Uncertainty and Debt Covenants

Transcription

1 Uncertainty and Debt Covenants Peter R. Demerjian* Goizueta Business School, Emory University First Draft: January 2012 This Draft: January 2013 Abstract I examine the relation between uncertainty and financial covenants in debt contracts. In the context of debt contracting, uncertainty refers to a lack of information about the borrower prior to contracting. One way to address uncertainty contractually is to renegotiate the contract when new information is received and uncertainty is resolved. I argue that financial covenants represent an ex ante commitment by the borrower and creditor to renegotiate the loan, allowing the contract to incorporate new (post-contracting) information. I find robust associations between financial covenant use and different proxies for uncertainty. I also consider the common assertion that agency conflicts related to debt drive financial covenant use. Using settings of exogenous shocks to uncertainty and agency, I find little evidence that financial covenant use is associated with agency conflicts. This result casts doubt on the agency explanation of financial covenant inclusion. *I appreciate the helpful comments of Jennifer Blouin, Asher Curtis, Kathryn Kadous, Melanie Millar, Shiva Rajgopal, Billy Strawser (AAA discussant), Jim Wahlen, Xue Wang, Donnie Young, Jingran Zhao, and workshop participants at Emory University, Indiana University, Louisiana State University, Southern Methodist University, University of Florida, University of Washington, the 2012 AAA Annual Meeting, the 2012 Penn State Accounting Research Conference, and the 2012 Southeast Summer Accounting Research Conference. I gratefully acknowledge the financial support of the Goizueta Business School. Phone: ; pdemerj@emory.edu.

2 1 Introduction In debt contracting, many questions are unanswered when a loan is initiated. Will the borrower adopt the optimal investment policy? Will his operating choices maximize the return on these investments? Will his value be sufficient to cover interest and principal payments? How will unexpected shocks affect the borrower s ability to make payments? The answers to all these questions are relevant to the creditor when he is pricing the loan. And while it is often assumed that the creditor can accurately predict future events and their implications on the borrower s value, it is likely that the creditor has some uncertainty pertaining to the borrower s future value prior to loan initiation. In this study, I explore the implications of uncertainty on loan contracting. Specifically, I contrast contracting when the creditor and the borrower know the distribution of the borrower s future value (which I term risk) against contracting when the creditor and borrower do not know the distribution (which I call uncertainty). My hypothesis is that financial covenants are in used in loan contracts to limit the effects of uncertainty. The logic is as follows. Prior to making a loan, a creditor is uncertain about the future value of the borrower: events that occur over the life of the loan will affect the borrower s value, but their likelihoods of occurring and value implications are difficult for the creditor to predict. For example, unanticipated macroeconomic shocks are by definition unpredictable, and often affect the borrower s value. Absent an objective measure of the borrower s future value, the creditor develops a subjective distribution. This distribution incorporates the creditor s information about the borrower, and also factors in the creditor s experience of pricing loans under uncertainty. Holding other things equal, uncertainty manifests as a wider range of expected values of the borrower at maturity. Due to the creditor s asymmetric payoff function, this wider range lowers the amount he expects to receive from the borrower. The creditor prices this lower expected payoff, with greater uncertainty resulting in a higher interest rate on the loan. Without provisions to reduce uncertainty, the borrower must pay higher interest costs. However, the effects of uncertainty can be mitigated following contract inception, when the creditor obtains previously unavailable information. Such information revelation oc- 1

3 curs when events are realized over the course of the loan; more fundamentally, when the borrower s operating performance is revealed (both through formal channels such as earnings reports and SEC filings, and informal ones like voluntary disclosures), the implications of these events on the borrower s value are clear and uncertainty is resolved. If the uncertainty could be resolved during initial contracting, the interest rate would be lower. However, since new information is not available until after the contract begins, it cannot be incorporated into the initial contract terms. Rather, any changes to the contract require renegotiation. Renegotiation requires the contracting parties to agree ex post to change the terms. The borrower, however, is unlikely to agree to a renegotiation that the creditor initiates. 1 Therefore, the contract requires a provision that forces both parties to commit ex ante to renegotiate under specific circumstances; that is, they agree to conditions requiring renegotiation prior to contract initiation (i.e. before receiving any post-contracting, uncertainty-resolving information). I argue that financial covenants provide such an ex ante commitment mechanism. Financial covenants are contract provisions that require the borrower to maintain a threshold level of a financial measure, such as interest coverage or net worth. If the borrower fails to maintain the threshold, the loan enters technical default. Technical default transfers control rights to the creditor, allowing him to attempt action against the borrower. Creditor actions vary, ranging from a simple waiver of the violation, to renegotiation of the loan terms, to acceleration of the loan maturity (Beneish and Press [1993]; Dichev and Skinner [2002]; Roberts and Sufi [2009]). The creditor s option to take action and specifically, to initiate renegotiation of the loan is at the heart of the theory in this study. As I model the debt contracting process, the loan is initially set with a low interest rate relative to the creditor s expected value of the borrower. 2 This low interest rate is 1 Creditors will want to renegotiate when new information reveals the borrower to be more likely to default relative to his original assessment (leading to stricter contract terms), while the borrower will prefer to maintain the original contract terms. 2 The initial interest rate of the loan must be set to provide incentive for the creditor to initiate renegotiation. If the initial rate is high, the incentive to renegotiate resides with the borrower. Unlike the creditor, the borrower does not need a trigger to force renegotiation; he can threaten the creditor with prepayment, which will induce the creditor to agree to renegotiate ex post. Since the creditor has no such plausible threat, a triggering event shifting control rights is needed to facilitate creditor-initiated 2

