratic utility function, then the optimal futures position is constant regardless of the parameter values and increases as the spot position or the conventional hedge ratio increases. When the capital allocation is small, the hedger tends to ignore this restriction and chooses a larger position. Consequently, the optimal position may decrease as the capital allocation increases. For a moderate capital allocation, the optimal position increases with an increasing capital allocation. Similar properties are established for exponential utility functions. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:603–613, 2003

Risk aversion, disappointment aversion, and futures hedging

AbstractThis article examines the effect of disappointment aversion on futures hedging. We incorporated a constant‐absolute‐risk‐aversion (CARA) utility function into the disappointment‐aversion framework of Gul (1991). It is shown that a more disappointment‐averse hedger will choose an optimal futures position closer to the minimum‐variance hedge than will a less‐disappointment‐averse hedger. The effect of disappointment aversion is stronger when the hedger is less risk averse. A small disappointment aversion will cause a near‐risk neutral hedger to take a drastically different position. In addition, a more‐risk‐averse or disappointment‐averse hedger will have a lower reference point. Numerical results indicate that the reference point of a disappointment‐averse hedger tends to be lower than that of a conventional loss‐averse hedger. Consequently, the disappointment‐averse hedger will act more conservatively, not exploiting profitable opportunities as much as the conventional loss averse hedger will. © 2002 John Wiley & Sons, Inc. Jrl Fut Mark 22:123–141, 2002

Futures Hedging Under Disappointment Aversion

AbstractThis article considers optimal futures hedging decisions when the hedger is disappointment‐averse (Gul, 1991). When the futures contract is a perfect hedge instrument, a disappointment‐averse hedger always holds a position closer to the full hedge than a nondisappointment‐averse hedger. In the presence of basis risk, the optimal futures position is either a partial hedge or a full hedge. Neither Texas hedge nor overhedge could be optimal. The effects of different degrees of disappointment aversion on futures trading are also analyzed. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:1029–1042, 2001

Price, Production, Storage and Futures Markets

We model seasonal, uncertain production of a commodity, with speculative storage. We allow agents to be risk averse, and we allow planned production to respond to price prospects. We also explicitly consider the presence or absence of a futures market in the commodity. Our technique involves a two phase extension of the usual dynamic program, to solve for the equilibrium price and inventory held by storers. In our extra phase, we numerically solve the First Order Conditions for the planned production and futures position taken by the producer. Our main conclusions are: First, we confirm that storage reduces the price volatility, but the availability of futures is important in making storage feasible. Second, the producer takes a longer futures position, in many cases positive (i.e. he hedges by going long the future), than he would in the absence of storage. Third, futures increase average production, but this effect is generally less when storage is available, and might be quite marginal in cases when the producer's optimal futures position is near zero.

Uncertain tax rules and futures hedging

This paper considers the optimal futures hedging decision under uncertain tax treatment. If the Corn Products (CP) rule applies, gains or losses from futures trading can offset business gains or losses. However, under the Arkansas Best (AB) doctrine, offsetting is not allowed. We show that the risk neutral firm will not trade futures contracts if the probability the CP rule prevails is small. When the probability is sufficiently large, the firm will assume an underhedge. A risk averse firm is likely to trade, even if the AB rule prevails. As long as the CP ruling is not a sure thing, the firm will engage in underhedge. The effects of average business profits, the volatility of business profits, and risk aversion on the optimal futures position are provided. Copyright © 1999 John Wiley & Sons, Ltd.

Seasonal patterns of futures hedging and the resolution of output uncertainty

Optimal futures hedging is examined in a two-good model with stochastic output and sequential information arrival. A producer's optimal hedge depends on demand elasticity, sensitivity of his output to weather, his correlation with aggregate output, and how rapidly his output uncertainty is resolved relative to other producers during different seasonal periods. Because regional output uncertainties are resolved at different times, the optimal futures position of a grower will commonly reverse in direction during the crop year. A producer with non-stochastic output who faces price risk arising from demand shocks may remain unhedged or even maintain a long position.

Determination of the Recommended Hedging Ratio

American Journal of Agricultural EconomicsVolume 65, Issue 3 p. 603-605 Note Determination of the Recommended Hedging Ratio Kandice H. Kahl, Kandice H. Kahl Manager of the Research Group in the Department of Economic Analysis and Planning Chicago Board of TradeSearch for more papers by this author Kandice H. Kahl, Kandice H. Kahl Manager of the Research Group in the Department of Economic Analysis and Planning Chicago Board of TradeSearch for more papers by this author First published: 01 August 1983 https://doi.org/10.2307/1240514Citations: 50AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL No abstract is available for this article.Citing Literature Volume65, Issue3August 1983Pages 603-605 RelatedInformation

The Time Pattern of Hedging and the Volatility of Futures Prices

The paper proposes a multi-period model of hedging which allows for a futures position to be revised within the cash holding period. Within this framework, we assess the robustness of the two-period theory of hedging when generalized to many periods. We characterize the normal time path of a hedge and the way it is affected by the requirement that futures accounts mark to market daily. Finally we show how the resolution of production uncertainty over time affects hedging behavior and determines the volatility of futures prices. In the large literature on hedging in futures markets the principal analytical accounts of hedging are framed in a two trade date setting. An agent commits himself now to a future purchase or sale of a good whose cash price later is uncertain. This risk is hedged by purchase or sale of an appropriate number of futures contracts and holding this futures position until the cash transaction is realized. In the present paper we formulate a multi-period model of hedging which allows for the futures position to be revised within the cash holding period. The resulting analysis captures an important institutional reality that is absent in a two trade date model, namely the fact that the day to day fluctuations of the futures price will generate a series of random cash flows over the period during which a futures position is held. This is due to the requirement that futures accounts mark to market daily. Within this framework we address a number of issues. First we assess the robustness of the two period theory of hedging when generalized to many periods. Second we characterize the normal time path of a hedge and contrast futures and forward contracts from the perspective of an individual hedger. Finally, we show how the resolution of production uncertainty over time affects hedging behaviour and determines the volatility of futures prices. While the literature on asset demand in a multiperiod setting is large, futures markets are specifically treated in a limited number of studies. Grauer and Litzenberger (1976) are concerned principally with characterizing the relation of spot and futures prices in a for a storable, periodically produced commodity. They offer a rationale for positive stock holding in markets where spot price exceeds the futures price. Richard and Sundaresan (1980) are also concerned primarily with characterizing price behaviour. Since they posit identical consumers, in equilibrium individual holdings of futures are zero. There is no hedging activity in the sense that we understand it. Breeden (1980b) analyzes the optimal futures position sizes in a multiperiod setting. His framework is more general than ours in that his is a multi-good, multi-asset model where preferences