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Accounting for Derivatives and Corporate Risk Management Policies*+
Ronnie Barnes
Assistant Professor of Accounting
London Business School
Sussex Place, Regents Park
London
NW1 4SA
email: [email protected]
Tel: +44 (0) 20 7262 5050
Current Draft, December 2001
* Preliminary: comments welcome. This work has been partially funded by scholarships from the Institute of Finance and Accounting at LBS and the Institute of Chartered Accountants in England and Wales. + This work constitutes part of my dissertation at LBS. Thanks are due to my transfer committee (Henri Servaes, Shiva Shivakumar and particularly Michel Habib), Dick Brealey, Bjorn Jorgensen, Arijit Mookherji and Pat O’Brien for useful comments and encouragement. I have also benefited from the comments of seminar participants at LBS, the University of North Carolina (Chapel Hill) and Lancaster University.
1
Accounting for Derivatives and Corporate Risk Management Policies
ABSTRACT: In this paper, I discuss the issue of how non-financial corporations should report
the results of their use of derivative financial instruments. Using the recently issued SFAS 133 as
a framework, I introduce three possible accounting regimes (mark to market, mark to market
hedge and deferral hedge) and characterize the information provided to users of financial
statements under each of the three alternatives. I then present a simple economic model with
which to analyze the effect (if any) on corporate risk management policies of the different
regimes. My main result is that hedging distortions (defined as deviations from the optimal
hedge position in the absence of any accounting considerations) may occur in a mark to market
regime but not in a mark to market hedge or deferral hedge regime. Finally, I discuss the policy
implications of this result and explain how the ability to make voluntary disclosures may
eliminate these distortions – this conclusion is, however, valid only if the underlying risk
exposures of firms are ex-post verifiable.
Key words: Corporate risk management, Hedging, Accounting for derivatives, Fair value
accounting
2
I. INTRODUCTION
In recent years, the corporate use of derivative financial instruments such as forwards, futures,
options and swaps has been subject to rapid growth, both in terms of the extent of use and the
complexity of the instruments employed. For example, a recent Bank for International
Settlements (BIS) survey showed that of the estimated US$ 74 trillion (in notional value terms)
of over the counter interest rate and foreign exchange derivatives outstanding in December 1999,
approximately 11% (US$ 8 trillion) were held by non-financial users. Similarly, in the Group of
Thirty report published in March 1994, over 80% of private sector corporations were reported as
considering that derivatives were important in implementing their financial policies. To illustrate
the increased complexity in the types of derivatives being used by corporations, one need look no
further than the well publicized losses incurred by Proctor and Gamble on leveraged swap
transactions.
Almost inevitably, this rapid growth in the use of the derivatives markets by corporate
end-users has not been matched by corresponding developments in the “financial infrastructure -
that is, the institutional interfaces between intermediaries and financial markets, regulatory
practices, organization of trading, clearing, back-office facilities and management-information
systems” (Merton (1996)). One important element of the infrastructure for which this is
unquestionably the case is the financial reporting environment. Accounting and disclosure
requirements1 in respect of the use of derivatives by non-financial corporations have been until
1 As a matter of terminology, I classify a particular requirement as “accounting” if it relates to the determination of the amounts which are included in the income statement and/or balance sheet and as “disclosure” if it relates to the more detailed information typically presented in the supplementary notes to the financial statements. Although I draw this distinction between accounting and disclosure requirements, my philosophy is that the value-relevance of a footnote disclosure (e.g. the fair value of the company's derivatives portfolio at the year-end) is identical to that of the same information included in the balance sheet or income statement unless the fact that the information is/is not included in a primary financial statement by itself has informational content. In other words, I adopt (at least as a starting point) the somewhat “purist” view that investors analyse the financial statements in their entirety, rather than simply focusing on a subset of the statements.
3
lately at best piecemeal, internally inconsistent, non-uniform across various types of derivatives
and incomplete (for example, the US) and at worst effectively non-existent (for example, the
UK). Further, the large derivatives-related losses experienced by companies such as Gibsons
Greetings, Metallgesellschaft and Proctor and Gamble led to the derivatives industry coming
under intense scrutiny from the media, regulators and politicians alike. As described by Benston
and Mian (1995), much of the debate surrounding these incidents focused on the use of
derivatives for what were apparently speculative purposes and the inadequacy of the then current
reporting requirements for communicating this information to shareholders, regulators and other
interested parties. Consequently, regulatory bodies such as the Financial Accounting Standards
Board (FASB) in the US and the Accounting Standards Board (ASB) in the UK came under
increased pressure to make the development of a comprehensive and consistent set of rules for
the reporting of corporate derivatives usage a matter of some priority.
Whilst few disagreed that these reporting requirements were in need of a major overhaul, the
level of consensus regarding the solution to the problem was considerably lower. From anecdotal
evidence, it is clear that the presentation of information relating to derivative securities in
financial statements is an issue of some concern to corporate users and that risk management
strategies are actually set with full consideration of the implications of these strategies for the
financial reporting process. For example:
(i) in a survey of 350 firms conducted in October 1995 (Bodnar, Hayt and Marston
(1996)), “qualifying for hedge accounting”2 was identified by 30% of those
respondents using derivatives as an issue over which the degree of concern was
2 A detailed discussion of the distinctions between hedge accounting and the main alternative, mark to market accounting, and of how they impact financial statements is provided in Section 2 of the paper. Loosely speaking, the principal feature of hedge accounting is that in many cases, gains and losses on a derivative position (and possibly
4
“high” - interestingly, only 9% had a high degree of concern over disclosure
requirements3;
(ii) a similar survey of 399 firms conducted in October 1997 (Bodnar, Hayt and
Marston (1998)) saw 74% of respondents claim that they has a “high or moderate
degree of concern” regarding the accounting treatment of their derivatives
activity;
(iii) when announcing in late 1994 that it had unwound derivatives with a total
notional value of $6 billion, Kodak explained the decision as an attempt to
prevent volatility in earnings as a result of using derivatives; at around the same
time, RJR Nabisco announced that it was discontinuing its use of derivatives that
were subject to mark to market accounting;
(iv) the FASB received over 250 responses to the Exposure Draft which preceded
SFAS 133: Accounting for Derivative Instruments and Hedging Activities, the
recently issued standard that is intended to unify the accounting and disclosure
requirements in this area - the contents of the Exposure Draft and the nature of
these responses are considered in detail later in the paper.
It is therefore apparent that these requirements are an important factor in determining
whether a non-financial corporation will choose to hedge the risks to which it is exposed and if
so, which risks should be hedged and which derivative instruments should be used to effect this
hedging and also whether derivatives should be used for speculative purposes. For example,
Montesi and Lucas (1996) note: “Derivatives are powerful and useful risk management tools,
even the position itself) do not appear in the financial statements until some time after the inception of the position - in other words, under hedge accounting such positions remain “off-balance sheet”.
5
and the inadequacy of financial reporting may discourage their legitimate use by contributing to
an atmosphere of uncertainty.” Similarly, Benston and Mian (1995) assert that “our analysis of
financial statements indicates that these rules have significantly constrained firms from using
derivatives optimally.”
In other words, the financial reporting environment is not economically “neutral” but in
many cases will be a significant economic variable in the corporation's decision making process.
Consequently, any proposed solution must take full account of these economic implications.
Whilst certainly necessary, it is not sufficient that reporting requirements for derivatives be
comprehensive and consistent - they must also be designed so as to discourage sub-optimal risk
management policies4.
At this point, it is worthwhile commenting on the terminology used in this paper. Within the
existing literature, the terms “hedging” and “risk management” are used somewhat
interchangeably. In this paper, I will use “risk management” to refer to any use of derivative
instruments for whatever purpose. In practice, corporations have alternative means of effecting
risk management strategies. For example, the exchange rate risk resulting from income
denominated in a foreign currency may be reduced by choosing a capital structure which
includes financing in that currency. Because of the focus of this paper, I will ignore this issue
and will concentrate solely on corporate risk management via the use of derivatives. The term
“hedging” will be reserved for those situations where such instruments are used by a corporation
to reduce its exposure to a particular risk factor, whilst “speculation” will be used to signify the
use of derivatives to increase the corporation's level of exposure to some risk factor.
