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Journal ArticleDOI

Financial Constraints, Competition and Hedging in Industry Equilibrium

01 Oct 2007-Journal of Finance (Blackwell Publishing Inc)-Vol. 62, Iss: 5, pp 2445-2473
TL;DR: In this paper, the authors analyze the hedging decisions of firms, within an equilibrium setting that allows them to examine how a firm's hedging choice depends on the hedge choices of its competitors.
Abstract: We analyze the hedging decisions of firms, within an equilibrium setting that allows us to examine how a firm's hedging choice depends on the hedging choices of its competitors. Within this equilibrium some firms hedge while others do not, even though all firms are ex ante identical. The fraction of firms that hedge depends on industry characteristics, such as the number of firms in the industry, the elasticity of demand, and the convexity of production costs. Consistent with prior empirical findings, the model predicts that there is more heterogeneity in the decision to hedge in the most competitive industries.

Summary (5 min read)

Introduction

  • Specifically, firms gain more from additional investment when other firms in the industry invest less, which implies that a firm has an incentive to make risk management choices that transfer cash flows to those states in which its competitors are relatively cash constrained.
  • In the Shleifer and Vishny model capital structure choices are interdependent because the bankruptcy costs of an individual firm are lower if other firms within the same industry are financially healthy, and compete to buy the assets of failing firms.
  • Géczy, Minton, and Schrand (1997) find that in industries with many firms there is more heterogeneity in hedging decisions than in industries with relatively few firms.
  • Section VII discusses the empirical implications of the model and Section VIII concludes.

A Technology and Production Costs

  • The production of the firm’s output requires two variable inputs, raw materials and labor, whose quantities are denoted respectively by X1 and X2.
  • The authors choose this specification of the production function so that the associated cost function is convex in output, and an increase in investment k reduces variable (and marginal) production costs.
  • For almost all their results, the authors need only the first term and hence only one variable input.
  • Labor and material, however, can be paid for when profits are realized, so the demand for these inputs is not constrained by the availability of financing.
  • Providers of external finance for capital investment are usually at “arms length” and are not able to monitor the firm’s managers easily.

B Hedging and Production Costs

  • For a given level of output q, the cost function (2) is convex in k, which implies that hedging reduces a firm’s expected production costs.
  • To determine the magnitude of the cost reduction achievable by hedging, the authors compare the cost functions of hedgers and nonhedgers.
  • Since γ(k) is a concave function, Jensen’s Inequality implies E(w) = E ( c γ(k) − c γ(k̄) ) > 0. (7) The fact that E(w) is positive implies that hedging reduces a firm’s expected production costs, where E(w) represents the expected cost reduction per unit of output.

E Competition

  • The authors assume that firms are Cournot competitors in the product market.
  • Each firm observes the hedging choices of the other firms as well as the realization of the common cash flow shock before deciding on its own output.
  • Equilibrium requires each firm’s output choice to be a best response to the output choices of all other firms.

II. The Profit Function of a Price-Taking Firm

  • 9,10 The fact that the output choice can be conditioned on the realizations of investment (or production cost), which the authors refer to as the production flexibility option, causes the profit function to be convex.
  • Intuitively, as the product price increases and the firm produces more, the benefit of the lower expected production cost associated with hedging increase.
  • 12 Perhaps less obvious, the benefit of production flexibility enjoyed by an unhedged firm does not also increase in price.
  • In the next section, the price level is determined by demand and supply.
  • The authors show that this has a material effect on the hedging decision of an individual firm, and hence firms’ hedging decisions are interdependent.

III. Subgame-Perfect Nash Equilibria (SPNE)

  • The authors model is a two-stage game with the following structure: Stage 1 : All firms simultaneously decide whether or not to hedge their cash flows, given the hedging strategies of all other firms.
  • After investing their cash flows and observing the investments made by other firms, all firms play a Cournot game in output, also known as Stage 2.
  • The equilibrium price and output depend on the number of firms that decide to hedge in the first stage and the realization of the cost shock w. Let Πu(w, mu) denote the profit of an unhedged firm in the second-stage game, and Πh(w, mu) denote the profit of a hedged firm.
  • Furthermore, let EΠu(w, mu) and EΠh(w, mu) denote the corresponding expected profits in the first stage.
  • In a pure strategy subgameperfect equilibrium (SPNE), no firm has an incentive to change its hedging strategy given the hedging strategies of all other firms.

