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Derivatives and Hedge Contracts: Identification

and Analysis Techniques for Audit Advisors Evaluating Financial Instruments Under Terms of ASC 815, ASC 820 and Other Guidance

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Presenting a live 110-minute teleconference with interactive Q&A

Steven Halterman, Director, PricewaterhouseCoopers, Florham Park, N.J.

Timothy Woods, Managing Director and Shareholder, CBIZ MHM, Denver

Michael Loritz, Managing Director and Shareholder, Mayer Hoffman McCann, Kansas City, Mo.

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Derivatives and Hedge Contracts: Identification and Analysis Techniques for Audit Advisors Seminar

Steven Halterman, PricewaterhouseCoopers

[email protected]

April 17, 2013

Michael Loritz, Mayer Hoffman McCann

[email protected]

Timothy Woods, Mayer Hoffman McCann

[email protected]

Today’s Program

Applicable Standards And Guidance

[Michael Loritz]

Common Derivative Instruments And Hedge Contracts

[Steven Halterman]

Derivatives, In Greater Depth

[Michael Loritz]

Hedge Contracts, In Greater Depth

[Steven Halterman]

Fair Valuation Practices With Derivatives

[Timothy Woods]

Slide 8 – Slide 13





Notice

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MAY BE IMPOSED ON ANY TAXPAYER OR (ii) PROMOTING, MARKETING OR

RECOMMENDING TO ANOTHER PARTY ANY MATTERS ADDRESSED HEREIN.

You (and your employees, representatives, or agents) may disclose to any and all persons,

without limitation, the tax treatment or tax structure, or both, of any transaction

described in the associated materials we provide to you, including, but not limited to,

any tax opinions, memoranda, or other tax analyses contained in those materials.

The information contained herein is of a general nature and based on authorities that are

subject to change. Applicability of the information to specific situations should be

determined through consultation with your tax adviser.

7

APPLICABLE STANDARDS AND GUIDANCE


9

Accounting For Derivatives: The History

• Why FASB Statement No. 133?

– A lack of transparency in the financial statements.

• Many derivative positions were not reflected in the financial

statements.

• As a result, investors were not aware of potentially significant

exposures from derivative instruments that ultimately resulted in the

recognition of significant losses (surprise factor).

• Lack of information about how companies used derivative

instruments and related strategies

– Many would assume that exposures were perfectly hedged,

when in reality they were not.

– It is very rare to have a “perfect hedge.”

10

Accounting For Derivatives: The History (Cont.)

• Accounting prior to SFAS No 133

– Deferral method: Gains or losses on a derivative position were

deferred as either an asset or a liability, and later amortized.

– Incurred/accrual method: Amounts actually receivable or payable

would be recorded, but there was nothing else reflected in the

financial statements (monthly settlements, for example).

– Fair value: Mark-to-market accounting

• Practice was diverse, and comparability was difficult!

11


• 1998: The Financial Accounting Standards Board (FASB) issued Financial Accounting Standard 133 (SFAS 133) on Accounting for Derivative Financial Instruments and Hedging Activities.�

– Original effective date of June 15, 1999

– Amended to June 15, 2000 (Jan. 1, 2001 for calendar-year companies)

• Also formed the SFAS 133 Derivatives Implementation Group (DIG) to help resolve particular implementation questions, especially in areas where the standard is not clear or allegedly onerous

– All have since been codified.

• One of the most confusing and complex accounting standards to date

– Established the notion of an “embedded derivative”

– Source of a significant number of restatements

– Very rules-based approach

http://www.rutgers.edu/Accounting/raw/fasb/

12


International Accounting Standards

• IAS 39: Financial Instruments, Recognition and Measurement

– Represents current standard for financial instruments - IFRS

• IFRS 9: Financial Instruments

– Phase I – Classification and measurement (amended 11/28/12)

– Phase II – Impairment (exposure draft issued 3/7/13)

– Phase III – Hedge accounting (exposure draft issued 9/7/12)

• More closely align accounting with risk management activities

• Improve ability of investors to understand risk management activities

• Improve ability of investors to assess the amounts, timing and uncertainty of future cash flows

• IFRS 9 is effective on Jan. 1, 2015.

– Early adoption is permitted.

13


Financial Accounting Standards Board

• On June 6, 2008, the FASB issued an exposure draft, Accounting for Hedging Activities

– Suggested some targeted changes to then-current hedge accounting guidance

• On May 26, 2010, the FASB issued a proposed accounting standards update, Accounting for Financial Instruments and Revisions to the Accounting for Derivative Instruments and Hedging Activities

– Feedback received from the 2008 draft was considered.