3 This could either mean that the content of the disclosures currently mandated in this area are considered to be unimportant, or that the respondents believe that investors, analysts and other users of accounts generally ignore footnote disclosures. 4 Exactly what objective function is being optimized will be discussed in Section 3 of the paper.
6
To illustrate the importance of this distinction and to create a feel for the inherent problems
faced by the standard setters, consider the case of an oil producer which sells forward 70% of its
total production volume. This may be considered simply as a partial hedge. Alternatively, it may
be instructive to decompose the position into a full hedge (selling forward of all production)
partially offset by a speculative position involving forward purchases amounting to 30% of
production volume. The reason why such a breakdown may be useful is that the motivation for
the two components may be significantly different. For example, market frictions such as
bankruptcy costs or taxes (see Section III below) may create a value for hedging such that the
fully hedged position is the optimal “passive” response; in addition, the company may have an
informational advantage concerning the future path of oil prices which it chooses to exploit by
taking a speculative position in the forward market. This dual motivation for risk management is
consistent both with the observation that many companies who utilize derivatives do not
necessarily adopt a fully hedged position and with (again anecdotal) evidence that a corporate's
risk management policies may well include an element which essentially amounts to “taking a
view” on the market. For example, in a survey of Fortune 500 companies carried out in 1992
(Dolde (1993)), only slightly more than 10% of companies using derivatives claimed never to
use them for taking a view5.
In this paper, I address the general issue of how the accounting and disclosure rules relating
to the corporate use of derivative financial instruments can actually affect the way in which
companies choose to use such instruments. The structure of the paper is as follows. In Section II,
I firstly describe the two main systems of accounting for derivatives, namely hedge accounting
and mark to market accounting. I then review the key elements of the recently issued SFAS 133:
5 Stulz (1996) argues that “the primary goal of risk management is to eliminate the probability of costly lower-tail outcomes” and that certain companies may have informational advantages which encourage selective hedging.
7
Accounting for Derivative Instruments and Hedging Activities (I choose to base my discussion
on the US simply because this is the jurisdiction in which the current rules are the most
developed and also because standard setting bodies in other jurisdictions, in particular the UK,
are likely to pay significant attention to the US requirements when developing their own
standards)6. Finally, I consider the responses to the Exposure Draft which preceded the standard
in order to delineate the issues which are of concern to derivatives end-users. The aim here is to
identify within the somewhat detailed requirements those factors which are of prime importance
to corporates when determining risk management policies.
In Section III, I briefly review the existing literature on possible economic rationales for
corporate risk management; I also discuss in somewhat more detail previous work which has
examined the interaction between the financial reporting environment and risk management. In
Section IV, I present a simple model of corporate risk management and use this model to analyze
how the incentives of corporations to use financial derivatives may be distorted by various
accounting regimes. Finally, Section V contains a summary of the paper and my conclusions.
II. INSTITUTIONAL FRAMEWORK
Hedge Accounting vs. Mark to Market Accounting
Much of the discussion concerning what form the accounting rules should actually take
centres around the relative merits of hedge and mark to market accounting and the question of
what the qualifying criteria for hedge accounting should be. Broadly speaking, hedge accounting
is the preferred method of accounting from the corporates' viewpoint. [The actions of Kodak and
RJR Nabisco described in Section 1 can be loosely interpreted as indicating an unwillingness to
6 In September 1998, the ASB issued FRS 13 – “Derivatives and Other Financial Instruments: Disclosures” in which they note that “work on measurement and hedge accounting is therefore continuing and the Board expects to publish
8
continue to hold derivative positions which had been afforded hedge accounting treatment but
which under the (at that time anticipated) new rules would be subject to mark to market
accounting]. By contrast, regulatory authorities have to date attempted to restrict the use of hedge
accounting by specifying often stringent conditions which must be met before this is permitted.
The model I present in Section IV can be seen as an attempt to explain and rationalize this
apparent aversion to mark to market accounting by considering what motivates the use of
derivatives by corporates in the first place and then analyzing how these incentives may be
changed as a result of changes in the reporting environment.
Since the distinction between hedge and mark to market accounting is crucial to the rest
of the paper, it is important at this stage that I define exactly what I mean by these terms.
Essentially, hedge accounting refers to a method of accounting for derivative instruments
whereby any gains or losses on a particular instrument are only recognized in the income
statement when the corresponding losses or gains on the item being hedged are recognized. The
basic idea underlying this method of accounting is that the hedged item and the hedge together
form an economic “package” and that it is this package which should be accounted for, not the
two individual elements.
Based on this underlying principle, there are three basic variants of hedge accounting:
(i) the fair value of the derivative is recorded on the balance sheet as an asset or
liability and any unrealized gains or losses which result are recorded in the
income statement immediately. This would only be appropriate if unrealized gains
or losses on the item being hedged are accounted for in this way; an example
would be the case of a marketable security held for trading purposes;
proposals on these subjects in due course.”
9
(ii) the fair value of the derivative is recorded on the balance sheet as an asset or
liability and any gains or losses are recorded as either a standalone balance sheet
item, an adjustment to the balance sheet value of the item being hedged or as
elements of comprehensive income (in the UK, this latter treatment would
correspond to gains or losses being recorded as movements in reserves and
disclosed in the Statement of Total Recognized Gains or Losses). This would be
the appropriate treatment for a derivative which is being used to hedge an existing
asset or liability which is recorded on the balance sheet but for which gains or
losses are only recognized in income when realized;
(iii) no accounting entries are made in respect of the derivative until some time after
the position is established - in other words, the derivative is treated as an off
balance sheet item until this time. This might be the case, for example, if the
derivative were a forward which was being used to hedge against the currency
exposure arising from the foreign purchase of a fixed asset - in this situation, the
asset and liability are not recorded until the contract is “completed” and the
concept of matching would require the hedge to be treated in the same way.
In contrast, under mark to market accounting the fair value of the derivative is recorded on
the balance sheet as an asset or liability and any unrealized gains or losses which result are
recorded in the income statement immediately, irrespective of the accounting treatment afforded
the item (if any) being hedged.
The focus in this paper is on the informational content of the various reporting regimes
encountered in practice. In this respect, it is important to note that the second variant of hedge
accounting discussed above is informationally equivalent to mark to market accounting (as
10
indeed is the third variant if the unrecognized gain or loss is reported via a footnote disclosure).
Consequently, in the theoretical model developed in Section IV, I adopt a slightly different
terminology:
(i) mark to market accounting refers to a system whereby the gain or loss on any
derivatives position is recognized immediately whereas that on the hedged item
(if any) is recognized only when realized;
(ii) under mark to market hedge accounting, gains and losses on both any
underlying exposure and the derivative are recognized immediately;
(iii) with deferral hedge accounting, any gain or loss on the derivative position is
deferred until realized to the extent that it is offset by a corresponding
unrecognized loss or gain on an underlying position - to the extent that there is no
such offset, the derivative gain or loss is recognized immediately.
SFAS 133 Requirements
In June 1998, the FASB released SFAS 133 – “Accounting for Derivative Instruments and
Hedging Activities” which represented the culmination of a six year program on the part of the
board to unify the reporting requirements in this area. In the Standard, four fundamental
decisions made by the FASB when formulating the proposals are described. These are as
follows:
(i) derivatives are assets and liabilities and should be reported in the financial
statements;
(ii) fair value is the most relevant measure for financial instruments and the only
relevant measure for derivative financial instruments; derivatives should be
11
measured at fair value and adjustments to the carrying amounts of hedged items
should reflect changes in their fair values (that is, gains and losses) arising while
the hedge is in effect;
(iii) only items that are assets or liabilities should be reported as such in the financial
statements;
(iv) hedge accounting should be provided for only qualifying transactions, and one
aspect of qualification should be an assessment of hedge effectiveness.