4 accompanied by a covenant that is triggered if future information reveals the borrower to be of low quality (i.e. likely to default). If the covenant is triggered, control rights revert to the creditor and he renegotiates a higher interest rate commensurate to the revealed quality of the borrower. If the covenant is not triggered, the loan continues at the initial rate, consistent with this rate being appropriate for a high quality (i.e. unlikely to default) borrower. The covenant facilitates the contingent transfer of control rights and the subsequent renegotiation of the loan s interest rate; hence, when a borrower agrees to a covenant, he is committing to a pay a higher interest rate if the covenant is triggered. For a covenant to be a useful commitment mechanism, it must have two features. First, it must provide a trigger for renegotiation. As discussed above, the transfer of control right accompanying technical default provides this. Second, the measure used in the covenant must be informative of future firm value, so that technical default is correlated with the new, uncertainty-resolving information. Most financial covenants are written on either earnings or net worth. Since the literature shows that each of these is associated with firm value (Hayn [1995]; Burgstahler and Dichev [1997]; Barth et al. [1998]), the second feature holds. I examine the relation between borrower-specific uncertainty and the inclusion of financial covenants. Following Jiang et al. [2005], I conceptualize uncertainty as the range, or variance, of the creditor s subjective distribution of the borrower s future value. 3 As empirical proxies, I select borrower features that either aid or hinder development of a precise estimate of the borrower s future value. These include the availability of historical financial information (borrower age), transparency of the borrower s information environment (when the borrower is rated by S&P), two trading measures from the equity market (stock price volatility and trading volume), a measure of cash flow uncertainty (implied equity duration, from Dechow et al. [2004]), and the number of analysts following the borrower s equity. For financial covenant use, I measure an index of financial covenants included in each deal, with values ranging from one to seven. The empirical tests show renegotiation. This is described in greater detail in Section Both uncertainty and a related concept, risk, are related to the variance of outcomes. I discuss similarities and differences, and why uncertainty is key to my prediction, in Section 2. 3

5 the predicted relation for five of the six uncertainty proxies. I also use principal components analysis to account for correlation between uncertainty measures and extract the underlying sources of variation. This procedure yields two principal components, each of which is significantly associated with financial covenant intensity. In addition to examining this study s hypothesis, it is important to consider alternative explanations for financial covenant use. Chief among these is that financial covenants limit the cost of agency conflicts related to debt. Following Smith and Warner [1979], many studies examine how different contract provisions limit the borrower s ability to expropriate wealth from the creditor. While Smith and Warner s analysis focuses on restrictive covenants (e.g. limits on dividend payments or asset sales) in bond indentures, subsequent studies apply their findings to financial covenants in private loans (Nash et al. [2003]; Bradley and Roberts [2004]; Billett et al. [2007]), despite significant differences in contract structures. While there are clear conceptual differences between agency and uncertainty, their measurement is endogenous, making separation in empirical tests difficult. To address this endogeneity, I run additional analysis focusing on two exogenous shocks, one to uncertainty and the other to agency. I find that following an exogenous shock to uncertainty the 9/11 Attacks financial covenant use increased, holding other factors equal. However, following an exogenous shock to agency inclusion of the borrower s stock in the S&P 500 Index financial covenant use was unchanged. In contrast, use of covenants restricting dividends (a provision directly linked to agency conflicts related to debt) was unchanged following the 9/11 Attacks, but increased when the borrower was included in the S&P 500. These results suggest that financial covenants serve a role in loan contracting distinct from addressing agency conflicts. The results of this study expand the literature on the the role of financial covenants in private debt contracts. Recent studies consider covenants as trip wires triggered by poor borrower performance (Dichev and Skinner [2002]), examine the association between accounting information and credit downgrades (Ball et al. [2008]), and measure the ability of accounting information to capture borrower performance (Christensen and Nikolaev [2012]). This study formalizes the intuition of these studies that accounting provides 4

