Corporate Hedging and Speculative Incentives:
Implications for Swap Market Default Risk
Abon Mozumdar¤
Pamplin College of Business
Virginia Tech
1016 Pamplin Hall-0221
Blacksburg, VA 24061
Tel:540-231-7379
e-mail: [email protected]
July 2000
¤
This paper is based on a chapter entitled `Swaps, Default Risk and the Corporate Hedging Motive' from
my PhD dissertation at New York University. I am grateful to the anonymous JFQA referee for exceptionally
constructive comments, the editor Jonathan Karpo®, Yakov Amihud, Don Chance, Zsuzsanna Fluck, Kose
John, Anthony Lynch, N.R. Prabhala, Anthony Saunders, Cli® Smith, Raghu Sundaram, Robert Whitelaw,
and seminar participants at NYU and Virginia Tech for comments and suggestions. I am especially grateful
to Marti Subrahmanyam for guidance, suggestions, and encouragement. Financial support from a summer
research grant at Virginia Tech is gratefully acknowledged. I am solely responsible for any remaining errors.
0
Corporate Hedging and Speculative Incentives:
Implications for Swap Market Default Risk
Abstract
This paper demonstrates a trade-o® between the risk-shifting and hedging incentives
of ¯rms and identi¯es conditions under which each dominates. A ¯rm may have the
incentive to hedge in a multi-period context, even if no such incentive exists in a singleperiod one. Unrestricted access to swaps in the presence of asymmetric information
about ¯rm type and the swapping motive would lead to unbounded speculation resulting
in breakdown in swap and debt markets. Price-based methods are unable to control
this and market makers have to rely upon additional exposure information or credit
enhancement devices to preserve equilibrium.
Corporate Hedging and Speculative Incentives:
Implications for Swap Market Default Risk
I
Introduction
The issue of default risk in swap markets continues to evoke concern, both in academic and
practitioner circles. In response to such concerns, recent years have seen the widespread
adoption of several `credit enhancement' devices such as netting, marking-to-market, collateralization, and credit triggers, ostensibly to protect the market against losses from
counterparty default. Yet, the frequency and extent of such losses have remained at negligible levels throughout the history of the swap market, and the market continues to record
explosive growth year after year. The impact of default risk seems to be small on swap
pricing practices too | quoted swap prices show little sensitivity to counterparty credit
ratings. It is therefore natural to ask if the problem of swap market default risk is indeed as
serious as has been commonly portrayed. Moreover, why does the market rely upon nonprice credit enhancement devices to control default risk instead of adjusting swap prices for
counterparty credit quality? This paper presents a simple framework for addressing these
questions.
The previous literature in the area can be broadly divided into two categories. The ¯rst
group of papers (Cooper and Mello (1991), Baz and Pascutti (1996), Du±e and Huang
(1996), Hentschel and Smith (1997)) theoretically models the default risk of swaps and
provides simulation evidence on its severity. The second group of papers (Sun, Sundaresan
and Wang (1993), Koticha (1993), Mozumdar (1996), Minton (1997), Du±e and Singleton
(1997)) uses actual swap market data to estimate the impact of default risk on interest rate
swap pricing. Both strands of the literature conclude that the impact of default risk on
swap pricing is small. For example, both Du±e and Singleton (1997) and Minton (1997)
¯nd only weak empirical evidence that default risk is important in swap markets. Similarly,
Du±e and Huang (1996) report that a 100 basis points di®erence in debt rates corresponds
to a 1 b.p. di®erence in swap rates, while Hentschel and Smith (1997) conservatively
estimate the expected annual loss rate to be 0.00025% of the notional principal. In view of
such microscopic estimates of the impact of default risk, it may seem that concerns about
catastrophic losses are gross exaggerations that can be safely ignored. We argue, however,
that jumping to such a conclusion may be incorrect and dangerous.
While it is certainly true that in equilibrium, the impact of default risk on swaps is
small, it is important to realize that this equilibrium does not arise automatically. Also,
while it may represent the most desirable equilibrium, it is not the only one possible. A
complete analysis of swap market default risk requires a clear understanding of why ¯rms
enter into swaps in the ¯rst place. The default risk of a swap is drastically higher if it is used
for speculation. The problem of swap market default risk is therefore directly related to the
more fundamental question of corporate hedging and speculative incentives. Drawing on
the hedging and risk-shifting literatures, we show that when there is risky debt outstanding,
the hedging motive dominates for pro¯table, well-capitalized ¯rms, while the speculative
1
motive does for less pro¯table, poorly-capitalized ones. We also show that the hedging
decision depends upon the planning horizon of the ¯rm | it may have the incentive to
hedge in a multi-period setting, even if it has no such incentive in a single period one.
When a swap market opens to satisfy the bona ¯de hedging needs of some ¯rms, it also
has to deal with the possible speculative intent of other ¯rms. Excluding all speculative
swaps is not possible since the ¯rm's true type and its swapping motive are not perfectly
observable to the market maker. Thus, the issue of swap market default risk essentially
revolves around resolving this information asymmetry, and several apparently enigmatic
features of the swap market can be explained as mechanisms for doing so.
We show that when ¯rms have such private information, price-based mechanisms are
unable to control default risk. Attempting to compensate the swap dealer for the default
risk of speculative swaps by raising the cost of swapping to the counterparty would only
exacerbate the speculative intent of the pool of counterparties, thereby further increasing
default risk and leading to a breakdown in the swap market. Moreover, the debt market
would also correctly infer the incentive for some ¯rms to speculate with borrowed money
and refuse to lend at any interest rate, leading to a breakdown in this market too. Nonprice methods are therefore necessary to control default risk and preserve equilibrium.
Such non-price methods may either be the production of additional information by the
market maker through long-term relationships and master swap agreements, or the use of
credit enhancement devices like netting, marking-to-market, and collateral. When such
mechanisms are in place, only hedging-motivated swaps are allowed, default risk ceases to
be an important concern, and price-sensitivity to credit rating is unnecessary.
While the analysis in this paper is done in the speci¯c context of swaps, the results can
be generalized to other derivative securities like forwards, futures, and collars. Like swaps,
these derivatives are zero-present-value securities in which cash in°ows in some future states
are paid for by cash out°ows in some other future states. Since the derivative payo® can
be positive or negative contingent on the realized state, the dealer is exposed to the risk of
default by the counterparty, as in a swap.1 Analysis similar to that presented here indicates
that non-price mechanisms are required to control default risk in markets for such other
derivatives as well. For exchange-traded futures, this function is served primarily by the
daily marking-to-market process. For over-the-counter derivatives like forwards and collars,
dealers rely upon credit-enhancement devices similar to those used for swaps.
The paper makes contributions in the following directions. It connects the risk-shifting
and hedging literatures to demonstrate the existence of a trade-o® between these two counteracting incentives and identi¯es conditions under which each dominates. It shows that
the hedging incentive becomes stronger as the number of time periods under consideration
increases. It highlights features of swap contracts that make them well suited for hedging
the risk of ¯nancial distress associated with risky debt. In a setting of asymmetric information about true ¯rm type, trying to control default risk of swaps through pricing would
1
In fact, a single-period swap is identical to a forward. Similarly, a multi-period swap can be seen as a
portfolio of forwards, some of which are in-the-money and the others out-of-the-money, so that the portfolio
as a whole has zero value.
2
lead to unbounded speculation by all ¯rms resulting in breakdown in both the swap and
debt markets. Consequently some form of non-price credit control mechanism is shown to
be necessary to attain equilibrium. Finally it shows how several institutional features of
the swap market are useful as such mechanisms and thus provides a complete theoretical
characterization of the swap contract.
II
A
Debt, Swaps, and Default Risk
Swaps: Some Stylized Facts
A swap is a ¯nancial contract between two counterparties under which each pays the other a
stream of cash °ows based on a certain notional principal, where the cash-°ows are indexed
to two publicly observable macroeconomic variables like interest rates, foreign exchange
rates, or commodity prices.2 In many swaps, payments by one counterparty are ¯xed, so
the net swap payments are contingent on only one index variable.3 A swap contract thus
embodies a positive exposure to one underlying economic risk factor and a negative exposure
to another. If it is of a ¯xed-for-°oating form, then it is a claim contingent upon only the
single risk factor to which the °oating leg is indexed. It is therefore a useful instrument
for a ¯rm that wishes to alter its risk exposure to one speci¯c factor, or to substitute it by
another factor.
In a perfect market, it is possible to create such pure individual factor claims even in the
absence of derivative securities like swaps. If there are N linearly independent sources of
risk in the economy, then in principle it is possible to create pure factor claims by forming
portfolios of N linearly independent primary securities. But such portfolios will in general
have short positions in some securities. In a world with short-sales constraints therefore,
the introduction of swaps increases the e®ective span of securities. The high degree of
liquidity in markets for several types of swaps, the availability of dealers willing to create
specialized swaps to suit individual client needs, and small transaction costs further enhance
the attractiveness of swaps as risk management instruments.
Short sales constraints are imposed by market-makers and regulators to minimize the
impact of default risk in the economy. Does a swap, which embodies a short position in
one of the two legs, violate this constraint and therefore expose the ¯nancial system to a
large degree of default risk? Our model shows that the answer to the problem lies in certain
apparently anomalous features of the swap market. First, among the pool of acceptable
counterparties there is little or no di®erence in pricing between higher and lower rated
¯rms: swap dealers quote the same rate to all counterparties. Second, until recently, there
used to be a strictly binary accept/reject rule regarding the acceptability of ¯rms as swap
counterparties. Only ¯rms with investment-grade credit rating were allowed to participate;
sub-investment-grade ¯rms were not. The situation has changed in recent years, but even
now, there are stringent credit-enhancement clauses (netting, collateral, credit triggers,
2
For a discussion of the legal aspects of swaps, see, e.g., Gooch and Pergam (1990).
In the terminology of the swap market, the ¯xed rate payer is called the buyer of the swap, the °oating
rate payer the seller, and the ¯xed rate the price of the swap.
3
3
marking-to-market etc.) imposed on sub-investment grade counterparties. Our analysis
indicates that both these features are directly related to insulating the swap contract from
default risk.