The key features of these proposals are that hedge accounting is again being restricted to
situations where certain criteria are met, all derivative positions must be included on the balance
sheet and any gains or losses must be reported in either earnings or other comprehensive income
(a separate component of equity outside of earnings) 7 - they cannot be carried on the balance
sheet as standalone “deferred” gains or losses or used to adjust the carrying value of the hedged
item8. If a gain or loss is initially reported in comprehensive income, it must at some later date be
transferred to earnings.
Response to Exposure Draft9
Overall, the response to the exposure draft preceding SFAS 133 from industrial firms was
extremely negative (whilst many changes were made in the final standard, the key requirements
are essentially unchanged and so these responses are equally relevant in the context of the
standard itself). 61% of respondents disagreed with the exposure draft's proposals whilst 24%
7 What the standard terms hedge accounting is really either mark to market or mark to market hedge accounting – the fact that a transaction qualifies for “hedge accounting” simply means that the unrealised gains or losses are recorded in other comprehensive income rather than in the income statement. Of course, the mere fact that a transaction qualifies for this treatment may in itself have informational content. 8 Additionally, deferral hedge accounting (whereby essentially nothing is recorded in respect of a derivatives position) is no longer possible. 9 The source of the information for this part of the paper is Boyd, Hayt, Reynolds and Smithson (1996).
12
agreed with the proposals subject to significant changes being made (the response from financial
firms was roughly similar whilst for the professional accounting firms, 37% disagreed and 37%
agreed subject to significant changes). Much of the criticism related to specific features of the
proposed standard (for example, the prohibition of basis adjustments on forecast transactions)
which, although of interest, are somewhat too detailed to be incorporated into a theoretical model
of the reporting process.
The response that I shall focus on and which is (with suitable interpretation) amenable to
inclusion within such a model relates to the impact of the proposals on volatility. 44% of
respondents mentioned increased balance sheet volatility and 62% earnings volatility as a source
of potential concern. As an example:
“Given the focus on earnings by analysts and shareholders, the earnings volatility potential presented by fair value hedge accounting, as proposed, may have a material impact on market valuation as well” (Providian Bancorp).
The crux of the argument appears to be that this increased volatility will make the firm
appear riskier than it really is. At first glance, such a response appears a little naive; given
adequate disclosure, investors will be able to “strip out” the source of this volatility which should
therefore have no value relevance. Suppose however that what this response is actually trying to
convey is a concern that the proposed standard will not enable firms that are using derivatives for
legitimate hedging purposes to properly distinguish themselves from firms which are using them
for speculative purposes. If this is the case, then increased volatility in earnings and/or the
balance sheet may be genuine (in the case of speculators) or spurious (in the case of hedgers) - if
investors are unable to identify into which category a particular firm falls, then this volatility
may indeed be value relevant. I will use this as the basic idea behind the theoretical model
developed in Section IV.
13
III. LITERATURE REVIEW
In this section, I first present a brief review of the existing theoretical literature which addresses
the motivations for non-financial corporations to engage in risk management activities. I then
discuss in somewhat more detail prior research on the impact of accounting and disclosure
requirements on such activities.
3.1 Motivations For Corporate Risk Management
In a Modigliani and Miller (1958) world of perfect capital markets (no taxes, no bankruptcy
costs, no asymmetric information), any corporate risk management is irrelevant. Consequently,
the various economic rationales which have been advanced in an attempt to explain corporate
hedging all depend on the violation of one or more of the restrictive conditions required for this
irrelevance proposition to be valid.
For example, Smith and Stulz (1985) note that hedging may lead to a reduction in expected tax
payments and/or expected bankruptcy costs whilst Froot, Scharfstein and Stein (1993) use the
costs of external financing compared to internally generated funds as a motivation for corporate
hedging. A somewhat different explanation is that of DeMarzo and Duffie (1991) who analyze a
setting where firms have proprietary information concerning their exposure to risk and where
hedging against these risks enables risk averse investors to make better portfolio choice
decisions. In Ljungqvist (1994), proprietary information is also the driving force behind
corporate risk management policies although in this case derivatives are used purely for
14
speculative purposes; such (costless) speculation acts as a “signal-jamming” mechanism which
allows existing shareholders to manipulate share prices to the detriment of potential new
investors. Degeorge, Moselle and Zeckhauser (1996) also use asymmetric information and the
desire to influence potential investors' perceptions concerning firm quality to explain corporate
risk management policies.
The papers discussed in the previous paragraph all have the maximization of (existing)
shareholder value as the firm's objective. By contrast, a number of papers have used managerial
utility maximization as the driving force behind corporate risk management policies. For
example, Stulz (1984) considers the case of a risk averse manager who also has an equity stake
in the firm that is somewhat larger then the optimal level suggested by modern portfolio theory -
particularly when human capital is taken into account, the manager is seen to have a very poorly
diversified portfolio. Earlier papers which adopt essentially the same line of reasoning include
Holthausen (1979) and Anderson and Danthine (1980, 1981). Campbell and Kracaw (1987) note
that as a result of the well-known agency problem between managers and shareholders, risk
sharing is sub-optimal. Hedging will reduce the unsystematic risks faced by the firm, risks which
are borne disproportionately by managers, and so shareholders may then actually benefit from
hedging since this risk reduction induces managers to be more productive. A second paper in a
similar spirit is DeMarzo and Duffie (1992). In Breeden and Viswanathan (1996), it is a concern
with communicating managerial ability to the labor market that is the motivation behind
corporate risk management programs. They analyze an economy where compensation contracts
are renegotiated at the start of each period with the compensation for any period being a fixed
amount which is equal to the expected profit for that period conditional on realized profits in
15
previous periods. These profits are comprised of two elements, the first of which is a function of
managerial ability and is thus in some sense under the control of the manager, whereas the
second is independent of ability and cannot be controlled. However, hedging instruments are
available which allow managers to eliminate the “noise” in profits caused by the uncontrollable
factor. Two other papers which also focus on managerial career concerns as the explanation for
risk management are DeMarzo and Duffie (1995) and Raposo (1996) - since these papers also
consider the impact of accounting and disclosure requirements, they are discussed in the
subsection below.
3.2 Impact of Financial Reporting Environment
To date, relatively little research has focused on the impact of the financial reporting
environment on the risk management activities of firms. Of this research, the two papers which
are closest in spirit to the current paper are Melumad, Weyns and Ziv (1999) (hereafter MZW)
and its (unpublished) predecessor, Weyns (1993).
The setting in MZW is of a two-period economy with a single firm with assets in place at
0=t which generate at 2=t a random operating cash flow
( )21 εεµ ++= xY
16
where x is the firm's exposure to the underlying risk factor, µ is the level of this risk factor at
0=t and 21,εε are the innovations to the risk factor in the first and second periods respectively.
Moreover
10 xxx +=
where 0x is common knowledge whilst 1x may be private information at 1=t ; x (and
therefore 1x ) is publicly observed at 2=t .
In this economy, all investors have mean-variance utility functions (so that the benefit from
hedging at the corporate level is the reduction in the variance of the payoffs to investors) and
managers are able to enter into forward contracts, the payoffs from which are perfectly correlated
with Y . As expected, when all shareholders are long-term (i.e. will hold their shares until 2=t
and are therefore interested only in the final (net) cash flow), the optimal hedging policy is to
hedge the expected exposure ( [ ]10 xEx + ) at 0=t and then to rebalance the position to hedge the
actual exposure at 1=t ; the accounting regime is irrelevant. A similar result obtains when 1x is
public information at 1=t .