6 information about the borrower s financial condition into a model linking uncertainty, information acquisition, and contract renegotiation. More broadly, this study is the first to show that uncertainty is a contracting problem that can be addressed using financial covenants. I develop the hypothesis in Section 2. I describe the sample and data in Section 3, and present empirical results in Section 4. I conclude in Section 5. 2 Hypothesis Development 2.1 Uncertainty Knight [1921] defines uncertainty as outcomes that are both unknown and unknowable. If a future outcome is completely uncertain, past history is no guide to prediction, and the person trying to make the prediction is reduced to simply guessing the outcome. Alchian [1950] defines uncertainty as lack of foresight of future events coupled with humans inability to process and solve complex problems with many variables. He argues that uncertainty poses a serious threat to the idea of optimization that guides much of economic thought, because it is impossible to optimize when the best outcome is not known and cannot be measured. Savage [1954] addresses the difficulty in measuring the likelihood of uncertain events by proposing personalistic or subjective probability. In his formulation, a decision maker does not attempt to explicitly determine numerical probabilities of outcomes. Rather, his actions reveal his underlying subjective assessment of the likelihood of uncertain events. In the traditional view of expected utility maximization (e.g. von Neumann and Morgenstern [1947]), the likelihood of future events is objectively measured, suggesting a distribution of future values would be agreed upon by all parties. In contrast, subjective probabilities mean parties can disagree, even when they are dealing with the same latent distribution of values, because the true distribution cannot be measured. Furthermore, Ellsberg [1961] notes that the probabilities revealed by choices reflect both that person s expectations of a future event as well as his preferences over the possible events. 5

7 Jiang et al. [2005] and Zhang [2006b] examine the relation between uncertainty and stock returns, while Zhang [2006a] tests the links between uncertainty and analysts forecasting behavior. In each of these studies, uncertainty is defined in terms of value ambiguity, essentially the precision with which firm value can be estimated by users of financial information. I adopt a similar definition of uncertainty for this study. In debt contracting, the users are the creditor and borrower: each uses information to determine the borrower s future value. More certain information leads to a more precise estimates, and hence a narrower distributions of borrower values Uncertainty and Risk Any discussion of uncertainty must also consider its conceptual counterpart, risk. There are two ways that Knightian Uncertainty is distinguished from risk, each inferred from the work of Knight [1921]. First, under risk the probabilities are known, while under uncertainty the probabilities are not known. That is, while both risk and uncertainty feature stochastic outcomes, the underlying distribution of outcomes is known for risk but unknown for uncertainty. Second, risk is objective while uncertainty is subjective. More precisely, following Savage [1954], any attempt to quantify probabilities under uncertainty must be subjective because no objective measure exists. 4 In this study I adopt these two perspectives in differentiating risk and uncertainty: risk indicates known distributions and objective measurements, while uncertainty indicates unknown distributions and subjective estimates. This distinction is important because new information and renegotiation has a role under uncertainty, but not under risk. 5 4 This perspective on Knight s definition of risk and uncertainty is pervasive in the literature; however, there is disagreement as to whether it is consistent with Knight s intent (LeRoy and Singell [1987]). 5 Put in a Bayesian framework, under risk the borrower and creditor have identical priors, while under uncertainty the borrower and creditor are likely to have diffuse priors. Further, under risk there is no updating of priors, while uncertainty allows updating. 6

8 2.2 Theory: Uncertainty and Debt Contracting Creditor s Pricing Consider a borrower seeking a loan from a creditor. The creditor wants to know the future value of the borrower to assess the likelihood of future default and possible recovery given default. Assume that the underlying distribution of the borrower s future value is risky. That is, the borrower s future value is stochastically linked the future state of the world, with some states leading to full repayment to the creditor and other states resulting in less than full repayment. If the distribution of the borrower s future value, which I term f(v), can be objectively determined and is known to the creditor, he will use it to price the loan. However, it is unlikely that this objective distribution is known by the creditor; there are many potential future events that are hard to predict, and their impact on the borrower s future value will be prohibitively difficult to determine ex ante. Hence, the creditor develops a subjective distribution of the borrower s future value leading to the following pricing expression for the potential loan: P r 0 V f c (V )dv + P r P r f c (V )dv = P (1) P is the principal of the loan, V is the value of the borrower s net assets at loan maturity, f c (V ) is the creditor s ex ante subjective expectation of the distribution of V, and r is one plus the interest rate. I make several simplifying assumptions. First, I assume no coupon payments, but rather that all interest is paid at maturity with the principal. Second, I assume zero time value of money. Third, I assume the creditor is risk-neutral. Fourth, I assume that uncertainty is solely related to the borrower s future value. 6 Fifth, I assume there are no agency conflicts between the borrower and the creditor. Specifically, I assume the borrower makes optimal decisions from the standpoint of the creditor (no moral hazard) and that the borrower credibly and costlessly communicates any private 6 Another source of uncertainty of interest to the creditor is the borrower s willingness to pay; that is, even if the borrower has sufficient funds at loan maturity, he chooses not to pay the creditor. I assume that, given sufficient value, the borrower always honors his contractual obligations. 7