A The Second Stage

  • Consider the output decision of an unhedged firm after the cost shock w has been realized.
  • In a Cournot-Nash equilibrium, each firm’s output decision must maximize profit, given the output decisions of all other firms.
  • Since E(w) is positive, as more firms decide not to hedge (mu increases), the expected equilibrium price increases and the expected output falls.
  • Aggregate hedging decisions also affect the volatility of the equilibrium price: Since P (w, mu) and w are positively correlated, as indicated by equation (24), they partially offset each other (a natural hedge).

B The First Stage

  • To decide whether or not to hedge in the first stage, a firm compares the expected profit of hedging with the expected profit of not hedging, given the hedging choices of all other firms.
  • (28) Equation (28) is similar to equation (16) except that here, the price is endogenous and affected by the hedging choices of all firms.
  • Lemma 1 shows that the difference in the payoff between an unhedged and a hedged firm is determined by two terms, one associated with E(w) and the other associated with E(w2).
  • Thus, the more the number of firms that remain unhedged, the greater is the incentive for an individual firm to hedge and vice versa.
  • In a state in which aggregate cash flows are relatively low, aggregate output will be low and the equilibrium price will be high if most firms are unhedged.

IV. Analysis of the Equilibrium

  • The following proposition gives necessary and sufficient conditions for the existence of an equilibrium.
  • If the lower of the two bounds exceeds unity, all firms remain unhedged.
  • These results - stated more formally below - are intuitive.
  • Thus, irrespective of the number of firms in the industry and the slopes of the demand and marginal cost curves, under the same set of parameters for which all firms in a price-taking industry would hedge (or remain unhedged), a majority of firms in any other industry would do the same.
  • It is also clear from this comparison that θ measures the relative dominance of the production flexibility versus the cost reduction effects if the aggregate hedging strategies have no impact on the equilibrium price.

V. Comparative Statics

  • The authors now consider how the proportion of firms that hedge, and hence the proportion that do not hedge depends on industry characteristics such as the number of firms in the industry (extent of competition), the convexity of the cost function, the slope of the demand function, and the size of the market.
  • To understand why the parameter changes have this implication, consider first the effect of a flatter industry demand curve (lower b) or steeper marginal cost curve (higher δ).
  • If the size of the market is sufficiently small (θ > 0), then the benefit from the cost-reducing effect is lower and remaining unhedged is more attractive.
  • Immediate from the expression in (31), also known as Proof.
  • Equation (24) suggests that the sensitivity of the industry price to cost shocks, dPdw = bmu nb+δ+b = nb(mu/n) nb+δ+b , depends on the proportion of firms that remain unhedged as well as the industry parameters n, b, and δ.

VI. Model Extensions

  • The authors first analyze the case of stochastic demand in order to clarify the relationship between their framework and that of FSS (1993).
  • Next, the authors investigate how the equilibrium changes if some firms are financially unconstrained.
  • Finally, the authors check whether their equilibrium continues to exist if firms can choose from a continuum of hedging strategies (partial hedging).

A Stochastic Demand

  • FSS (1993) show that given a profit function that is concave in investment, a financially constrained firm prefers to hedge its cash flows as long as the covariance between cash flows and investment opportunities is not too high.
  • In their framework, the concavity of the profit function gives the firm a natural incentive to hedge.
  • Thus, if the covariance between cash flows and investment opportunities is sufficiently high, then even with concave profit functions financially constrained firms are better off remaining unhedged.
  • FSS (1993) do not explicitly model the production decisions of firms, but choose instead to work in terms of a “reduced-form” profit function that is concave in investment.
  • To see this more formally, let the industry demand curve be denoted by.

B Unconstrained Firms

  • The authors analysis above assumes that all firms are financially constrained and thus they always invest less than their unconstrained optimum.
  • The authors now consider the possibility that muc firms in the industry are unconstrained and thus they invest at the first-best levels.
  • In general, the first-best investment levels of these firms depend on the hedging and investment decisions of the other firms in the industry, and are determined as part of a Nash equilibrium.
  • It is clear, however, that in equilibrium, the unconstrained firms will invest more in states of nature in which the constrained firms invest relatively less, that is, their cash flows are lower.
  • This is because the industry price is higher if the investment and cash flows are lower, providing the unconstrained firms greater incentive to invest more.