B
Factor Risks and Financial Distress
The major utility of swaps lies in ameliorating costs of ¯nancial distress associated with
debt by making risky debt less risky. Debt has some characteristics that make it attractive
as a ¯nancing choice, viz., tax deductibility of interest and removal of free cash-°ow from
`empire-building' managers. However, it carries with it the risk of ¯nancial (as distinct from
economic) distress which occurs when the cash in°ows of the ¯rm are insu±cient to meet
its debt obligations at speci¯c points in time, even if the going-concern value is positive.4
Financial distress arises due to mismatch between the ¯rm's cash in°ows and out°ows.
Debt represents ¯xed or exogenously indexed claims on the ¯rm. The ¯rm's ability to
service the debt, however, depends on its operating performance which in turn depends on
its exposure to risk factors in the economy such as interest-rate risk, currency risk, price of
oil risk, etc. Let there be N risk factors X1 ; X2 ; ::::XN and let the sensitivity of the ¯rm's
project return Y to factor Xi be ¯i . Then,
Y =®+
N
X
¯i Xi + e
(1)
i=1
where e is idiosyncratic risk, with E(e) = E(ejXi ) = 0; 8i: Let the cost of debt be R, with
P
E(Y ) = ®+ ¯i E(Xi ) > R so that the ¯rm is able to service its debt on average. However,
P
if the variance of project returns, V ar(Y ) = ¯i2 V ar(Xi ) + V ar(e) is large, then default
will occur in some states. If ¯xed-for-°oating swaps exist for each one of the N factors,
then the ¯rm can use them to reduce this default possibility. A ¯xed-for-°oating swap
indexed to Xi has payo® Si = Xi ¡ X i , where X i is the swap rate, and to hedge completely,
the ¯rm takes a position wi = ¡¯i in Si . Assuming risk-neutrality (see the next section),
X i = E(Xi ). Then the combined cash-°ow YS on the project and the swap is
YS = Y ¡
N
X
¯i Si = ® +
i=1
N
X
i=1
¯i Xi + e ¡
P
N
X
i=1
¯ i Si = ® +
N
X
¯i E(Xi ) + e
(2)
i=1
As before, E(YS ) = ® + ¯i E(Xi ) > R, so that the mean pro¯tability of the ¯rm remains
the same, but V ar(YS ) = V ar(e) ∙ V ar(Y ). Thus, an appropriate set of swaps reduces
the possibility of default by e®ectively indexing the net debt obligations to the same risk
factors to which the operating cash-°ows are exposed.
Most swaps are associated with some outstanding issue of debt. A swap's maturity,
coupon dates, and notional principal are often the same as those of the associated debt.
Some swaps originate in conjunction with the issuance of new debt, while others are used
to alter the risk characteristics of preexisting debt. In keeping with the existence of nonstandard debt structures, there exist non-standard swaps too, e.g., amortizing swaps, accreting swaps, etc. A swap is particularly useful in a dynamic context: even if the debt is
4
See John(1993) for a survey.
4
indexed to the appropriate risk factors at origination, changes in the ¯rm's business operations over time alter the risk pro¯le of its cash-°ows, thus increasing the risk of ¯nancial
distress. Replacing old debt with new debt on a regular basis would entail large transaction
costs while an appropriate swap attains the same objective inexpensively.
The possibility of default on debt may also be reduced by using related derivative
securities like futures or forwards. However, to hedge the risk associated with coupon debt,
the ¯rm has to enter into several forward/futures contracts, one for each individual coupon
payment and one for the terminal cash-°ow. A swap on the other hand hedges the risk
of all payment obligations in one transaction. In a world with transaction costs, swaps
are therefore more attractive hedging vehicles. In this sense, a swap is a security that is
designed to provide the least-cost hedging solution to the default risk of risky debt.
C
Variance Reduction versus Risk-Shifting
Reducing cash-°ow variance appears to be a plausible explanation for the use of swaps,
but it runs against the traditional concept of risk-shifting. In particular, the con°ict of
interest between debt and equity arising from equity payo® being bounded from below at
zero induces equityholders to increase the riskiness of the ¯rm's cash-°ows and not reduce
it (Merton (1974), Jensen and Meckling (1976)).
More recently, however, a distinct strand of literature seeking to explain corporate hedging has emerged. The risk-shifting result holds only in the absence of all dissipative costs of
¯nancial distress and externalities related to loss of control. The hedging literature explores
situations where this assumption is not valid. The underlying reason to hedge has been variously identi¯ed as managerial risk aversion, a progressive tax schedule, bankruptcy costs,
and excessive costs of external ¯nancing when internal cash °ows are insu±cient to meet
positive NPV investment requirements (Stulz (1984,1990), Smith and Stulz (1985), Smith,
Smithson and Wilford (1990), Froot, Scharfstein and Stein (1993), DeMarzo and Du±e
(1995), Breeden and Viswanathan (1996)). The common feature here is that the payo® to
the insider/decisionmaker is a concave function of the ¯rm's cash °ows, which counteracts
the convex call option-like feature of equity. Bessembinder (1991) shows that even in the
absence of direct ¯nancial distress costs or progressive taxes, hedging may increase ¯rm
value by reducing underinvestment caused by agency problems between equityholders and
senior claimants like creditors. Hedging redistributes new investment payo®s across states
in such a way that equityholders receive positive payo®s in more states, increasing their
incentives to make those (positive-NPV) investments. In a di®erent setting, John and John
(1993) show that when the agency cost of debt is high, it is in shareholders' interest to
precommit to reducing ¯rm cash-°ow variance by means of a suitably designed concave
management compensation contract. Diamond (1991) makes a similar point by modeling
the private bene¯ts derived by the insider by simply being in control and `excessive' liquidations by debtholders who do not take these control rents into account. Minton (1993)
extends Diamond's framework to the interest-rate risk hedging context. Franke, Stapleton,
and Subrahmanyam (1998) distinguish between hedgeable and unhedgeable risks, and show
that ¯rms having di®erent degrees of relative exposures to them will have incentives to buy
5
and sell hedging products like options.
These papers clearly demonstrate the existence of conditions which mitigate the ex-post
risk-shifting incentive of equity in the presence of risky debt. Our analysis builds on it and
the traditional risk-shifting idea to show that a trade-o® exists between these con°icting
incentives. Proposition 1 in Section IV-A shows that a corporate motive to hedge systematic
risks may or may not arise endogenously for a ¯rm, depending upon the relative sizes of
the predictable and unpredictable components of the ¯rm's returns. Further, Proposition
2 shows that the possibility of positive equity payo®s in future periods may induce a ¯rm
to hedge in a multi-period context, even if is not optimal to do so in a single-period one.
III
The Model
Our basic model is a simple single-period (2-date) one. At time-0, the ¯rm has an opportunity to invest $1 in a project. To ¯nance the investment, the ¯rm issues debt claims against
the (uncertain) time-1 cash-°ows from the project. The riskfree single-period interest-rate
is Rf . The promised Interest-rate on a ¯rm's debt is R(R > Rf ) if the debt is seen as being
risky by lenders. All ¯nancing is provided by a large, risk-neutral market.
To concentrate on the impact of hedgeable, systematic risks in the economy, we assume
an exact linear factor structure of returns generated by the project. Using an inexact factor
structure, i.e., including an error term in the returns generating process, would introduce
an additional unhedgeable risk in the model and make perfect hedging impossible, but
would not a®ect the basic analysis of hedging and speculation with systematic risks. For
simplicity, assume there is only a single source of risk X in the economy. The risk factor
has zero expected return5 and positive variance. The total gross cash-°ow (Y ) from the
project is given by
Y = m + ¯X
(3)
where m is the expectation, or the predictable component of Y , and ¯ the sensitivity of
Y to the risk factor X. Let the required rate of return on the project be ¹. In general,
¹ = Rf +¯¸ where ¸ is the market price of risk X. Under our assumption of risk neutrality,
¸ = 0 ) ¹ = Rf . The expected return m measures the special skill or knowledge of the
¯rm in its line of business, and its quality in ¯nancial markets.
Assumption 1: m(t) is distributed uniformly over the interval [Lm ; Hm ] where Lm < Rf
and Hm > Rf . The superior quality of a better ¯rm is represented by its higher expected
return from its project.
The risk factor X refers to an economic variable that is not speci¯cally related to the
business of the ¯rm but a®ects returns in a general, macro sense. A typical example would
be the short-term interest-rate risk for a manufacturing ¯rm. The ¯rm has no particular
advantage in working with this factor. However, returns from every project (except lending
at the risk-free rate) are necessarily correlated with it. Let s be the state of the world
realized at time-1. Then X(s) represents the risk-factor realization.
5
This is without any loss of generality. If X has nonzero expectation, we simply need to adjust m in
equation (3) by adding ¯E(X).
6
Assumption 2: X(s) is distributed uniformly over the interval [¡K; K], K ¸ 0:
Note that m is a function of the ¯rm type while X is a function of the realized state
at time-1, i.e., for each ¯rm type, m has a ¯xed value and no variability, while X has
0 expectation and variance = K 2 =3: Also note the irrelevance of the sign of ¯ for the
risk-return pro¯le of the ¯rm. A ¯rm with exposure ¯ and one with exposure ¡¯ both
have an expected return m and volatility ¯ 2 K 2 =3. While the sign of ¯ determines the
ex-post realization of cash-°ows, only its magnitude is relevant for determining the ex-ante
distribution of those cash-°ows. This point plays an important role in our analysis later.
We assume the following information structure. The ¯rm observes its expected project
return m with perfect precision. This is private information and is not observable to the
market. What is public knowledge, instead, is the ¯rm's credit rating » which is m plus a
random, zero-mean noise ². The credit rating represents the external market's expectation
of the ¯rm's ability to service its debt, i.e., its expected future cash-°ow position. We make
the following distributional assumption about ².
Assumption 3: ² is distributed uniformly in the range [¡e; e].
The complete sequence of events can now be summarized. At time-0, the ¯rm observes
the expected return on the project m while the market observes a noisy credit rating »
based on which it sets a debt rate R(»). Based on m and R(»), the ¯rm decides (a) whether
to borrow and invest and (b) whether to hedge. Conditional on the ¯rm's borrowing and
investing, the project matures at time-1, cash-°ows are generated and claims are paid o®.
Appendix A provides a summary of symbols used in the model.
IV
A
Incentives for Hedging....
