Accounting for Financial Instruments
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Abstract This paper tries to analyze and compare the three different theories on financial instruments, namely Evidence Based Accounting Theory (EBAT), IASC Exposure Draft E62, and FASB Statement No.133. In the first section, I briefly discussed the Evidence Based Accounting Theory (EBAT) proposed by Smieliauskas [1996]. In this section, I tried to use EBAT to analyze and measure derivative securities (forward, futures and options). In the second section, I introduced the methodology of IASC Exposure Draft D62 - Financial Instruments: Recognition and Measurement. Then, in section three, I briefly introduced the underlying concepts of the FASB 133. Then, I illustrated the principles of recognition of derivatives and measurement of derivatives and hedged items in FASB 133. In the fourth section, I introduced another major critique of IASC E62 and FASB 133. In summary, EBAT is more consistent with the accounting and auditing framework. Table of Contents

Evidence Based Accounting Theory for Derivatives
Forward and Future Securities Analysis

Valuation at contract inception
Valuation during and at expiration of forward contract term
Analysis with EBAT
Illustration with EBAT
    Situation 1
    Situation 2
    Situation 3 Option Contracts At origination
Valuation during and at expiration of option contract term
EBAT Reasoning
    Payoff pattern of options
    Lognormal distribution
Illustration with EBAT
    Situation 1
    Situation 2
    Situation 3
Comparison of EBAT, IAC E62 and FASB 133
    Hedge Accounting IASC Exposure Draft E62 - Financial Instruments: Recognition and Measurement Scope
Initial Recognition and Measurement
Subsequent Measurement
Derecognition
In-Substance Defeasance
Hedge Accounting Statement of Financial Accounting Standards No. 133 Recognition and Measurement of Derivatives
Hedge Accounting Another Major Critique of Fair Value Accounting

Reference

Appendix 1 - Source code and illustration with mathematica for EBAT

appendix 2 -  Black-Scholes option pricing model with MS Excel 97

Appendix 3 - IASC exposure draft E62: Financial Instrument: Recognition and Measurement
 

Evidence Based Accounting Theory for Derivatives

Lam and Smieliauskas [1996] proposed a reporting model based on a concept of measurement which is dependent on what is verifiable. They integrated audit reasoning, accounting theory, and behavior finance theory into the Evidence Based Accounting Theory (EBAT) framework. In other words, they limited accounting measure to what is auditable.

The Evidence Based Accounting Theory (EBAT) can be summarized as follows:

In summary, if audited financial statements are to be made more useful for financial statement users they should treat all sources of forecast error consistently with respect to the risk associated with these errors. Since audit risk is the risk associated with misstatements, audit risk is the risk that should also be associated with omissions of material future events. Thus, the only material future events that should be omitted are those that have less than audit risk possibility of occurring. The accounting principle of conservatism suggests that this should be especially true of future events that have adverse consequences to the firm.

Smieliauskas [1998] classified the financial instruments into three regions. Region I: those that require recognition. Region II: those that do not require recognition, but should disclose. Disclosure is assumed needed because this region represents contingencies which while not recognized have sufficiently high probability of occurring that most people would consider it misleading if the item were not disclosed. Region III: those risks and uncertainties that do not require even disclosure because they are so remote.

In EBAT framework, we have the disclosure criteria and measurability criteria. Disclosable events are those with a cumulative after audit probability of material misstatement in excess of planned audit risk if the item were not disclosed. Measurable events are those which have the added condition that the posterior probability distribution of error without recording the event is such that one minus audit risk probability is within material amount of at least one point estimate.

Figure 1 shows conditions of events that are disclosable and measurable, because the probability of misstatement is less than audit risk if we record it as 10.

Figure 1 - Disclosable and Measurable Items

Figure 2 shows conditions of events that are disclosable but not measurable.

Figure 2 - Posterior Description of Items that is disclosable but not measurable.

The measurement issue from the auditor's point of view is that the point estimate cannot result in material differences from other possible values more than audit risk percentage of times (e.g., not more than audit risk probability of materially different outcomes). Therefore, whether to record, disclose, or not depends on three major factors for financial derivatives, namely, materiality, audit risk, and the probability distribution of the underlying assets.

