Corporate risk management and asymmetric information

The Quarterly Review of Economics and Finance 44 (2004) 727–750

Corporate risk management and asymmetric information Longkai Zhao∗ Sauder School of Business, University of British Columbia, 2053 Main Mall, Vancouver, BC, Canada V6T 1Z2 Received 14 October 2003; received in revised form 5 April 2004; accepted 7 April 2004 Available online 12 October 2004

Abstract We discuss the effect of information on corporate risk management decisions when the information is asymmetric between the insider and the market. We suggest an explanation for previous contradiction between existing theories and empirical findings, which state that fewer small firms choose to hedge. We consider two different scenarios of information revelation to the market, and find hedging cost is not the main reason preventing firms from hedging. Rather asymmetric information plays the decisive role in a firm’s risk management policy. One of the empirical implications we find is that cash flows with high variances may discourage firms from hedging even when they face high financial distress costs. © 2004 Board of Trustees of the University of Illinois. All rights reserved. JEL classification: D82; G30 Keywords: Risk management; Asymmetric information; Signaling

1. Introduction Risk management has received much attention in the theory of corporate finance, and is playing an increasingly important role in corporate financial management with the rapid development of derivative securities. Many surveys show that risk management is ranked ∗

Tel.: +1 604 8272553. E-mail address: [email protected].

1062-9769/$ – see front matter © 2004 Board of Trustees of the University of Illinois. All rights reserved. doi:10.1016/j.qref.2004.04.001

728

L. Zhao / The Quarterly Review of Economics and Finance 44 (2004) 727–750

by financial executives as one of their most important objectives, and hedging is frequently used by large and widely held companies. Managers are becoming more concerned about their risk management strategies. Theories such as Black-Scholes’ option pricing model have provided some good instructions on how to implement a firm’s hedging strategies. However, we still need more insight into the mechanism of hedging on firms’ behavior. Some theories have explained why corporations need hedging and what the benefits of risk management are. These theories suggest that some companies facing large exposures to interest rates, exchange rates or commodity prices can increase their market values by using derivative securities to reduce their exposures. One fundamental direct goal of using hedging is to reduce the variability of cash flows, thus reduces various costs. According to Modigliani and Miller’s (1958) irrelevant theory, if hedging can increase firm values, it must do it through taxes, contracting costs, the impact on the firm’s investment decision, etc. Otherwise, the investors can diversify their risks through the same hedging strategies. In fact, most risk management theories focus on some aspects of relaxing the irrelevant theorem and study the effect of hedging on the firm’s value or financial decisions. According to Smith and Stulz (1985), firms can hedge by trading certain securities contracts or by altering real operating decisions. Therefore, hedging reduces the dependence of firm value on the changes of state variables. Hedging can reduce the volatility of taxable cash flow, which has an impact on a firm’s value if the tax code is convex. Smith and Stulz (1985) state that risk management can reduce taxes if effective marginal tax rates on corporations are an increasing function of the firm’s pre-tax value. Because of the convexity of the tax code in most countries, there are benefits to managing the taxable income in an optimal range. By reducing the fluctuations in taxable income, risk management can lead to lower tax payments since it ensures that the largest possible proportion of corporate income falls in the optimal range of tax rates. Smith and Stulz (1985), Stulz (1997), and Bessembinder (1991) also discuss the impact of hedging on bankruptcy costs. Investors become concerned if the variability of cash flow increases the probability of financial distress, since the distress cost will be reflected in the current market value. This, therefore, decreases the value. However, given a level of debt, hedging can reduce the probability that a firm will find itself in a situation where it is unable to repay that debt. In extreme cases, risk management eliminates the risk of bankruptcy effectively, reducing the costs to zero and, in so doing, increases the value of the firm. In general, by shifting individual future states from default to non-default outcomes, hedging increases the proportion of future states in which equity holders are the residual claimants. Froot, Scharfstein, and Stein (1993) develop this idea to show that hedging adds value to such an extent that a firm has sufficient internal funds available to take advantage of attractive investments. They argue that if capital market imperfection makes externally obtained funds more expensive than those generated internally, there is a rationale for risk management. Their theory is still rooted in the understanding that risk management can reduce the variability of cash flows. It will also indirectly reduce the variability in the amount of money raised externally and the variability in the amount of investment. Since the marginal return to investment usually decreases and the marginal cost of fund goes up with the amount raised externally, the reduction in the variability by hedging is very meaningful to firm value. By reducing the probability of financial distress, risk management has the

L. Zhao / The Quarterly Review of Economics and Finance 44 (2004) 727–750

729

potential to increase debt capacity and facilitate larger equity stakes for management. In a certain sense, risk management can be viewed as a direct substitute for equity capital. The more a firm hedges its exposure, the less equity it needs to support its business. So the use of risk management to reduce exposure effectively increases a company’s debt capacity as discussed in Smith and Stulz (1985) and Stulz (1997). A firm’s hedging decision should be jointly made with the corporate capital structure decision. By considering “asset substitution problem”, Gavish and Kalay (1983), Green and Talmor (1986) have formally demonstrated how the existence of risky debt generates an incentive for managers to substitute low-risk assets for high-risk assets. Campbell and Kracaw (1990) also show that the incentive to shift risk increases monotonically with the use of risky debt. They further their research by separating the risk into observable risk, which can be written by hedging contracts, and unobservable risk, such as operating risk, which cannot be hedged using derivative instruments. By studying the impact of observable risk on asset substitution, they conclude that when two types of risks are sufficiently positively correlated the managerequityholders should benefit from hedging. This provides another explanation for hedging. Because of asset substitution problem, given debt in place, if hedging is unrestricted, the borrower will have an incentive to increase the risk by avoiding hedging and thereby shift the wealth from the lender to the borrower. Hence, the lender needs a contract that compels the borrower to choose a level of hedging that allows the lender to break even at least. This leads to the managerial incentive for hedging. Stulz (1984) partly touches this problem, but its focus isn’t on the incentive contract. He derives the optimal hedging policies under the assumption that managers maximize their expected lifetime utility, and their income from the firm is an increasing function of the changes in the value of the firm. Here, the manager compensation contract is given by the shareholders without considering the agency costs. Smith and Stulz (1985) also discuss the compensation contracts between the manager and the shareholders. Their results show that making the managerial wealth a concave function of firm value bonds the firm to a hedging policy, which is also important for a firm with debt or other fixed claims. It ensures that firm will hedge as long as that compensation policy is followed. Campbell and Kracaw (1990) show that the incentive to shift risk and the associated agency costs of debt increase with the use of risky debt, thus it may be optimal to include covenants which require that borrowers hedge an observable risk in debt contracts. Bessembinder (1991) argue that independent of effects on investment, hedging increases value by improving contracting terms. In his paper, the beneficial effects of hedging are attainable only to the extent that a firm can credibly commit to maintaining the hedge over the life of the senior claim. There, he predicts that firms will devise methods to make such credible commitments. The most obvious is to include covenants defining a firm’s hedging policies in contracts with senior claimants. DeMarzo and Duffie (1995) investigate the role of managerial career concerns in determining corporate financial hedging policy. They find standard hedging accounting can improve a firm’s future investment decisions. In addition, standard hedge accounting may also increase a manager’s incentive to make an optimal initial investment decision. Under full disclosure, hedging positions have real effects primarily because they act as a signal and reveal private information known to the manager. If hedging positions are not disclosed, hedging has a more direct impact on the risks of a firm’s profits and managers’

