Exhibit 4

FAS 138 Benchmark Interest Value-Locked Debt Accounting Case:
Glossary of Key Terms

Bob Jensen at Trinity University

This is a very small subset of Bob Jensen's large FAS 133 and IAS 39 Glossary.  That large Glossary can be accessed at http://www.trinity.edu/rjensen/acct5341/speakers/133glosf.htm

Amortization of Basis Adjustments
In Example 2 of Appendix B of FAS 133, you will see values for "Amortization of Basis Adjustments" in the table in Paragraph 117.  These are simply put into the table, along with "Interest Accrued" amounts without any explanation from the FASB as to how to calculate those values or what they really mean.  In the Excel workbook accompanying this case you can trace how they are calculated and how they impact the journal entries.  They seem to add more confusion than they benefit users of financial statements since the amortization amounts have to be reset each year due to changing benchmarked carrying values of the debt.

The theory behind the amortization of basis adjustments is that, whenever carrying value of debt is revalued due to changes in benchmark rates, that change in value should be amortized over the remaining life of the debt rather than be charged each period.  Thus the change in the value of the debt due to changed benchmark rates can be amortized using the PMT function in Excel to compute the payment for each remaining period that will amortize that change in value.  As indicated above, however, the amortization must be reset each period that the rates change.

In the Excel workbook you are allowed to view the journal entries with or without the amortization of basis adjustments.  Basis adjustment in this case is simply a fancy way of saying that the i(t) index upon which carrying value of debt is being revalued changes and requires an adjustment in the carrying value.  In Excel, you can use the PMT function to compute the amortization each period as a function of the i(t) ex post benchmarked interest rate index, the I(t-1)-I(t) change in the value of the debt that is being amortized, and the number of periods remaining to maturity.  However, this PMT amount is only used one time, because the amortization amount (PMT) must be reset every period for changes in the i(t) index.

Benchmark Interest Rate =

FAS 138 Amendments expand the eligibility of many derivative instrument hedges to qualify FAS 133/138 hedge. Such qualifications in accounting treatment that reduces earnings volatility when the derivatives are adjusted for fair value. 

The term "swap spread" applies to the credit component of interest rate risk.  Assume a U.S. Treasury bill rate is a  risk-free rate.  You can read the following at http://www.cbot.com/ourproducts/financial/agencystrat3rd.html 

The swap spread represents the credit risk in the swap relative to the corresponding risk-free Treasury yield. It is the price tag on the actuarial risk that one of the parties to the swap will fail to make a payment. The Treasury yield provides the foundation in computing this spread, because the U.S. Treasury is a risk-free borrower. It does not default on its interest payments.

Since the swap rate is the sum of the Treasury yield and the swap spread, a well-known statistical rule breaks its volatility into three components:

Swap Rate Variance = Treasury Yield Variance
                                    + Swap Spread Variance
                                    + 2 x Covariance of Treasury Yield and Swap Spread

Taken over long time spans (e.g., quarter-to-quarter or annual), changes in the 10-year swap spread exhibit a small but reliably positive covariance with changes in the 10-year Treasury yield. For practical purposes this means that as Treasury yield levels rise and fall over, say, the course of the business cycle, the credit risk in interest rate swaps tends to rise and fall with them.

However as Figure 1 illustrates, high-frequency (e.g., day-to-day or week-to-week) moves in swap spreads and Treasury yields tend to be uncorrelated. Their covariance is close to zero. Thus, for holding periods that cover very short time spans, this stylized fact allows simplification of the preceding formula into the following approximation:

 

This rule of thumb allows attribution of the variability in swap rates in ways that are useful for hedgers. For example, during the five years from 1993 through 1997, 99% of week-to-week variability in 10-year swap rates derived from variability in the 10-year Treasury yield. Variability in the 10-year swap spread accounted for just 1%.

It is very popular in practice to have a hedging instrument and the hedged item be based upon two different indices.  In particular, the hedged item may be impacted by credit factors.  For example, interest rates commonly viewed as having three components noted below:

·        Risk-free risk that the level of interest rates in risk-free financial instruments such as U.S. Treasury T-bill rates will vary system-wide over time.

·        Credit sector spread risk that interest rates for particular economic sectors will vary over and above the risk-free interest rate movements.  For example, when automobiles replaced horses as the primary means of open road transportation, the horse industry’s credit worthiness suffered independently of other sectors of the economy.  In more recent times, the dot.com sector’s sector spread has suffered some setbacks.  In this case of interest rate swaps, this is the swap spread defined above.

·        Unsystematic spread risk of a particular borrower that varies over and above risk-free and credit sector spreads.  The credit of a particular firm may move independently of more system-wide (systematic) risk-free rates and sector spreads.

Suppose that a hedge only pays at the Treasury rate for hedged item based on some variable index having credit components.  FAS 133 prohibited “treasury locks” that hedged only the risk-free rates but not credit-sector spreads or unsystematic risk.  This was upsetting many firms that commonly hedge with treasury locks.  There is a market for treasury lock derivatives that is available, whereas hedges for entire interest rate risk are more difficult to obtain in practice.  It is also common to hedge with London’s LIBOR that has a spread apart from a risk-free component.

The DIG confused the issue by allowing both risk-free and credit sector spread to receive hedge accounting in its DIG Issue E1 ruling.  Paragraph 14 of FAS 138 states the following:

Comments received by the Board on Implementation Issue E1 indicated (a) that the concept of market interest rate risk as set forth in Statement 133 differed from the common understanding of interest rate risk by market participants, (b) that the guidance in the Implementation Issue was inconsistent with present hedging activities, and (c) that measuring the change in fair value of the hedged item attributable to changes in credit sector spreads would be difficult because consistent sector spread data are not readily available in the market. 

In FAS 138, the board sought to reduce confusion by reducing all components risk into just two components called “interest rate risk” and “credit risk.”  Credit risk includes all risk other than the “benchmarked” component in a hedged item’s index.  A benchmark index can include somewhat more than movements in risk-free rates.  FAS 138 allows the popular LIBOR hedging rate that is not viewed as being entirely a risk-free rate.  Paragraph 16 introduces the concept of “benchmark interest rate” as follows:

Because the Board decided to permit a rate that is not fully risk-free to be the designated risk in a hedge of interest rate risk, it developed the general notion of benchmark interest rate to encompass both risk-free rates and rates based on the LIBOR swap curve in the United States.

FAS 133 thus allows benchmarking on LIBOR.  It is not possible to benchmark on such rates as commercial paper rates, Fed Fund rates, or FNMA par mortgage rates.

Readers might then ask what the big deal is since some of the FAS 133 examples (e.g., Example 5 beginning in Paragraph 133) hedged on the basis of LIBOR.  It is important to note that in those original examples, the hedging instrument (e.g., a swap) and the hedged item (e.g., a bond) both used LIBOR in defining a variable rate.  If the hedging instrument used LIBOR and the hedged item interest rate was based upon an index poorly correlated with LIBOR, the hedge would not qualify (prior to FAS 138) for FAS 133 hedge accounting treatment even though the derivative itself would have to be adjusted for fair value each quarter.  Recall that LIBOR is a short-term European rate that may not correlate with various interest indices in the U.S.  FAS 133 now allows a properly benchmarked hedge (e.g., a swap rate based on LIBOR or T-bills) to hedge an item having non-benchmarked components.