In EBAT framework, probability of management intent is very important. If management intends to sell the financial instrument, then fair value may be more relevant. However, such probabilities of intent may be quite difficult to access.

In the next section, I will introduce forward and futures contracts first and analyze them using fair value accounting and EBAT respectively.

Forward and Future Securities Analysis

Forward contracts are negotiated between two parties to purchase and sell a specific quantity of a commodity, a foreign currency, or a financial instrument at a specified price, with delivery or settlement at a specified future date. Because forward contracts are not formally regulated by an organized exchange, each party to the contract is subject to the default of the other party.

Valuation at contract inception

Forward contracts are priced at-the-money at origination, which means that the fair value of the contracts is zero. The pricing formula at inception is calculating the agreed-upon forward price. Pricing concepts for forward contracts (excluding foreign exchange) are simple. The forward agreed-upon price is calculated based on the existing spot price, the interest cost of carrying the item over the term of the contract, storage costs, and any yield on the item. The interest cost or rate is determined by reference to the risk-free Treasury rate. The formula is as follows: Forward Price = [Spot price × (1 + interest rate + carrying costs – yield)] The yield refers to income that the holder of the underlying would receive, such as a dividend related to a common stock.

Foreign currency forward price calculations are complicated by the need to factor in the interest rate differential between two countries. The relationship between currency spot rates and currency forward rates is expressed by the following formula:

FXt = Spott (1 + R1t / 1 + R2t),
where FXt = Forward foreign exchange price (FX1/FX2) in period t
        Spott = Spot foreign exchange price (FX1/FX2) in period t
        R1t = Interest rate for country 1 in period t
        R2t = Interest rate for country 2 in period t. If this relationship did not hold, arbitrage opportunities would be present. Just as arbitrage arguments dictate the relationship between forward foreign exchange prices and interest rates, these relationships must also hold true for currency prices among countries. For example, assume the following interest rates for 90-day Treasury instruments:
 
U.S.
Japan
Annual rate 4.93% 0.48%
Quarterly rate 1.21% 0.12%
Spot rate 140.22 J¥ / U.S. $
Given these assumptions, the forward foreign exchange rate at the end of the first quarter must be:

FX = 140.22 × (1.0012/1.0121) = 138.71 J¥/U.S. $

If the forward foreign currency rate is higher or lower than 138.71 J¥/U.S. $, an investor could make alternative investment decisions and obtain a risk-free incremental (arbitrage) profit.

Valuation during and at expiration of forward contract term

The value after the forward contract is entered into is determined by four factors: A futures contract is a type of forward contract with highly standardized and closely specified contract terms. We usually value futures contracts using forward formula, because forward and futures prices are equal when interest rates are constant as proved by Hull [1997].

Analysis with EBAT

Under EBAT, the valuation of financial instruments highly depends on the materiality, audit risk, and probability distribution of the underlying assets. We need to estimate the probability distribution of the underlying assets, and estimate the point estimate. Then, we could compare the probability of misstatement if record at the point estimate.

Illustration with EBAT

We want to buy 1,000 gold forward contract at futures price of $440
Spot price of gold: $400
Interest rate: 10%
Future price of gold (for delivery in 1 year): F = S (1 + r) = 400 ´ (1 + 10%) = $440
Materiality = $10,000
Audit risk = 5%
Situation 1
The probability distribution of gold price in 1 year is normal distribution with mean of $440 and standard deviation of $5 (See Figure 3). Then the probability of $10 deviation from $440 is 4.55%. Therefore, if we record the 1,000 futures contract at $440, than the probability of material misstatement is only 4.55%. Therefore, we should record at $440. The following analysis is using MathematicaÒ Professional Programming Language as shown in Appendix 1.
Situation 2
The probability distribution of gold price in 1 year is normal distribution with mean of $440 and standard deviation of $10 (See Figure 4). Then the probability of $10 deviation from $440 is 31.73%. Therefore, if we record the 1,000 futures contract at $440, than the probability of material misstatement is 31.73%, which is greater than audit risk of 5%. Therefore, we should not record this asset and only disclose it.
Situation 3
The probability distribution of gold price in 1 year is normal distribution with mean of $440 and standard deviation of $180 (See Figure 5). Then the probability of $10 deviation from $440 is 95.57%. Therefore, if we record the 1,000 futures contract at $440, than the probability of material misstatement is 95.57%, which means not recording it wills result probability of material misstatement of 4.43% (less than audit risk of 5%). Therefore, we should not record or even disclose this asset.