Exogenous Cost of Debt
As discussed in Section II-C, theoretical explanations of corporate hedging have sought
to identify ¯nancial market imperfections and tax-related reasons that create incentives
for hedging. Proposition 1 describes the trade-o® between the hedging and risk-shifting
incentives of the ¯rm in the presence of such imperfections, and shows that its resolution
depends upon the relative magnitudes of the predictable and risky components of the ¯rm's
cash-°ows. In this section, we consider hedging-motivated swaps only, i.e., swap positions
that reduce cash-°ow sensitivity to the risk factor X. An unhedged position thus refers to
a zero swap position. Speculative swaps are introduced in Section V. For simplicity, the
(gross) cost of debt R is assumed to be exogenously given in this subsection and the next.
We relax this assumption and endogenize R in subsection C.
Proposition 1a considers the case when the insider receives control rents which are lost
in the event of bankruptcy, or equivalently when deadweight costs of bankruptcy exist.6
Proposition 1a:Let the insider derive private bene¯t B by being in control of the ¯rm.
Then,
6
The case of ¯nancial distress costs outside bankruptcy is similar. A proof using a linear ¯nancial distress
cost schedule is available on request.
7
(a) Being completely hedged is optimal for ¯rms with quality m ¸ m¤
(b) Being completely unhedged is optimal for ¯rms with quality m < m¤
where the threshold quality level m¤ = R + °1 and °1 = max(¯K ¡ 2B; 0).
Proposition 1b considers the other reasons that have been suggested for corporate hedging, i.e., the various causes of concavity of the insider's payo® as a function of the ¯rm's
cash-°ows (managerial risk aversion, progressive taxes, underinvestment when external ¯nance is more costly, etc.). Thus we assume that the insider's payo® f (¢) is a positive,
increasing, and concave function of the ¯rm's net cash-°ow m + ¯X ¡ R.
Proposition 1b:Let the ¯rm insider's payo® be f (m + ¯X ¡ R) where f (¢) is positive,
increasing, and concave, i.e., f (0) = 0; f (y) > 0; f 0 (y) > 0 and f 00 (y) < 0; 8y > 0. Then,
(a) Being completely hedged is optimal for ¯rms with quality m > m¤
(b) Being completely unhedged is optimal for ¯rms with quality m < m¤
where the threshold quality level m¤ = R + °2 and °2 2 (0; ¯K).
Unlike °1 in Proposition 1a, an explicit expression for °2 is not possible because no speci¯c
functional form for f (¢) has been assumed.
Proposition 1 (a,b) considers various sources of pecuniary and non-pecuniary costs to
the insider that provide an incentive to hedge.7 In combination with the powerful riskshifting incentive of equity in the presence of risky debt, this leads to a similar result in
both cases: given a cost of debt R, it is optimal for ¯rms with quality m greater than a
cut-o® level m¤ = R + ° to hedge, while not hedging is optimal for ¯rms with m below
this level. Proposition 1a is illustrated in Table 1 for the following set of parameter values:
R = 1:05; K = 0:2; ° = max(¯K ¡ 2B; 0); B = 0:05; m 2 [0:85; 1:25]; ¯ 2 [0; 1].
Note that while the proposition implicitly assumes a positive exposure ¯ to the risk
factor X, an identical result holds when the exposure is negative. As described in Section III,
the direction of the exposure is unimportant for the ex-ante mean-variance characteristics
of the ¯rm. Since the distribution of X is symmetric about zero, a ¯rm with unhedged
cash-°ows m ¡ ¯X (¯ > 0) also has the incentive to hedge if m > R + ° and not to hedge
otherwise, where ° is as de¯ned in the proposition.
The economic intuition behind Proposition 1 is as follows. The payo® function to the
¯rm insider has both a convex and a concave section. The convexity arises due to the payo®
being bounded from below at zero, while the concavity is due to bankruptcy costs/control
rents in (a), and managerial risk aversion, progressive taxation, underinvestment when
external funds are costlier, etc. in (b). In each case, the concavity induces a hedging
motive which is stronger when expected ¯rm cash-°ows are larger, i.e., for ¯rms with
superior quality m. The incentive e®ect of the convexity, on the other hand, can be seen in
terms of the well-known equivalence between equity and a call option on the assets of the
¯rm which induces the insider to increase risk. When the call is deep in-the-money, i.e.,
the expected ¯rm cash-°ow is far greater than the required debt payment (m > R + °),
the option vega (option value sensitivity to volatility) is low and the variance-increasing
7
This result can be generalized to include distributions other than the uniform distribution for X. For
m to exist it is su±cient that limX!1 f (m + ¯X ¡ R)g(X)dX = 0, where g(¢) is the density function for
X. This condition imposes a mild restiction on f 0 (¢), one that is trivially satis¯ed for any concave f (¢) and
non-fat-tailed g(¢).
¤
8
incentive of the insider is small. Therefore, the hedging incentive induced by the concave
section of the payo® function dominates. On the other hand, when the call is close to being
at-the-money, (m < R + °), vega is high and the risk-shifting incentive dominates.
B
Extension to Multi-Period Settings
The above results are based on a single-period analysis. The next proposition shows that
when the analysis is extended to a multi-period framework, the threshold level of expected
project return for which hedging becomes optimal (m¤ ) is reduced. To illustrate the impact of extending the decision horizon of the ¯rm, assume that none of the conditions of
Proposition 1 hold, i.e., B = 0 and f 00 (¢) = 0. Under such conditions it would never be
optimal for the equityholders to hedge in a single-period context. Yet, in a repeated game,
hedging is shown to be optimal for equityholders for a very large range of values of m.
Proposition 2: Let the ¯rm face the single-period problem described above repeatedly
for T successive periods. Then it is optimal for it to hedge in the ¯rst period i® its quality
m > m¤ (T ), where the threshold quality level m¤ (1) = R + ¯K > m¤ (2) > m¤ (3) > :::: >
limT !1 m¤ (T ) = R + R¡1
R+1 ¯K.
When T = 1, the condition for hedging to be optimal is m > R + ¯K. But for
m > R + ¯K, the equityholder's payo® is linear in X and the ¯rm is indi®erent between
hedging and not hedging. Therefore, it is not optimal for any ¯rm to hedge. When T > 1
however, m¤ (T ) < R +¯K, and for ¯rms with m 2 (m¤ (T ); R + ¯K), it is optimal to hedge.
The quality threshold level m¤ (T ) is a decreasing function of T which implies that the set
of ¯rms for which hedging is optimal expands as T increases. In the limit, ¯rms with even
marginally positive NPV projects ¯nd it optimal to hedge.8 The intuition here is simple: in
a one-shot game, the equityholders clearly have an incentive to increase cash-°ow variance.
Even though this increases default risk, the equityholder is not averse to it since the ¯rm is
liquidated at the end of the period anyway. In a repeated game, however, the equityholder
has an incentive to keep the ¯rm going in later periods also. If the game is repeated a
su±cient number of times, it is in the interest of the equityholder to cooperate with the
bondholder and not to increase default risk by increasing cash-°ow variance.
C
Endogenizing the Cost of Debt
The analysis has so far considered the debt market rate R to be exogenously speci¯ed.
Given the distributions of the ¯rm types m and observation error ², and the decision rule of
¯rms with respect to hedging (propositions 1 and 2), R can be endogenized in equilibrium.
To be speci¯c, we assume that the structure of Proposition 1a holds, i.e., a ¯rm hedges if its
quality m exceeds m¤ = R + °, where ° = max[¯K ¡ 2B; 0] and B represents bene¯ts lost
in default. Also, in order to highlight the e®ect of observation error, we restrict attention
to one speci¯c value of risk exposure ¯. In particular, let ¯ = 1 and assume ¯ > 2B
K . The
¯rst assumption is without any loss of generality as none of the results are qualitatively
8
As in Proposition 1, here too an identical result holds for ¯rms with a negative exposure (¡¯) to the
risk factor X.
9
dependent upon ¯. The second assumption helps to focus on the more interesting case of
the possible pool of ¯rms including all three types | those that are inherently infeasible
(m < Rf ), those that have positive NPV but do not have the incentive to hedge, and those
that have the incentive to hedge.9 We also de¯ne a new variable ± = » ¡ R(») to obtain
closed-form representations of R(»). In intuitive terms, ± represents the external market's
perception of the expected future cash-°ow accruing to the equityholder. A high value of ±
indicates that the ¯rm's equity o®ers a substantial bond of compliance on its debt, making
the debt safer.
Proposition 3: Let the market observe a noisy version » of ¯rm quality m, » = m + ²,
with ² distributed uniformly over the interval [¡e; e], and e < K. Assume ¯ = 1 ¸ 2B
K . If a
swap market for hedging is available, then the equilibrium cost of debt R(») is given by the
following implicit closed-form representations
f or ± < ¡e ¡ K
R(») : Not Feasible;
2
R(») = Rf + (±+e)(±+e¡4K)+7K
; f or
12K
3(K¡±)2 +e2
R(») = Rf +
;
f or ±
12K
(K+e¡±)3 ¡(K¡°)3
R(») = Rf +
; f or
24eK
± 2 [¡e ¡ K; e ¡ K]
(4b)
2 [e ¡ K; ° ¡ e]
(4c)
± 2 [° ¡ e; ° + e]
f or ± ¸ ° + e
R(») = Rf ;
(4a)
(4d)
(4e)
If a swap market for hedging is not available, then the equilibrium cost of debt R(») is given
by
R(») : Not Feasible;
f or ± < ¡e ¡ K
2
R(») = Rf + (±+e)(±+e¡4K)+7K
; f or ± 2 [¡e ¡ K; e ¡
12K
2
2
+e
R(») = Rf + 3(K¡±)
;
f or ± 2 [e ¡ K; K ¡ e]
12K
3
R(») = Rf + (K+e¡±)
f or ± 2 [K ¡ e; K + e]
24eK ;
R(») = Rf ;
where ± = » ¡ R(»)
f or ± ¸ K + e
(5a)
K] (5b)
(5c)
(5d)
(5e)
Proposition 3 shows that the introduction of a swap market for hedging unambiguously
improves welfare. Some ¯rms for which the variable ± lies in the range (° ¡ e; K + e)
have the incentive to hedge with swaps in their own ex post interest. The debt market
correctly infers their incentive to hedge, perceives debt issued by these ¯rms to be riskfree,
and reduces their required debt rate R. Thus for this set of ¯rms, default risk and cost of
debt are reduced by the availability of swaps.