The short-cut method of relieving hedge ineffectiveness testing may no longer be available.  Paragraph 23 of FAS 138 states the following:

For cash flow hedges of an existing variable-rate financial asset or liability, the designated risk being hedged cannot be the risk of changes in its cash flows attributable to changes in the benchmark interest rate if the cash flows of the hedged item are explicitly based on a different index.  In those situations, because the risk of changes in the benchmark interest rate (that is, interest rate risk) cannot be the designated risk being hedged, the shortcut method cannot be applied.  The Board’s decision to require that the index on which the variable leg of the swap is based match the benchmark interest rate designated as the interest rate risk being hedged for the hedging relationship also ensures that the shortcut method is applied only to interest rate risk hedges.  The Board’s decision precludes use of the shortcut method in situations in which the cash flows of the hedged item and the hedging instrument are based on the same index but that index is not the designated benchmark interest rate.  The Board noted, however, that in some of those situations, an entity easily could determine that the hedge is perfectly effective.  The shortcut method would be permitted for cash flow hedges in situations in which the cash flows of the hedged item and the hedging instrument are based on the same index and that index is the designated benchmark interest rate.

In other words, any hedge item that is not based upon only a benchmarked component will force hedge effectiveness testing at least quarterly.  Thus FAS 138 broadened the scope of qualifying hedges, but it made the accounting more difficult by forcing more frequent effectiveness testing.

FAS 138 also permits the hedge derivative to have more risk than the hedged item.  For example, a LIBOR-based interest rate swap might be used to hedge an AAA corporate bond or even a note rate based upon T-Bills.

There are restrictions noted in Paragraph 24 of FAS 138:

This Statement provides limited guidance on how the change in a hedged item’s fair value attributable to changes in the designated benchmark interest rate should be determined.  The Board decided that in calculating the change in the hedged item’s fair value attributable to changes in the designated benchmark interest rate, the estimated cash flows used must be based on all of the contractual cash flows of the entire hedged item.  That guidance does not mandate the use of any one method, but it precludes the use of a method that excludes some of the hedged item’s contractual cash flows (such as the portion of interest payments attributable to the obligor’s credit risk above the benchmark rate) from the calculation.  The Board concluded that excluding some of the hedged item’s contractual cash flows would introduce a new approach to bifurcation of a hedged item that does not currently exist in the Statement 133 hedging model.

Derivative Financial Instrument =

a financial instrument that by its terms, at inception or upon the occurrence of a specified event, provides the holder (or writer) with the right (or obligation) to participate in some or all of the price changes of an underlying (that is, one or more referenced financial instruments, commodities, or other assets, or other specific items to which a rate, an index of prices, or another market indicator is applied) and does not require that the holder or writer own or deliver the underlying.  A contract that requires ownership or delivery of the underlying is a derivative financial instrument if (a) the underlying is another derivative, (b) a mechanism exists in the market (such as an organized exchange) to enter into a closing contract with only a net cash settlement, or (c) the contract is customarily settled with only a net cash payment based on changes in the price of the underlying.  What is most noteworthy about derivative financial instruments is that in the past two decades, the global use of derivatives has exploded exponentially to where the trading in notional amounts is in trillions of dollars.  Unlike FAS 133, IAS 39 makes explicit reference also to an insurance index or catastrophe loss index and a climatic or geological condition. 

 The FASB provides a free 95-page document that defines derivatives in greater detail and provides summaries of various types of derivatives.  The document can be downloaded from "Summary of Derivatives Types from FASB" at http://www.rutgers.edu/Accounting/raw/fasb/derivsum.exe.  A somewhat simpler definition is given at http://www.finpipe.com/derivatives.htm (I recommend visiting that website to learn more about derivatives and how they are used.)

A derivative financial product is a contrived instrument, the value of which depends indirectly on the price of a cash instrument. The price of the cash instrument is referred to as the "underlying" price, quite often. Examples of cash instruments include actual shares in a company, physical stocks of commodities, cash foreign exchange, etc.

Why use derivatives and not just cash instruments? Derivatives exist to solve specific positioning, accounting and regulatory problems.

Recommended Tutorials on Derivative Financial Instruments (but not about FAS 133 or IAS 39)

• You might start at http://www.finpipe.com/derivatives.htm.  
  
  

• Then you can try Financial Derivatives in Plain English --- http://www.iol.ie/~aibtreas/derivs-pe/ 
  
  

• For details on products and how they work in practice, I like the following tutorial/education websites:

CBOE --- http://www.cboe.com/education/ 

CBOT --- http://www.cbot.com/ourproducts/index.html 

CME --- http://www.cme.com/educational/index.html 

Recommended Tutorials on FAS 133

• The Appendix B examples in FAS 133.  You can also download Excel worksheet tutorials on the first 10 examples in files 133ex01a.xls through 133ex10.xls at http://www.cs.trinity.edu/~rjensen/ 
  Instructions are given at http://www.cs.trinity.edu/~rjensen/13300tut.htm 
  
  

• Bob Jensen's cases indexed at http://www.trinity.edu/rjensen/caseans/000index.htm 
  
  

• The FASB's CD-ROM Self-Study CPE Training Course and Research Tool http://www.rutgers.edu/Accounting/raw/fasb/CDROM133.html 
  
  

• Summary of Derivatives Types from FASB at http://www.rutgers.edu/Accounting/raw/fasb/derivsum.exe 
  
  

• The FASB provides some new examples illustrating the FAS 138 Amendments to FAS 133 at http://www.rutgers.edu/Accounting/raw/fasb/derivatives/examplespg.html
  
  

• Implementation Guidelines on IAS 39 --- http://www.iasc.org.uk/frame/cen2_139.htm 
  
  

• The excellent tutorials entitled Introductory Cases on Accounting for Derivative Instruments and Hedging Activities by Walter R. Teets and Robert Uhl available free from http://www.gonzaga.edu/faculty/teets/index0.html.
  
  

• Accounting Firm Helpers
  
  • KPMG Book  Derivatives and Hedging Handbook issued by KPMG Peat Marwick LLP in July 1998). The book in hard copy or PDF versions can be ordered at http://www.us.kpmg.com/fs/publications/banking/deriv.html.
    
  • PwC Book that I cannot find an online reference to is the PricewaterhouseCoopers book entitled A Guide for Derivative Instruments and Hedging Activities.   PwC also has a book entitled FAS 133:  New Rules for Derivatives by Robert Sullivan and Lou Le Guyader. Another PwC book is entitled Derivatives and the Internal Auditor. You can order all PwC books and other risk publications at http://www.riskpublications.com/. 

