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: rbarnes@london.edu

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.

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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

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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.

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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

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“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”.

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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.

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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.

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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

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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.”

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(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

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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

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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).

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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.

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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

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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

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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

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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

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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.

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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.

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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 .

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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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