9 information to the creditor (no information asymmetry). 7 Sixth, I assume that the creditor s subjective distribution f c (V ) is wider than the objective distribution f(v), in the sense of having wider boundaries or a higher variance. 8 In Eq. (1), the left-hand side of the expression represents the value the creditor expects to receive based on his subjective distribution of V. The first integral is the value the creditor expects to get if the borrower defaults; if he expects the value of the borrower at maturity to be less than Pr, the creditor assumes he can costlessly take control of and liquidate the borrower. The second integral is the value to the creditor when the borrower is not expected to default; as long as the value of the borrower at maturity exceeds Pr, this is the amount the creditor expects to receive. The creditor determines the interest rate r based on f c (V ), and uses this to equate the left- and right-hand sides of Eq. (1). In other words, the creditor sets the interest rate so the expected payment he receives, given the possible values of the borrower and their expected likelihoods, is equal to the initial principal; I call this interest rate ˆr. Uncertainty about the future value of the borrower shapes the creditor s subjective distribution f c (V ). The degree of uncertainty is a function of how much information about the borrower is available. Following Jiang et al. [2005], I characterize uncertainty in terms of the precision of the creditor s estimate of the borrower s future value V : more information indicates less uncertainty and a narrower distribution, while less information indicates greater uncertainty and a wider distribution. Uncertainty is priced in Eq. (1). With payoffs to the creditor being asymmetric, the creditor stands to lose his entire principal if the the loan defaults, though his upside payoff is capped at the principal and interest. As f c (V ) gets wider (holding the mean expected borrower value equal), the expected likelihood of extreme good and bad outcomes increases. Thus, the potential for losses increases, but without a commensurate increase in potential gains. 9 It follows that 7 I make these stylized assumptions in the model to understand the effects of uncertainty absent agency conflicts. To address agency conflicts in the empirical tests, I employ both controls (in cross-sectional tests) and specific settings. 8 This assumption follows Jiang et al. [2005], who model uncertainty as the the precision of information. The objective, risk-based distribution forms the base for the creditor s estimate, and any incremental uncertainty leads to a wider distribution. 9 This is the case described in Myers [1977], where shareholders benefit by increased volatility in firm net assets; the increased volatility widens the distribution of outcomes to firm value, and equity holders 8

10 the creditor prices uncertainty, with a wider range of expected borrower values leading to a higher value for ˆr. I illustrate this with a mathematical example in Appendix A Borrower s Pricing and Decision If the distribution of V is objectively determined, the borrower should accept the ˆr offered by the creditor. However, in the same way that the creditor makes a subjective assessment of the borrower s future value, so does the borrower assess his own future value. In other words, similar to the creditor, the borrower assesses the following expression when considering a loan: P r 0 V f b (V )dv + P r P r f b (V )dv = P (2) Eq. (2) is a quasi-pricing expression; it represents how the borrower would price the loan if he were setting the interest rate. The subscript of f b (V ) indicates the borrower s subjective distribution rather than the lender s. If the borrower and creditor agree about the distribution of V (either due to the distribution being objectively known, or by chance the subjective distributions yielding identical values over the domain of the distribution), the borrower will agree to the creditor s offered rate of ˆr. Congruence between subjective distributions, however, is unlikely; the borrower and creditor may have different information sets, and even when they are dealing with the same information they are likely to interpret it differently (e.g. the value of investment opportunities). In the remainder of this section, I consider the case where the borrower has a higher expected future value for V (over the entire distribution of outcomes) than the creditor. 10 The borrower always perceives that he is overpaying. More formally: P ˆr 0 V f b (V )dv + P ˆr P ˆr f b (V )dv = P (3) P is the borrower s expected repayment amount given f b (V ), the borrower s subjective distribution, and ˆr, the offered interest rate. When the borrower has a higher valuation enjoy most of the upside benefit while sharing the downside risk with creditors. 10 Due to asymmetry in payoffs, I expect creditors put greater weight on the low end of the distribution of borrower value, whereas borrowers will focus on the entire distribution. Additionally, behavioral explanations, such as overconfidence or self-attribution bias, will tilt the borrower s expectations higher. 9

11 over the distribution of V, P is greater than P. As such, due to disagreement in their subjective distributions, the borrower is unwilling to accept the creditors interest rate. Moreover, the degree of overpayment, P P, is increasing in the creditor s uncertainty. This is due to the asymmetric payoffs to the creditor: greater creditor uncertainty results in a greater likelihood of low outcomes, which increases ˆr. Holding the f b (V ) equal, this increases P P. In Appendix A.2 I calculate the degree of borrower overpayment and its relation to uncertainty Creditors Pricing with a Covenant The information friction, in this setting, is lack of information by the creditor about the borrower s future value. When new information is received, some of the creditor s uncertainty is resolved; that is, he becomes incrementally better informed about V. If the creditor had access to this information prior to loan contracting, it would affect his pricing. However, Eq. (1) only allows information available prior to contract inception to influence the interest rate. In other words, unless ex ante uncertainty about the borrower s future value can be remedied, the credit market may fail to allocate capital to a borrower who is in fact a good credit risk. One solution is renegotiation, where the creditor and borrower agrees to change contract terms ex post. Consider the following simple example where a prospective borrower can be one of two types. A good borrower will not default, while a bad one will. The creditor cannot determine the borrower s type ex ante, so he develops a subjective distribution over the two types. 11 Assume that there is an information signal related to the borrower s type that is unavailable prior to the start of the contract, but is revealed after the contract has begun. The signal, while not fully revealing of the borrower s type, does provide the creditor clarity about the borrower: a low signal means the borrower is more likely to be bad, and a high signal means the borrower is more likely to be good. As long as the signal is predictive of the future value V it resolves uncertainty and hence would 11 It is also possible, if not likely, that the borrower will not know his actual type. Following the earlier discussion, I assume only that the borrower s subjective distribution is weighted more heavily towards his being the good type. 10