Recommended Glossaries

Bob Jensen's FAS 133 Glossary on Derivative Financial Instruments and Hedging Activities

Also see comprehensive risk and trading glossaries such as the ones listed below that provide broader coverage of derivatives instruments terminology but almost nothing in terms of FAS 133, FAS 138, and IAS39:

• http://risk.ifci.ch/SiteMap.htm
  
  

• http://www.margrabe.com/Dictionary.html 
  
  

• http://www.adtrading.com/glossary/glossary.htm
  
  

• Related glossaries are listed at http://www.trinity.edu/rjensen/bookbus.htm 

A nonderivative financial instrument fails one or more of the above tests to qualify as a derivative in FAS 133.  Nonderivatives do not necessarily have to be adjusted to fair value like derivative instruments.  However, they may be used for economic hedges even though they do not qualify for special hedge accounting under FAS 133.  Exceptions in FAS 133 that afford special hedge accounting treatment for nonderivative instruments that hedge foreign currency fair value and/or hedge foreign currency exposures of net investment in a foreign operation.  See FAS Paragraphs 6c, 17d, 18d, 20c, 28d, 37, 39, 40, 42, 44, 45, 246, 247, 255, 264, 293-304, 476, 477, and 479.  Also see foreign currency hedge.

It is important to note that all derivatives in finance may not fall under the FAS 133 definition.  In FAS 133, a derivative must have a notional, an underlying, and net settlement.  There are other requirements such as a zero or minimal initial investment as specified in Paragraph 6b and Appendix A Paragraph 57b of FAS 133 and Paragraph 10b of IAS 39.  Examples of derivatives that are explicitly excluded are discussed in Paragraph 252 on Page 134 of FAS 133.  Paragraph 10c of IAS 39 also addresses net settlement.  IASC does not require a net settlement provision in the definition of a derivative.  To meet the criteria for being a derivative under FAS 133, there must be a net settlement provision.  

For a FAS 133 flow chart, go to http://www.trinity.edu/rjensen/acct5341/speakers/133flow.htm

There must also be zero or small net investment to meet the definition of a derivative financial instrument  (FAS 133 Paragraphs 6b and Appendix A Paragraph 57b.  Also see IAS 39 IAS 39: Paragraph 10b)

Also see other DIG issues under net settlement.

Paul Pacter states the following at http://www.iasc.org.uk/news/cen8_142.htm 

IAS 39 A derivative is a financial instrument— (a) - whose value changes in response to the change in a specified interest rate, security price, commodity price, foreign exchange rate, index of prices or rates, a credit rating or credit index, or similar variable (sometimes called the ‘underlying’); (b) - that requires no initial net investment or little initial net investment relative to other types of contracts that have a similar response to changes in market conditions; and (c) - that is settled at a future date.

FAS 133 (a) – same as IAS 39 (b) – same as IAS 39 (c) – FASB definition requires that the terms of the derivative contract require or permit net settlement.

FAS 133 Paragraph 408 reads as follows:

The Board recognizes that entities are commonly exposed to a variety of risks in the course of their activities, including interest rate, foreign exchange, market price, credit, liquidity, theft, weather, health, catastrophe, competitive, and business cycle risks. The Exposure Draft did not propose detailed guidance on what risks could be designated as being hedged, other than to note in the basis for conclusions that special hedge accounting for certain risk management transactions, such as hedges of strategic risk, would be precluded. In redeliberating the issue of risk, the Board reaffirmed that hedge accounting cannot be provided for all possible risks and decided to be more specific about the risks for which hedge accounting is available.

Various exceptions are dealt with in Paragraph 58 of FAS 133.  For example, Paragraph 58c reads as follows:

Certain contracts that are not traded on an exchange. A contract that is not traded on an exchange is not subject to the requirements of this Statement if the underlying is:

(1) A climatic or geological variable or other physical variable. Climatic, geological, and other physical variables include things like the number of inches of rainfall or snow in a particular area and the severity of an earthquake as measured by the Richter scale.

(2) The price or value of (a) a nonfinancial asset of one of the parties to the contract unless that asset is readily convertible to cash or (b) a nonfinancial liability of one of the parties to the contract unless that liability requires delivery of an asset that is readily convertible to cash.

(3) Specified volumes of sales or service revenues by one of the parties. That exception is intended to apply to contracts with settlements based on the volume of items sold or services rendered, for example, royalty agreements. It is not intended to apply to contracts based on changes in sales or revenues due to changes in market prices.

If a contract's underlying is the combination of two or more variables, and one or more would not qualify for one of the exceptions above, the application of this Statement to that contract depends on the predominant characteristics of the combined variable. The contract is subject to the requirements of this Statement if the changes in its combined underlying are highly correlated with changes in one of the component variables that would not qualify for an exception.

Also see "regular-way" security trading exceptions in Paragraph 58a if FAS 133.  Also note the exception in DIG C1.  Some general DIG exceptions to the scope of FAS 133 are listed in the "C" category at http://www.rutgers.edu/Accounting/raw/fasb/derivatives/issuindex.html 

DIG exceptions at http://www.rutgers.edu/Accounting/raw/fasb/derivatives/issuindex.html  Section C: Scope Exceptions *Issue C1—Exception Related to Physical Variables (Cleared 02/17/99) *Issue C2—Application of the Exception to Contracts Classified in Temporary Equity (Cleared 02/17/99) *Issue C3—Exception Related to Stock-Based Compensation Arrangements (Cleared 02/17/99) *Issue C4—Interest-Only and Principal-Only Strips (Cleared 02/17/99) *Issue C5—Exception Related to a Nonfinancial Asset of One of the Parties (Cleared 02/17/99) *Issue C6—Derivative Instruments Related to Assets Transferred in Financing Transactions (Cleared 03/31/99) *Issue C7—Certain Financial Guarantee Contracts (Cleared 07/28/99) *Issue C8—Derivatives That Incorporate an Underlying on the Issuer's Equity Price (Released 10/99)

A nice review of the theory and application (aside from accounting) of derivative financial instruments appears in Myron Scholes' Nobel lecture that is reprinted as "Derivatives in a Dynamic Environment," American Economic Review, June 1998, 350-370.   Types of embedded derivative  instruments are often indexed debt and investment contracts such as commodity indexed interest or principal payments, convertible debt, credit indexed contracts, equity indexed contracts, and inflation indexed contracts.  By "indexed" it is meant that an uncertain economic event that is measured by an economic index (e.g., a credit rating index, commodity price index, convertible debt, or inflation index) defined in the contract.  An equity index might be defined as a particular index derived from common stock price movements such as the Dow Industrial Index or the Standard and Poors 500 Index.   Derivative instruments may also be futures contracts, forward contracts, interest rate swaps, foreign currency derivatives, warrants, forward rate agreements, basis swaps,  and complex combinations of such contracts such as a circus combination.    Interest rate swaps are the most common form of derivatives in terms of notional amounts.  There are Paragraph 6b initial investment size limitations discussed under the term premium.

Derivatives that are covered by FAS 133 accounting rules must remeasured to fair value on each balance sheet date.  Paragraph 18 on Page 10 of FAS 133 outlines how to account gains and losses on derivative financial instruments designated for FAS 133 accounting.  See hedge accounting.

FAS 133 does not change the requirement banning the netting of assets and liabilities in the balance sheet (statement of financial position) unless there is a right of  setoff.  This rule goes back to APB 10, Omnibus Opinion.  Hence the aggregate of positive valued derivative financial instruments cannot be netted against those with negative values.  The only exception would be when there are contractual rights of offset.  FAS 133 is silent as to whether derivatives expiring in the very near future are cash equivalents in the cash flow statement.  KPMG argues against that in terms of SFAS 95 rules.  See Example 6 beginning on Page 347 of of the Derivatives and Hedging Handbook issued by KPMG Peat Marwick LLP in July 1998.