The role of the accounting regime arises only when 1x is not public information at 1=t and a
fraction of the firm's existing shareholders are short-term in the sense that they will sell their
shares at this intermediate date. The price that potential new investors are willing to pay depends
17
on their assessment of the distribution of the firm's terminal cash flows; this in turn depends on
the information contained in the 1=t financial statements. MZW show that, in this case,
hedging distortions will occur under a mark to market or a deferral hedge regime but not under a
mark to market hedge regime.
However, their results are critically dependent upon the assumption that disclosure of the firm's
hedging position is not required and that voluntary disclosures are not permitted. These
assumptions are rather implausible – as noted earlier, SFAS does in fact require disclosure of
derivatives positions whilst voluntary disclosures are an important mechanism for
communicating information.
Weyns (1993) also considers a variant of this basic model in which investors are uncertain as to
whether firms are in fact hedging optimally. More specifically, he assumes that the economy
consists of two types of firm, both of which have the same underlying exposure which is known
to investors; however, whilst one type of firm (H) continues to hedge optimally, the other type (I)
non-strategically overhedges during the first period10 - this induces additional uncertainty into
the intermediate share price of the type-H firms to the detriment of the short-term shareholders.
Using a numerical example, Weyns shows that the optimal response of the type-H firm is to
underhedge during the first period11. By doing so, a type-H firm is able to probabilistically
separate itself from the type-I firms - by underhedging, the type-H firm will generate first period
earnings which are less likely to have originated from a type-I firm. The optimal degree of
10 In this variant of the model, any deviation from optimal hedging is motivated solely by a desire to influence investors' beliefs (and therefore the share price) at 1=t ; consequently, any such deviations are corrected in the second period.
18
underhedging will represent a trade-off of the interests of the long-term and the short-term
shareholders - once again, any underhedging will be eliminated in a mark to market hedge
accounting regime and the distortions could be easily eliminated by allowing voluntary
disclosure (in this case of the actual position in forward contracts).
Although Weyns notes that “imperfectly hedging” firms may be explained by (for example) an
inability to correctly estimate the true risk exposure or speculative motives arising from
heterogeneous beliefs concerning the evolution of the risk factor, he does not attempt to
endogenize the actions of the type-I firms. By contrast, the model presented in Section 4 of this
paper (which also analyzes hedging distortions arising from an inability on the part of investors
to distinguish between two types of firm) does explicitly endogenize the behavior of each type as
the rational response to the actions of the other.
By contrast, Fischer (1997) considers corporate hedging as a means of eliminating the variability
in accounting earnings which arise from factors that are beyond a manager's control and analyzes
whether such hedging leads to an improvement in the incentive effects of contracts which are
written on these earnings. Within a standard principal-agent framework with a risk-neutral
principal and a risk-averse agent, he finds that when the effects of uncontrollable events can be
perfectly hedged, perfect hedging should be undertaken and the optimal earnings number for
contracting purposes is one derived under “symmetric” accounting12. The paper then goes on to
analyze a setting in which pre-hedged earnings depend both directly and indirectly on a
11 It seems intuitively obvious that overhedging in the first period would be the optimal response if the type-I firms were to non-strategically underhedge.
19
hedgeable risk factor. The author finds that the optimal strategy is to hedge the overall (i.e. direct
plus indirect) exposure and that this choice of optimal hedge is actually independent of the
accounting regime.
Jorgensen (1998) also analyzes the interaction of corporate hedging decisions and the financial
reporting environment using a two-period principal-agent model. In this paper, a group of risk-
averse shareholders hire a similarly risk-averse manager to acquire (at a cost to the manager)
information concerning the correlation between the firm's second period operating income and
the gains or losses on a forward contract which must be initiated at 0=t 13. As in Fischer (1997),
accounting earnings in this model are of importance since they are used for contracting purposes.
Consequently, deferral hedge accounting (earnings in the first period reflect only that period's
operating income, not the unrealized gain or loss on the forward position) is distinguishable from
mark to market accounting (earnings in the first period reflect both that period's operating
income and the unrealized gain or loss on the forward position) - this compares to the situation in
Weyns (1993) where, as discussed above, the importance of an earnings number derives from its
informational content and these two regimes are essentially equivalent. However, in the
Jorgensen model, mark to market hedge accounting and mark to market accounting are identical
since the underlying risk exposure which is being hedged affects only the second period
operating income; therefore, the first period change in the value of this underlying exposure is,
by definition, zero.
12 Using the terminology of this paper, symmetric accounting may be identified with deferral hedge accounting i.e. the earnings number used for contracting includes neither the change in value of the underlying exposure nor the change in value of the hedge position. 13 i.e. in order to hedge the risk inherent in the second period operating income, the manager must establish and maintain a position in the forward contract at 0=t .
20
Within this setting, Jorgensen finds similar results to Fischer (1997) i.e. that if performance
measures are generated using deferral hedge accounting, there are no hedging distortions, but
that such distortions may occur if mark to market accounting is used to determine accounting
earnings.
Jorgensen also investigates the demand for separate disclosures of operating income and hedging
gains or losses in the context of a single period model with risk-neutral shareholders and a risk-
averse manager. He finds that, given linear compensation contracts, the shareholders have no
demand for such separate disclosures but that this may not be the case if the manager has private
information regarding the hedge instrument.
Two other papers which consider how hedging and its reporting are interrelated (DeMarzo and
Duffie (1995) and Raposo (1996)) also focus on this somewhat narrower issue of the demand for
a split of total accounting earnings between operating and hedging activities. DeMarzo and
Duffie (1995) (a paper which is similar to Breeden and Viswanathan (1996) in that the
motivation for corporate hedging stems from managerial career concerns) focus directly on the
informational role of hedging. They find that with disclosure only of aggregate accounting
earnings, managers will always choose a policy of full hedging. However, if separate disclosure
of the two components of earnings is mandated, this is no longer the case and indeed no hedging
may occur in equilibrium. Moreover, they show that, by eliminating extraneous noise, hedging
improves the informativeness of earnings as an indicator of management ability and project
quality and thereby enables shareholders to make better future investment decisions. This
increase in the informativeness of earnings may well outweigh the informational content of a
21
separate disclosure of the results of hedging activity, leading shareholders to prefer a regime
where only aggregate disclosure is mandated.
Raposo (1996) is essentially an extension of DeMarzo and Duffie (1995) which allows for, inter
alia, renegotiation of managerial compensation contracts, managerial input into project choice
and voluntary disclosure. Once more, the model characterizes the possible accounting regimes as
aggregate or separate disclosure of operating and hedging profits and, as such, is less relevant to
the model in the current paper than those of MZW, Weyns (1993), Fischer (1997) and the two-
period model of Jorgensen (1998).
Finally, Kanodia et al. (1999) consider (at a macroeconomic level) the interaction between the
disclosure of risk exposures and real production decisions - their main result is that disclosing
risk exposures leads to a higher futures price and increased price efficiency.
4. Accounting for Derivatives: A Theoretical Model
4.1 Introduction
In this section, I develop a simple economic model with which to analyze the effect on corporate
risk management policies of various accounting regimes. Specifically, I consider an economy in
which there are two distinct types of firm, namely “high” and “low” quality. A high quality firm
has a (risky) terminal operating cash flow that can be decomposed into a firm-specific element
(which cannot be hedged) and a market-wide or systematic element (which can be hedged); by
22
contrast, the terminal operating cash flow of a low quality firm is entirely firm-specific. All
investors are risk-averse. Consequently, a high quality firm has an incentive to access the
derivatives market in order to hedge its systematic risk, whereas a low quality firm has an
incentive to avoid this market – it is not exposed to systematic risk and so any use of the
derivatives market will lead to an increase in risk which is harmful to its shareholders.