– Less rigorous qualitative assessment to qualify for hedge accounting

• No significant progress on the hedging project since the 2010 exposure draft

COMMON DERIVATIVE INSTRUMENTS AND HEDGE CONTRACTS


PwC

Formalities

The following materials were developed for this presentation and not for other purposes. This content is for general information purposes only, and should not be used as a substitute for consultation with professional advisors.

PwC United States helps organizations and individuals create the value they’re looking for. We’re a member of the PwC network of firms in 158 countries with more than 180,000 people. We’re committed to delivering quality in assurance, tax and advisory services. Tell us what matters to you and find out more by visiting us at www.pwc.com/us

Copyright © 2013 PricewaterhouseCoopers LLP, a Delaware limited liability partnership. All rights reserved. PwC refers to the United States member firm, and may sometimes refer to the PwC network. Each member firm is a separate legal entity. Please see www.pwc.com/structure for further details.

Slide 15

April 17, 2013 Hedges

http://www.pwc.com/us

http://www.pwc.com/structure

PwC

What Hedge Designations Are Most Common?

Forecasted transactions of fixed rate or variable rate debt (CF)

- Do not qualify for shortcut, not an existing asset or liability

- Likely to own the perfect hypothetical, but negotiations or strategy may cause the debt to change, requiring subsequent quantitative assessments

Variable rate debt (CF)

- Issues qualifying for shortcut, as the debt is frequently pre-payable at par while swap is pre-payable at fair value

- Qualitative methods to own the perfect hypothetical, but negotiations or strategy may cause the hypothetical to be different than your actual hedge, creating possible ineffectiveness

Fixed rate debt at issuance (FV)

- May not qualify for shortcut, if the debt is prepayable at a fixed price (say, 102%) and the feature is not mirrored in the swap

• Late hedges of fixed rate debt (FV)

- May have issues proving an on-market hedge is highly effective, if the debt is now significantly off-market

Slide 16


PwC

What Hedge Designations Are Most Common? (Cont.) • Forecasted foreign currency-denominated, inter-company sales or expenses (CF)

- Typically executed as layered fx forward contracts, settling each month in the future

- Since sales occur each day, derivative does not mature each day; do not own perfect hedge

- Kviz or boxing analysis performed at inception to support a critical terms (perfect hypothetical) qualitative assertion, but regression could also be done.

• Forecasted foreign currency payments for assets purchased (CF)

- Typically executed as a single or layered fx forward contract(s) settling in month of purchase or milestone payment due; be cautious for changes in your fact pattern that indicate that you no longer hold the perfect hypothetical

• Hedges of AFS debt securities for changes in FX rates (FV)

- Hedge of typically the recorded fair value (works like a dynamic hedge)

- Hedge of cost basis is much more difficult to calculate the basis adjustment of the bond

Slide 17


Slide Intentionally Left Blank

DERIVATIVES, IN GREATER DEPTH


20

Why Are Derivatives Used?

• Increased friction between buyers and sellers of underlying assets in

established debt, equity, currency and commodities markets put

pressure on the securities industry to develop innovative solutions.

• Synthetic assets that derived their value from these underlying

assets but allowed for more flexible timing, risk, pricing and

contractual arrangements were developed by private parties and

market-making firms.

• These synthetic securities increased the number of buyers and

sellers coming into the marketplace to transact for a variety of

reasons.

• This increased volume of activity allows more efficient markets, and

greater liquidity for all investors in both the derivative and underlying

asset markets.

21

Why Are Derivatives Used? (Cont.) • Risk management

– Derivatives are used by many companies to manage the risk of

changing market conditions on assets/liabilities or variable cash

flows on operations.

– Hedge accounting can apply.

• Arbitrage

– Lock in riskless profits (excluding credit risk)

– Generally the use by large banks

• Speculation

– Trading derivative products in order to take a position in the

market (betting on future movements)

22

Why Are Derivatives Used? (Cont.)

Derivatives used as speculation

• Companies and investors utilize derivatives as investments, because derivatives provide an extreme amount of leverage that can be utilized to magnify investment gains (and losses).

• Example: Futures contract on oil

• Notional amount = 40,000 barrels of oil

• Company purchases a futures contract to purchase 40,000 barrels of oil at a price of $70 per barrel for a term of three months.