FAS 133 requires disclosures of hedging gains and losses by risk type.  Paragraph 45 on beginning on Page 27 does require that aggregate net amounts be reported by type of hedge.  Disclosure by market risk category is required by the SEC. 

In this FAS 133 Glossary, there are added conditions to become a qualified derivative financial instrument under FAS 133 rules.   In certain instances a nonfinancial derivative will also suffice for accounting under FAS 133 rules.  Unless noted otherwise it will be assumed that such instruments meet the FAS 133 criteria.  The formal definition of a derivative financial instrument for purposes of FAS 133 is given in Paragraph 249 on Page 133.  Such an instrument must have all three of the following attributes:

a. 
It has (1) one or more underlyings and (2) one or more notional amounts or payment provisions or both.

b.
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.

c.
Its terms require or permit net settlement, it can readily be settled net by 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.

Initial investment is an important criterion for distinguishing a derivative instrument from a nonderivative instrument.  See Paragraph 6b on Page 3 of FAS 133.  Paragraph 256 on Page 135 contains the following example:

A party that wishes to participate in the changes in the fair value of 10,000 shares of a specific marketable equity security can, of course, do so by purchasing 10,000 shares of that security.  Alternatively, the party may enter into a forward purchase contract with a notional amount of 10,000 shares of that security and an underlying that is the price of that security. Purchasing the shares would require an initial investment equal to the current price for 10,000 shares and would result in benefits such as the receipt of dividends (if any) and the ability to vote the shares. A simple forward contract entered into at the current forward price for 10,000 shares of the equity instrument would not require an initial investment equal to the notional amount but would offer the same opportunity to benefit or lose from changes in the price of that security.

Paragraph 10c of IAS 39 also addresses net settlement.  IASC does not require a net settlement provision in the definition of a derivative.  To meet the criteria for being a derivative under FAS 133, there must be a net settlement provision.  

In FAS 133, derivative financial instruments come in three basic types that are listed in Paragraph 4 on Page 2 of FAS 133:

Paragraph 4 on Page 2 of FAS 133.
This Statement 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. If certain conditions are met, an entity may elect to designate a derivative instrument as follows:

a.
A hedge of the exposure to changes in the fair value of a recognized asset or liability, or of an unrecognized firm commitment, \2/ that are attributable to a particular risk (referred to as a fair value hedge)
==========================================================================
Footnote 2
\2/ An unrecognized firm commitment can be viewed as an executory contract that represents both a right and an obligation. When a previously unrecognized firm commitment that is designated as a hedged item is accounted for in accordance with this Statement, an asset or a liability is recognized and reported in the statement of financial position related to the recognition of the gain or loss on the firm commitment. Consequently, subsequent references to an asset or a liability in this Statement include a firm commitment.
==========================================================================

b.
A hedge of the exposure to variability in the cash flows of a recognized asset or liability, or of a forecasted transaction, that is attributable to a particular risk (referred to as a cash flow hedge)

c.
A hedge of the foreign currency exposure of

(1) an unrecognized firm commitment (a foreign currency fair value hedge), (

(2) an available-for-sale security (a foreign currency fair value hedge),

(3) a forecasted transaction (a foreign currency cash flow hedge), or

(4) a net investment in a foreign operation.

With respect to Section a above, a firm commitment cannot have a cash flow risk exposure because the gain or loss is already booked.  For example, a contract of 10,000 units per month at $200 per unit is unrecognized and has a cash flow risk exposure if the payments have not been made. If the payments have been prepaid, that prepayment is "recognized" and has no further cash flow risk exposure. The booked firm commitment, however, can have a fair value risk exposure.

With respect to Section c(1) above, firm commitments can have foreign currency risk exposures if the commitments are not already recognized.  See Paragraph 4 on Page 2 of FAS 133. If the firm commitment is recognized, it is by definition booked and its loss or gain is already accounted for. For example, a purchase contract for 10,000 units per month at 100DM Deutsche Marks per unit is unrecognized and has a foreign currency risk exposure if the payments have not been made. If the payments have been prepaid, that prepayment is "recognized" and has no further foreign currency risk exposure.  Similar reasoning applies to trading securities that are excluded in c(2) above since their gains and losses are already booked.  These gains have been deferred in comprehensive income for available-for-sale securities.

Cash flow hedges must have the possibility of affecting net earnings.  For example, Paragraph 485 on Page 211 of FAS 133 bans foreign currency risk hedges of forecasted dividends of foreign subsidiary.  The reason is that these dividends are a wash item and do not affect consolidated earnings.  For reasons and references, see equity method.

Section c(4) of Paragraph 4 on Page 2 of FAS 133 makes an exception to  Paragraph 29a on Page 20 for portfolios of dissimilar assets and liabilities. It allows hedging under "net investment" criteria under Paragraph 20 of SFAS 52. The gain or loss is reported in other comprehensive income as part of the cumulative translation adjustment. Reasons are given in Paragraph 477 on Page 208 of FAS 133:

The net investment in a foreign operation can be viewed as a portfolio of dissimilar assets and liabilities that would not meet the criterion in this Statement that the hedged item be a single item or a group of similar items. Alternatively, it can be viewed as part of the fair value of the parent's investment account. Under either view, without a specific exception, the net investment in a foreign operation would not qualify for hedging under this Statement. The Board decided, however, that it was acceptable to retain the current provisions of Statement 52 in that area. The Board also notes that, unlike other hedges of portfolios of dissimilar items, hedge accounting for the net investment in a foreign operation has been explicitly permitted by the authoritative literature.

For a derivative not designated as a hedging instrument, the gain or loss is recognized in earnings in the period of change.  Section 4(c) of Paragraph 4 of FAS 133 amends SFAS 52 on Foreign Currency Translation, to permit special accounting for a hedge of a foreign currency forecasted transaction with a derivative.  For more detail see foreign currency hedge.

Paragraph 42 on Page 26 reads as follows:

.A derivative instrument or a nonderivative financial instrument that may give rise to a foreign currency transaction gain or loss under Statement 52 can be designated as hedging the foreign currency exposure of a net investment in a foreign operation. The gain or loss on a hedging derivative instrument (or the foreign currency transaction gain or loss on the nonderivative hedging instrument) that is designated as, and is effective as, an economic hedge of the net investment in a foreign operation shall be reported in the same manner as a translation adjustment to the extent it is effective as a hedge. The hedged net investment shall be accounted for consistent with Statement 52; the provisions of this Statement for recognizing the gain or loss on assets designated as being hedged in a fair value hedge do not apply to the hedge of a net investment in a foreign operation. 

These Section c(4) confusions in Paragraph 4 are illustrated in Examples 11-13 beginning on Page 270 of the Derivatives and Hedging Handbook issued by KPMG Peat Marwick LLP in July 1998.