12 be useful for contracting. However, since it is not available ex ante, the contract must be renegotiated to incorporate the new information. The key question is how to effectively facilitate renegotiation. To start, it is important to consider the ex ante allocation of control rights and how this allocation relates to renegotiation. When a loan is made, the borrower receives funds from the creditor; this gives the borrower relative control in the lending relationship and a plausible threat to force renegotiation. Consider a loan with a high initial interest rate. Subsequent to loan inception, new information reveals the borrower to be the good type; this makes the initial interest rate too high, and the borrower has incentive to get the rate lowered. Since the borrower holds the funds from the loan, he can seek alternative funding (i.e. a loan from a different bank). 12 If the original lender wants to keep the borrower s lending business, he will be compelled to renegotiate when the borrower demands it. In contrast, the creditor lacks a plausible threat to terminate the loan due to his lack of control rights. In other words, the creditor has little control (since the borrower holds the cash from the loan) to force a renegotiation that the borrower does not want. For this reason, the contract must include a provision that facilitates creditor-initiated renegotiation. Consider a loan provision which is triggered if an information signal reveals that the borrower is likely to be of the bad type. In practical terms, such a provision (a covenant) requires the borrower to maintain a financial measure at or above c. The level of c can be viewed as a partition on the future value V ; with any realization of the information signal below c the creditor may want to renegotiate the loan terms, whereas the creditor strictly does not want to renegotiate for any realization c or above. By including a covenant of this type, the creditor can set a low initial interest rate (commensurate to the good type) under the assumption that if the covenant is triggered a new, higher interest rate can be negotiated. In this way, the covenant represents a conditional reallocation of control rights, facilitating creditor-initiated renegotiation. To understand how adding a covenant 12 Roberts and Sufi [2009] show that prepayment restrictions are seldom used in private loans. 11

13 affects pricing, I augment Eq. (1): P r2 0 V f c (V )dv + P r 2 c P r 2 f c (V )dv + P r 1 c f c (V )dv = P (4) Eq. (4) features two interest rates: r 1 is the initial interest rate, and r 2 is the rate the creditor expects to get in renegotiation; r 2 can be viewed as a punishment rate if the borrower fails to maintain the threshold c. I assume the relation r 2 > r > r 1 holds. The left-hand side of Eq. (4) can be broken into two parts based on the state of the covenant and the expected payments from the borrower conditional on the expected covenant state. If V c, the borrower is in compliance and pays P r 1, the principal plus the initial interest rate. If V < c, the loan is in technical default and the creditor expects to receive either P r 2 (if V is sufficiently high) or V (if the borrower value value is low). Eq. (4) links the subjective distribution f c (V ), the interest rates of the loan, and the covenant level: holding r 2 and c equal, the initial interest rate r 1 is increasing in uncertainty. The logic is similar to the pricing of uncertainty without a covenant. I illustrate this in Appendix A.3. Finally, it is important to note that, given r 1 and r 2, the level of c will be set so that the creditor s expected receipt from the borrower is the same regardless of whether a covenant is used. This follows from the relation r 2 > r > r 1. In other words, the creditor is indifferent between having and not having a covenant, because any pricing effects are passed on to the borrower. Hence, for a covenant to be used in a loan contract, it must reduce the amount the borrower expects to pay Borrower s Pricing and Decision with a Covenant Similar to above, define ˆr 1 and ˆr 2 as the calculated rates from the creditor s pricing equation. The borrower s expected payout with a covenant is: P ˆr2 0 V f b (V )dv + P ˆr 2 c P ˆr 2 f b (V )dv + P ˆr 1 c f b (V )dv = P (5) 12

14 Eq. (5) shows how much the borrower expects to pay under the creditor s pricing, in this case with a covenant in the contract. As illustrated earlier, P is greater than P, so when there is no covenant, the borrower always overpays under the creditor s pricing, and the degree of overpricing (P P ) is increasing in the creditor s uncertainty. To accept having a covenant, the amount the borrower overpays when a covenant is in place (P P ) must be less than the overpayment without a covenant (P P ). In other words, a borrower will agree to include a covenant when: (P P ) > (P P ) = P P > 0 (6) That is, since the creditor is indifferent about having a covenant, the borrower will choose a covenant when it results in a lower expected payment. By offering ˆr 1 < ˆr, the creditor is trading a lower interest rate for contingent control rights. When will the borrower accept? Recall that the borrower has a higher expected value over the entire distribution of V. Consider the extreme case where the borrower expects he will never violate the covenant. In this case, his expected payout is P ˆr 1 < P ˆr, and he will prefer the covenant. The borrower s higher subjective value means his expected likelihood of technical default is lower than the creditor s, and hence his expected payment is lower, meaning he will choose to take the loan with the covenant. Furthermore, the greater the difference between P and P, the greater the borrower s incentive to agree to a covenant. Finally, as I illustrate in Appendix A.4, the difference between P and P is increasing in creditor uncertainty (holding the borrower s uncertainty equal). Recall that P P is increasing in uncertainty, due to disagreement between the creditor s and borrower s subjective distributions. P P is also increasing in uncertainty. However, the borrower s perceived overpayment in this case is increasing less in uncertainty than in the no-covenant case. As when there is no covenant, the creditor s uncertainty is priced into the offered interest rate. The different subjective distributions also affect the borrower s perceived likelihood of triggering the covenant. Other things equal, greater uncertainty leads to greater disagreement between the borrower and the creditor; given a covenant, the borrower s expected likelihood of entering technical default is decreasing in the creditor s 13