730

L. Zhao / The Quarterly Review of Economics and Finance 44 (2004) 727–750

wages. Thus, accounting issues are likely to have important consequences for hedging policy. Leland (1998) considers the interaction between agency cost, capital structure and risk management. To my knowledge it is the first work that studies the joint determinant of capital structure and investment risk. Using simulation, he provides some quantitative guidance on the amount and maturity of debt, financial restructuring, and the firm’s optimal risk strategy. He finds, for realistic parameters, the agency costs of debt related to asset substitution are far less than the tax advantages of debt. It can be very costly for owners to monitor a firm’s risk management activities. Managers need to be given the right incentives for choosing the risk management policy preferred by the owner. Tufano (1996) studies the hedging behavior of 48 publicly traded North American gold mining companies. The bottom line of his study is that the only important systematic determinants of the 48 corporate hedging decisions are managerial ownership of shares and the nature of the managerial compensation contract. His evidence seems to suggest that hedging can alleviate agency problem by reducing the noise in managerial compensation. It is consistent with the theory above in a certain sense. But no work has shown us how to design a manager compensation package to make the managers use hedging to increase the firm value, though some implications are discussed for some particular packages. In this paper, we try to answer a different question: why don’t firms hedge? Though hedging costs play an important role in the answer, we argue that when market asymmetric information exists between a manager and outside investors, some firms will want to hedge less or not hedge in order to give a signal to the market about their quality, even if hedging cost isn’t a concern. The revelation of signals depends on accounting requirements. So, we consider two cases when the market can easily verify the hedge ratio or when the categorized data — hedge or non-hedging are available to the market. We find in the first case it is possible to have a separating equilibrium in which firms hedge less than the necessary ratio to eliminate all the financial distress costs. In the second situation, we can have two pooling equilibria of hedging firms and non-hedging firms separated by two signals. Our results show that fewer firms will hedge, even they are facing higher uncertainties in future cash flows, as long as the divergence of firm quality is severe. We suggest that the proportion of hedging firms is negatively related with the extent to which the information is asymmetric. The implications from our model are consistent with some available empirical results. We also suggest more tests for future empirical study. We analyze the welfare of the whole economy in two scenarios and discuss the policy implication. In both scenarios, good type firms are exposed to higher expected bankruptcy cost as the cost of signaling. In Ross (1977), higher leverage firms are perceived as higher value firms. In his incentive-signaling model, high debt level increases the risk that a manager receives penalty in his compensation. However, given his compensation contingent on the firm’s value, a manager signals information to the market by setting debt levels. In Ross’s (1977) incentive-signaling equilibrium, expected bankruptcy cost can be thought as the signaling cost though it is actually reflected by the penalty in managers’ compensations. In our model, the debt level is fixed. Risk management policies alter expected bankruptcy costs. When corporate hedging decisions can also signal information of a firm’s value to the market, the equilibrium in Ross (1977) would be broken. Only leverage is no longer enough to sustain the signaling equilibrium, because both leverage and risk management

L. Zhao / The Quarterly Review of Economics and Finance 44 (2004) 727–750

731

policy can affect expected bankruptcy costs. Our model shows that risk management can have the same effect as the choice of capital structure because of the existence of bankruptcy costs. However, our model does not merely rely on bankruptcy costs. The implication in our model can be easily extended to other value-increasing effects of hedging such as tax. This paper suggests signaling can be a motive for firms not to hedge. This is realistic. The cost of changing capital structures can be very high, and the adjustment to the target debt level is slow. As discussed above, risk management can provide the same signaling effect as the capital structure in Ross (1977), but in a shorter time period. When the debt level is difficult to adjust because of the constraints such as debt covenants, firms may change their risk management strategies to give signals to the market. In this sense, risk management strategies are easier to implement. The existing literature has a difficulty to explain why fewer small firms choose to hedge than large firms do, though small firms have more volatile cash flows. There are fewer financial analysts following small firms. The information of small firms is difficult to be received by the market. Asymmetric information can play an important role here. By telling the market: “the firm is doing so well that we do not need to hedge”, firms do reveal more information to the market. A motive like that is stronger for small firms. However, there has been no empirical study to provide direct evidence that firms do use risk management strategies as signals. In our model, we suggest some empirical implications to look further into this problem. We explain our model in Section 2. First, we design a simple example to illustrate the basic idea. After setting up the basic structure of our model, we derive some results where hedge ratio is unverifiable and verifiable respectively. We also discuss the impact of hedging cost on this model and do the welfare analysis in Section 3. In Section 4, we discuss some empirical implications. We conclude and discuss the future research in Section 5.

2. Model 2.1. An example If the market is as complete as in M–M’s framework, risk management cannot alter a firm’s value because investors can diversify the risk themselves. However, former research finds that corporate policy of risk management can increase firm value if financial distress or bankruptcy cost is considered. This is because risk management reduces the variance of the future cash flow, which in turn may reduce the probability of bankruptcy or financial distress. The effects of risk management on tax shield, agency cost, etc. are also examined. One conclusion common to all these effects is that risk management can increase firm value. But empirical results show that though the trading in some derivatives markets is mainly for corporate purpose, the proportion of firms using risk management is not as high as we predict. And the proportion is even lower for small firms, which is contrary to the theory that small firms usually have higher variances of cash flow, and that risk management should be more beneficial. Different hedging costs might be one reason for this finding. Here, we are trying to explore the possibility that if risk management decisions can convey more information to the market when there exists asymmetric information between the outside