A more confusing, at least to me, portion of Paragraph 36 reads as follows:

The criterion in paragraph 21(c)(1) requires that a recognized asset or liability that may give rise to a foreign currency transaction gain or loss under Statement 52 (such as a foreign-currency-denominated receivable or payable) not be the hedged item in a foreign currency fair value or cash flow hedge because it is remeasured with the changes in the carrying amount attributable to what would be the hedged risk (an exchange rate change) reported currently in earnings.  Similarly, the criterion in paragraph 29(d) requires that the forecasted acquisition of an asset or the incurrence of a liability that may give rise to a foreign currency transaction gain or loss under Statement 52 not be the hedged item in a foreign currency cash flow hedge because, subsequent to acquisition or incurrence, the asset or liability will be remeasured with changes in the carrying amount attributable to what would be the hedged risk reported currently in earnings. A foreign currency derivative instrument that has been entered into with another member of a consolidated group can be a hedging instrument in the consolidated financial statements only if that other member has entered into an offsetting contract with an unrelated third party to hedge the exposure it acquired from issuing the derivative instrument to the affiliate that initiated the hedge.

Investments accounted for under the equity method cannot be hedged items under FAS 133 accounting for reasons explained under the term "equity method."   Recall that the magic percentage of equity ownership is 20% of more.  Lower ownership share accounted for under the cost as opposed to equity method can be hedged. 

In summary, the major exceptions under FAS 133 are discussed in the following FAS 133 Paragraphs:

• Business combinations APB Opinion No. 16 (FAS 133Paragraph 11c)

• Shareholders' equity (FAS 133 Paragraph 11a)

• Leases (FAS 133 Paragraph 10f)

• Employee benefits (SFAS 123 (Paragraph 11b)

• Insurance contracts (note exceptions in FAS 133 Paragraph 10c)

• Financial guarantees (note exceptions in FAS 133 Paragraph 10d)

• Physical indices (FAS 133 Paragraphs 10e, 58c)

• Regular-way trades (FAS 133 Paragraphs 10b, 58b)

Exceptions are not as important in IAS 39, because fair value adjustments are required of all financial instruments.  However, exceptions or special accounting for derivatives are discussed at various places in IAS 39:

• Business combinations )IAS 39 Paragraph 1g --- Also note  IAS 22 Paragraphs 65-76)

• Shareholders' equity IAS 39 Paragraph 1e)

• Leases IAS 39 Paragraph 1b)

• Employee benefits IAS 39 Paragraph 1c)

• Insurance contracts IAS 39 Paragraph 1d)

• Financial guarantees IAS 39 Paragraph 1f)

• Physical indices (IAS 39 Paragraph 1h)

• Regular-way trades (Not an explicit exception in IAS 39)

For a FAS 133 flow chart, go to http://www.trinity.edu/rjensen/acct5341/speakers/133flow.htm 

See hedge and financial instrument.

Yahoo Finance is Bob Jensen's Favorite Place to learn more about the mechanics and widespread use of derivative financial instruments.  That web site, however, will not help much with respect to accounting for such instruments under FAS 133 and IAS 39.  Also see CBOE, CBOT, and CME for some great tutorials on derivatives investing and hedging.

DIG = 

the Derivatives Implementation Group established by the FASB for purposes of helping firms implement FAS 133.  The web site is at http://www.rutgers.edu/Accounting/raw/fasb/derivatives/digmain.html . 

The Derivatives Implementation Group is a task force that was created to assist the FASB in answering questions that companies will face when they begin implementing Statement 133, Accounting for Derivative Instruments and Hedging Activities. The FASB’s objective in forming the group was to establish a mechanism to identify and resolve significant implementation questions in advance of the implementation of Statement 133 by many companies.

The role of the Derivatives Implementation Group is different from that of other task forces previously assembled by the FASB because it was established to address issues related to a new Statement that has not yet been implemented by most companies. The responsibilities of the Derivatives Implementation Group are to identify practice issues that arise from applying the requirements of Statement 133 and to advise the FASB on how to resolve those issues. In addition to members of the implementation group, any constituent or organization may submit questions to be debated by the group by sending a detailed letter to the group chairman, FASB Vice Chairman Jim Leisenring. The FASB staff also seeks input from the implementation group on selected technical inquiries that it resolves.

The model for the Derivatives Implementation Group is the Emerging Issues Task Force (EITF) with the key difference being that the Derivatives Implementation Group does not formally vote on issues to reach a consensus. Instead, it is the responsibility of the Chairman to identify an agreed-upon resolution that emerges based upon the group’s debate. Implementation group members are free to submit written objections to any issue where the group reaches an agreed-upon resolution. In instances where no clear resolution of an issue emerges, the issue may be further discussed at a future meeting or handled by the FASB staff.

After each meeting of the Derivatives Implementation Group, the FASB staff has the responsibility of documenting tentative conclusions reached by the group. Those tentative conclusions are publicly available on the FASB web site approximately three weeks after a meeting of the Derivatives Implementation Group. Those conclusions will remain tentative until they are formally cleared by the FASB and become part of an FASB staff implementation guide (Q&A). The Board is typically not asked to formally clear the staff's tentative conclusions at a public Board meeting until those conclusions have been publicly available on the web site for at least one month. That delay provides constituents the opportunity to study those conclusions and submit any comments before the Board considers formal clearance.

Meetings of the Derivatives Implementation Group are held at the FASB offices in Norwalk, CT and are open to public observation. The group will meet bimonthly during 1998 and 1999 when companies are planning for transition to the new accounting requirements. The need for meetings of the group in the year 2000 will be assessed at a later date.

DIG Issue E1 =

QUESTION (In DIG Issue E1)

In a fair value hedge (or cash flow hedge) where the hedged risk is the change in the fair value (or variability in cash flows) attributable to market interest rates, may the changes in fair value (or variability in cash flows) attributable to changes in the risk-free interest rate be designated as the hedged risk and be the sole focus of the assessment of hedge effectiveness?

RESPONSE (of the DIG)

No. Changes in the fair value (or variability in cash flows) attributable to changes in only the risk-free rate cannot be designated as the hedged risk in a fair value hedge (or cash flow hedge). Paragraphs 21(f) and 29(h) of Statement 133 permit the designated risk in a fair value hedge (or cash flow hedge) to be one of the following: (1) risk of changes in the overall fair value (or cash flows) of the entire hedged item, (2) risk of changes in the fair value (or cash flows) attributable to changes in market interest rates, (3) risk of changes in the fair value (or functional-currency-equivalent cash flows) due to changes in foreign currency rates, or (4) risk of changes in the fair value (or cash flows) due to changes in the obligor’s creditworthiness. The term credit risk in paragraph 21(f) is used to refer only to the risk of changes in fair value attributable to changes in the obligor’s creditworthiness, which can be measured by changes in the individual company’s credit rating.

The risk of changes in fair value (or cash flows) due to changes in market interest rates encompasses the risk of changes in credit spreads over the base Treasury rate for different classes of credit ratings. Therefore, if market interest rate risk is designated as the risk being hedged in either a fair value hedge or a cash flow hedge, that hedge encompasses both changes in the risk-free rate of interest and changes in credit spreads over the base Treasury rate for the company’s particular credit sector (that is, the grouping of entities that share the same credit rating). The risk of changes in the fair value (or cash flows) attributable to changes in the risk-free rate of interest is a subcomponent of market interest rate risk. Statement 133 does not permit designation of a risk that is a subcomponent of any of the four risks identified in paragraphs 21(f) and 29(h) in Statement 133 as the risk being hedged. An entity may designate a contract based on the base Treasury rate (for example, a Treasury note futures contract) as a cross-hedge of the forecasted issuance of corporate debt. However, hedge ineffectiveness may occur to the extent that credit sector spreads change during the hedge period. As a result, in designing a hedging relationship using a contract based on the base Treasury rate as a cross-hedge, the risk of changes in credit sector spreads should be considered in designating the hedged risk.