Suppose, however, that shareholders are interested not only in the terminal cash flow of a firm
but also in its share price at some intermediate date. If the accounting regime is such that
investors are unable to distinguish between the two types of firm, it may make sense for a low
quality firm to use the derivatives market for speculation. This will be the case if the higher share
price which results from being “pooled” with the high quality firms at the intermediate date
outweighs the adverse effect of the increase in risk. Obviously, such pooling will be detrimental
to the high quality firms who may therefore attempt to “separate” themselves by choosing a
derivatives position that the low quality firms have no incentive to copy. This will be the case if
the gain from not being pooled with the low quality firms exceeds the loss from having to choose
a sub-optimal hedging strategy. In either case, the accounting regime has a direct impact on
corporate risk management policies.
4.2 Basic set-up
As described above, the economy under consideration consists of a large number N of firms, of
which a proportion θ are of typeH and a proportion θ−1 are of typeL . The economy lasts for
two periods; the first of these runs from the current date 0=t to the intermediate date 1=t
23
whilst the second runs from 1=t to the final date 2=t . At 0=t , firm n ( Nn ,....,1= ) has
assets in place that will generate (at 2=t ) a random operating cash flow nZ where
YXXZ nnn ++= 21
If firm n is of typeH , then
( )
21
2,~
εεµ ++=Y
smNX Hnt
where 0, >µHm and ( )2,0~ σε Nt .
If firm n is of typeL , however, then
( )
0
,~ 2
=Y
smNX Lnt
Further, I assume that all random variables in the set 2,1;,....,1:, == tNnX tnt ε are pairwise
independent.
In the remainder of the analysis, I shall focus on a representative firm of typeH and a
representative firm of typeL and write, with a slight change in notation
24
LLL
HHH
XXZ
YXXZ
21
21
+=
++=
All investors in the economy have a negative exponential utility function with a coefficient of
absolute risk aversion of ρ i.e. the utility from a random cash flow W is given by
( ) ( )WWu ρ−−= exp
Since
( )( )
( )2
22
2,2~
2,2~
smNZ
smNZ
LL
HH σµ ++
the expected utility accruing to a shareholder who owns firmH (and is intending to retain this
shareholding until 2=t ) is
( ) ( )[ ] ( ) ( )( )2222expexp σρµρρ +++−−=−−= smZEZU HHH
Similarly,
( ) ( )222exp smZU LL ρρ +−−=
25
- note that
( ) ( )
( ) ( )
( ) 2
22222
2
22
ρσµ
ρρσρµρ
>−+⇔
−>+−+⇔
>
LH
LH
LH
mm
smsm
ZUZU
I shall impose this latter inequality as a parametric restriction in order that the interpretation of
H and L as “high” and “low” quality respectively is somewhat meaningful.
Henceforth, I shall assume that each of the firms under consideration is owned by a single
shareholder. Whilst somewhat unrealistic, this assumption simplifies the analysis considerably
and will not affect the qualitative implications of the model. I also assume (as in Miller and Rock
(1985) and numerous studies since) that the existing shareholder in firm i ( LHi ,= ) will retain
(with probability iλ ) her holding until 2=t and receive the firm's terminal cash flow iZ .
However, with probability iλ−1 , the shareholder will sell (for liquidity reasons, say) this
holding14 at 1=t at the prevailing market valueiP . Consequently, using iM to denote the cash
flow accruing to this shareholder, her expected utility is
( ) ( ) ( ) ( )iiiii ZUPUMU λλ +−= 1
14 An alternative formulation is one in which the single shareholder of firm i will, with probability one, sell a
fraction iλ−1 of the firm at 1=t and retain the remaining fraction iλ until 2=t . This formulation is less tractable than the one developed here although I would expect it to generate (at least qualitatively) similar results. Similar remarks apply to a second alternative formulation whereby firm i is owned by multiple shareholders, a fraction
iλ−1 of which are “short-term” and will sell their shares at 1=t whilst
the remaining fraction iλ are “long-term” and will retain their shares until 2=t .
26
Assuming the absence of any moral hazard issues, this is the objective function that the manager
of firm i will maximize at 0=t .
Now consider the question of the proceeds the shareholder would receive from selling her
holding at 1=t . Suppose that a fraction π of the firm is offered to a potential new investor.
Based on his information, this investor will have a conditional probability distribution over the
terminal cash flow M of the firm. The conditional expected utility from a purchase of this
fraction is15
( )[ ] [ ] [ ]
+−−=−− MVarMEME 1
2211 2
1expexp πρρπρπ
Consequently, the price ( )πP at which, assuming for simplicity a risk-free interest rate of zero,
the investor is indifferent between this investment and one in risk-free securities (which would
generate expected utility of ( )( )πρP−− exp is then
( ) [ ] [ ]MVarMEP 12
12
1 ρπππ −=
which is obviously a function of π . As an immediate corollary of this observation, the total
proceeds from a sale of the firm depend crucially on the number of new investors to which the
shares are sold and the fraction of the firm which each of them receives. This raises interesting
but (for the purposes of this analysis at least) irrelevant side issues such as optimum trade sizes
27
and the strategic interactions between the various agents; consequently, I make a further
simplifying assumption that any sale of shares is made to a single new investor. I also assume
that there are a large number of competitive potential investors who will bid away any increase
in utility. In summary, therefore, with probability iλ the existing shareholder of a type i firm
sells her entire shareholding in the firm to a single new investor at a price [ ] [ ]MVarME 11 2
1 ρ− .
The managers of either firm are able (at zero cost) to enter into an unrestricted number of long or
short positions in a forward contract that pays off
µ−Y
at 2=t . Here, I am implicitly assuming that µ denotes the 0=t spot price of some traded asset
or commodity, that1ε and 2ε denote the innovations to this price over the first and second periods
respectively, and that it is possible to calculate the forward price using the standard no-arbitrage
relationship which equates (the present value of) this forward price to the 0=t spot price -
hence, setting the forward price equal toµ is not inconsistent with my assumption of risk averse
investors.
Denoting by iφ the position taken by firm i , the operating cash flows of the two firms are now
15 Henceforth, the subscript 1 will be used to denote expectations and variances evaluated conditional on the information available to the new shareholder at 1=t . The use of an operator without a subscript indicates that this is an unconditional operator evaluated at 0=t .
28
( )
( )µφ
µφ
−++=
−+++=
YXXZ
YYXXZ
LLLL
HHHH
21
21
and have distributions
( )( )( )
( )( )( )222
222
2,2~
12,2~
σφ
σφµ
LL
L
HH
H
smNZ
smNZ
+
+++
so that
( ) ( ) ( )( )( )2222 12exp; σφρµρφ HH
HH smZU ++++−−=
whilst
( ) ( )( )( )22222exp; σφρρφ LL
LL smZU ++−−=
4.3 Accounting Disclosures
Now consider the information available to investors at 1=t under each of the three accounting
regimes i.e. mark to market hedge, deferral hedge and mark to market. In all cases, I assume that
disclosure of the derivatives position is required.
29
Under mark to market hedge accounting, the gain or loss on the forward contract and the gain or
loss on the underlying position (if any) are both recognized in earnings i.e.
111 εφε HHHMTMH Xearnings ++=
- the three components are, respectively, the firm-specific element of the first period operating
earnings, the market-wide element of those earnings (i.e. the gain or loss on the underlying
position) and the gain or loss on the forward contract. Similarly,
11 εφ LLLMTMH Xearnings +=
Given that firms are required to disclose their derivatives positions and the fact that 1ε is public
information and under the assumption that firmH does not report separately the two components
of its operating earnings, the investors' information set is
LLHHMTMH XXI φφε ,;, 111 +=
- note that if LH φφ = , my assumption that the distribution of any component of operating
earnings has a support equal to the entire real line means that investors will be unable to
distinguish between the two firms. If, however, firmH does report separately the two
components of its operating earnings, investors are able to make this distinction, even if
LH φφ = ; for the remainder of the analysis, I shall assume that this is the case. This assumption
is critical to my results and I shall discuss it in more detail at the end of the section.