732

L. Zhao / The Quarterly Review of Economics and Finance 44 (2004) 727–750

investors and the firm managers, in some situations firms will choose no hedging or partial hedging as a signal to tell the market that they have better quality. We use a simple one period model to illustrate the basic idea. Let’s assume that this is a risk-neutral world, where all the agents are risk neutral. For notational simplicity, we assume the risk-free rate is zero here. There are two firms: A and B, and one project is available for them that begins at t = 0 and ends at t = 1. Firms A and B both have identical initial value V at t = 0 and they have to pay debt or pre-decided cash payment at t = 1. Let’s assume the amount is L. If the firms have no enough cash for the payment, they have to go bankruptcy and a cost: b will occur. So if either firm doesn’t take the project, it will face bankruptcy at the end of the period. To exclude this situation, we simply set the project to have positive NPV. Thus, two firms will be willing to take the project. Also, we assume there are only two states at t = 1 for this project, s = 0 and s = 1. In the state 0, the output will be 0; in the state 1, the firms will have a positive cash flow of X. Further, we assume the probability that firm A is in state 1 is p + ∆ (∆ > 0), and the probability that firm B is in state 1 is only p. Here, firm A is considered to be the good type since it has a better chance to reach the good state 1. In order to focus on the effect of hedging, we assume the accruement from V is 0, which will avoid the discussion of underinvestment problems. As in Stulz (1984), we define hedging as eliminating all the uncertainty in cash flow and also assume hedge cost is zero. So, the payoff at t = 1 will be (p + ∆)X, pX respectively if two firms choose to hedge. Further, we assume that hedging can reduce the bankruptcy cost to zero, which means pX > L, it should be optimal for two firms to hedge their future cash flow. However, this conclusion is based on the assumption that the market knows all the information of future cash flow for two firms. Otherwise, if only the manager knows the state probability for his firm and his purpose is to maximize the social welfare function (Miller & Rock, 1985), he might behave differently. The social welfare function is: WV = kVM + (1 − k)E[V ]

(1)

where VM is the firm’s market value, which might be different from the intrinsic value E[V] if the market cannot distinguish the firms’ qualities. k can be thought as the weight on the firm’s market value and is between 0 and 1. Let’s suppose the investors in the market cannot distinguish A from B if no signal is given, but know all the other information. To focus on the risk management policy, we assume the firms can only use hedging or non-hedging as a signal. Or, we can think of the case as if the firm has made other financial decisions such as capital structure and it is up to the decision of its risk management policy. It is easy to conclude that if firm A has decided to hedge and firm B knows that, firm B will always hedge. (Here, firm A is the good firm.) It is always optimal for firm B to mimic firm A’s risk management policy if it only considers the market value. But if its mimic behavior brings some extra cost to its intrinsic value, firm B will have to balance the trade-off between the market value and the intrinsic value. What we are interested in is whether there is a separating equilibrium here. If there is, it must be the case that A has no hedging activity and B has. Proposition 1. If a separating equilibrium exists with signals of hedging or non-hedging, firms with lower expected bankruptcy costs (good firms) do not hedge.

L. Zhao / The Quarterly Review of Economics and Finance 44 (2004) 727–750

733

In this setting, firm A and B are distinguished by their risk management polices. The firm that hedges is considered to be the bad type firm B, otherwise it will be considered as the good type firm A. In the separating equilibrium, the market gets the correct signal of firms’ quality and gives it the corresponding market value. It must be the case that the market value is equal to the expected intrinsic value. In order to satisfy the conditions for the existence of a separating equilibrium, we will make sure that neither type has the incentive to mimic the other one. For the good type firm A, the condition would be: WVA|no hedge ≥ kVM |hedge + (1 − k)E[VA ]|hedge ⇒ (p + ∆)X − (1 − p − ∆)b ≥ kpX + (1 − k)(p + ∆)X

(2)

The left hand side is the social welfare function if firm A doesn’t hedge. Giving the signal of no hedging, firm A’s market value is equal to its intrinsic value since a correct signal is given. The right hand is the function value if firm A hedges. The first term on the right hand side is the market value. The second part is the intrinsic value because given the signal of hedging, the market thinks of firm A as a bad type. Though its intrinsic value is increased under the hedging policy, as long as the increment cannot compensate the decrease in the market value, the good type firm has no incentive to give a wrong signal. Another condition would be that the bad type firm B has no incentive to mimic A’s behavior: WVB |hedge ≥ kVM |no hedge + (1 − k)E[VB ]|no hedge pX ≥ k[(p + ∆)X − (1 − p − ∆)b] + (1 − k)[pX − (1 − p)b]

(3)

From the right hand side, we can see the bad type firm might increase its market value by giving a signal of no hedging, but decrease its intrinsic value. As long as the overall effect of giving a wrong signal is negative, the bad type firm B will always choose to hedge. From (2) and (3), we can see a separating equilibrium exists under the conditions: k∆ k∆ X = b- < b < b¯ = X 1 − p − k∆ 1−p−∆

(4)

In the separating equilibrium, the market value of the bad type firm B is pX, which is equal to the intrinsic value since hedging strategy is adopted. The market value of the good type firm A is (p + ∆)X − (1 − p − ∆)b, since given the signal the market believes a firm without hedging is the good type firm. When the bankruptcy cost: b ∈ [0, b- ], there may be many equilibria. In the range of ¯ ∞), there is a pooling equilibrium in which both firms choose to hedge. The range of [b, bankruptcy costs for the existence of separating equilibrium is: b¯ − b- =

k(1 − k)∆2 X (1 − p − ∆)(1 − p − k∆)

(5)

Under some parameters, there exists the possibility that the exogenous bankruptcy cost might drop into this range. This is not a Pareto-optimal equilibrium. The good firm has to give up the benefit from hedging and use it as the signaling cost. Here, non-hedging becomes a signal by the good type firm. The non-hedging decision conveys the true quality of the firm to the market but at the same time increases the expected bankruptcy cost. The good firm decides the trade-off between cost and benefit. When the bankruptcy cost is so

734

L. Zhao / The Quarterly Review of Economics and Finance 44 (2004) 727–750

small that increasing this cost cannot prevent the bad firm from mimicking the good one or the increased value from hedging is insignificant, there would not be equilibrium. Another extreme case would be that the bankruptcy cost is so high that it overwhelms the signaling effect. The implication from (5) is consistent with our intuition. We find that the better the good firm is (larger ∆), the wider the range is, which leads naturally to a higher probability that the separating equilibrium may occur. We can consider p and X as the characteristics of the project. The higher they are, the wider the range is. It is interesting because increasing p or X is equivalent to increasing the variance of this project in this example. A more volatile project might leave more space for signaling. This implication is consistent with the survey result that fewer small firms choose to hedge than large firms. It is normally accepted that small firms usually have more volatile cash flows, which might lead them to use signals more often. Bankruptcy cost is exogenous in this example. It includes indirect cost and direct cost, the sum of which is often estimated as a ratio of the firm value. So, let b = αV (it is not strict since we use the initial value as the firm value here). Then the range of α is negatively related with the firm value. This is also consistent with the phenomena that fewer small firms hedge than large firms, because the range of the ratio is wider. It is necessary to discuss two extreme cases: k = 0 and k = 1. In both cases, the range of b is zero. However, when k = 0, the managers focus only on the intrinsic value. In this case, all firms should hedge since it eliminates the dangers of bankruptcy. There is a pooling equilibrium. When k = 1, there cannot exist any separating equilibrium, since B firm can mimic A firm without any cost, and can increase its market value. However, the assumption that the manager is attempting to maximize the social welfare function is essential to this conclusion. There are many arguments about this assumption. However, there are at least two reasons. (1) Firms are often issuing new issues. If the market value is lower than the true value, it is always disadvantageous for the current shareholders. (2) There are no reasons to expect that the current shareholders are going to hold the shares indefinitely. In fact, it is easy to extend the example above to a case where a firm has to raise funds for the project by issuing new shares and the managers behave as maximizing the current shareholders’ value. 2.2. The structure of the model We hope to extend the essentials of signaling effects of risk management decisions to be included in a generalized model. One important factor is whether risk management policy is a feasible signal to the market, and to which extent it can be conceived by investors, which is related to the accounting code for corporate risk management. The revelation of a hedging position is always reflected in the footnote of accounting report, which is required by the Financial Accounting Standards Board (FASB). Though the accounting standards are revised gradually and more strict accounting treatments are imposed upon the corporate hedging reports, it is still arguable that a firm’s risk exposures can be fully conceived by the market. In some sense, firms are not willing to reveal their hedging positions, which is intuitively consistent with the example above. However, in this section, we are going to discuss the signaling effect in a more strictly defined model. Two situations are considered here: the first is that firms can only reveal if they have a risk management policy that is