Table 2 illustrates the result for a set of parameter values. Note that the extreme values
of R(»; e) are the same for all levels of measrement error: Rf + K when » = R ¡ e ¡ K and
Rf when » ¸ Rf +° +e. Also, » is seen to have a self-ful¯lling prophecy-like property: ¯rms
which receive an incorrectly low rating face a higher cost of debt R(») which (a) increases
9
The pool of ¯rms in case of ¯ <
subset of that with ¯ > 2B
K .
2B
K
consists of only the ¯rst and third types and the analysis there is a
10
the possibility of their cash-°ows being less than the required debt payment and (b) in
some cases makes it optimal for them not to hedge while it would have been optimal to
hedge if their cost of debt had been at the perfect information level R(m)(< R(»)).
V
A
....and Incentives for Speculating
Speculation and Default Risk with Asymmetric Information
The previous section presents a very comforting picture of swap use. High-quality ¯rms
(m ¸ R + °) use swaps for hedging, thereby reducing their default risk and cost of debt.
Low-quality ¯rms (m < R + °) stay away from the swap market. Overall, swaps improve
welfare by reducing expected bankruptcy costs etc. for those ¯rms for which the hedging
motive dominates the risk-shifting incentive. In particular, given our model's assumption
of an exact factor structure of returns, there is no risk of swap default and the swap rate X
equals E(X) = 0. In a more realistic case of including an error term in the returns process,
there exists some residual default risk, but it is likely to be negligibly small (Du±e and
Huang (1996), Hentschel and Smith (1997)).
This analysis is valid only if speculative swaps are assumed not to exist. In reality,
however, bad ¯rms (i.e., ¯rms with quality m < R + °) will not only not have an incentive
to hedge, but by the same risk-shifting argument, have an incentive to increase cash-°ow
variance by participating in speculative swaps. This is the crux of the problem of default
risk in swap markets: speculative swaps expose the swap dealer to the risk of counterparty
default in those states where the risk factor X has low realizations.
The problem of speculation arises from the information asymmetry between the ¯rm
and the swap dealer about the ¯rm's operating exposure ¯ to the underlying risk factor
X. If the dealer knows the direction of the exposure, it can use this knowledge and the
sign of the proposed swap position w to infer if the swap is intended for hedging or for
speculation. For example, it is plausible that a dealer knows that a short-funded S&L is
exposed to the risk of interest rates increasing.10 Therefore, such an S&L's attempt to buy
a ¯xed-for-°oating interest rate swap (i.e., pay ¯xed and receive °oating) would likely be
interpreted as a hedge by the dealer, while trying to sell such a swap (i.e., pay °oating and
receive ¯xed) would be seen as speculation, and therefore disallowed.
Unfortunately however, dealers do not have this information in all cases, i.e., for all
counterparties, for all risk factors, and at all times. For example, while a dealer may reliably
infer the interest rate sensitivity of a short-funded S&L as mentioned above, the exposures
of manufacturing and retailing ¯rms to interest rates, exchange rates, and commodity prices
are likely to be more ambiguous and subject to °uctuations over time. In such situations
then, dealers have to rely upon the observed counterparty credit rating » to infer the
swapping motive. As shown in the previous section, it is impossible to precisely distinguish
between hedgers and non-hedgers on this basis due to the noisiness of observed credit
quality ». The problem is more severe now because non-hedgers use swaps to speculate,
10
We are indebted to Cli®ord W. Smith for this example.
11
which increases the probability and severity of default.
Lemma 1: High-quality ¯rms (m ¸ R + ° + wX) use swaps to hedge. Low-quality ¯rms
(m < R + ° + wX) use swaps to speculate.
The swap market observes the swap position w of the counterparty, but does not know
if it is motivated by hedging or speculative incentives. It therefore pools all such counterparties and charges a common swap price X. Within the pool of counterparties, for a given
swap position w and swap rate X, the higher-quality ¯rms (m ¸ R + ° + wX) have the
incentive to hedge, and the lower-quality ¯rms (m < R + ° + wX) to speculate.
Consider, as in the previous section, the case where the size of the exposure ¯ is 1, but
its direction is unknown, i.e., cash°ow Y = m § X, and speculative swaps are possible.
When a ¯rm proposes a swap position w = 1, the dealer cannot infer if (1) the ¯rm's true
quality m > R + ° + X, its exposure ¯ = ¡1, and the swap is intended to be a hedge, or
(2) the ¯rm's true quality m < R + ° + X, its exposure ¯ = +1, and the swap is intended
to speculatively `double up' the pre-existing exposure. Proposition 4 describes swap and
debt market equilibria in this case. Following previous literature in the area (Cooper and
Mello (1991), Baz and Pascutti (1996)), here we assume swaps to be junior to debt in case
of default. However, we show in the next subsection that the main results on the incentives
to hedge or speculate are insensitive to the speci¯c seniority structure assumed.
Proposition 4: Let the market observe a noisy version » of ¯rm quality m, » = m + ²,
with ² distributed uniformly over the interval [¡e; e], and e < K. Firms with quality
m > R + ° + X have exposure ¯ = ¡1 and take swap position w = 1 to hedge, while
¯rms with quality m < R + ° + X have exposure ¯ = +1 and take swap position w = 1 to
speculate. The equilibrium debt rate R(»; e) and swap rate X(»; e) are described by equations
(A1a|A4b) in Appendix A.
Unfortunately, we are unable to obtain closed-form expressions for R(»; e) and X(»; e) from
equations (A1a,A1b) and (A3a,A3b). However, it is easy to solve for them numerically for
speci¯c parameter values. Table 3, Panels A and B present debt rates R(»; e) and swap
rates X(»; e), respectively, for a set of parameters. The impact of speculative swaps can be
clearly seen by comparing the net cost of debt, R(»; e) + X(»; e), with the debt rate R(»; e)
reported in Table 2A, where speculative swaps are assumed not to exist.
There are two points here worth noting. First, when speculative swaps are allowed, the
probability of default by a non-hedger (speculator) as well as the extent of debt and swap
losses in case of default are higher. Consequently, the required net debt rate, R(»; e) +
X(»; e) is higher. The second point concerns the incentives of ¯rms to hedge or speculate.
Since the overall cost of debt is higher when speculative swaps are allowed, the quality
threshold, m¤ = R(»; e) + X(»; e) + °, above which it is optimal to hedge is also higher.
Therefore, the set of ¯rms for which hedging is optimal becomes smaller when speculative
swaps are allowed. As a second-order e®ect, this further raises the net cost of debt.
These results are illustrated in Figure 1. The curve hh represents the quality threshold
¤
m = R(») + ° as a function of observed credit quality », when speculative swaps are
not allowed (Proposition 3/Table 2A). The curve ss shows m¤ = R(») + X(») + ° when
speculative swaps are allowed (Proposition 4/Table 3A, B). Region B in the ¯gure consists
12
of ¯rms that have the incentive to hedge if speculative swaps are somehow excluded; but
if such speculation cannot be prevented, then the very presence of such swaps distorts the
incentive structure of these ¯rms and makes it optimal for them to speculate.
Note that a similar result holds for swap position w = ¡1. Firms with quality m >
R + ° + X and exposure ¯ = +1 take swap positions w = ¡1 to hedge. They are pooled
with by ¯rms with quality m < R + ° + X and exposure ¯ = ¡1 that take identical swap
positions (w = ¡1) to speculate. Swap and debt rates are identical to those described in
Proposition 4. Figure 2 summarizes the various combinations of m; ¯; and w possible.
B
Relative Seniority of Debt and Swap Contracts
The analysis of the previous subsection assumes that in case of default, swaps are junior
to debt. While earlier papers too have typically made this assumption, the actual legal
position is less clear. Claims on a defaulted party are governed by the Bankruptcy Code
for non-¯nancial ¯rms, and the Federal Deposit Insurance Act (FDIA) for ¯nancial institutions, which place several restrictions on such claims if a bankruptcy petition has been
¯led. In view of the adverse impact this has on swaps and similar contracts, the Financial
Institutions Reforms, Recovery and Enforcement Act (1989) and the 1990 amendments to
the Bankruptcy Code have relaxed many of these restrictions for swaps and similar quali¯ed
¯nancial contracts, making the juniority of swaps questionable. Further, the geographical
location of incorporation of the defaulted ¯rm, and the legal jurisdiction under which it falls
are often unclear. Therefore, it is important to examine how our results may be a®ected if
the assumption of swap juniority is not valid.
It turns out, however, that the main results on the incentive structure of hedging and
speculation are completely insensitive to changes in the seniority of swaps vis-a-vis debt.
Both swaps and debt represent external claims on the ¯rm's cash-°ows. While their relative
seniority impacts the state-contingent payo®s to the individual claims, the total payo® is
always max(m+X; R+X¡X), with the total expected payout equaling expected debt payo®
plus expected swap payo® = Rf + 0 = Rf . Therefore, while the debt rate R and the swap
rate X assume di®erent values for di®erent seniority structures, their sum, R + X, remains
constant. Consequently, the quality cut-o® level for hedging to be optimal, m¤ = R+X +°,
is insensitive to changes in swap seniority relative to debt.
For example, when the swap is senior to the debt, R and X are as described by equations
(A5a|A10b) in Appendix A. Table 3, Panel C reports R for the earlier set of parameters.
Note that the juniority of the debt raises the debt rate and lowers the swap rate (X = 0)
compared to the junior swap case. However, the sum of swap and debt rates when the
swap is junior (Panels A and B) equals the debt rate when the swap is senior (Panel C),
the swap rate being 0 in that case.
C
Unbounded Speculation and Market Failure
Speculative swaps become even more problematic when we relax our simplifying restriction
of j¯j = 1. If ¯rms have arbitrary levels of exposure ¯, then ¯rms with quality m >
13
R + ° + wX will hedge by taking swap positions w = ¡¯. This provides the cover necessary
for bad ¯rms (m < R+° +wX) with exposures in the opposite direction to take speculative
swap positions w = ¡¯. Lemma 2 shows that in the absence of size restrictions on swap
positions, speculators will seek to take unboundedly large positions in swaps.