15 uncertainty, leading to lower expected payment. In total, the positive relation between uncertainty and the offered interest rate is counteracted by the negative relation between uncertainty and the borrower s expected likelihood of violating the covenant. This makes the the borrower s preference for a covenant increasing in uncertainty, leading to the hypothesis: H1: The use of financial covenants is increasing in the creditor s uncertainty about the future value of the borrower. 2.3 Why Contract on Uncertainty? A fundamental issue to this study and its prediction is whether uncertainty is a contracting problem; that is, should contracts include provisions to address uncertainty, or should the creditor simply price this cost in the interest rate, like risk? To start, consider how risk and uncertainty manifest in debt contracting. Each indicates stochastic outcomes for the borrower, and can be operationalized as a wider range of values. The key difference is the nature of the underlying distributions. As defined in this study, risk has a known distribution, while uncertainty has an unknown, and hence subjective, distribution. When a distribution is objectively known (e.g. Knight s a priori probability), new information does not change subjective assessments of that distribution. In contrast, subjective assessments of an unknown distribution are updated when new information arrives. The difference between risk and uncertainty as it relates to contracting and updating information is best illustrated with an example. Consider a multi-round game where a six-sided die is thrown. If the throw reveals a five the player wins, and otherwise the player loses. This is a risky game; assuming a fair die, the player has a one-in-six chance of winning and a five-in-six chance of losing. Say the first throw of the die yields a four. Since the underlying distribution of outcomes is known, and die throws are independent events, receiving a four does not alter the player s expectation of winning future rolls: this remains one-in-six. In other words, information received in the throw of the die does not change the player s expected odds of winning. 14

16 Now consider a similar game, where again five is the winning throw. However, the die being thrown cannot be observed, and it can be either six-sided or ten-sided. Assume that the same die is used in each round of the game. The two dice represent uncertainty; the player s odds of winning are one-in-six or one-in-ten depending on which die is actually used. Prior to the first throw, the player subjectively determines his odds of winning. The odds should be somewhere between one-in-six and one-in-ten, but can differ from player to player. Now, say that the first throw is a seven. This throw indicates unambiguously that the die is ten-sided: the player should update his expectation of winning future throws to one-in-ten. Any throw between seven and ten completely resolves the uncertainty, and the objective odds are known. If a four was thrown on the first throw (rather than a seven), the effect on resolving uncertainty is less clear, because four belongs to both distributions. However, a series of throws all six or under should convince a player that he is dealing with a six-sided die. 13 Returning to debt contracting, realizations of information subsequent to loan inception resolve uncertainty about borrower type. Realization of a low information signal helps the creditor narrow down the set of possible distributions; on seeing such a signal, he removes the best potential distributions and waits for the next signal to learn more. A series of information signals updates the creditor s subjective view of the borrower s value. In contrast, if the distribution of the borrower s value is objectively known, new information does not affect the creditor s view, and hence the original pricing of the risk is appropriate; there is no incentive to have covenants because renegotiation is never demanded. In total, the subjective nature of uncertain distributions motivates future acquisition of information and renegotiation of debt contracts, making uncertainty a contracting problem. 13 In this example, a player can infer that a six-sided die is being used with 99% confidence after nine throws between one and six. 15

17 3 Sample and Data 3.1 Sample The sample consists of all private debt agreements to publicly-traded borrowers on the LPC/Dealscan database initiated from 1995 to Accounting data are from the Compustat quarterly Xpressfeed, and stock trading and returns data are from the CRSP daily file. I match the Dealscan data to Compustat and CRSP using the matching table from Chava and Roberts [2008]. Finally, I exclude deals from the sample which have no covenants reported on Dealscan; Drucker and Puri [2009] show that these observations are often data errors. This reduces the sample by 273 observations, consistent with the majority of private loans including financial covenants. Dealscan is organized on the facility- and deal-level. Facilities are individual loans, such as terms loans and revolving lines of credit. Deals are groups of facilities issued at the same time by the same lead lender. All the facilities in a deal are covered by the same set of covenants, so the analysis in this study is at the deal-level. The sample consists of 15,120 deal-observations. 3.2 Variable Measurement The hypothesis examines the relation between covenant use and uncertainty. One way to measure covenant use is to sort borrowers with no financial covenants from those with at least one. However, since this sample by design includes only deals with financial covenants, this is not possible. 14 Instead, I define FINANCIAL COVENANT INTEN- SITY as the number of financial covenants included in each deal. 15 I present statistics on FINANCIAL COVENANT INTENSITY in Table 1. The index ranges from one to 14 Even including these deals, 98% of Dealscan deals in the sample period have financial covenants, meaning there is insufficient variation in covenant inclusion to use a dichotomous sorting. 15 Murfin [2009] correctly notes that financial covenant intensity captures only one dimension of the deal s covenant portfolio; two other aspects, the covenants initial slack (initial value less threshold value of the covenant financial measure) and the correlation between covenant measures also contribute to the frequency of technical default. To the extent that initial slack and correlation vary between borrowers and deals, this confounds this measure as a proxy for overall covenant protection. However, covenant intensity is commonly used in the literature (Bradley and Roberts [2004]; Billett et al. [2007]; Christensen and Nikolaev [2012]). 16