Index (Indices) =

is a term used in FAS 133 to usually refer to the underlying (e.g., a commodity price, LIBOR, or a foreign currency exchange rate) of a derivative contract. By "indexed" it is meant that an uncertain economic event that is measured by an economic index (e.g., a credit rating index, commodity price index, convertible debt, equity index, or inflation index) defined in the contract. An equity index might be defined as a particular index derived from common stock price movements such as the Dow Industrial Index or the Standard and Poors 500 Index. FAS 133 explicitly does not allow some indices such as natural indices (e.g., average rainfall) and contingency consideration indices (e.g., lawsuit outcomes, sales levels, and contingent rentals) under Paragraphs 11c and 61).

Paragraph 252 on Page 134 of FAS 133 mentions that the FASB considered expanding the underlying to include all derivatives based on physical variables such as rainfall levels, sports scores, physical condition of an asset, etc., but this was rejected unless the derivative itself is exchange traded.  For example, a swap payment based upon a football score is not subject to FAS 133 rules.  An option that pays damages based upon the bushels of corn damaged by hail is subject to insurance accounting rules (SFAS 60) rather than FAS 133.  A option or swap payment based upon market prices or interest rates must be accounted for by FAS 133 rules.  However, if derivative itself is exchange traded, then it is covered by FAS 133 even if it is based on a physical variable that becomes exchange traded.

The following Section c in Paragraph 65 on Page 45 of FAS 133 is of interest with respect to a premium paid for a forward or futures contract:

c. Either the change in the discount or premium on the forward contract is excluded from the assessment of effectiveness and included directly in earnings pursuant to Paragraph 63 or the change in expected cash flows on the forecasted transaction is based on the forward price for the commodity.

KPMG notes that if the hedged item is a portfolio of assets or liabilities based on an index, the hedging instrument cannot use another index even though the two indices are highly correlated.  See Example 7 on Page 222 of the Derivatives and Hedging Handbook issued by KPMG Peat Marwick LLP in July 1998.

Ineffectiveness =

degree ex ante to which a hedge fails to meet its goals in protecting against risk (i.e., degree to which the hedge fails to correlate perfectly with the underlying value changes or forecasted transaction prices. According to Paragraphs 20 on Page 11 and 30 on Page 21 of FAS 133, ineffectiveness is to be defined ex ante at the time the hedge is undertaken. Hedging strategy and ineffectiveness definition with respect to a given hedge defines the extent to which interim adjustments affect interim earnings. Hedge effectiveness requirements and accounting are summarized in Paragraphs 62-103 beginning on Page 44 of FAS 133. An illustration of intrinsic value versus time value accounting is given in Example 9 of FAS 133, Pages 84-86, Paragraphs 162-164. In Example 9, the definition of ineffectiveness in terms of changes in intrinsic value of a call option results in changes in intrinsic value each period being posted to other comprehensive income rather than earnings. In Examples 1-8 in Paragraphs 104-161, designations as to fair value versus cash flow hedging affects the journal entries. 

One means of documenting hedge effectiveness is to compare the cumulative dollar offset defined as the cumulative value over a succession of periods (e.g., quarters) in which the cumulative gains and losses of the derivative instrument are compared with the cumulative gains and losses in value of the hedged item.  n assessing the effectiveness of a hedge, an enterprise will generally need to consider the time value of money according to FAS 133 Paragraph 64 and IAS 39 Paragraph 152.

Neither the FASB nor the IASC specify a single method for either assessing whether a hedge is expected to be highly effective or measuring hedge ineffectiveness.  Tests of hedge effectiveness should be conducted at least quarterly and on financial statement dates.  The appropriateness of a given method can depend on the nature of the risk being hedged and the type of hedging instrument used.  See FAS 133 Appendix A, Paragraph 62 and IAS 39 Paragraph 151.  

Paragraph 63 of FAS 133 reads as follows:

In defining how hedge effectiveness will be assessed, an entity must specify whether it will include in that assessment all of the gain or loss on a hedging instrument. This Statement permits (but does not require) an entity to exclude all or a part of the hedging instrument's time value from the assessment of hedge effectiveness, as follows:

a. If the effectiveness of a hedge with an option contract is assessed based on changes in the option's intrinsic value, the change in the time value of the contract would be excluded from the assessment of hedge effectiveness.

b. If the effectiveness of a hedge with an option contract is assessed based on changes in the option's minimum value, that is, its intrinsic value plus the effect of discounting, the change in the volatility value of the contract would be excluded from the assessment of hedge effectiveness.

c. If the effectiveness of a hedge with a forward or futures contract is assessed based on changes in fair value attributable to changes in spot prices, the change in the fair value of the contract related to the changes in the difference between the spot price and the forward or futures price would be excluded from the assessment of hedge effectiveness.

Paragraph 69 of FAS 133 reads as follows [also see (IAS 39 Paragraph 152)]:

The fixed rate on a hedged item need not exactly match the fixed rate on a swap designated as a fair value hedge. Nor does the variable rate on an interest-bearing asset or liability need to be the same as the variable rate on a swap designated as a cash flow hedge. A swap's fair value comes from its net settlements. The fixed and variable rates on a swap can be changed without affecting the net settlement if both are changed by the same amount. That is, a swap with a payment based on LIBOR and a receipt based on a fixed rate of 5 percent has the same net settlements and fair value as a swap with a payment based on LIBOR plus 1 percent and a receipt based on a fixed rate of 6 percent.

Paragraph 10c of IAS 39 also addresses net settlement.  IASC does not require a net settlement provision in the definition of a derivative.  To meet the criteria for being a derivative under FAS 133, there must be a net settlement provision.  

The following Section c in Paragraph 65 on Page 45 is of interest with respect to a premium paid for a forward or futures contract:

c. Either the change in the discount or premium on the forward contract is excluded from the assessment of effectiveness and included directly in earnings pursuant to Paragraph 63 or the change in expected cash flows on the forecasted transaction is based on the forward price for the commodity.

Delta ratio D = (D option value)/ D hedged item value)
range [.80 < D < 1.25] or [80% < D% < 125%]      (FAS 133 Paragraph 85)
Delta-neutral strategies are discussed at various points (e.g., FAS 133 Paragraphs 85, 86, 87, and 89)

A hedge is normally regarded as highly effective if, at inception and throughout the life of the hedge, the enterprise can expect changes in the fair value or cash flows of the hedged item to be almost fully offset by the changes in the fair value or cash flows of the hedging instrument, and actual results are within a range of 80-125% (SFAS 39 Paragraph 146).  The FASB requires that an entity define at the time it designates a hedging relationship the method it will use to assess the hedge's effectiveness in achieving offsetting changes in fair value or offsetting cash flows attributable to the risk being hedged (FAS 133 Paragraph 62).  In defining how hedge effectiveness will be assessed, an entity must specify whether it will include in that assessment all of the gain or loss on a hedging instrument.  The Statement permits (but does not require) an entity to exclude all or a part of the hedging instrument's time value from the assessment of hedge effectiveness. (FAS 133 Paragraph 63).