Figure 3: Normal distribution with mean = 440 and standard deviation = 5

Figure 4: Normal distribution with mean = 440 and standard deviation = 10


Figure 5 - Normal distribution with mean = 440 and standard deviation = 180

Options Contract

In this section, I will introduce option contract first, and use Black-Scholes Option Pricing Model to analyze European options. Then, I use EBAT framework to analyze options.

The purchaser of an option has the right, but not the obligation, to buy or sell a specified quantity of a particular commodity, a foreign currency, or a financial instrument, at a specified price, during a specified period of time (American option) or on a specified date (European option). There are two types of option contracts, call options and put options.

Call options provide the holder the right to acquire an underlying at an exercise or strike price, throughout the option term. The holder pays a premium for the right to benefit from the appreciation in the underlying. Put options provide the holder the right to sell the underlying at an exercise or strike price, throughout the option term. The holder gains as the market price of the underlying falls below the strike price.

This fair value is composed of the following components:

 The intrinsic value of a call option on common stock, for example, is equal to the excess of the market price of the stock over the exercise price, times the specified number of shares of stock that can be purchased with the option. An option purchased at- or out-of-the-money has no value from the intrinsic value component of the option because it is zero. The intrinsic value of a put option on common stock is equal to the excess of the exercise price over the market price of the stock, times the specified number of shares that can be sold.

The combination of the effect of discounting and the volatility value of an option is commonly referred to as the time value because these components converge to a zero value as the option expires.

 An American option allows the holder to exercise at any time before expiration, whereas a European option allows exercise only at expiration of the contract. Because the American option gives its owner all the rights and privileges of a European option, plus the additional right to exercise anytime before expiration, the former would be worth at least as much as the latter before the expiration date is reached and in some cases is worth more.

At origination

The premium that a writer of an option receives and that the buyer pays is made up of the intrinsic value of the option and both components of the time value.

A common option pricing method uses the Black-Scholes Model. That model uses a complex mathematical formula that computes the value of an option at a given point in time. It can be applied without adjustment to both European options and American call options on stocks that do not pay dividends and is based on a number of highly limiting assumptions such as:

 As a result of the above restrictive assumptions, the original Black-Scholes Model did not accurately value options on dividend-paying stock. Therefore, the Model has been adjusted to reflect the impact of dividends. (However, another model, the Binomial Pricing Model, more accurately values American options on dividend-paying stocks, and is therefore also used to value options). A detailed discussion of option pricing formulas is beyond the scope of this paper. For a complete explanation of the option pricing models, please refer to Cox and Rubinstein (1985), Jarrow and Rudd (1983) and Hull (1997).

At a high-level view, it is important to recognize that the value of an option depends on the following basic variables:

IIASC Exposure Draft D62- Financial Instruments

The following is a summary of the key principles included in E62.

Scope

The Standard would apply to all companies whose securities are publicly traded. Rights and obligations rising under insurance contracts would be excluded, but derivatives embedded in insurance contracts would be included. An enterprise's own equity instruments would also be excluded, but a derivative that can be settled in cash or in the enterprise's shares, at the issuer's option, is not an equity instrument. Commodity contracts that can be settled for cash and that are not entered into to meet the enterprise's normal inventory needs would be treated as financial instruments.

Initial Recognition and Measurement

All financial assets and financial liabilities would be recognized on the balance sheet, including all derivatives.

The initial measurement of all financial assets and liabilities, including derivatives, would be at the fair value of consideration paid or received. This is no different from any other asset. Transaction costs would be included for those financial assets that will subsequently be carried at amortized cost; transaction costs would be excluded for those financial assets that will subsequently be re-measured to fair value (see below).