L. Zhao / The Quarterly Review of Economics and Finance 44 (2004) 727–750

735

lacking more details about how much they hedge. The other is the extreme case in which detailed hedging information such as the hedging ratio is conveyed to the market. The first case can also be thought as a situation where audit cost is too high for investors so that they wouldn’t bother to find out the detailed risk management policy. Considered in a one period context and in a risk neutral world, at time 0, a project P is offered to all firms and eventually will be taken by all. To maximize the social welfare of their individual firms, managers decide what risk management policy they are going to use for this project and report it to the market. Since the market will only take hedging or no hedging as the meaningful signal, the managers only need to tell the market they hedge (H = 1) or not (H = 0). At time 1, the payoff from the project is realized. Without loss of generality, we assume this project is the only cash flow source for all the firms in this period. For firm i, the project has a random payoff at t = 1: P˜ i = Ri + z˜

(6)

where Ri is a constant, and z˜ is a random variable. We assume z˜ is the risk that firms are facing. Particularly, we think z˜ is the risk that firms would like to hedge and can be hedged with a financial instrument provided in the financial market with zero cost. The probability density function of z˜ is f(˜z). We also assume E[˜z] = 0 and 0 ≤ Var(˜z) < ∞. The risk is common knowledge to the market, but a firm type is characterized by Ri which is only known to the manager when the project is taken. Higher Ri means a better quality firm. Managers know all the distribution of their own firms’ future cash flow. Outsiders know the mean of the distribution but not individual firm’s realization. We assume firms go bankrupt if P˜ i = Ri + z˜ < L.

(7)

It is either because of pre-decided cash payment or debt payment. We can think of L as a cash flow level under which firms have to go bankrupt. However, it would be interesting to endogenize L with a capital structure problem and discuss the relationship between hedging and other financial policies. We will discuss this later. Here, L is exogenous. Also, we assume Pr(P˜ i < L) > 0 for any i, which means all the firms face bankruptcy risk no matter how good they are. This assumption is purely for convenience, making us focus on the trade-off between the bankruptcy cost and the signaling effect later. If a firm goes bankrupt, additional bankruptcy costs will be burdened on the firm. We suppose the bankruptcy cost, b, is the same for all the firms. In order to make sure the project is taken by all the firms, we further assume that E[P˜ i = bPr(P˜ i < L)] > 0,

(8)

which is equivalent to Ri − bPr(P˜ i < L) > 0

(9)

for all firms. We can think of the condition above as a project that has a positive NPV for any firm. When the project is taken, managers have a better knowledge of the distribution of future cash flow, which is reflected by that they know exactly what Ri would be. Behaving

736

L. Zhao / The Quarterly Review of Economics and Finance 44 (2004) 727–750

as maximizing the social welfare function: max(WV = kVM + (1 − k)E[V ]), h

the manager will decide what kind of risk management policy, h, he would choose. Here, VM is the firm’s market value, and E[V] is the intrinsic value. Different weights are attached to them to balance the two groups, of which one is holding the shares and the other is going to sell. We suppose all the managers have the same weight on the market value. The manager can alter the variance of future cash flow by hedging some risk. Defining hi as a hedge ratio for firm i, then the payoff of the project is: P˜ i = Ri + (1 − hi )˜z

(10)

where 0 ≤ hi ≤ 1. Apparently, a positive hedge ratio can reduce the variance of the cash flow. From the result in Smith and Stulz (1985), reduction of the variance can increase a firm’s intrinsic value because it reduces the expected bankruptcy cost. But trade-off arises here if hedge ratio is considered as a signal of a firm’s quality. A firm’s market value is decided by the signal received by the market. As we have discussed in the example above, the manager has to decide the trade-off between the market value and the intrinsic value. 2.3. Scenario 1 How well a signal of hedge ratio can be transferred to the market is still arguable. We would like to study two extreme cases. In the first case, a hedge ratio is unverifiable but whether a firm hedges or not can be verified. This is a realistic scenario because it is fairly easy to find out if a firm adopts a risk management policy, but the cost is always too high to verify the exact hedge ratio. Non-financial firms don’t report their risk management instruments on their balance sheets. The existing evidence on corporate derivatives activity typically takes the form of categorical data — whether firms hold any derivatives or not. In the second case, a hedge ratio is verifiable at a low cost, which can exist when strict accounting treatment is implemented. Then financial institutions have to file more detailed reports on derivatives holdings to their supervisory agencies, which is very close to the second situation we will discuss later. When hedge ratio is unverifiable, the market will take the signal as: H = 0, H = 1,

if hi = 0; if 0 < hi < 1.

(11)

Outside investors only know whether a firm hedges or not. Since there are two signals in the market and outsiders can only take their valuation upon the two signals, the market value of firms can be categorized into two groups: VM,H=1 and VM,H=0 . A firm’s intrinsic value is still only known to the manager after he decides a hedge ratio, which is: E[V ] = Ri − bPr(Ri + (1 − hi )˜z < L).

(12)

L. Zhao / The Quarterly Review of Economics and Finance 44 (2004) 727–750

737

Notice, without loss of generality we normalize the initial value of the firm to be zero, and the risk-free rate to be zero. First, we can get the proposition below: Proposition 2. If hedge ratio is unverifiable, firms who hedge always keep their bankruptcy risk exposure fully hedged. The proposition is straightforward. A firm hedges with hedge ratio h > 0, then H = 1. Changing the hedge ratio has no effect on its market value. The manager only needs to maximize the intrinsic value, which can be highest when the manager uses a hedging strategy to eliminate the bankruptcy cost completely. Thus, if outside investors know a firm hedges, they know the firm must have hedged away all the bankruptcy risk. Proposition 2 shows that if there is a separating equilibrium, the firm that gives a signal of hedging will fully hedge their hedgeable bankruptcy risk. It is unnecessary to make the hedge ratio 1, but in the view of the market, it makes no difference. The market will always understand that hedging firms hedge away all possibilities of future bankruptcy. However, the separating equilibrium is not in a strict sense, since there are only two signals to the market, which results in only two market values. Now we are trying to discuss the conditions for the existence of such a signaling equilibrium. Further, for the simplicity, suppose the firms with different qualities are uniformly dis¯ and R, where R ¯ > R. We use the constant component in the payoff of tributed between R the project to stand for the quality. And z˜ is well distributed (continuous, differentiable). We have: Proposition 3. If and only if a firm of type R∗ is indifferent to hedging or not, there exists a quasi-separating equilibrium such that firms with Ri > R∗ choose no hedging; firms with Ri < R∗ choose to hedge.1 In this signaling equilibrium, signals only convey limited information to the market. Good firms can only tell the market at least how good it is, but cannot give the exact information of its quality to the market. We can call this a quasi-separating equilibrium. Below or above a certain quality, different firms are still pooled with the same market value. Accepting the outsiders are rational, the market value should be the average intrinsic value of the group with the same signal. We have: VM,H = E{E[V ]|H }, which is a function of

R* .