C Continuous Hedging Strategies

  • Up to this point the authors have assumed that firms follow discrete hedging strategies, that is, firms either completely hedge their cash flows or they do not hedge at all.
  • The authors briefly describe the consequences of relaxing this particular assumption.
  • Assume that firms can choose from a continuum of hedging strategies and let h ∈ [0, 1] represent a firm’s hedge ratio.
  • The equilibrium can be characterized as the intersection of the reaction function of each firm.
  • The authors find that for a range of parameter values, the reaction functions are discontinuous, so that an interior equilibrium does not exist.

VII. Empirical Implications and Relationship

  • The authors model is motivated by the observed heterogeneity of hedging practices that is typical of many industries.
  • Another dimension of hedging behavior that has been noted - but not extensively studied - is that of “between-industry” variation in the proportion of firms that hedge.
  • Specifically, the model implies that the sensitivity of the industry price to common shocks that affect cash flows, and hence the production costs of firms in an industry, will be higher if:27 The industry is more competitive (more firms in an industry).
  • Allayannis and Weston (1999) find that firms operating in industries with lower price-cost margins are more likely to use foreign currency derivatives, as shown in Figure 1.
  • It is easy to check from equation (31) that when the fraction of firms that hedge is less than one-half, θ must exceed zero.

VIII. Conclusion

  • The existing literature explores how financial constraints impact the incentive for firms to hedge.
  • In the spirit of Maksimovic and Zechner (1991) and Shleifer and Vishny (1992), the authors show that the proportion of firms that hedge is determined within the equilibrium.
  • The authors analysis helps us understand why the authors observe extensive diversity in risk management strategies even within the same industry.
  • Tufano (1996) suggests that this diversity is due to differences in managers’ compensation packages, which in turn provide different incentives to hedge.
  • The authors analysis predicts that in industries with more competition, more inelastic demand, and less convexity in production costs, the authors should observe more heterogeneity in hedging choices.

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Financial Constraints, Competition, and
Hedging in Industry Equilibrium
TIM ADAM, SUDIPTO DASGUPTA, and SHERIDAN TITMAN
ABSTRACT
We analyze the hedging decisions of firms, within an equilibrium setting that allows us to examine how
a firm’s hedging choice depends on the hedging choices of its competitors. Within this equilibrium
some firms hedge while others do not, even though all firms are ex ante identical. The fraction of
firms that hedge depends on industry characteristics, such as the number of firms in the industry, the
elasticity of demand, and the convexity of production costs. Consistent with prior empirical findings,
themodelpredictsthatthereismoreheterogeneityinthedecisiontohedgeinthemostcompetitive
industries.
Adam is from the MIT Sloan School of Management, Dasgupta from the Hong Kong University of Science
& Technology (HKUST), and Titman from the University of Texas. We are grateful to Axel Adam-M¨uller,
ohnke Bartram, Nittai Bergman, Dirk Jenter, Peter Mackay, Gordon Phillips, James Vickery, Keith Wong,
and an anonymous referee for valuable suggestions that greatly improved the paper. We would also like to
thank seminar participants at HKUST, MIT, National University of Singapore, Tel Aviv University, University
of Mainz, and the annual meetings of the American, European, and Western Finance Associations for their
comments and discussions. Any remaining errors are our own.

Risks have costs as well as benefits. The costs have been the focus of a growing literature on
corporate risk management and hence are well understood.
1
In contrast, the idea that risk
can also be beneficial has been recognized in the real options literature but has largely been
ignored in the risk management literature.
Theobjectiveofthispaperistoanalyzethehedgingdecisionsoffirmsthattakeinto
account both the costs and the benefits of their risk exposures. To do so we develop a model
in the spirit of Froot, Scharfstein, and Stein (1993) (henceforth, FSS). FSS assume that
internal funds are less costly than external funds. Consistent with this view, we consider the
extreme case in which firms must rely solely on internal funds to finance their investments.
In contrast to FSS, however, we model a firm’s output decision explicitly. In particular, we
assume that firms have the flexibility to adjust their output levels in response to realized
production costs after making their investment choices. Within this setting, the volatility of
cash flows, which affect investment and in turn production costs, can benefit firms that have
the flexibility to produce more when costs are low and less when costs are high. We show
that because of this flexibility, a firm’s profit function can be convex in investment, which
provides financially constrained firms an incentive not to hedge.
A further contribution of our model is that it analyzes how these incentives affect firms’
risk management decisions within the context of an industry equilibrium in which the equi-
librium price is determined endogenously. Since the equilibrium output price is a function
of aggregate investment and hedging decisions, a firm’s risk management choice is affected
by the investment/hedging decisions of other firms in the industry. Specifically, firms gain
more from additional investment when other firms in the industry invest less, which implies
1