30
Now recall that under a deferral hedge accounting regime, any gain or loss on the forward
contract is deferred until realized to the extent that it is offset by a corresponding unrecognised
loss or gain on an underlying position - to the extent that there is no such offset, the forward
contract gain or loss is recognized immediately. In this case, reported earnings are16
HHDH Xearnings 1=
whilst
11 εφ LLLDH Xearnings +=
However, under the assumption that firmH is also required to disclose that it has deferred the
gain or loss on the forward contract, investors will be again be able to distinguish between the
two firms even if LH φφ = .
Finally, under mark to market accounting, the gain or loss on the forward contract is recognized
immediately whereas that on the hedged item (if any) is recognized only when realized. Thus
11
11
εφ
εφ
LLLMTM
HHHMTM
Xearnings
Xearnings
+=
+=
16 Strictly speaking, this is true only if 1≤Hφ i.e. the forward contract has genuinely been taken out as a hedge. However, given the ability of investors to distinguish between the two firms, firmH will have no incentive to
choose a position other than 1−=Hφ and so the case of 0>Hφ need not be considered.
31
and
LLHHMTMH XXI φφ ,;, 11=
i.e. the information available to investors will not enable them to distinguish firmH from firm L
in the event that LH φφ = .
4.4 Optimal Risk Management: Case I
Consider first the case where the utility of a firm's existing shareholder depends only upon the
firm's terminal cash flow (i.e. 1=iλ ). In this case, the optimum positions in the forward contract
are
0ˆ
1ˆ
=
−=
L
H
φ
φ
To see this, note that in this case, ( ) ( )iiii ZUMU φφ ;; = ; differentiating ( )iiZU φ; with respect
to iφ and setting the resulting expression to zero immediately yields the above result. This should
be intuitively obvious: entering into a forward contract affects only the variance of the terminal
cash flow, not the mean and so the optimum position is that which minimizes this variance. For
firm H , this amounts to choosing a position which is equal and opposite to its underlying
exposure; for firmL , any position will serve to increase the variance and so the optimum
position is zero.
32
4.5 Optimal Risk Management: Case II
Now consider the case where, in addition to the terminal cash flow, the ex-ante utility of the
existing shareholder of firm i is also impacted by its market value iP at the intermediate date
1=t ; in other words, 1<iλ .
Given the realizations of HX1 and 1ε and a derivatives position Hφ , the conditional distribution
of the terminal cash flow of firmH is
( ) ( )( )22211 1,1~ σφεφµ HHH
HH sXmNZ ++++++
Suppose that firm type is public information at 1=t . Then, in the event that firmH is sold at this
date, and usingfiP as shorthand for the full information price
[ ] [ ]
( ) ( )( )22211
11
121
1
2
1
σρεµ
ρ
HHHH
HHHfi
sXm
ZVarZEP
Φ++−Φ++++=
−=
where HΦ denotes the belief of the new investor concerning Hφ . Given that under all of the
accounting regimes I consider, firms are required to disclose their derivatives position at 1=t ,
there is no need to distinguish further between Hφ and HΦ .
Hence
33
( ) ( )( ) ( )( )
( ) ( )( )( )( )H
HH
HHH
Hfi
ZU
sm
ssmPU
=
++++−−=
+++
++−+−−=
2222
2222222
12exp
12
11
2
12exp
σφρµρ
σφρσφρµρ
so that
( ) ( )HH ZUMU =
Similarly, for firmL , the conditional distribution of the terminal cash flow is
( )( )22211 ,~ σφεφ LHL
LL sXmNZ +++
whilst the full information price is
[ ] [ ]
( )( )22211
11
2
1
2
1
σφρεφ
ρ
LLLL
LLLfi
sXm
ZVarZEP
+−++=
−=
and the ex-ante expected utility of the existing shareholder is calculated as
34
[ ] ( )( )
[ ] ( )
( ) ( ) ( ) ( )( )( )2222
222
222
2exp
21
2
σφρρ
σφ
σφρ
LL
LLfi
L
LLfi
LL
Lfi
smZUPUMU
sPVar
smPE
++−−===
+=
+−=
Consequently, it is again the case that ( )HMU is maximized by choosing 1−=Hφ and that
( )HMU will be maximized if 0=Lφ . Hence the following
Proposition 1.
In a mark to market hedge or deferral hedge accounting regime, there are no hedging
distortions.
Proof:
This follows immediately from the above discussion given that under a mark to market hedge or
a deferral hedge accounting regime, firmH is required to disclose information which enables
investors to distinguish between the two firms.
The intuition behind this result should be obvious. The only incentive for firmL to deviate from
its optimum position is so that it can be pooled with firmH - the requirement to separately
disclose either the two components of operating earnings or the deferral of the hedge gain or loss
35
means that such pooling will not occur and firmL will not wish to deviate. Since the only
incentive for firmH to deviate is to separate itself from firmL , firm H will also not wish to
deviate from its optimum position.
Suppose, however, that firm type is not public information at 1=t ; i.e., the market is unable to
make the distinction between the two firms - this will be the case under a mark to market
accounting regime. In this case, both firms will have the same market valuePat 1=t . In order to
calculate what this market value is, I need to again impose the condition that a potential new
investor is indifferent between an investment in the firm and an investment in the risk free asset.
LetZ denote the terminal cash flow accruing to this investor. Then, from the investor's
perspective, HZZ = with probability qand LZZ = with probability q−1 where
( )( ) ( )( )LH
H
qλθλθ
λθ−−+−
−=111
1
is the conditional probability that the firm is of typeH given that the existing shareholder is
selling.
Thus the indifference condition may be written as
( )[ ] ( ) ( )PPuZuE ρ−−== exp1
But
36
( )[ ] ( )[ ] ( ) ( )[ ]LH ZuEqZuqEZuE 111 1−+=
and soP is given by
( ) ( )( ) ( ) ( )( )Lfi
Hfi PqPqP ρρρ −−+−=− exp1expexp
Hence
( ) ( )[ ] ( ) ( ) ( )Lfi
Hfi PUqPqUPEPU −+=−= 1exp
Given this, I can now investigate whether hedging distortions will occur in the mark to market
accounting regime. My first result is:
Proposition 2.
In a mark to market accounting regime, there is no pooling equilibrium.
Proof:
Suppose that firmH has chosen φφ =H . Let ( )LHiU φφ , be the ex-ante expected utility of the
existing shareholder of firm i , given that the derivatives position chosen by firm )(LH is
( )LH φφ . Then firmL will choose φφ =L provided
37
( ) ( )0,, φφφ LL UU >
i.e. it will choose to mimic firmH rather than choose its own optimum if by doing so it can
increase the level of its shareholder's utility. Now:
( ) ( ) ( ) ( )
( ) ( )( ) ( ) ( )( )( ) ( )
( ) ( )( ) ( )( )( ) ( )
( ) ( ) ( )( )( )( )( )( ) ( )( )2222
2222
2exp11
12exp1
;111
;11
;;1,
σφρρλλσφρµρλ
φλλφλ
φλφφλ
φλφλφφ
++−+−−−
++++−−−=
+−−+−=
+−+−=
+−=
smq
smq
ZUqPqU
ZUPUqPqU
ZUPUU
LLL
HL
LLLHfi
L
LLLfi
Hfi
L
LLLL
whilst
( ) ( ) ( ) ( ) ( ) ( )222exp0;0;0;10, smZUZUPUU LLLLL
fiLL ρρλλφ +−−==+−=
Hence, dividing throughout by ( )222exp smL ρρ +−− , the condition for firmL to mimic can be
reduced to
( )( ) ( ) ( ) 1exp11exp 222222 <−+++− σφρσφρ∆ρ LL kk
where
38
( )
( )LH
LL
mm
qk
−+=∆
−=
2
1
µ
λ
Now denote the left hand side of this inequality by( )φf and note that
( ) ( ) ( ) 11exp0 22 <−++∆−= LL kkf σρρ
since by assumption 2ρσ>∆ .