(13)

Substitute (13) into:

kVM,H=0 (R∗ ) + (1 − k)E[V (R∗ )]H=0 = kVM,H=1 (R∗ ) + (1 − k)E[V (R∗ )]H=1 .

(14)

If we can solve (14) and get the solution R* , we obtain a quasi-separating equilibrium. The existence of a feasible solution depends on the parameters of the economy. We will use a numerical example to show the relationship. 1

The proof is available upon request. In the proof of Proposition 3, we find that the cost associated with signaling is negatively related to the firm type, which is consistent with the Spence condition.

738

L. Zhao / The Quarterly Review of Economics and Finance 44 (2004) 727–750

Fig. 1. Illustration.

In the numerical example, we set z˜ uniformly distributed between [−a, a].We have: R∗ =

¯ − R) − (1/2)kR ¯ L + a − (a/b)k(R . 1 − (k/2)

(15)

If there is a partial signaling equilibrium, we should have: ∗ ¯ R - < R < R.

(16)

Suppose (16) is satisfied, we show the social welfare function in Fig. 1. ¯ firms will not hedge. The line C–D shows the function value of Notice from R∗ to R, firms that do not hedge, while the line A–E shows the value of hedging firms. Notice that the solid part B–C is above the dotted line B–E, which shows that in this range firms have no incentive to choose hedging. The opposite result is obtained from line A–B and line D–B. The function is quasi-convex. We are more interested in the proportion of firms that report hedging in this economy, since many empirical surveys provide the evidence that fewer small firms use risk management as predicted. The proportion of hedging firms in this economy is given as:
 R∗ − R 1 a k L+a−R p= − + (17) = ¯ −R (1 − k/2)S 2 b 1 − k/2 R ¯ − R. where S = R Comparative static shows us: (a) Higher L or b would cause more firms to choose hedge. These two factors are associated with the bankruptcy risk. A high level of pre-determined cash payment exposes firms to a high probability of bankruptcy. And high bankruptcy cost increases a firm’s signaling cost. These two variables can be understood to show the effect that hedging can increase a firm’s intrinsic value. However, if there is no market asymmetric information, all firms will hedge the bankruptcy risk. Changes of bankruptcy costs cannot alter a firm’s decision. But when firms have to consider the trade-off between the signaling effect and the effect on the intrinsic value, the change of the bankruptcy cost can disturb the

L. Zhao / The Quarterly Review of Economics and Finance 44 (2004) 727–750

739

former balance. We also have ∂2 p/∂b2 < 0. The change of the proportion is negatively related to the change of the bankruptcy cost. Higher than expected bankruptcy costs cause more firms to hedge, but the signaling effect is still there. ¯ − R is larger, p decreases. Fewer firms would hedge in the economy (b) When S = R where the quality divergence is significant if the bottom line of the bad quality is fixed. In other words, when there are more good quality firms, fewer firms hedge. It is the result of the signaling effect dominating the value increasing effect. (c) When managers put more weight on the market value in their consideration, the proportion of hedging firms should be lower. We can find ∂p/∂k and ∂2 p/∂k2 < 0. Usually when firms are going to raise external funds, managers are more concerned with the market value. Different from the result found in Froot et al. (1993) in which they suppose hedging can decrease funding costs by relying more on internal funds, but there is no effect on external funding, our results imply that hedging might increase external funding costs. The equilibrium is a result of a trade-off between a firm’s intrinsic value and possible future funding costs. One empirical implication would be that the firms that are more likely to raise external funds in the future would have a high probability of no hedging. (d) The only ambiguous result of comparative static is the project’s variance, here a as a proxy. We have:
 ∂p 1 k 1 = − . ∂a S b 1 − k/2 When the quality divergence is significantly large, ∂p/∂a < 0, which implies a riskier project, the result is fewer hedging firms. This is contradictory to the former literature, but consistent with empirical evidence that fewer small firms hedge than larger firms. Small firms are usually not so well followed by analysts in the market. Less information about their quality is available, which results in the perception of a small firm’s greater quality divergence. Though small firms always have higher volatility of cash flow, a small proportion will hedge according to our result. If the quality divergence is insignificant, the benefit from signaling might not exceed the cost of decreasing intrinsic value especially when the bankruptcy risk is higher with a riskier project. This finding can explain the contradiction reported in some empirical studies. Small firms are normally not very information efficient in the sense that fewer analysts follow small firms and asymmetric information is more commonly observed. Our model predicts that even if small firms have more volatile cash flows, there will still be a proportion of firms that choose not to hedge in this separating equilibrium. 2.4. Scenario 2 In the section above, we assume the market can only perceive if the firm hedges or does not hedge. Investors can only have a range and not exact information of a firm’s type. However, if a manager can use more signals or a more detailed signal, he can reveal more information of its type to the market. Based on the information equilibrium by Riley (1979), we explore the possibility of a complete separating equilibrium when hedge ratio is verifiable by the outsiders.

740

L. Zhao / The Quarterly Review of Economics and Finance 44 (2004) 727–750

Now, we consider h as a continuous variable. Receiving the signal about how much risk a firm is going to hedge, outside investors make their judgments about a firm’s quality, which will also determine the firm’s market value. Let RM (h) be the market perceived quality of firm i given the hedge ratio h. We assume RM (h) is differentiable in h between a reasonable range. If the signal is effective, we can have: RM (h) = Ri .