that a firm has an incentive to make risk management choices that transfer cash flows to
those states in which its competitors are relatively cash constrained. This in turn implies
that an individual firm’s incentive to hedge increases as more firms in the industry choose
not to hedge and vice versa. As a result, an industry equilibrium can exist in which some
firms hedge and others do not, even though all firms are ex ante identical.
The model developed in this paper is related to existing research that explores why
similar firms in the same industry often choose different capital structures. In particular,
our equilibrium analysis is related to Maksimovic and Zechner (1991), who show that ex-
ante identical firms may choose different debt-equity ratios, and De Meza (1986), who shows
that otherwise identical firms may choose different production technologies in an industry
equilibrium. Our model is also closely related to Shleifer and Vishny (1992), who examine
how a firm’s bankruptcy/liquidation costs depend on the financial health of its competitors.
In the Shleifer and Vishny model capital structure choices are interdependent because the
bankruptcy costs of an individual firm are lower if other firms within the same industry are
financially healthy, and compete to buy the assets of failing firms. Similarly, the firms in our
model have an incentive to generate cash flows in those situations in which other industry
participants are financially constrained.
2
Our model generates a number of predictions that relate industry characteristics to the
fraction of firms that hedge.
3
We find that in equilibrium approximately half of the firms use
derivatives, while the other half do not. This is consistent with empirical studies that show
that on average “hedging” and “not hedging” are equally common in the nonfinancial sector.
4
The exact fraction of derivatives users depends on industry characteristics such as the number
2

of firms in the industry (degree of competition), the elasticity of demand, the convexity of
production costs, and market size. For example, our model implies that in industries with
more competitors, steeper industry demand curves, and flatter marginal cost curves, there
is more heterogeneity in firms’ hedging choices, that is, the fraction of firms that hedge in
industry equilibrium moves towards 50% (the point of maximum heterogeneity). In addition,
we find that larger market size results in a larger fraction of firms hedging in equilibrium.
These predictions are consistent with several empirical studies. Allayannis and Weston
(1999), for example, find a positive correlation between mark-ups, which proxy for the degree
of competition in an industry, and the extent of derivatives usage in that industry. G´eczy,
Minton, and Schrand (1997) find that in industries with many firms there is more hetero-
geneity in hedging decisions than in industries with relatively few firms. In addition, the
idea that hedging choices affect product market prices is consistent with Nain (2004), who
documents that output prices are less volatile in industries in which more firms hedge their
foreign exchange rate risks.
The rest of the paper is organized as follows. In Section I, we outline the basic model
and show that given our assumptions a firm’s profit function is convex in investment and
the equilibrium output price. In Section II, we consider the special case of a price-taking
firm and illustrate how the profit function can be convex as well as concave in investment.
Sections III and IV outline the subgame-perfect Nash equilibrium for our two-stage game.
In Section V we discuss the comparative static results and in Section VI we consider several
extensions of the model. Section VII discusses the empirical implications of the model and
Section VIII concludes.
3

I. The Model
Consider an industry with n identical firms. At date 1, all firms receive identical but
uncertain cash flows, which they can invest in productive capital that generates returns at
date 2.
5
At date 0, firms decide whether or not to hedge their cash flows. If a firm does not
hedge, the amount of funds available for investment at date 1 will be y y + ,where
is a common shock to all firms and E(y)=¯y. If a firm hedges, then the amount of funds
available for investment at date 1 will be y y.
6
While firms can hedge at fair terms, we assume that they cannot raise external finance.
Further, we assume that for all values of y, the marginal return to investment is higher than
the opportunity cost of funds, which is normalized to one. This implies that firms will invest
their entire cash flows, that is, k = y,wherek denotes a firm’s investment.
7
The above discussion is summarized in the following timeline of events:
T=0 Firms only know the exogenous distribution of their cash endowments y at T=1, not
the realization. Each firm decides whether or not to hedge their cash flows given the
hedging strategies of all other firms. That is, hedging is determined within a Nash
equilibrium.
T=1 Cash flows are realized, and firms invest all of their cash flows. Each firm observes the
investment decisions of all other firms. Firms then choose their outputs in the context
of a Cournot equilibrium.
T=2 Profits are realized.
4

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