Lemma 2: Let all swap positions be allowed. Then it is optimal for a bad ¯rm to take an
unboundedly large position w in the swap.
If ¯rms could credibly commit to not exceeding given swap positions w, equilibrium
would obtain at those levels. However, given the speculative intent of bad ¯rms as characterized in Lemma 2, such commitments are not credible. In all cases, debt and swap
rates increase with the swap position w.11 For any given cost of debt R¤ (»), a speculating
¯rm has incentive to take a large enough speculative position w in the swap such that
R(»; w) > R¤ (»). Therefore in the absence of ex-ante limits on swap position w, no value
of R will provide the necessary expected return of Rf to lenders.
Further, the incentive of bad ¯rms to take on large swap position w leads to a high
value of X as well as R. This raises the threshold level of m (m¤ = R + ° + wX), and
reduces the proportion of ¯rms for which hedging is optimal. In other words, if large swap
positions are allowed, and if the swap dealer cannot identify and exclude speculators, then
the resultant increase in R and X will distort the incentives for even some of those ¯rms for
which it was originally optimal to hedge, and induce them to speculate as well. For large
enough w, there will be no counterparties with genuine hedging motives (m ¸ R + ° + wX),
leading to breakdowns in both swap and debt markets. Thus, in the absence of limits on
w, the original welfare-improving objective of the swap market, viz., to provide hedging
instruments to good ¯rms, is not attained. Attempting to compensate the swap dealer for
the additional default risk of a doubtful counterparty thus has the reverse e®ect of further
increasing the default risk of the swap. Price-based mechanisms by themselves are therefore
unable to control swap market default risk arising from speculative swaps.
Figure 3 illustrates this point. An observed credit rating » implies that true ¯rm quality
in the pool ranges from » ¡ e to » + e. If w is small, ¯rms in the pool with m ¸ m¤ (w)
(region A in the ¯gure) have the incentive to hedge. As w increases, so does m¤ , so that
beyond a certain value of w, all ¯rms in the pool have m < m¤ , i.e., the speculative incentive
dominates.
D
Mechanisms to Control Swap Market Speculation
Attempts to control speculation and the resultant default risk therefore have to rely upon
non-price mechanisms. The explosive growth of the swap market and the remarkably few
instances of default indicate that such mechanisms do exist and are e®ective in excluding
speculative swaps. The empirical literature also supports the view that ¯rms use swaps
almost always to hedge and seldom, if ever, to speculate. (See, e.g., Geczy, Minton, and
Schrand (1997), Mian (1996) and Nance, Smith, and Smithson (1993).) However, our analysis shows that this happy outcome does not arise automatically | as Hentschel and Smith
11
Larger speculative positions increase the probability and severity of default. Therefore, creditors and
swap dealers require higher debt and swap rates in equilibrium.
14
(1997) note, \derivatives dealers have incentives to monitor customers' use of derivatives
to ensure that they use derivatives to hedge."
How do dealers ensure this? First, as mentioned before, dealers often have access to
information about counterparty characteristics which mitigates the information asymmetry
concerning the motive behind the swap. Speci¯cally, the dealer may know the direction of
the counterparty's operating exposure to the underlying risk factor, based on which, it can
infer whether the swap is meant to be a hedge or not. Unfortunately however, dealers do
not always have such information and have to rely upon the observed counterparty credit
rating » to infer the swapping motive.
When the measurement error ² is limited, it is possible to implement the simple accept/reject decision rule based on » that guarantees the exclusion of speculative swaps.
This was indeed the case in swap markets until recently. Swap dealers did not discriminate between counterparties of di®erent credit ratings so long as they were above a certain
threshold level (usually investment-grade). Counterparties of lower credit ratings were simply excluded from the market. Our model o®ers an explanation for such a scheme. A high
enough credit rating (» > » ¤ = Rf + ° + e) means that all ¯rms in the pool have true
quality m > Rf + °. This implies low default risk not only because the ¯rms' projects are
inherently safer, but also because such ¯rms have the endogenous incentive to hedge and
thus reduce their default probabilities even further. There is thus no reason for swap dealers
to charge higher rates from less-than-perfect counterparties so long as they are rated above
this cut-o® level. Unfortunately, such a decision rule denies the opportunity to swap to a
set of good ¯rms (m > m¤ ) with genuine hedging motives, but whose credit rating » lies
below the cuto® level » ¤ . This represents the unavoidable e±ciency loss of a second best
solution due to asymmetric information about ¯rm quality.
More recently however, sub-investment-grade counterparties have been allowed to enter
into swap contracts, largely due to two developments. First, much of the business has moved
away from investment banks to commercial banks which have long term relationships with
swap counterparties. Such a relationship provides the bank with better information about
(a) the nature of the underlying operating exposure and (b) the true ¯rm quality than is
provided by only the credit rating of the ¯rm. This alleviates the asymmetric information
problem and enables some of the sub-investment-grade ¯rms to be correctly identi¯ed as
having the hedging incentive. Second, the market has increasingly come to rely on non-price
credit enhancement mechanisms to limit swap exposures, especially with counterparties of
doubtful quality. The most commonly used credit enhancement devices are:
Credit triggers: The dealer has the right to terminate all swaps with a counterparty if
the counterparty's credit rating falls below a prespeci¯ed level or if it defaults on some other
obligation to another party. It thus o®ers the swap dealer an early exit from a deteriorating
credit situation.
Collateral: The counterparty has to put up collateral to cover possible dealer losses in
case of default. Unlike margin requirements for futures contracts, most swaps and related
OTC contracts do not require collateral when the credit exposure is small, but only when
it exceeds some prespeci¯ed level. The nature and extent of collateral varies from case to
15
case, and are naturally more restrictive for weaker counterparties.
Marking-to-market: The swap's market value is calculated on a regular basis and the
change in value since the last evaluation is transferred between the dealer and the counterparty. The swap is `recouponed', i.e., the swap rate is reset so that the new exposure
becomes equal or close to zero. Gains and losses are thus settled up regularly, and large
credit exposures are not allowed to build up. A variation on this practice combines recouponing with collateralization: at intermediate points between scheduled recouponings,
the swap value is measured and additional collateral has to be put up if necessary.
Netting: Since a dealer and a ¯rm usually have several swap contracts between them at
any one time, it is customary to consolidate the treatment of all mutual swaps through a
master agreement. Given the unsettled legal position, netting protects the dealer against
the ¯rm strategically `cherry-picking' those swaps that are in-the-money for it, and seeking
bankruptcy protection on those that are out-of-the-money for it.
Wakeman (1996) provides a detailed survey of credit enhancement techniques. The
common objective of all these mechanisms is attenuating the credit exposure of the swap
position w, thereby reducing the market-maker's value-at-risk as well as mitigating the
counterparty's incentive to speculate by limiting the gains from speculation.
As swap markets have become more liquid and competitive, it has become increasingly
important for dealers to provide quick quotes without exhaustive analyses of individual
counterparties. Dealers have therefore come to rely upon credit enhancement clauses to
take care of default risk concerns, resulting in such clauses becoming standard features of
swap contracts today. This assures participants in both debt and swap markets that all
realized swap transactions are undertaken for hedging purposes and default risk ceases to
be important. Given our assumption of the swap variable being the same as the underlying
risk factor X, our model implies a default probability of zero and consequently, complete
insensitivity of swap prices to counterparty credit rating. In reality the swap variable and
the risk factor may be less than perfectly correlated resulting in some residual default risk,
but its magnitude would be negligibly small. Hentschel and Smith (1997), for example,
report a conservative estimate of 0.05% default probability per annum. Similarly, Du±e
and Huang (1996) provide simulation evidence suggesting that a di®erence of 100 b.p. in
debt markets translates into a 1 b.p. di®erence in interest rate swap rates.
The result on the insensitivity of swap prices to credit ratings and reliance on nonprice mechanisms to control default risk is similar in spirit to the Stiglitz and Weiss (1981)
explanation of credit rationing in debt markets. The analysis becomes somewhat more
complex because now equilibrium has to be jointly determined in swap and debt markets.
Interestingly, non-price devices to control default risk are required not in the debt market,
but in the swap market. The existence of these mechanisms limits the ability of bad ¯rms
to risk-shift and is able to sustain equilibrium in both markets.
16
VI
Conclusion
In recent years there has been much concern about default risk in swap markets. This paper
presents a simple theoretical framework for analyzing the incentive structure underlying the
issue. It argues that the basic utility of a swap lies in its ability to ameliorate the direct
and indirect costs of risky debt. A swap is a zero-present-value repackaging of cash-°ows
across states of nature that results in indexing the net external claims on the ¯rm (the
combined cash-°ows on the debt and the swap) to the appropriate sources of risk in the
economy. Better alignment of the risk pro¯les of the cash in°ows and out°ows results in a
lower probability of ¯nancial distress and thus reduces the ¯rm's cost of issuing debt.
This bene¯t has to be weighed against the insider's incentive to risk-shift. Our model
predicts that the resolution of the trade-o® depends upon the relative magnitudes of the
predictable and risky components of cash in°ows: good ¯rms hedge, bad ¯rms do not.
Moreover, the incentive to hedge becomes stronger as the number of time periods under
consideration increases. The debt market recognizes this and sets the lending rate accordingly. Thus, other things remaining the same, the introduction of hedging instruments like
swaps reduces the incidence of default and cost of debt in the economy.
Unfortunately however, the availability of these very instruments o®ers low-quality ¯rms
a vehicle to speculate with. If not controlled, this would combine with their strong risk
shifting incentives to cause breakdowns in both the debt and derivative markets. For
a nontrivial equilibrium to exist therefore, the derivative market has to control default
risk somehow. We show that this function is performed by swap market makers by (a)
interpreting the information in operating risk exposures of end-users, (b) sorting on credit
rating and excluding counterparties which fall below a certain level, (c) maintaining longterm relationships with counterparties to reduce the degree of information asymmetry, and
(d) relying on other credit enhancement devices like credit triggers, netting, and markingto-market to severely limit the exposure of swap positions, as indeed observed in the swap
market. In the presence of such mechanisms, our model predicts insensitivity of swap rates
to credit rating among the pool of acceptable counterparties, thus providing a theoretical
justi¯cation of this observation in earlier papers.