18 seven, with an average of 2.5 financial covenants per deal. To measure uncertainty, I identify borrower features that reflect the borrower s information environment. AGE is the number of months the firm has been listed on CRSP. Firms with long histories are likely to be better known, and there is more information available to analyze and use in projections. RATED is an indicator variable with a value of one if the firm has an S&P senior unsecured debt rating, and a zero otherwise. The presence of a rating suggests a more transparent information environment for the firm. There is less uncertainty about older firms and firms with debt ratings, so I predict a negative relation between each of these variables and covenant use. Following Jiang et al. [2005], I use additional measures from the equity market to capture uncertainty. VOLATILITY is the 60-day standard deviation of the firm s stock price, multiplied by the inverse of leverage. 16 VOLUME is the 25-day average trading volume of the firm s stock, scaled by the total shares outstanding. 17 Greater uncertainty about a firm manifests as less agreement on its value among investors, which leads to a more volatile stock price and more trading. The third equity market measure is DURA- TION, the implied equity duration from Dechow et al. [2004]. Similar to debt duration, equity duration measures the weighted-average time expected to receive cash flows. Cash flows to be received further in the future are measured with less precision, so longer duration indicates greater uncertainty. Since each of these equity market measures has a positive association with uncertainty, I expect each to have a positive association with financial covenant use. The sixth measure is ANALYSTS, the number of analysts listed on I/B/E/S making at least one earnings estimate for the borrower s stock in the quarter preceding the loan. Greater analyst coverage should lead to less uncertainty, so I predict a negative association with covenant use. I present summary statistics on uncertainty variables in Table 2, Panel A. There are a number of other variables used in the literature to measure uncertainty that I do not use in this study. Kothari et al. [2002] use both firm size (the natural 16 Holding other things equal, higher leverage firms have more volatile equity values; delevering volatility abstracts away from the effects of financing policy. 17 Similar to Jiang et al. [2005], I use a different measurement window to reduce correlation between VOLATILITY and VOLUME. 17

19 logarithm of the market value of equity) and financial leverage (debt-to-market value of assets) as predictors of earnings variability. I do not use these because both have alternative interpretations: size proxies for many things, including agency conflicts and borrower negotiating strength, while leverage may measure agency conflicts, capital market access, or default risk. I include these as controls. Zhang [2006a], in addition to using firm age, stock price volatility, analyst coverage, and size, includes analyst forecast dispersion and cash flow volatility as uncertainty proxies. I do not use forecast dispersion due to data constraints: over 40% of sample borrowers have zero or one analysts covering their stock. I do not use cash flow volatility because the measure is earnings-based, which may confound its meaning as a proxy for uncertainty. Specifically, more volatility may cause accounting-based financial measures to be less useful in covenants, indicating a negative relation. This runs counter to the prediction that more volatility, and hence greater uncertainty, is positively associated with covenant use. I use several borrower-level control variables in the tests, each potentially associated with financial covenant use. LEVERAGE is the ratio of total debt to total assets. EBITDA is the ratio of earnings before interest, taxes, depreciation, and amortization to average total assets. This controls for operating performance, which indicates the sufficiency of cash flows to cover debt payments. SIZE is the natural logarithm of the market value of the firm (the market value of equity plus the book value of debt). MARKET- TO-BOOK is the ratio of the market value of the firm to the book value of the firm, and is a common proxy for growth opportunities and agency conflicts. EDF, the distance to default (based on Merton [1974]), measures default risk based on the borrower s leverage and asset volatility. RATING is the borrower s S&P Senior Unsecured Debt rating on a 22-point scale (AAA = 1, AA+ = 2, etc.). Some tests use loan-level controls including LENDERS, the number of syndicate members; CAPITAL EXPENDITURE, an indicator for presence of a covenant restricting fixed asset purchases; PERFORMANCE PRICING, an indicator for a pricing grid linked to stock rating or an accounting ratio; COLLAT- ERAL, an indicator if the loan requires security; and MATURITY, the stated term to maturity of the loan in days. I present descriptive statistics for each of these variables in 18