(18)

which is equivalent to saying that the market value is equal to the intrinsic value. Here, we do not know the exact function form of RM (h) yet, so we only can write the market value and the intrinsic value as: VM = VM (RM (h), h); E[V ] = E[V (Ri , h)]. Suppose VM is infinitely differentiable in RM , and E[V] is infinitely differentiable in h. We have the objective function: max(WV = kVM (RM (h), h) + (1 − k)E[V (Ri , h)]). h

The first order condition is: 
∂VM ∂RM dE[V ] ∂VM + + (1 − k) = 0. k ∂h ∂RM ∂h dh

(19)

Suppose the second order condition is satisfied. ∂2 WV <0 ∂h2

(20)

If a boundary condition is given, we can solve the first order condition as a differential equation to get the function of RM (h). We use the same setting as the numerical example in the section above, except that the manager can choose hedge ratio h. The market can observe this by evaluating the variance after the implementation of the risk management policy. For example, the manager can use a basket of forward contracts to reduce their variance. This assumption is closely related to the accounting requirement for risk management disclosure. More strict requirements in accounting will make this kind of signal more practical. We leave the discussion of this for later. In the example, we assume the manager can use risk management to change the cash flow to uniform distribution [R − (1 − h)a, R + (1 − h)a]. The reason we use uniform distribution in the numerical example is for the existence of a closed solution in this section with the same setting. However, one distinct difference between the two assumptions is the concept of full hedging. If the hedge ratio is unverifiable, the market can assume firms choose hedge ratio to be 1 as long as firms choose to hedge. The market values are the same. But in this numerical setting, firms only need to choose 1 − hi ≥ ((Ri − L)/a). So, we make another assumption that firms are only willing to eliminate bankruptcy risk when they

L. Zhao / The Quarterly Review of Economics and Finance 44 (2004) 727–750

741

consider their intrinsic value, or they can only eliminate their own bankruptcy risk. It is not only convenient for mathematical reasons, but also realistic in some situations such as that the hedging instruments or contracts are customized and the providers are only reluctant to take the bankruptcy risk for some reasons. However, we will find this assumption is not crucial to the whole problem, but is used only for the convenience of the boundary condition. In this numerical setting, the firm’s intrinsic value is E[V ] = R −

L + (1 − h)a − R b 2(1 − h)a

(21)

Suppose the second order condition is satisfied. Substituting Eq. (18) in to the first order condition, Eq. (19), and using Eq. (21), yields dE[V ] ∂VM dRM =− ∂RM dh dh

(22)

or k

dRM [2(1 − h)a + b](1 − h) = (R − L)b dh

(23)

The ordinary differential Eq. (23) has the solution: k ln(RM − L) = − ln

2a(1 − h) + C0 . 2a(1 − h) + b

(24)

C0 is a constant needed to be solved from boundary conditions. Let us look at the worst firm R - . Its incentive for hedging is that it wants to eliminate bankruptcy, so we have the boundary condition:
 R −L RM 1 − =R -. a Then we have the solution:   a(1 − h)(2R − 2L + b) 1/k RM = L + (R . - − L) (2a(1 − h) + b)(R − L) -

(25)

Inversing (25) and using Eq. (18), we have the function h(R). h(R) = 1 −

1−k b (R − L)k (R - − L) 1−k k − (R − L)k ] + b/2 2a (R − L) [R − L] -

(26)

The relation between the quality and the hedge ratio is no longer linear as in our assumption. When a firm’s quality is high enough, we might even have a negative hedge ratio. In this situation, firms are willing to expose more to bankruptcy risk to signal their quality. In some empirical studies, such phenomenon is reported. Here, we provide one reason for a firm’s decision to increase rather than reduce risk exposure. Restricted to the (20), not all the parameters can satisfy the existence of such a signaling mechanism. In Fig. 2, we show the function with some feasible parameters. In Fig. 2, the straight line stands for the minimum hedge ratio for different quality firms to fully eliminate bankruptcy risk. The function curve will always lie under the straight line

742

L. Zhao / The Quarterly Review of Economics and Finance 44 (2004) 727–750

Fig. 2. The relation between the hedge ratio and a firm’s quality in a separating equilibrium when hedge ratio is completely verifiable. We set the worst firm as R = 12, a = 8, b = 5, L = 10, and k = 0.6.

otherwise the signaling mechanism will be broke because firms will not face any signaling cost. In the area under the straight line, firms do not eliminate all the expected bankruptcy cost by hedging. Instead they choose to retain some bankruptcy risk as the cost for signaling in this signaling equilibrium. The function is concave in the figure above, which shows good quality firms need to expose more to the bankruptcy risk in an increasing speed. This is reasonable because good firms have a higher expected cash flow to bear a higher cost for signaling. Because of the concavity, for some parameters, good firms might even have a negative hedge ratio. Firms intend to increase the uncertainty of their future cash flow. The idea is straightforward: “our firm is so good that we would not care if we have a higher risk”. Unlike the case that hedge ratio is unverifiable, here quality and hedge ratio is in a one-to-one relation. It is a complete signaling equilibrium. The exact quality is conveyed to the market by hedge ratio. In some sense, each firm takes its own signaling cost. When hedge ratio is unverifiable, good firms are taking on some signaling costs for worse firms in two pooling groups. In Figs. 3–5, we check the effect of different parameters on the signaling function. The basic comparative static is consistent with scenario one. When the social welfare function has more weight on the market value, firms choose to hedge less, though in the signaling mechanism, market value is equal to intrinsic value. And the signaling function is more concave with higher k. For bankruptcy cost, it is just the opposite. The function is more concave with lower bankruptcy cost, since firms choose to hedge more when they are facing a high bankruptcy cost. In Fig. 5, we can see lower cash flow variance increases the concavity of the signaling function. Comparing the quasi-separating equilibrium and the separating equilibrium, a distinct difference is that we assume the market knows the upper and lower levels of qualities when

L. Zhao / The Quarterly Review of Economics and Finance 44 (2004) 727–750

743

Fig. 3. The effect of different weights in the social welfare function on the signaling function. We set the worst firm as R = 12, a = 8, b = 5, L = 10, and k = 0.5, 0.6, 0.7.

a hedge ratio is unverifiable. As we have shown, in the group of no hedging, relatively worse firms transfer some signaling cost to better firms. However, when the hedge ratio is verifiable, firms have to bear their own cost. According to the present accounting requirement, we think the situation that hedge ratio is not completely verifiable without high audit cost is closer to reality.

Fig. 4. The effect of different bankruptcy costs on the signaling function. We set the worst firm as R = 12, a = 8, k = 0.6, L = 10, and b = 4, 5, 6.

744

L. Zhao / The Quarterly Review of Economics and Finance 44 (2004) 727–750

Fig. 5. The effect of project variance on the signaling function. We set the worst firm as R = 12, b = 5, k = 0.6, L = 10, and a = 6, 8, 10.