Since ( )φf is a continuous function of φ with
( ) +∞=±∞→
φφ
flim
there is an open interval ( )βα,− (with 0, >βα ) over which ( ) 1<φf and firmL has the
incentive to deviate.
However, in order for ( )φφ , with ( )βαφ ,−∈ to be a pooling equilibrium, it must also be the
case that firmH has no incentive to deviate i.e.
( ) ( ) ( )ψφψφφφψφψ
;max,max, HHH ZUUU≠≠
=>
39
- in other words, given that firmL has chosenφ , firm H should mimic and also chooseφ since the
value of its objective function by doing so is higher than the maximum value it can achieve by
not mimicking.
Suppose that 1−≠φ . Then it is evident that firmH will wish to deviate since by doing so it can
achieve its unconstrained maximum and so )1,1( −− is the only potential pooling equilibrium. For
this to be feasible, I need 1>α i.e.
( ) ( ) ( ) ( ) 1exp1exp1 22 <−+∆−=− σρρ LL kkf
Now
( ) ( ) ( ) ( )
( ) ( )( ) ( ) ( )( )( ) ( )
( )( ) ( )( ) ( )( ) ( )
( )( ) ( )( )( )( ) ( )( )
( )( ) ( ) ( )( )22222
22
222
2exp12exp
2exp1
2exp11
1;1111
1;1111
1;1;11,1
smksmk
smq
smq
ZUqPUq
ZUPUqPqU
ZUPUU
HH
LH
HHH
LH
HHLLfi
H
HHLfi
Hfi
L
HHHH
ρµρσρρρµρλλσρρλ
λλλ
λλ
λλ
++−−−++−−=
++−+−−
++−−−−=
−+−+−−−=
−+−−+−−=
−+−−=−−
where
( )( )qk HH −−= 11 λ
40
Let
δφ +−= 1H
denote the position taken by firmH . Then
( ) ( ) ( )( )22222exp1; σδρµρδ +++−−=+− smZU HH
so that the condition for firmH not to deviate (and for )1,1( −− to be a pooling equilibrium) is
that for all 0≠δ
( ) ( )1,11; −−<+− HH UZU δ
or
( ) ( )( )
( )( ) ( ) ( )( )22222
2222
2exp12exp
2exp
smksmk
sm
HH
LH
H
ρµρσρρ
σδρµρ
++−−+++−
>+++−
i.e.
( )( ) ( ) ( ) 1exp11exp 222222 >−−+−+∆− σδρδσρρ HH kk
When 1=δ , the left hand reduces to
( ) ( ) ( ) ( ) 1expexp1exp 2222 <−<−−+∆− σρσρρ HH kk
41
where the first inequality again that follows from my assumption that 2ρσ∆ > .
Hence, in the mark to market accounting regime, there is no pooling equilibrium i.e. any
equilibrium will be separating. In other words, in all cases the benefits to firmL from being
pooled with firmH at 1=t are outweighed by the adverse effect of the increased variance of its
terminal cash flow.
The final question I need to address is whether these equilibria induce any hedging distortions. In
this regard, consider the following two propositions:
Proposition 3.
If αα≤≤1, then a mark to market accounting regime does not induce any hedging distortions.
Proof:
42
If 1≤α , then from the proof of the previous proposition, if firmH chooses its own optimum
1H −=φ , firm L has no incentive to deviate from its own optimum of zero. Consequently, the
unique separating equilibrium is
0ˆ
1ˆ
=
−=
L
H
φ
φ
i.e. both firms choose their own optima and there are no hedging distortions.
Proposition 4.
If αα>1 , then hedging distortions will occur under a mark to market accounting regime.
Proof:
Suppose that 1>α . By definition, if firmH were to choose 1−=Hφ , then firmL would choose
to mimic (and, as has been shown, this is not an equilibrium). In this case, the only potential
separating equilibria are ( )0,Hφ for ( ] [ )+∞∪−∞−=∈ ,, βαφ αβAH Since αβA∉−1 , this means
that whilst firm L chooses its own optimum of zero, firmH will deviate from its optimum of –1.
Proposition 5.
43
If hedging distortions occur in a mark to market accounting regime, they are of a overhedging
nature i.e. the position chosen by firm H is φφH = -αα with αα > 1.
Proof
Recall that the loss to firmH when deviating from its unconstrained optimum is
( )( ) ( ) ( )( )222222 2exp2exp σδρµρρµρ +++−−++− smsm HH
which increases as δ (the deviation from -1) increases; hence the candidate equilibria can be
reduced to ( )0,α− and ( )0,β . If 11 +>− βα then the latter will be the unique separating
equilibrium, whereas if 11 +=− βα both will be possible; finally, ( )0,α− will be the only
separating equilibrium if 11 +>− βα .
Suppose that 11 +≥− βα . Then 2−≤ αβ and ( ) 12 ≥−αf i..e.
( )( ) ( ) ( )( ) 12exp11exp 222222 ≥−−+−+∆− σαρσαρρ LL kk
By definition, ( ) 1=−αf or
( )( ) ( ) ( ) 1exp11exp 222222 =−+−+∆− σαρσαρρ LL kk
44
For both of the previous two equations to be compatible, it must be the case that ( ) 222 αα ≥− or
1≤α - this is obviously inconsistent with the condition for hedging distortions to occur in the
first place, namely that 1>α . Consequently, although a mark to market accounting regime may
induce hedging distortions, they do not involve firmH taking a “perverse” long derivatives
position – rather, the position chosen will still be of a hedging nature (i.e. negative) but will be
somewhat larger than the optimum position of –1.
To complete the analysis of the mark to market regime, I address two final questions. Firstly, are
there values of the model parameters for which α is indeed greater than 1? Secondly, how does
the equilibrium change as the parameters change?
To answer the first of these questions, recall that 1>α is equivalent to ( ) 11 <−f . To simplify
the notation, write
( ) ( ) ( ) ( )22exp1exp1 σρρ LL kkfD −+∆−=−=
Then the condition 1<D reduces to
( )( ) ( )∆−−
−>ρσρ
σρexpexp
1exp22
22Lk
45
and since ( ) ( )22exp1exp σρρ <<∆− , the right hand side of this inequality lies somewhere
between 0 and 1 i.e. there are indeed values of the model parameters for which the “distortion”
condition 1<D is satisfied.
In order to investigate the relationship between the nature of the equilibrium and the model
parameters, recall that ( )φf is defined by
( ) ( )( ) ( ) ( )222222 exp11exp σφρσφρρφ LL kkf −+++∆−=
where
( )( )( ) ( )( )
( )LH
LH
HLL
mm
k
−+=∆
−−+−−−=
2
111
11
µ
λθλθλλθ
For a fixed φ , we can regard this as a functionφf of the set of model parameters
22 ,,,,,,,, σρµλλθ smm LHLH=Ω . If we differentiate this with respect toµ , we have
( )( ) 01exp 222 <++∆−−=∂∂ σφρρρ
µ
φLk
f
i.e. a small increase inµ leads to a downward shift in the curve of ( )φf . The implication of this
result is that α , the solution to
46
( ) 0;1 >=− ααf
has increased – in other words, a small increase inµ leads to an increase in the magnitude of any
hedging distortion. This is intuitive – an increase inµ (the expected value of the market-wide
element of the high quality firm’s terminal operating cash flow) serves to widen the “quality
gap” between the two types of firm. This increases the incentives of the low quality firm to
mimic which in turn increases the extent of the hedging distortion needed to render such
mimicking counter-productive.
Similarly,
( )( )
( )( ) 01exp2
01exp2
222
222
>++∆−=∂∂
<++∆−−=∂∂
σφρρρ
σφρρρ
φ
φ
L
L
L
H
km
f
km
f
i.e. the magnitude of any hedging distortion is increasing/decreasing in the expected value of the
firm-specific element of the high/low quality firm’s terminal operating cash flow – the intuition
for these results is exactly the same as that for the response to small changes inµ .