Subsequent Measurement

Subsequent measurement of all financial assets would be at fair value, except that the following would be at amortized cost:

Fixed maturity securities (debt, loans, receivables, and mandatorily redeemable preferred shares) that the enterprise has the intent and ability to hold to maturity, and those financial assets for which fair value cannot be reliably measured. Those financial assets should be measured at amortized cost using the effective interest rate method (with fixed maturity) or cost (without fixed maturity).

The Standard would impose strict tests for intent and ability to hold a security to its fixed maturity. Within a broad category of fixed maturity securities, a single sale of prior to maturity would call into question the enterprise's intent to hold the rest of that category of securities to maturity.

Subsequent measurement of all financial liabilities except derivatives and liabilities held for trading purposes would be at the original recorded amount less amortization of any premium or discount. Derivatives and trading liabilities, however, would be re-measured to fair value.

For those financial assets and liabilities that are re-measured to fair value, an enterprise would have the option either to:

Recognize the entire adjustment in net profit or loss for the period, or recognize in net profit or loss for the period only the portion of the adjustment relating to securities held for short-term trading, with the remainder of the adjustment reported as a separate component of equity until the financial asset is sold or liability is extinguished, at which time the realized gain or loss would then be reported in net profit or loss.

For financial assets carried at amortized cost, a strict asset impairment test would apply, with the impairment write-down to net profit or loss and reversal of impairment to net profit or loss, up to cost. Impairment is the difference between carrying amount and estimated recoverable amount (present value of cash flows discounted at the loan's original effective interest rate).

Derecognition

An enterprise should remove a financial asset from its balance sheet ('derecognize' the asset) when it realizes the benefits from that asset or surrenders or loses control of the rights inherent in the asset. An enterprise should derecognize a financial liability when it is extinguished or when primary responsibility is transferred to another party.

If a financial asset or liability is sold or transferred, the difference between the carrying amount of the asset or liability sold and the proceeds is included in net profit or loss.

If part of a financial asset or liability is sold or extinguished, the carrying amount is split based on relative fair values. If fair values are not determinable, a cost recovery approach to profit recognition is taken. Similar treatment is required if a new financial asset or liability is created as a result of a transfer. The standard would provide guidance on when fair value is reliably measurable.

In-Substance Defeasance

The proposal would propose to prohibit "in-substance defeasance accounting", a practice that has come to be applied when an enterprise transfers essentially risk-free assets to an irrevocable defeasance trust. The cash flows from those assets, which closely approximate the scheduled interest and principal payments of a specified financial liability, are earmarked for such payments, but the creditor does not release the enterprise from its primary obligation. Under in-substance defeasance accounting, the liability would be treated as having been extinguished. Under the draft proposal, however, the enterprise would not remove the liability from its balance sheet but, rather, would continue to report both the assets in the trust and the liability on its balance sheet.

Hedge Accounting

Hedging involves designating a derivative or other financial instrument whose value or cash flows are expected to move inversely and approximately proportionately with changes in the value or cash flows of an asset or liability, a firm commitment, or an uncommitted but probable future transaction to offset the change in the value or cash flows of the hedged item. Hedge accounting means recognizing and measuring the hedging instrument and related item being hedged on symmetrical bases, so that offsetting gains and losses are reported in income in the same periods.

Under the draft interim standard, hedge accounting would be permitted in certain circumstances, provided that the hedging relationship is clearly defined, measurable, and actually effective. Guidance is provided on when a hedge is effective.

For a fair value hedge of an existing asset or liability using a derivative, any gain or loss on the hedging instrument and on the hedged item would be included in net profit or loss for the period. The carrying amount of the hedged item is adjusted even if that asset or liability is otherwise carried at cost.

For a cash flow hedge of an existing asset or liability, a commitment, or an uncommitted forecasted transaction, the gain or loss on the hedging instrument is reported as a separate component of equity until the hedged transaction affects net profit or loss. In the case of a hedge of a forecasted asset or liability acquisition, a key question, still to be resolved, is whether the amount reported as a separate component of equity becomes part of cost of the asset or liability at the time it is actually acquired (sometimes called 'basis adjustment'), or whether it remains a separately amortizable component of equity.