Hedge ineffectiveness would result from the following circumstances, among others:

a) difference between the basis of the hedging instrument and the hedged item or hedged transaction, to the extent that those bases do not move in tandem.

b) differences in critical terms of the hedging instrument and hedged item or hedged transaction, such as differences in notional amounts, maturities, quantity, location, or delivery dates.

c) part of the change in the fair value of a derivative is attributable to a change in the counterparty's creditworthiness (FAS 133 Paragraph 66).

The method an enterprise adopts for assessing hedge effectiveness will depend on its risk management strategy.  In some cases, an enterprise will adopt different methods for different types of hedges.  For instance, an interest rate swap is likely to be an effective hedge if the notional and principal amounts, term, repricing dates, dates of interest and principal receipts and payments, and basis for measuring interest rates are the same for the hedging instrument and the hedge item (IAS 39 Paragraph 147).  Sometimes the hedging instrument will offset the hedged risk only partially.  For instance, a hedge would not be fully effective if the hedging instrument and hedged item are denominated in different currencies and the two do not move in tandem.
(IAS 39 Paragraph 148).

Interest Rate Swap =

a transaction in which two parties exchange interest payment streams of differing character based on an underlying principal amount. As in all other swaps, the swap is a portfolio of forward contracts. Swaps are the most common form of hedging risk using financial instruments derivatives. The most typical interest rate swaps entail swapping fixed rates for variable rates and vice versa. For instance, in FAS 133, Example 2 beginning in Paragraph 111 illustrates a fair value hedge and Example 5 beginning in Paragraph 131 illustrates a cash flow hedge. These are explained in greater detail in the following documents:

http://www.trinity.edu/rjensen/caseans/294wp.doc 
The Excel workbook is at http://www.cs.trinity.edu/~rjensen/133ex02a.xls 

http://www.trinity.edu/rjensen/caseans/133ex05.htm 
The Excel workbook is at http://www.cs.trinity.edu/~rjensen/133ex05a.xls 

A short tutorial on interest rate swaps is given at http://home.earthlink.net/~green/whatisan.htm.  A good place to start in learning about how interest rate swaps work in practice is the CBOT  tutorial at http://www.cbot.com/ourproducts/financial/agencystrat3rd.html.  A very interesting (not free) swap calculator is given by TheBEAST.COM at http://www.thebeast.com/02_products/beast_help/ScreenSwapCalculator.htm 
A tutorial can be found at http://www.thebeast.com/02_products/beastonline_gettingstarted.html 

LIBOR =

the London InterBank Offering Rate interest rate at which banks borrow in London. The rate is commonly used as an index in floating rate contracts, interest rate swaps, and other contracts based upon interest rate fluctuations.

LIBOR Swap Rate =

The fixed rate on a single-currency, constant-notional interest rate swap that has its floating-rate leg referenced to the London Interbank Offered Rate (LIBOR) with no additional spread over LIBOR on that floating-rate leg. That fixed rate is the derived rate that would result in the swap having a zero fair value at inception because the present value of fixed cash flows, based on that rate, equate to the present value of the floating cash flows. See Interest Rate Swap.

SFAS 133 and FAS 138  = 

a standard issued by the Financial Accounting Standards Board (FASB) in June 1998.  SFAS 133 (or FAS 133) was amended by SFAS 138 (FAS 138) released on June 15, 2000.  You can read more about FAS 133 and FAS 138  and other FASB standards at http://www.rutgers.edu/Accounting/raw/fasb/st/stpg.html.  Note that the FASB's FAS 133 becomes required for calendar-year companies on January 1, 2001.  Early adopters can apply the standard prior to the required date, but they cannot apply it retroactively.   The January 1, 2001 effective date follows postponements from the original starting date of June 15, 1999 stated in Paragraph 48 on Page 29 of FAS 133.   For fiscal-year companies, the effective date is June 15, 2000.  The international counterpart known as the IASC's IAS 39 becomes effective for financial statements for financial years beginning on the same January 1, 2001.  Earlier application permitted for financial years ending after March 15, 1999.  

Publication Number 186-B, June 1998, Product Code S133
FASB Statement No. 133, Accounting for Derivative Instruments and Hedging Activities
Telephone (800) 748-0659 or go to web site http://www.rutgers.edu/Accounting/raw/fasb/home2.html
Copies are $11.50 each and are subject to academic discounting.

The FASB created a special Derivatives Implementation Group (DIG).  Some general DIG exceptions to the scope of FAS 133 are listed in the "C" category at http://www.rutgers.edu/Accounting/raw/fasb/derivatives/issuindex.html 

A number of important issues that surfaced in the DIG have resulted in a new standard FAS 138, Accounting for Certain Derivative Instruments and Certain Hedging Activities an amendment of FASB Statement No. 133, Released June 15, 2000 --- http://www.rutgers.edu/Accounting/raw/fasb/public/index.html

My introduction to FAS 138 (Amendments to FAS 133) and some key DIG issues at http://www.cs.trinity.edu/~rjensen/000overview/mp3/138intro.htm 

The FASB has a CD-ROM course at http://www.rutgers.edu/Accounting/raw/fasb/ 

The FASB's Derivatives Implementation Group website is at http://www.rutgers.edu/Accounting/raw/fasb/digsum.html

FAS 133 replaces the Exposure Draft publication Number 162-B, June 1996.

The International Accounting Standards Committee (IASC) later came out with IAS 39 which is similar to but less detailed than FAS 133. 

The FASB address is Financial Accounting Standards Board, P.O. Box 5116, Norwalk, CT 06856-5116. Phone: 203-847-0700 and Fax: 203-849-9714.  The web site is at http://www.rutgers.edu/Accounting/raw/fasb/

The for-free IASC comparison study of IAS 39 versus FAS 133 (by Paul Pacter) at http://www.iasc.org.uk/news/cen8_142.htm

The non-free FASB comparison study of all standards entitled The IASC-U.S. Comparison Project: A Report on the Similarities and Differences between IASC Standards and U.S. GAAP
SECOND EDITION, (October 1999) at http://www.rutgers.edu/Accounting/raw/fasb/IASC/iascus2d.html

Term Structure =

yield patterns in which returns of future cash flows are not necessarily discounted at the same interest rates.  Yield curves may have increasing or decreasing yield rates over time.  However, it is much more common for the rates yields to increase over time.  Theories vary as to why.  One theory known as expectations theory based on the assumption that borrowers form long-term expectations and then choose a rollover strategy if short-term rates are less than long-term expectations and vice versa.  Lenders form their own expectations.   Expectations theory postulates that long-term interest rates are a geometric average of expected short term interest rates.   Liquidity preference theory postulates that investors add a liquidity preference premium on longer-term investments that gives rise to an upward sloping yield curve.  Liquidity preference theory is not consistent with the averaging process assumed in expectations theory.  Market segmentation theory is yet another theory used to explain term structures.  That theory postulates that the supply and demand for money is affected by market segments' demands for short term money that in turn affects the cost of coaxing short term lenders into making longer commitments.  Whatever the reasons, yield vary with the time to maturity, and this relationship of yield to time is known as term structure of interest rates.  See yield curve.