Turning to the “risk” parameters in the model, we have:
47
( ) ( )( ) ( ) ( ) 0exp11exp1
0
22222222222
2
>−+++∆−+=∂∂
=∂∂
σφρφρσφρρφρσ
φ
φ
LL kkf
s
f
The result with respect to 2s is trivial – the decision of the low quality firm to mimic is
unaffected by the variance of the firm-specific element of firms’ terminal operating cash flows.
We would expect 2σ
φ
∂∂f
to be positive. Mimicking introduces unwanted volatility into the
terminal cash flow of the low quality firm, and so the higher 2σ is, the lower is the incentive to
mimic and the lower the hedging distortion needed to prevent such mimicking.
Next, note that
( )( ) ( )222222 exp1exp σφρσφρρφ
−++∆−=∂∂
Lk
f
This will be negative provided that
−∆< 1
2
122σρ
ρφ . Since by assumption 2ρσ>∆ , the right-
hand side of this inequality is positive – hence, it is certainly the case that for φ negative (the
region in which we are interested), Lk
f∂∂ φ
is negative.
To relate this to the basic model parameters, notice that
48
( ) ( ) ( )( )( )
( ) ( )( )[ ]( )
( ) ( )( ) 0111
1
0111
1
0111
11
2
2
2
<
−−+−
−−=∂∂
>−−+−
−=∂∂
>
−−+−
−−=∂∂
LH
H
L
L
LHH
L
LH
LH
L
k
k
k
λθλθλθ
λ
λθλθθθ
λ
λθλθλλ
θ
so that 0<∂∂
θ
φf, 0<
∂∂
H
fλ
φ
and 0>∂∂
L
fλ
φ
i.e. the magnitude of any hedging distortion increases as
either θ (the proportion of high quality firms) or Hλ (the probability that the shareholder of the
high quality firm retains her holding until 2=t ) increases but falls as Lλ (the probability that
the shareholder of the low quality firm retains her holding until 2=t ) increases. Once again,
these results are intuitively obvious. An increase in θ increases the market’s perceived
probability that a firm being sold at 1=t is high quality – this therefore increases the incentives
of the low quality firm to mimic, and the extent of the hedging distortion needed to dissuade the
low quality firm from mimicking in this way. The arguments with respect to Hλ and Lλ are
identical.
Finally, let us consider the impact of ρ (the risk aversion parameter). We have
( )( ) ( )( ) ( ) ( )2222222222 exp121exp12 σφρσρφσφρρσφρρ
φLL kk
f −+++∆−++∆−=∂∂
which increases as φ becomes increasingly negative and tends to ∞+ as −∞→φ .
Consequently, if it is positive at 1−=φ , it remains positive for all 1−≤φ i.e. an increase in the
49
risk aversion parameter will reduce the mimicking incentives and the hedging distortions. If,
however, it is negative at 1−=φ , it will remain negative up to some critical point 1* −<φ when
it will become positive. This result arises from the fact that mimicking increases both the
expected share price at 1=t and the volatility of the terminal payoff – given the assumption of a
negative exponential utility function, the benefit of the former effect (in terms of an increase in
expected utility) and the cost of the latter are both increasing inρ and so the overall effect is
ambiguous. This can be seen if we inspect the condition that the expression is positive at 1−=φ ,
namely
( ) ( ) ( )222 exp12exp σρρσρ LL kk −+∆−∆−
or
( )( )1
22exp2
1−
+∆−∆+< σρρ
ρLk
i.e. if the conditional probability of being able to sell at a higher price at 1=t is sufficiently low,
the incentive to mimic is decreasing in the risk aversion parameterρ .
4.6 Discussion
In the above analysis, I have shown that hedging distortions do not occur under a mark to market
hedge or deferral hedge accounting regime but may occur under a mark to market regime. It
50
would therefore seem that regulators such as the FASB should favor either variety of hedge
accounting if they wish to ensure that the accounting regime does not distort the economic
activity that it is designed to report. However, I would argue that this is somewhat of an
oversimplification.
To see this, let me first consider under what conditions hedge accounting is a feasible alternative.
Recall that the non-distortionary nature of such a regime is critically dependent upon the
assumption that firmH either reports separately the two components of its operating earnings or
discloses the fact that it has deferred its derivatives gain or loss - by doing so, investors are able
to distinguish it from firmL in the event that LH φφ = . If operating earnings or the deferral of the
hedge gain or loss are not disclosed in this way, investors are (informationally) in exactly the
same position as in the mark to market regime and distortions may occur. Let me now make the
seemingly plausible assumption that the FASB requires disclosure only of information which is
ex post verifiable; further, firms are also at liberty to make voluntarily any non-mandated
disclosure which is similarly verifiable. However, the FASB will neither require nor permit
disclosures which are ex post unverifiable - and penalizes such disclosures to an extent that firms
will never have the incentive to make them. Similar penalties also apply in respect of disclosures
which are ex post verifiable but untruthful. This is arguably rather a strong assumption but in
some sense is nothing more than an extension of the FASB's desire for financial statement
amounts to be “reliable”.
Given this assumption, it would seem reasonable to claim that hedge accounting is feasible only
if the systematic risk exposure of firmH can be verified ex post. This would be the case, for
51
example, if this exposure related to sales denominated in a foreign currency; ex post, the level of
these sales can be measured without error and it is easily checked whether or not a position in the
forward contract was initiated as a hedge against these sales. Suppose that the FASB mandated
mark to market accounting as the required regime. In this case, firmH could simply voluntarily
disclose that the derivatives position it holds was taken out as a hedge; given the assumption
above, investors will know that this disclosure is reliable and will therefore be able to perfectly
distinguish the two firms. Informationally, therefore, the mark to market regime together with the
ability to make voluntary disclosures regarding underlying exposures is equivalent to either
variety of hedge accounting and any hedging distortions are eliminated.
Suppose however that systematic risk exposure of firmH is ex post nonverifiable. Now, deferral
hedge accounting and mark to market hedge accounting (at least with separate disclosure of the
components of operating earnings) are simply not realistic options. Consequently, either mark to
market hedge accounting (with operating earnings reported only in total) or mark to market
accounting are the only viable alternatives and distortions may occur.
Hence, it is less the actual regime and more the information available to investors which is
crucial to determining whether or not distortions occur. Further, the information which can be
made available is highly dependent upon the nature (in particular, the ex post verifiability) of any
hedgeable risk exposure.
5. Summary and Conclusions
52
In this paper, I discuss the recent heated debate concerning how non-financial corporations
should report the results of their use of derivative financial instruments. Using the recently issued
SFAS 133 as a framework, I introduce three possible accounting regimes (mark to market hedge,
deferral hedge and mark to market) and described the information provided to investors in
financial statements under each of the three alternatives. I then introduce a simple economic
model with which to analyze both the motivation for hedging and how this motivation might be
affected by the financial reporting environment and showed that hedge distortions may occur
under a mark to market regime but not under a mark to market hedge or deferral hedge regime.
Finally, I discuss how these results were essentially driven by a single factor, namely whether or
not the existence or otherwise of a hedgeable risk exposure was ex post verifiable.
The bottom line is as follows. Given the ex post verifiability of this risk exposure, the accounting
regime chosen is essentially irrelevant provided that firms are allowed to make voluntary
disclosures - in this case, hedging distortions will not occur. Under the alternative scenario, only
mark to market hedge accounting (with operating earnings reported only in total) or mark to
market accounting are viable alternatives and distortions may occur. However, this conclusion
depends crucially on the assumption that voluntary disclosures by management form part of the
information set that investors use. The question as to whether investors do indeed behave in this
way is essentially an empirical one. Given that SFAS 133 will require firms to include “on
balance sheet” items which are currently disclosed but are “off balance sheet”, the introduction
of the standard effectively presents an opportunity to directly examine this very question - this is
an item for
future research.
53
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