FASB 133 - Accounting for Derivatives

FASB 133 gives a definition for a derivative instrument as a financial instrument or other contract with all three of the following characteristics:
        • It has (1) one or more underlyings and (2) one or more notional amounts or payment provisions or both. Those terms determine the amount of the settlement or settlements, and, in some cases, whether or not a settlement is required.
        • It requires no initial net investment or an initial net investment that is smaller than would be required for other types of contracts that would be expected to have a similar response to changes in market factors.
        • Its terms require or permit net settlement, it can readily be settled net by a means outside the contract, or it provides for delivery of an asset that puts the recipient in a position not substantially different from net settlement.
In developing the standards in FASB 133, the Board concluded that the following four fundamental decisions should serve as cornerstones underlying those standards:
The FASB 133 standardizes the accounting for derivative instruments, including certain derivative instruments embedded in other contracts, by requiring that an entity recognize those items as assets or liabilities in the statement of financial position and measure them at fair value. In addition, if certain conditions are met, an entity may elect to designate a derivative instrument as follows:
FASB 133 generally provides for matching the timing of gain or loss recognition on the hedging instrument with the recognition of (a) the changes in the fair value of the hedged asset or liability that are attributable to the hedged risk, or (b) the earnings effect of the hedged forecasted transaction.

Recognition and Measurement of Derivatives

An entity shall recognize all of its derivative instruments in its statement of financial position as either assets or liabilities depending on the rights or obligations under the contracts. All derivative instruments shall be measured at fair value. The guidance in FASB Statement No. 107, Disclosures about Fair Value of Financial Instruments, as amended by FASB 133, shall apply in determining the fair value of a financial instrument (derivative or hedged item). If expected future cash flows are used to estimate fair value, those expected cash flows shall be the best estimated based on reasonable and supportable assumptions and projections. All available evidence shall be considered in developing estimates of expected future cash flows. The weight given to the evidence shall be commensurate with the extent to which the evidence can be verified objectively. If a range is estimated for either the amount or the timing of possible cash flows, the likelihood of possible outcomes shall be considered in determining the best estimate of future cash flows.

Hedge Accounting

The accounting for changes in the fair value (that is, gains or losses) of a derivative depends on whether it has been designated and qualifies as part of a hedging relationship and, if so, on the reason for holding it. Either all or a proportion of a derivative may be designated as the hedging instrument. The proportion must be expressed as a percentage of the entire derivative so that the profile of risk exposures in the hedging portion of the derivative is the same as that in the entire derivative. Alternatively, two or more derivatives, or proportions thereof, may also be viewed in combination and jointly designated as the hedging instrument. Gains and losses on derivative instruments are accounted for as follows:

Another Major Critique of Fair Value Accounting

One of the major critiques of fair value accounting for financial instruments is proposed by the financial services industry. As pointed out by Paul Salfi, "Accounting policy makers are pushing for fair value before demonstrating that it is the right answer".

In 1993, the Group of Thirty (G30) - a worldwide group of representatives from industry, law, accounting, academia, and the public sector - built a framework of practices and principles for derivatives. It quickly became an industry standard as financial institutions used it to re-evaluate internal controls for derivatives trading and risk management activities. US banking regulators used it as a basis for guidance. Today, it still provides a comprehensive introduction to derivative activities and internal controls.

However, G30 recommendations unfulfilled the accounting policy for derivatives, instead, G30 recommended:

 Different from G30 recommendation, FASB developed SFAS 133, which requires fair value accounting for derivatives and hedging. FASB 133 is different from the practices of most financial institutions - the largest providers and users of derivatives. In Salfi [1998]'s opinion, the biggest drawbacks of FASB 133 are as follows: There is concern that FASB may be leading the EASC astray. The IASC proposes adopting most of FASB 133 in IAC E62. It also proposes to use the framework of FASB 115: Accounting for Certain Investments in Debt and Equity Securities.

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