20 Table 2, Panels B (borrower features) and C (loan features). In Table 3, Panel A, I present univariate correlations for the six uncertainty measures. A number of the uncertainty measures have strong correlations with each other; for example, the pairs AGE-RATED, RATED-VOLATILITY, and VOLATILITY-VOLUME all have correlations (in absolute terms) of at least Hence, multicollinearity could affect the inferences from tests. To more precisely measure the underlying sources of uncertainty, I use principal components analysis on the six uncertainty variables. Following convention, I retain the two principal components with eigenvalues greater than one. I present the component loadings in Table 3, Panel B. Based on the signs and magnitudes of the standardized loadings, I predict a negative sign and a positive sign for the first and second principal components (PCA1 and PCA2) respectively. I present summary statistics for the two principal components in Table 3, Panel C. 4 Empirical Tests and Results 4.1 Univariate Results As initial descriptive evidence, I sort borrowers by financial covenant intensity and examine the level of the six measures of uncertainty as well as the two principal components. Since there are few deals with either six or seven covenants, I group these into a category with deals having five covenants. I present the results in Table 4. Both AGE and RATED display the predicted negative trend over financial covenant intensity; borrowers whose deals have one covenant are, on average, over twice as old as those in the highest group (224 versus 112 months), and nearly twice as likely to be rated (52.4% to 28.3%); both are statistically significant differences. VOLATILITY displays the predicted increasing pattern, though the relation is relatively weak: the lowest covenant intensity group has volatility only 10% lower than the highest group (2.2% versus 2.4%). VOLUME and DURATION do not show any clear pattern. ANALYSTS is nearly three times higher in the lowest covenant intensity group than the highest (5.865 to 2.020). PCA1 has a clear negative trend from lowest to highest intensity, while PCA2 has the predicted positive 19

21 (though not monotonic) trend. 4.2 Multivariate Results To formally test the hypothesis and control for alternative drivers of covenant use, I use multivariate analysis. The test takes the form: F incovintensity i = f(α + BUncertainty i + ΓControls i + ɛ) (7) Since FINANCIAL COVENANT INTENSITY is a count variable, the regression uses the negative binomial function. I run four specifications. In the first, I include the six separate uncertainty proxies and the borrower-level controls (LEVERAGE, EBITDA, SIZE, MARKET-TO-BOOK, and EDF). In the second specification I include all the variables from the first, and add RATING and loan-level controls (LENDERS, CAPEX, PERFORMANCE PRICING, and COLLATERAL). The third and fourth specifications are similar to the first and second, but include the two principal component variables rather than the six separate uncertainty variables. All regressions include indicators for year and industry (based on Fama and French [1997]). I present the regression results in Table 5. The table shows coefficient estimates and Z-statistics (clustered by borrower and year to address cross-sectional and intertemporal correlation). In the first specification, five of the six uncertainty variable coefficients have the predicted sign and are statistically significant; only VOLATILITY deviates, with a negative but insignificant coefficient. The controls suggest that small, profitable, and highly levered firms, on average, have more financial covenants. The second specification yields similar results, with signs of the coefficients being the same (though with diminished significance in some instances). The coefficient on RATED is over seven times larger in the second specification. This is likely due to its significant, positive correlation with RATING (ρ = 0.94); for this reason I do not included RATING as a control in subsequent tests, though inferences are not altered when I do include it. Additionally, both PERFORMANCE PRICING and COLLATERAL requirements are positively associated 20

22 with covenant use. The third and fourth specifications show significant coefficients in the predicted direction for both principal components, and the coefficients on the controls are similar to the first two specifications. These results show that uncertainty, as captured by a variety of measures, has a strong association with the number of covenants included in private loans. There is one particulary notable coefficient from the controls, the MARKET-TO- BOOK ratio. While this ratio has a variety of interpretations in the literature, a common one is that it proxies for growth opportunities, or agency costs (Smith and Watts [1992]; Skinner [1993]); higher values represent greater growth opportunities, and hence more serious agency problems. Agency conflicts are a common explanation for financial covenant use. If agency conflicts explain financial covenant use, the coefficient on MARKET-TO- BOOK should be positive. The fact that it is not positive in any of the four specifications (and negative and significant in two) casts doubt on the agency explanation. However, since MARKET-TO-BOOK is an ambiguous proxy for agency conflicts, I explore this issue in greater depth in the next section. All the regressions in Table 5 include EDF as a control for risk, and the two extended specifications also include RATING. However, as discussed in Section 2.1, risk and uncertainty are related concepts; both are based on the idea of stochastic outcomes, with a wider range of outcomes indicating greater risk and greater uncertainty, respectively. This makes differentiating risk and uncertainty with empirical measures difficult. For example, if uncertainty is reflected in empirical measures as a wider range of values incremental to risk, higher value of uncertainty proxies could be a function either of greater uncertainty or of greater risk (or potentially both). It is unlikely that including control variables for risk in multivariate regression fully controls for this issue. To address the influence of risk more directly, I use regression to create a set of uncertainty measures orthogonalized to risk. Specifically, I run each of the uncertainty measures through the following OLS regression: 21