3. Discussion We want to address two issues in the discussion section: hedging cost and economy welfare analysis. 3.1. Hedging cost We have assumed that the hedging cost is zero. The assumption of no hedging cost is reasonable only in the situation that credit risk is not priced into the instruments for hedging. Or, we can think of this in another way: there is a competitive market in which the providers of hedging instruments face no bankruptcy risk at all. But risk management packages are sometimes customized by large institutions, which are in monopoly status because only they have the access to the firms that face bankruptcy costs. They like to add extra charges for providing customized instruments to maximize their own profits. When hedge ratio is unverifiable, they cannot distinguish between different quality firms that hedge. Suppose they charge hedging firms extra c. One direct influence of that would be that fewer firms would want to hedge because of higher hedging costs. But the instrument provider is a monopolist whose objective function is: 

max(R − R -)·c c



(27)

Here, R is the firm that is indifferent to hedge or not when the hedging cost c occurs.  Notice that R is also decided by c. This is similar to that the provider knows the reaction

L. Zhao / The Quarterly Review of Economics and Finance 44 (2004) 727–750

745

function of the firms and chooses c. We get: R∗ = 21 (R∗ + R - ), 



where R∗ is the firm that is indifferent to hedge or not when c∗ is the optimal solution of (27), R* is the firm who is indifferent to hedging or non-hedging when there is no hedging cost. The hedging proportion is reduced to: 

R∗ − R - = 1 p. ¯ −R R 2 Introducing exogenous costs discourages firms from hedging. However, it does not change the signs of comparative static in scenario one. Our previous conclusions still hold. The hedging costs are actually on worse firms. It narrows the range of bad firms under a crucial quality; on the other hand, the pooling group of better firms becomes larger, which alleviates the signaling effect. p =

3.2. Welfare analysis We have discussed the effect of asymmetric information in two economies. The difference between two economies is because of risk management reporting requirements: one is stricter than the other. We can also think of the situation as if the audit cost in the economy of scenario one is too high while the other is low. It would be interesting to analyze welfare in the two economies since it would provide us with more policy implications. We choose the benchmark to be the economy in which there is no asymmetric information, such that every firm will hedge away its bankruptcy risk. The total welfare of this economy is: 1 ¯2 2 (R

2 −R - ).

(28)

Here, economy welfare is the intrinsic value created in the economy. It is the long-term intrinsic value of the whole economy. In the economy of scenario one, better firms will not hedge, which decreases the welfare of the economy. The total economy welfare is: 
∗ ¯ ¯ 2 − R2 R - + b (R ¯ − R∗ ) R − L − a + R − L − a . (29) 2 2a 2 2 The second term is always negative. When the quality divergence in the economy is large, the economy welfare loss due to the signaling cost is higher. The welfare of the economy in scenario two is:  R¯ ¯ 2 − R2 R L − R + (1 − h)a - − b dR, (30) 2 2a R 1−h where h is given as a function of R in Eq. (26). Comparing them with the benchmark economy, the economies with asymmetric information have lower intrinsic values because of signaling costs. Firms in two economies have to bear some expected bankruptcy costs. Which economy has higher welfare? Or

746

L. Zhao / The Quarterly Review of Economics and Finance 44 (2004) 727–750

what risk management reporting requirement better encourages the long term valueincreasing in an economy? The answer will rely on the characteristics of the economies. Here, we provide some numerical simulations of different economies in the table below:2 ¯ R

¯ − R)/R (%) (R - -

Welfare of economy 1

Welfare of economy 2

15.25 15.50 15.75

27.1 29.2 31.3

0.9884 0.9781 0.9689

0.9790 0.9764 0.9738

16.00 16.25

33.3 35.4

0.9603 0.9526

0.9711 0.9683

16.50 16.75

37.5 39.6

0.9454 0.9388

0.9655 0.9627

When the quality divergence is not large, the economy with less strict reporting requirements has a higher total value than the economy with stricter risk management reporting requirements. This reverses when the quality divergence gets bigger. In the first economy, there is a group of firms that fully hedge away their bankruptcy risks. In the second economy, no firm uses full hedging strategies, but each firm hedges a proportion of the risk. As we discussed in the previous section, small quality divergence causes more firms to fully hedge in the first economy, which is why welfare in the first economy is higher than in the second economy when the quality divergence is small. Our welfare analysis does not support the notion that stricter risk management reporting is always socially better than less strict reporting. The policy making of risk management reporting requirements should consider the quality divergence in the market. Stricter requirements are more suitable for a market where the asymmetric information of a firm’s qualities is significant.

4. The empirical implications Our model suggests an explanation for why firms do not hedge or hedge less even when they face bankruptcy risk. The model identifies the trade-off between the two effects of hedging. One trade-off is the value-increasing effect because hedging can decrease the expected bankruptcy cost, which in turn leads to a higher expected intrinsic value. The other trade-off is the signaling effect which arises in the situation when the market cannot obtain full information about a firm’s quality. We examined the signaling equilibrium under different accounting requirements, since the present accounting standards still cannot pinpoint various risks in certain formal statements. This model has some empirical implications, some of which have been reported in the former empirical work. However, some Here, we set the parameters of the economies as R - = 12, a = 8, b = 5, L = 10, and k = 0.5. The welfare in the table has been scaled by the welfare in the benchmark economy. 2

L. Zhao / The Quarterly Review of Economics and Finance 44 (2004) 727–750

747

new tests are suggested to verify whether risk management policy can reveal information to the market. It is always difficult to verify the motivations of managers who adopt risk management policies. The essential prerequisite of this model is based on the beliefs that hedging can eliminate or decrease bankruptcy costs. So whether managers realize that or whether some risk management policies are designed for this purpose is the premier question. Up until now, empirical results have been mixed with firms hedging in response to expected financial distress costs. Graham and Rogers (2000) studied the derivative holdings of firms facing interest rate and/or currency risk. Their results indicate firms hedge in response to higher financial distress costs. The evidence in Haushalter (2000) shows that the extent of hedging is related to financial costs. Tufano (1996) examined the corporate risk management activity in the North American gold mining industry. He finds little support. Mian (1996) uses a large database and finds that the evidence is inconsistent with financial distress cost models. In this model, we assume a manager’s objective is the social welfare function, which is reasonable in the sense that managers have to balance the requirement of two groups of shareholders: one is going to sell stocks, the other is holding stocks. Different weights are imposed on the market value and on the intrinsic value according to the welfare of the two groups, respectively. The weights are not constant, which may vary because of financial situations that firms are dealing with. For example, when firms are going to issue new shares to raise funds, it would not be preferred that the market value is too low. Consider that, the weight on the market value will always be higher before firms have seasoned issues. In this situation, our model predicts that firms would hedge less than before because they want to give a more accurate signal of their quality to lower their costs before new equity issues. Froot et al. (1993) studied the relationship between hedging and the cost of raising funds. However, they focused on the internally generated funds and suggested that “firms will want to hedge less, the more closely correlated are their cash flows with future investment opportunities”. This requires that the empirical test of our model be able to separate the effects of signaling and generating more internal funds. The risk management policy in Froot et al. (1993) should be static since “future investment opportunities” contain all the possibilities of funds needs, but our model predicts a change in a firm’s risk management decision when an investment opportunity is going to be undertaken. The market asymmetric information is in the core of this model. Our model is consistent with the intuition that the more severe the uncertainty of the information, the more effective signaling will be. When the divergence of firm quality is significant, we can draw the conclusion from the model that fewer firms will hedge. It provides the implication that small firms have a lower hedging proportion than large firms do. Usually small firms are not so well followed by the analysts and less information is available to investors in the market. This phenomenon has been reported in many empirical papers. For example, Nance, Smith, and Smithson (1993), Mian (1996), Geczy, Minto, and Schrand (1997), Graham and Rogers (2000), etc. used accounting data; Culp and Miller (1995) conducted a survey of 1999 companies and got responses from 530 firms. One clear finding that emerged from that survey was that large companies make greater use of derivatives than smaller firms. This phenomenon has also been explained by the idea of economies of scale. But one further implication of our model has not been tested before and can be used to separate the cost

