On the optimal mix of corporate hedging instruments: Linear versus nonlinear derivatives

Abstract

We examine how corporations should choose their optimal mix of linear and nonlinear derivatives. We present a model in which a firm facing both quantity (output) and price (market) risk maximizes its expected profits when subjected to financial distress costs. The optimal hedging position generally is comprised of linear contracts, but as the levels of quantity and price-risk increase, the use of linear contracts will decline due to the risks associated with overhedging. At the same time, a substitution effect occursThe authors acknowledge the helpful comments and conversations we have had with Mike Rebello, Steve Smith, Alan Tucker, P. V. Viswanath, Jayant Kale, Tom Webster, and seminar participants at Pace University and the University of South Florida. They also are appreciative of the comments provided by an anonymous reviewer. Smithson (1998) for an excellent summary and also the seminal articles of DeMarzo and Duffie (1995), Froot, Scharfstein, and Stein (1993), and Smith and Stulz (1985. 2 A professional version of this article, with anecdotal and empirical support for our hypotheses, appears in Gay, Nam, and Turac (2002). toward the use of nonlinear contracts. The degree of substitution will depend on the correlation between output levels and prices. Our model also allows us to provide insight into the relation between a firm's derivatives usage and its transaction-cost structure.

Risk Management in Energy Markets

“…This theorem supports results obtained in Brown and Toft (2002) and Gay et al (2003). These authors considered long commodity case and assumed that µ = 0.…”

“…It is important to note that although the distributions and objective functions in Brown and Toft (2002), Gay et al (2003) and this paper are different the conclusions are strikingly similar. This reassures that the results depend on the general features of distribution (randomness of price and quantity and their correlation) and objective function (penalization only of lower tail of cash-flow distribution) and do not depend on specifics of the problem.…”

“…The theorem shows that options and futures can be effectively used to hedge away almost all price risk even though price and quantity are combined in nonlinear way. It shows that even with naive hedge n F = 1 semivariance can be greatly reduced, but in this situation the position generally overhedges (as was pointed out in Gay et al (2003)). The better reduction of risk can be obtained by fine tuning the futures position and introducing option.…”

“…This result was obtained in Gay et al (2003), who have shown that when MPR equals zero and "when firms face only price risk, the optimal hedging position will be comprised strictly of linear instruments (e.g., forwards). "…”

“…Restricting hedging to options only, Ahn, Boudoukh, Richardson, and Whitelaw (1999) discuss optimal hedging with Value-at-Risk as an objective function. The hedging of price and quantity risks with options and futures is considered in Brown and Toft (2002) and Gay, Nam, and Turac (2003). These authors considered the case when futures prices are unbiased predictors of spot prices, and they arrived at similar results concerning relevance of correlation between quantity and price and influence of other parameters on choice between option and futures in hedging.…”