Yield (Swap) Curve =

the graphical relationship between yield and time of maturity of debt or investments in financial instruments.  In the case of interest rate swaps, yield curves are also called swaps curves.  Forward yield (or swaps) curves are used to value many types of derivative financial instruments.   If time is plotted on the abscissa, the yield is usually upward sloping due to term structure of interest rates.  Term structure is an empirically observed phenomenon that yields vary with dates to maturity. 

FAS 133 refers to yield curves at various points such as in Paragraphs 112 and 319.   The Board also referred to by analogy at various points such as in Paragraphs 162 and 428.  Financial service firms obtain yield curves by plotting the yields of default-free coupon bonds in a given currency against maturity or duration. Yields on debt instruments of lower quality are expressed in terms of a spread relative to the default-free yield curve.   Paragraph 112 of SFAS 113 refers to the "zero-coupon method."   This method is based upon the term structure of spot default-free zero coupon rates.  The interest rate for a specific forward period calculated from the incremental period return in adjacent instruments. A very interesting web site on swaps curves is at http://www.clev.frb.org/research/JAN96ET/yiecur.htm#1b  

In the introductory Paragraph 111 of FAS 133, the Example 2 begins with the assumption of a flat yield curve. A yield curve is the graphic or numeric presentation of bond equivalent yields to maturity on debt that is identical in every aspect except time to maturity. In developing a yield curve, default risk and liquidity, for example, are the same for every security whose yield is included in the yield curve. Thus yields on U. S. Treasury issues are normally used to plot yield curves. The relationship between yields and time to maturity is often referred to as the term structure of interest rates.

As explained by the expectations hypothesis of the term structure of interest rates, the typical yield curve is gradually increase relative to maturity. That is, in normal economic conditions short-term rates are somewhat lower than longer-term rates. In a recession with deflation or disinflation the entire yield curve shifts downward as interest rates generally fall and rotates indicating that short-term rates have fallen to much lower levels than long-term rates. In an economic expansion accompanied by inflation, interest rates tend to rise and yield curves shift upward and rotate indicating that short-term rates have increased more than long-term rates.

The different shapes of the yield curve described above complicate the calculation of the present value of an interest rate swap and require the calculation and application of implied forward rates to discount future fixed rate obligations and principal to the present value. Fortunately Example 2 assumes that a flat yield curve prevails at all levels of interest rates. A flat yield curve means that as interest rates rise and fall, short-term and long-term rates move together in lock step, and future cash flows are all discounted at the same current discount rate.

A yield curve is the graphic or numeric presentation of bond equivalent yields to maturity on debt that is identical in every aspect except time to maturity. In developing a yield curve, default risk and liquidity, for example, are the same for every security whose yield is included in the yield curve. Thus yields on U. S. Treasury issues are normally used to plot Treasury yield curves. The relationship between yields and time to maturity is often referred to as the term structure of interest rates. Similarly, an unknown set of estimated LIBOR yield curves underlie the FASB swap valuations calculated in all FAS 133/138 illustrations.  The FASB has never really explained how swaps are to be valued even though they must be adjusted to fair value at least every three months. Other than providing the assumption that the yields in the yield curves are zero-coupon rates, the FASB offers no information that would allow us to derive the yield curves or calculate the swap values in Examples 2 and 5 in Appendix B of FAS 133 and in other examples using FAS 138 rules.

The typical yield curve gradually increases relative to years to maturity. That is, historically, short-term rates are somewhat lower than longer-term rates. In a recession with deflation or disinflation the entire yield curve shifts downward as interest rates generally fall and rotates counter-clockwise indicating that short-term rates have fallen to much lower levels than long-term rates. In rapid economic expansion accompanied by inflation, interest rates tend to rise and yield curves shift upward and rotate clockwise indicating that short-term rates have increased more than long-term rates.

The different shapes of the yield curve described above complicate the calculation of the present value of an interest rate swap and require the calculation and application of implied forward rates to calculate future expected swap cash flows. Example 2 in Appendix B of FAS 133 assumed that a flat yield curve prevails at all levels of interest rates. A flat yield curve means that as interest rates rise and fall, short-term and long-term rates move together in lock step, and future cash flows are all discounted at the same current discount rate. The cash flows and values in the Appendix B Example 5, however, are developed from the prevailing upward sloping yield curve at each reset date.

The accompanying Excel workbook used the tool Goal Seek in Excel to derive upward sloping yield curves and swap values at the reset dates that generated the $4,016,000 swap value used in the FASB's Example 1 of Section 1 of the FAS 138 examples at  http://www.rutgers.edu/Accounting/raw/fasb/derivatives/examplespg.html.

Yield curves are typically computed on the basis of a forward calculated in the following manner using the y(t) yield curve values:

ForwardRate(t) = [1 + y(t)]t/[1 + y(t-1)]^t-1 – 1

The ForwardRate(t) is the forward rate for time period t, y(t) is the multi-period yield that spans t periods, and y(t-1) is the yield for an investment of t-1 periods. For example, if 6.5% is y(t) and 6.0% is y(t-1). Thus, ForwardRate(2), the forward LIBOR for year 2, is calculated as follows

ForwardRate(2) = (1.065)2/1.06 – 1 = 0.07 or 7.0%

Having calculated a forward rate for each quarter from the rates in the trial yield curve, we can then ask Excel to give us the values of an upward sloping yield curve with forward rates that would calculate future expected swap cash flows whose present value is zero. The resulting yield curve,  equivalent rates, forward rates, expected swap cash flows are shown in the base examples in the Excel workbook.

In practice, investors and auditors often rely upon the Bloomberg swaps curve estimations.   The contact information for Bloomberg Financial Services is as follows: Bloomberg Financial Markets, 499 Park Avenue, New York, NY 10022; Telephone: 212-318-2000; Fax: 212-980-4585; E-Mail: feedback@bloomberg.com; WWW Link: <http://www.bloomberg.com/> and <http://www.wsdinc.com/pgs_www/w5594.shtml>. Various pricing services are available such as Anderson Investors Software at  http://www.wsdinc.com/products/p3430.shtml    Cutter & Co. provides some illustrations yield curves at http://www.stocktrader.com/summary.html    Discussion group messages about yield curves are archived at http://csf.colorado.edu/mail/longwaves/current-discussion/0086.html

Links to various sites can be found at http://www.eight.com/websites.htm    You may also want to view my helpers at http://WWW.Trinity.edu/rjensen/acct5341/index.htm  

Also see my interest rate accrual comments my "Missing Parts of FAS 133" document.

Bob Jensen provides free online tutorials (in Excel workbooks) on derivation of yield curves, swap curves,  single-period forward rates, and multi-period forward rates. These derivations are done in the context of FAS 133, including the derivations of the missing parts of the infamous Examples 2 and 5 of FAS 133.  Since these tutorials contain answers that instructors may want to keep out of the hands of students in advance of assignments, educators and practitioners must contact Jensen for instructions on how to find the secret URL.  The key files on yield curve derivations are yield.xls, 133ex02a.xls, and 133ex05a.xls. Bob Jensen's email address is rjensen@trinity.edu