748

L. Zhao / The Quarterly Review of Economics and Finance 44 (2004) 727–750

effect and the signaling effect. We find that a more volatile project may lead to less hedging when the quality divergence is great. On a cross-sectional basis, hedging activities are predicted to be greater at firms that are going to have a lower return. We predict that there is a negative relation between the hedge ratio and a firm’s quality when a hedge ratio is easy to verify. Even if the ratio is unverifiable, we may still have this negative relation on average. This provides a direct implication to test whether signaling is one of the considerations for companies before they make any risk management decisions. Also, in our model, there are always firms who hedge less than the amount necessary to cover all the risks that will decrease their intrinsic value. It implies that incomplete hedging is common in the market. In fact, studies have discovered this phenomenon in many markets. Empirical studies also show that many firms buy derivatives that only expose firms more to the risks instead of alleviating the impact of uncertainty. Hentschel and Kothari (1999) use data from financial statements of 425 large US corporations. They find that many firms manage their exposures with large derivative positions and some reduce risks with derivatives, while others increase risks. We predict this can happen when firms are so good that in the signaling mechanism, they have to increase risk to give a signal to the market. So in a future empirical test, we would like to see if there exists a strong relation between good quality and a negative hedge ratio.

5. Conclusion Previous theories provide many explanations for why firms hedge. Our work tries to understand the risk management problem from a different perspective. Since much empirical evidence show us that risk management policy is not always implemented by firms, we hope to explore why not. We suggest that signaling effect might explain part of this phenomenon. Under the bankruptcy risk, firms choose hedging or non-hedging to convince the market that they are a certain type. By facing more bankruptcy costs, good firms use non-hedging as a signal to the market. We discuss two cases where a hedge ratio is easy to verify or not. If the hedge ratio is unverifiable, we cannot have a complete separating equilibrium. But hedging or non-hedging as a signal divides firms into two groups distinguished by a certain level of type. In the case that a hedge ratio is verifiable, we obtain a separating equilibrium with different type firms choosing different hedge ratios. However, the hedge ratio in the signaling equilibrium is always smaller than the necessary ratio to cover all the bankruptcy risk. Our model has some results that are consistent with the observations in the market. We find it is very possible that projects with high variance might lead fewer firms to hedge, which is contradictory to previous theories but has been reported widely. At the same time, we also suggest more empirical implications for future empirical tests. Since we focus solely on the bankruptcy risk, some assumptions in the model might not be very general. But we find it is easy to extend the idea to deal with the effects of convex tax code on risk management. We only consider linear financial instruments in hedging in this model, non-linear ones such as options can be easily included if we suppose firms use options to eliminate the unsymmetrical risk. Another interesting problem arises from this model,

L. Zhao / The Quarterly Review of Economics and Finance 44 (2004) 727–750

749

which is that it is more reasonable to assume that the level of financial distress should be endogenized. We fixed the debt level in this model, but by relaxing this assumption, we have more space to discuss the relationship between the dynamic capital structure and risk management policy.

Acknowledgement I am grateful to Matthew Clements, Gilles Chemla, Adlai Fisher, Ron Giammarino, Rob Heinkel, Alan Kraus, Tan Wang and seminar participants at UBC. The author would also like to thank the anonymous referee for the helpful comments.

References Bessembinder, H. (1991). Forward contracts and firm value: Investment incentive and contracting effects. Journal of Financial and Quantitative Analysis, 26, 519–532. Campbell, T. S., & Kracaw, W. A. (1990). Corporate risk management and the incentive effects of debt. Journal of Finance, 45, 1673–1686. Culp, C., & Miller, M. (1995). Hedging in the theory of corporate finance: A reply to our critics. Journal of Applied Corporate Finance, 8, 121–127. DeMarzo, P. M., & Duffie, D. (1995). Corporate incentives for hedging and hedging accounting. Review of Financial Studies, 8, 743–771. Froot, K. A., Scharsfstein, D. S., & Stein, J. C. (1993). Risk management: Coordinating corporate investment and financing policies. Journal of Finance, 48, 1629–1658. Gavish, B., & Kalay, A. (1983). On the asset substitution problem. Journal of Financial and Quantitative Analysis, 18, 21–30. Geczy, C., Minton, B. A., & Schrand, C. (1997). Why firms use currency derivatives. Journal of Finance, 52, 1323–1354. Graham, J. R., & Rogers, D. A. (2000). Does corporate hedging increase firm value? An empirical analysis (Working Paper). Northeastern University. Green, R. C., & Talmor, E. (1986). Asset substitution and the agency costs of debt financing. Journal of Banking and Finance, 10, 391–399. Haushalter, G. D. (2000). Financing policy, basis risk, and corporate hedging: Evidence from oil and gas producers. Journal of Finance, 55, 107–151. Hentschel, L., & Kothari, S. P. (1999). Are corporations reducing or taking risks with derivatives? (Working Paper). University of Rochester. Leland, H. E. (1998). Agency costs, risk management, and capital structure. Journal of Finance, 53, 1213– 1243. Mian, S. L. (1996). Evidence on corporate hedging policy. Journal of Financial and Quantitative Analysis, 31, 419–437. Miller, M., & Rock, K. (1985). Dividend policy under asymmetric information. Journal of Finance, 40, 1031– 1051. Modigliani, F., & Miller, M. (1958). The costs of capital, corporate finance, and the theory of investment. American Economic Review, 48, 261–297. Nance, D. R., Smith, C. W., & Smithson, C. W. (1993). On the determinants of corporate hedging. Journal of Finance, 48, 267–284. Riley, J. G. (1979). Informational equilibrium. Econometrica, 47, 331–360. Ross, S. A. (1977). The determination of financial structure: The incentive signaling approach. The Bell Journal of Economics, 7, 23–40.

750

L. Zhao / The Quarterly Review of Economics and Finance 44 (2004) 727–750

Smith, C. M., & Stulz, R. M. (1985). The determinants of firms’ hedging policies. Journal of Financial Quantitative Analysis, 20, 391–405. Stulz, R. M. (1984). Optimal hedging policies. Journal of Financial and Quantitative Analysis, 19, 127–140. Stulz, R. M. (1997). Rethinking risk management (Working Paper). Ohio State University. Tufano, P. (1996). Who manages risk? An empirical examination of risk management practices in the gold mining industry. Journal of Finance, 51, 1097–1137.