There are several other empirically testable implications of the model. First, the results
that (a) high quality ¯rms have the incentive to hedge, and (b) that the market is able
to exclude speculative swaps, together imply that among the pool of ¯rms with similar
(imprecisely observed) ex-ante quality, those that are allowed to swap should subsequently
be revealed to be of superior quality | either through rating upgrades or through better
operating performance. However, a test of this hypothesis has to be implemented carefully:
the model also predicts that a properly designed swap may directly improve the performance
of the ¯rm by reducing its cash-°ow volatility. Therefore, it is important to control for such
ex-post swap bene¯ts while testing for di®erences in ex-ante quality.
Second, if a swap indeed reduces direct and indirect costs of ¯nancial distress associated
with risky debt, then a ¯rm that uses swaps in equilibrium should be able to raise its debt
capacity. Thus, our model predicts that the opening and deepening of a swap market in an
economy should be accompanied by an increase in the debt ratios of ¯rms, especially those
17
with high credit ratings, since they enjoy easy access to the swap market.
Third, since the possibility of speculative swaps is higher for poorly-rated ¯rms, our
model predicts that highly-rated ¯rms should be able to do swaps with many relatively
unknown swap dealers, while the poorly-rated ¯rms would be restricted to fewer dealers,
typically commercial banks, with which they have long-standing credit relationships.
Fourth, the model predicts a connection between the use of credit enhancement devices
and the reliability of the legal system. Since most credit enhancement devices take the
form of clauses included in the swap contract, their e®ectiveness directly depends on the
ease with which such clauses can be enforced. Therefore, swap markets in countries with
more developed legal systems should rely more on credit enhancement devices, while those
in countries with less developed ones should have to rely on long-term relationships with
swap counterparties or rationing out lower-rated counterparties altogether.
Casual empiricism seems to be in line with our explanation of the economic role of
swaps. Growth in the swap market has occurred concurrently with debt becoming more
popular as a ¯nancing choice. However, rigorous tests of the empirical implications of this
model can be done only with ¯rm-level ¯nancing and hedging data. We leave that exercise
for future research.
18
Appendix A
Summary of model variables and parameters
Y : Project payo® at time-1.
m: Expected component of project returns/ Firm quality.
X: Risk factor realization.
K: Size of risk factor distribution.
¯: Exposure of the ¯rm's returns to the risk factor.
R: Required (gross) interest-rate on the ¯rm's debt.
Rf : Riskfree (gross) interest-rate.
»: Observed ¯rm quality/ Credit rating.
²: Noise in observing ¯rm quality.
e: Size of noise distribution.
m¤ : Firm quality threshold for hedging.
°: Excess of m¤ over required debt rate.
½: Single-period discount factor.
±: Excess of observed ¯rm quality over required debt rate.
w: Swap position.
X: Swap rate.
Debt and swap rates when debt is senior
For observed ¯rm quality » 2 [R + X ¡ e ¡ 2K; R + X + e ¡ 2K]
(»+e¡R¡X¡K)2 +6X(»+e¡R)¡3K 2
=0
24K
2
3K [»+e+3(R+X)]¡(»+e¡R¡X¡K) ¡3X(»+e¡R)
¡
12K
(A1a)
K = Rf
(A1b)
For observed ¯rm quality » 2 [R + X + e ¡ 2K; R + X + ° ¡ e]
X=K+
q
12K(»¡Rf )¡e2
3
R=»+K ¡
q
¡
q
24K(»¡Rf )¡e2
3
(A2a)
12K(»¡Rf )¡e2
3
(A2b)
For observed ¯rm quality » 2 [R + X + ° ¡ e; R + X + ° + e]
X+
(R+e¡X¡»)3 +(°+X)3 +6(K+X)2 (»¡e¡R¡°)+3X [°(3X+°)¡2K(K¡2X)]+X
48eK
(°+X¡K)3 ¡(»¡e¡R¡K)3
R¡
= Rf
24eK
3
=0
(A3a)
(A3b)
For observed ¯rm quality » > R + X + ° + e
X=0
(A4a)
R = Rf
(A4b)
19
Debt and swap rates when swap is senior
For observed ¯rm quality » 2 [R + X ¡ e ¡ 2K; R + X + e ¡ 2K]
Z
»+e
1
Á(m)dm = 0
» + e ¡ R ¡ X + 2K R+X¡2K
Z »+e
1
Ã(m)dm = Rf
» + e ¡ R ¡ X + 2K R+X¡2K
(A5a)
(A5b)
For observed ¯rm quality » 2 [R + X + e ¡ 2K; R + X + ° ¡ e]
1
2e
1
2e
Z
Z »+e
Á(m)dm = 0
(A6a)
Ã(m)dm = Rf
(A6b)
»¡e
»+e
»¡e
For observed ¯rm quality » 2 [R + X + ° ¡ e; R + X + ° + e]
1
2e
1
2e
Z R+X+°
Á(m)dm +
»¡e
Z R+X+°
Z »+e
X
dm = 0
2e
(A7a)
R
dm = Rf
2e
(A7b)
R+X+°
Ã(m)dm +
»¡e
Z »+e
R+X+°
For observed ¯rm quality » > R + X + ° + e
where
Á(m) =
(A8a)
R = Rf
(A8b)
Z max(¡K; X¡m )
2
m+X
¡K
and
X=0
Ã(m) =
2K
Z
R+X¡m
2
max(¡K; X¡m
)
2
dX +
Z K
max(¡K; X¡m
)
2
m + 2X ¡ X
dX +
2K
Z K
X ¡X
dX
2K
(A9b)
R
dX
2K
(A10b)
R+X¡m
2
Appendix B
Proposition 1a
Proof: Expected payo® from a completely unhedged position
= E [max(m + ¯X ¡ R; 0)] + B ¢ P r [m + ¯X ¡ R ¸ 0] ; R + ¯K > m > R ¡ ¯K (B1a)
Z K
Z K
m + ¯X ¡ R
1
= R¡m
dX + B R¡m
dX; R + ¯K > m > R ¡ ¯K (B1b)
2K
2K
¯
¯
Expected payo® from a completely hedged position equals 0 for m < R and m ¡ R + B for
m > R. Therefore, bene¯t of complete hedging can be shown to be (2B + m ¡ R ¡ ¯K)(R +
¯K ¡ m)=(4¯K) for m 2 [R; R + ¯K], and ¡(2B + m ¡ R + ¯K)(m ¡ R + ¯K)=(4¯K) for
20
m 2 [R ¡ ¯K; R]. When m > R, the critical value of m for which the bene¯t of hedging is
0 is given by m¤ = R + ¯K ¡ 2B. When m > (<)m¤ , the bene¯t from hedging is positive
(negative), and it is in the equityholders' interest to completely hedge (not hedge). When
¯ ∙ 2B=K, ¯K ¡ 2B < 0 and m¤ = R. When m < R, the bene¯t from hedging is always
negative and it is never optimal for equityholders to hedge. 2
Proposition 1b
Proof: Expected payo® from a completely unhedged position = E [max(f (m + ¯X ¡ R; 0))]
8
0
>
>
>
>
>
< R
f (m+¯X¡R)
K
=
dX
R¡m
2K
>
¯
>
>
>
>
: R K f (m+¯X¡R)
¡K
m < R ¡ ¯K
R + ¯K > m > R ¡ ¯K
m > R + ¯K
dX
2K
Expected payo® from a hedged position equals 0 if m < R and f (m ¡ R) if m > R.
Therefore, bene¯t of complete hedging
=¡
= f (m ¡ R) ¡
Z K
R¡m
¯
Z K
= f (m ¡ R) ¡
R¡m
¯
=0
f (m + ¯X ¡ R)
dX
2K
f (m + ¯X ¡ R)
dX
2K
Z K
f (m + ¯X ¡ R)
¡K
2K
dX
m < R ¡ ¯K
(B2a)
R > m > R ¡ ¯K
(B2b)
R + ¯K > m > R
(B2c)
m > R + ¯K
(B2d)
In equation (B2b), f (¢) > 0 ) bene¯t of hedging is negative. In equation (B2d), bene¯t of
1 RK
hedging ­(m) = 2K
¡ f (m + ¯X ¡ R)]dX. Using the Mean Value Theorem,
¡K [f (m ¡ R)
1 RK 0
0
~
^
it can be shown that ­(m) = 2K
0 [f (m ¡ ¯X ¡ R) ¡ f (m + ¯X ¡ R)]¯XdX, for some
00
0
0
^
~
~
^
~ X
^ > 0. Therefore,
X; X 2 (0; X). But f (¢) < 0 ) f (m ¡ ¯X ¡ R) > f (m + ¯X ¡ R); 8X;
­(m) > 0. In equation (B2c), it can be shown that 9 a unique m¤ 2 (R; R + ¯K) such that
the bene¯t of hedging ­(m) < 0; m < m¤ and ­(m) > 0; m > m¤ . Combining the above
results, we get ­(m) = 0 for m < R ¡ ¯K, ­(m) < 0 for m¤ > m > R ¡ ¯K, and ­(m) > 0
for m > m¤ , for some m¤ 2 (R; R + ¯K). Thus, it is optimal for ¯rms with m > m¤ to
hedge and for ¯rms with m < m¤ not to hedge. 2
Proposition 2
Proof: Let the T periods be indexed by t. The control variable c(t) 2 fH; N Hg indicates if
it is optimal to hedge in period t. p(t) is the probability that the ¯rm survives from period
RK
m+¯K¡R
1
t¡1 to period t. [p(t)jc(t¡1) = H] = 1 and [p(t)jc(t¡1) = N H] = R¡m
.
2K dX =
2¯K
¯
The Value Function V (t; T ) is the present value of the insider's claim at the end of period
t, if the optimal hedging policy is adopted over the remaining periods. ½ = 1=R is the
one-period discount factor, i.e., the price of a one-period unit face value discount bond.
[V (t) j c(t) = H] = m ¡ R + ½V (t + 1; T )
21
R < m < R + ¯K
[V (t) j c(t) = N H] =
(m ¡ R + ¯K)2 m ¡ R + ¯K
+
½V (t + 1; T )
4¯K
2¯K
R ¡ ¯K < m < R + ¯K
Therefore, c(t) = H is optimal i® m > R + ¯K ¡ 2½V (t + 1; T ). Note that V (t; T ) is
a monotone decreasing function of t, since an (s + 1)-period game is equivalent to an speriod one plus one additinal time period with a non-negative cash-°ow payo®. Therefore,
V (t + 1; T ) < V (t; T ); 8t. For T = 1, V (1; T ) = V (1; 1) = 0. Then the optimality condition
implies that c(0) = H is optimal i® m > R + ¯K. But m < R + ¯K by de¯nition.
Therefore, it is never optimal to hedge when T = 1. For T > 1, V (1; T ) > V (T; T ) = 0,
which implies that c(0) = H is optimal i® m > m¤ (T ) = R + ¯K ¡ 2½V (1; T ). Further,
using the argument that an s-period game is less valuable than an (s + 1)-period one, we
have V (1; T1 ) > V (1; T2 ) i® T1 > T2 . Together with the optimality condition for c(0), this
implies that m¤ (T ) > m¤ (T + 1). In the limit, in an in¯nitely repeated game, c(0) = H is
P1 t
optimal i® c(1) = c(2)::::c(t) = H are also optimal. Then limT !1 V (0; T ) = t=0
½ (m¡R)
¤ (T ) = R + 1¡½ ¯K = R + R¡1 ¯K. 2
= m¡R
=)
lim
m
T !1
1¡½
1+½
R+1
Proposition 3
Proof: The pool of ¯rms with observed credit quality » have m 2 [» ¡ e; » + e] = [R(») + ± ¡
e; R(») + ± + e]. Also, a ¯rm of true type m realizes end-of-period project cash-°ow in the
range [m ¡ K; m + K]. In (4a), ± = » ¡ R(») < ¡e ¡ K. No ¯rm in the pool can service the
debt, so borrowing is infeasible. In (4b), ¯rms with m 2 [R + ± ¡ e; R ¡ K] can never pay
R and so do not participate in the pool of borrowers. Firms with m 2 [R ¡ K; R + ± + e]
default when m + X < R, i.e., X < R ¡ m, and are able to pay R when m + X > R, i.e.,
X > R ¡ m. The debt market therefore sets R(») to satisfy
Z R+±+e
R¡K
1
K+±+e
"Z
R¡m m + X
2K
¡K
dX +
Z K
R¡m
#
R
dX dm = Rf
2K
(B3)
Solving for R yields the result. In (4c), the argument is as in (4b), except that all ¯rms
with observed quality » participate. The debt market equilibrium condition is similar to
(B3) but with m 2 [R + ± ¡ e; R + ± + e]. In (4d), ¯rms with m 2 [R + °; R + ± + e] hedge,
making their debt riskfree. Poorer ¯rms in the pool, i.e., ¯rms with m 2 [R + ± ¡ e; R + °]
default when X < R ¡ m. R(») is set to satisfy
Z R+°
R+±¡e
1
2e
"Z
R¡m m + X
¡K
2K
dX +
Z K
R¡m
#
R
dX dm +
2K
Z R+±+e
R
R+°
2e
dm = Rf
(B4)
Solving yields the result. In (4e), the hedging incentive prevails for all ¯rms in the pool
with observed credit quality ». The debt market correctly infers this and sets R = Rf .
When a swap market for hedging is not available, ¯rms with m > R + ° cannot hedge
even though they have the incentive to do so. Equations (5a-5e) then follow from reasonings
similar to those for equations (4a-4e). 2
Proposition 4
Proof: In (A1a-A1b), some ¯rms in the pool have true quality m < R + X ¡ 2K while the
others have m > R + X ¡ 2K. Firms in the former group always default, since for them
cash-°ow Y = m + X < R + X ¡ X, 8X. Therefore they do not borrow, swap, or invest.
22
Firms in the latter group have m < R + X + °, since e < K. Therefore, by Lemma 1, they
do not have the incentive to hedge and all take speculative swap position w = 1. There is
default on both debt and swap, i.e., payo® to debt equals m + X and payo® to swap equals
0 when m + X < R, i.e., X < R ¡ m. There is default on swap but not on debt, i.e., debt
payo® is R and swap payo® is m + X ¡ R when m + X ¡ R < X ¡ X, i.e., X < R+X¡m
.
2
Thus, the equilibrium conditions in swap and debt markets are
3
Z K
m+X ¡R
X ¡X
dX +
dX 5 dm = 0
R+X¡m
2K
2K
R+X¡2K
R¡m
2
"Z
#
Z »+e
Z K
R¡m
1
m+X
R
dX +
dX dm = Rf
2K
» + e ¡ R ¡ X + 2K R+X¡2K ¡K
R¡m 2K
Z
1
» + e ¡ R ¡ X + 2K
»+e
2
Z
4
R+X¡m
2
(B5a)
(B5b)
In (A2a-A2b), all ¯rms have m > R + X ¡ 2K and m < R + X + °, so they all have the
incentive to speculate. Swap and debt market equilibrium conditions are similar to (B5a)
and (B5b), with m 2 [» ¡ e; » + e]. In (A3a-A3b), some ¯rms have m < R + X + °, while
others have m > R + X + °. From Lemma 1, the former (latter) group has the incentive to
speculate (hedge). Swap and debt payo®s for speculators are similar to the previous cases,
while for hedgers they are X ¡ X and R in all states. Therefore, swap and debt market
equilibrium conditions are
Z
1
2e
1
2e
R+X+°
»¡e
Z
R+X+°
»¡e
2
Z
4
R+X¡m
2
R¡m
"Z
R¡m
¡K
m+X ¡R
dX +
2K
m+X
dX +
2K
Z
K
R¡m
Z
3
K
X ¡X
dX 5 dm
2K
Z »+e Z K
1
X ¡X
+
dXdm = 0
2e R+X+° ¡K 2K
#
Z »+e Z K
R
1
R
dX dm +
dXdm = Rf
2K
2e R+X+° ¡K 2K
:
R+X¡m
2
(B6a)
(B6b)
Evaluating the integrals and collecting terms, we get equations (A1a)-(A3b). Finally, for
m > R + X + ° + e, all ¯rms have m > R + X + °, all ¯rms hedge, X = 0, and R = Rf . 2
Lemma 1
Proof: An equilibrium swap rate X and a swap position w makes the overall e®ective cost
of borrowing R + wX. The result follows from Proposition 1. 2
Lemma 2
Proof: Let the ¯rm take
h a speculative position w in swap Si = X ¡X. Then expected payo®
to the ¯rm, P (w) = E max(m + (1 + w)X ¡ wX ¡ R; 0) . We have m + (1 + w)X ¡ wX ¡
R = 0 when X =
R+wX¡m
.
1+w
dP
dw = [w(w +
R+wX¡m
< K )
1+w
and
h
i
Therefore, P (w) = (K(1 + w) + m ¡ R ¡ wX)2 =(4K(1+w))
2)(K ¡ X)2 ¡ (K + R ¡ m ¡ 2X)(R ¡ m ¡ K)]=(4K(1 + w)2 ). But
w > R¡m¡K
) dP
dw (w) > 0. Therefore the expected payo® to the
K¡X
speculator P (w) grows without bound with w, implying that it is optimal to take an
unboundedly large position in the swap, given a swap rate and debt rate, (X; R). 2
23
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25
Table 1
Bene¯t of Hedging
¯
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.85
0
0
0
0
0
0
0
0
0
0
0
0.9
0
0
0
0
0
0
0
0
-0.0017
-0.0054
-0.0094
0.95
0
0
0
0
0
0
-0.0050
-0.0100
-0.0150
-0.0200
-0.0250
1.0
0
0
0
-0.0046
-0.0122
-0.0187
-0.0248
-0.0305
-0.0361
-0.0415
-0.0469
m
1.05
0
-0.0300
-0.0350
-0.0400
-0.0450
-0.0500
-0.0550
-0.0600
-0.0650
-0.0700
-0.0750
1.1
0
0
0
0.0038
0.0066
0.0063
0.0044
0.0016
-0.0017
-0.0054
-0.0094
1.15
0
0
0
0
0
0
0.0033
0.0043
0.0037
0.0022
0
1.2
0
0
0
0
0
0
0
0
0.0014
0.0029
0.0031
1.25
0
0
0
0
0
0
0
0
0
0
0
This table reports the bene¯t of hedging over not hedging for di®erent combinations of ¯rm quality
m and risk factor sensitivity ¯. Realized cash-°ows for the ¯rm are m + ¯X, where X is the risk
factor realization, distributed uniformly over the range [¡K; K]. The ¯rm insider/equityholder
incurs direct bankruptcy costs/ loss of control rents B in bankruptcy. The (gross) cost of debt Rf is
exogenously speci¯ed. Cases in which it is optimal for the ¯rm to hedge, i.e., the bene¯t of hedging
is positive, are reported in boldface. The parameter values used are: Rf = 1:05; K = 20%; B =
0:05; ° = max(¯K ¡ 2B; 0); m 2 [0:85; 1:25]; ¯ 2 [0; 1].
26
Table 2
Equilibrium Debt Rate in the Absence of Speculative Swaps
e
1.00
1.025
1.05
0.0
0.025
0.05
0.075
0.10
0.125
0.15
0.175
0.20
*
*
1.25
1.2269
1.2072
1.1902
1.1754
1.1626
1.1515
*
*
1.2269
1.2072
1.1902
1.1754
1.1626
1.1515
1.1418
*
1.2269
1.2072
1.1902
1.1754
1.1626
1.1515
1.1418
1.1335
0.0
0.025
0.05
0.075
0.10
0.125
0.15
0.175
0.20
*
*
1.25
1.2269
1.2072
1.1902
1.1754
1.1626
1.1515
*
*
1.2269
1.2072
1.1902
1.1754
1.1626
1.1515
1.1418
*
1.2269
1.2072
1.1902
1.1754
1.1626
1.1515
1.1418
1.1335
»
1.075
1.10
1.125
1.15
1.175
Panel A:Hedging with Swaps Possible
1.1336
1.100
1.0801
1.0672
1.05
1.1343
1.1005
1.0805
1.0641
1.05
1.1366
1.1021
1.0818
1.0643 1.0549
1.1403
1.1047
1.0818 1.0669 1.0582
1.1459
1.1085
1.0842 1.0701 1.0614
1.1515 1.1123 1.0883 1.0741 1.0649
1.1418 1.1176 1.0935 1.0787 1.0687
1.1335 1.1263 1.0997 1.0839 1.0730
1.1263
1.1202
1.1071 1.0899 1.0779
Panel B:Hedging with Swaps Not Possible
1.1336
1.100
1.0801
1.0672
1.0588
1.1343
1.1005
1.0805
1.0675
1.0591
1.1366
1.1021
1.0818
1.0686
1.0601
1.1403
1.1047
1.0839
1.0705
1.0618
1.1459
1.1085
1.0870
1.0731
1.0641
1.1515
1.1135
1.0909
1.0765
1.0670
1.1418
1.1197
1.0959
1.0807
1.0706
1.1335
1.1274
1.1019
1.0857
1.0747
1.1263
1.1202
1.1090
1.0915
1.0794
1.20
1.225
1.25
1.05
1.05
1.05
1.0531
1.0558
1.0587
1.0618
1.0653
1.0693
1.05
1.05
1.05
1.05
1.0522
1.0545
1.0570
1.0598
1.0630
1.05
1.05
1.05
1.05
1.05
1.0517
1.0537
1.0559
1.0584
1.0536
1.0539
1.0548
1.0563
1.0583
1.0607
1.0635
1.0668
1.0707
1.0508
1.0511
1.0519
1.0530
1.0545
1.0564
1.0586
1.0612
1.0643
1.05
1.0501
1.0505
1.0512
1.0522
1.0535
1.0552
1.0572
1.0596
This table reports equilibrium debt rates R(»; e) for di®erent combinations of observed ¯rm quality
» and observation error size e. Observed quality » equals true quality m plus a random zero-mean
noise ², i.e. » = m+², with ² distributed uniformly over the range [¡e; e]. Realized cash-°ows for the
¯rm are m+ X, where X is the risk factor realization, distributed uniformly over the range [¡K; K].
Panel A reports results for the case where a market for hedging with swaps is available, and Panel B
for the case where such a market is not available. It is optimal for the ¯rm to hedge in equilibrium if
its true quality m exceeds m¤ = R(»; e)+°. The debt market sets the debt rate R(»; e) such that the
expected return on debt equals the risk-free rate Rf . Cases in which it is optimal for some ¯rms to
hedge are reported in boldface. In these cases, the presence of the swap market reduces default risk
and consequently, the equilibrium debt rate R(»; e). * indicates that debt market equilibrium is not
feasible. The parameter values used are: Rf = 1:05; K = 20%; ° = 0:1; » 2 [1:0; 1:25]; e 2 [0; 0:2].
27
Table 3
Debt and Swap Rates when Speculative Swaps are Possible
e
0
0.025
0.05
0.075
0.1
0.125
0.15
0.175
0.2
e
0
0.025
0.05
0.075
0.1
0.125
0.15
0.175
0.2
e
0
0.025
0.05
0.075
0.1
0.125
0.15
0.175
0.2
1.00
1.025
1.05
*
*
*
1.2364
1.2242
1.2133
1.2036
1.195
1.1873
*
*
1.2364
1.2242
1.2133
1.2036
1.195
1.1873
1.1805
1.25
1.2364
1.2242
1.2133
1.2036
1.195
1.1873
1.1805
1.1746
*
*
*
0.1896
0.1797
0.1701
0.1608
0.1518
0.143
*
*
0.1896
0.1797
0.1701
0.1608
0.1518
0.143
0.1345
0.2
0.1896
0.1797
0.1701
0.1608
0.1518
0.143
0.1345
0.1262
*
*
*
1.426
1.4039
1.3834
1.3644
1.3467
1.3303
*
*
1.426
1.4039
1.3834
1.3644
1.3467
1.3303
1.315
1.45
1.426
1.4039
1.3834
1.3644
1.3467
1.3303
1.315
1.3008
»
1.075
1.10
1.125
1.15
1.175
Panel A:Debt Rates (Senior Debt)
1.1336
1.1
1.0801 1.0672
1.05
1.1343 1.1005 1.0805 1.0675 1.0591
1.1366 1.1021 1.0818 1.0686 1.0601
1.1404 1.1047 1.0839 1.0705 1.0611
1.1459 1.1085
1.087
1.0731 1.0635
1.1534 1.1135 1.0909 1.0764 1.0666
1.1632 1.1197 1.0959 1.0806 1.0702
1.1746 1.1274 1.1019 1.0856 1.0743
1.1694 1.1367
1.109
1.0913 1.0791
Panel B:Swap Rates (Senior Debt)
0.1414 0.1172 0.0985 0.0828
0
0.1412
0.117
0.0984 0.0827 0.0689
0.1405 0.1165
0.098
0.0824 0.0686
0.1394 0.1157 0.0974 0.0819 0.0432
0.1376 0.1146 0.0965 0.0811 0.0408
0.1351
0.113
0.0953 0.0676 0.0405
0.1315
0.111
0.0937 0.0609 0.0408
0.1262 0.1084
0.088
0.0574 0.0411
0.1181 0.1051 0.0782 0.0551 0.0414
Panel C:Debt Rates (Senior Swap)
1.275
1.2172 1.1786
1.15
1.05
1.2755 1.2175 1.1789 1.1503
1.128
1.2771 1.2186 1.1798
1.151
1.1287
1.2797 1.2205 1.1813 1.1524 1.1043
1.2835 1.2233 1.1834 1.1542 1.1043
1.2885 1.2265 1.1862
1.144
1.1071
1.2947 1.2307 1.1896 1.1415 1.1109
1.3008 1.2358 1.1899
1.143
1.1154
1.2876 1.2418 1.1871 1.1465 1.1205
1.20
1.225
1.25
1.05
1.05
1.05
1.0543
1.0571
1.0598
1.0629
1.0663
1.0702
1.05
1.05
1.05
1.05
1.0528
1.0552
1.0577
1.0605
1.0637
1.05
1.05
1.05
1.05
1.05
1.0521
1.0541
1.0564
1.0589
0
0
0
0.0148
0.0212
0.0251
0.0278
0.0299
0.0315
0
0
0
0
0.0088
0.0144
0.0183
0.0213
0.0237
0
0
0
0
0
0.0063
0.0109
0.0145
0.0174
1.05
1.05
1.05
1.0691
1.0783
1.0849
1.0907
1.0962
1.1017
1.05
1.05
1.05
1.05
1.0616
1.0696
1.076
1.0819
1.0875
1.05
1.05
1.05
1.05
1.05
1.0584
1.065
1.0709
1.0763
This table reports equilibrium debt and swap rates R(»; e) and X(»; e) for di®erent combinations
of observed ¯rm quality » and observation error size e, when the motive for the swap is unknown.
Observed quality » equals true quality m plus a random zero-mean noise ², i.e. » = m + ², with ²
distributed uniformly over the range [¡e; e]. All ¯rms take swap position w = 1. Realized cash-°ows
for the ¯rm are m ¡ R ¡ X if the swap is used for hedging, and m + 2X ¡ X ¡ R if it is used for
speculating, where X is the risk factor realization, distributed uniformly over the interval [¡K; K]. It
is optimal for a ¯rm to hedge in equilibrium if its quality m exceeds m¤ = R(»; e)+X(»; e)+°, and to
speculate otherwise. The debt market sets R(»; e) such that the expected return on debt equals Rf .
Similarly, the swap market sets the swap rate X(»; e) such that the expected payo® to the swap equals
zero. Panels A and B report debt and swap rates, respectively, for the case when the debt is senior to
the swap. Panel C reports debt rates for the case when the swap is senior to the debt. In the latter
case, the swap is riskfree, so X = 0. * indicates that debt and swap market equilibria are not feasible.
The parameter values used are: Rf = 1:05; K = 20%; ° = 0:1; w = 1; » 2 [1:00; 1:25]; e 2 [0; 0:2]:
28
Figure 1
Regions of optimality for hedging and not hedging
in the absence and presence of speculative swaps.
This ¯gure illustrates the incentive to hedge in the absence and presence of speculative swaps. The
two upward-sloping straight lines mark the boundaries of true ¯rm quality m possible, (» ¡ e; » + e),
given an observed ¯rm quality ». The curve hh indicates m¤ = R(»; e)+°, the minimum level of true
¯rm quality m for hedging to be optimal, when speculative swaps are absent. The curve ss indicates
m¤ = R(»; e) + X(»; e) + ° when speculative swaps are present. Region A represents ¯rms for which
it is optimal not to hedge both in the presence and absence of speculative swaps. Similarly, region C
represents ¯rms for which it is optimal to hedge under both scenarios. However, for ¯rms in region
B, it is optimal to hedge when speculative swaps are excluded, and to speculate when such swaps are
allowed. Parameter values used are: Rf = 1:05; K = 20%; ° = 0:1; w = 1; e = 0:1; » 2 [1:00; 1:25]:
29
Figure 2
Possible combinations of ¯rm quality,
operating exposure, and swap position.
This ¯gure shows the possible combinations of ¯rm quality m and operating exposure ¯ for ¯rms,
given a swap position w. There are two groups in the pool of ¯rms with w = +1 (the shaded cells):
one group has quality m < m¤ , ¯ = +1, and swaps to speculate; the other group has m > m¤ ,
¯ = ¡1, and swaps to hedge. Similarly, there are two groups in the pool of ¯rms with w = ¡1 (the
unshaded cells): one group has quality m < m¤ , ¯ = ¡1, and swaps to speculate; the other group
has m > m¤ , ¯ = +1, and swaps to hedge.
30
Figure 3
Regions of optimality for hedging and not hedging
when speculative swaps are possible.
The ¯gure shows combinations of ¯rm quality m and swap position w for which it is optimal to
hedge/not hedge. Realized cash-°ows for the ¯rm are m + X where X is the risk factor, distributed
uniformly over [¡K; K]. The market observes the imprecise version » of true quality m, i.e., » =
m + ², where the observation error ² is distributed uniformly over [¡e; e]. Based on observed » and
w, the swap market sets the swap rate X. A represents ¯rms with quality m greater than the cut-o®
level m¤ = R + wX + ° and it is optimal for these ¯rms to hedge. Firms in region B have quality
m less than m¤ and it is optimal for such ¯rms not to hedge. For large enough w, all ¯rms in the
pool lie in B.
31