• Except for initial margin (typically 5% of notional amount, $140,000), company does not need to put up any capital, and it controls $2.8 million of oil. If oil closes at $80, company made $400,000l; if it closes at $60, it lost $400,000. So, on a 14.28% move in oil, the company makes 186%, plus it gets the $140,000 margin back.

23

Why Are Derivatives Used? (Cont.) Risk management

• Companies utilize derivatives to offset (HEDGE) risks that are inherent in their business models.

• Examples include:

– Futures contracts to lock in sales prices for commodities being sold (hedging the volatility in sales prices); e.g., copper futures for sales of copper

– Foreign exchange contracts to lock in a fixed exchange rate on its international sales in Europe (hedging the volatility in exchange rates)

– Interest rate swaps to lock in a fixed interest rate for a company’s variable-rate debt (hedging the volatility in interest rates)

• Upon entering into these derivative contracts, the company is satisfied with the price that it will receive upon settlement of the derivative. Ideally, any gain or loss on the derivative contract is offset by the loss or gain from the item being hedged. The company has received the market rate on the date into which the derivative contract was entered.

Common Interest Rate Swap Agreement

Company A

Issues $100

Million In debt

Bond

Holders

Swap

Agreement

With Bank

A

24


Accounting Model For Derivatives

• A derivative instrument is recorded on the balance sheet as either

an asset or liability measured at its fair value. Changes in the

derivative instrument’s fair value must be recognized currently in

earnings , unless specific hedge accounting criteria are met.

• An entity that does not report earnings, such as a not-for-profit

entity, generally is required to report such changes as part of the

change in its net assets.

26

HEDGE CONTRACTS, IN GREATER DEPTH


Assessing Effectiveness And Measuring Ineffectiveness

PwC

Hedge Effectiveness Assessment Qualitative Long-Haul

“Long-haul” to many persons familiar with hedge accounting means performing involved calculations. It does

frequently, but also not necessarily. Many of these methods are illustrated using interest rate hedges of debt but are applied widely by analogy.

The use of qualitative methods of asserting high effectiveness are common. Terms are oftentimes misused to mean effectively the same thing. This can be perilous in a form-driven standard.

Shortcut: A qualitative method for assessing the effectiveness of a cash flow or fair value hedge of an existing asset or liability for changes in the identified benchmark interest rate, when using an interest rate swap as the hedging instrument. Anything that is not shortcut is, by definition long-haul.

Critical terms match: A qualitative method for assessing the effectiveness of both cash flow and fair value hedges. It is generally understood to apply to forward contracts of existing items and forecasted transactions, but has been more widely applied. Oftentimes, it is combined with limiting changes to only those due to spot rates. This and the items below are long-haul methods, as anything that is not shortcut is long-haul.

Changes in variable cash flows method (CVCF): A qualitative or quantitative method for cash flow hedges of existing liabilities, or assets or forecasted asset or liability transactions, for interest rate risk using interest rate swaps but applied by analogy to commodity hedges and combinations of interest rates and currency

Hypothetical derivative method: Only for cash flow hedges; may be qualitative or quantitative, similar to CVCF method above but refers to selected criteria in shortcut to assert that the hedge will result in no ineffectiveness; used widely by analogy in commodity and currency hedges as well as for options under former DIG Issue G20

Slide 29


PwC

Fair Value Hedges

Cash Flow Hedges

Notes

Shortcut method Qualitative Qualitative Not as useful for cash flow hedges

Long-haul methods

Changes in variable cash flows method

Both Fine when assessing qualitatively but difficult quantitatively

Hypothetical derivative method

Both Most common, both qualitative and quantitative refers to shortcut criteria to define the hypo

Change in fair value method

Quantitative Risk of “small numbers” phenomenon so paired with regression

Change in fair value method

Quantitative Same, discount rate is often different for the derivative and hedged item

Qualitative Vs. Quantitative Tests Of Interest Rates More options for CF hedges

Slide 30


PwC

Hedge Effectiveness Assessment Vs. Ineffectiveness Measurement

A confusing aspect of the literature is that all the methods described are technically measurements of ineffectiveness.

Since many of these methods allow a possible conclusion of no ineffectiveness, one could only logically conclude that the hedge must be assessed as being effective.

Ineffectiveness is always measured by the change in fair value of each item, as defined in the hedge documentation, subject to the OCI limitation for cash flow hedges on overhedges (or overperformance).

Off-market derivatives contain a financing component that should be viewed as an embedded loan payable or receivable combined with a zero fair value derivative. View the embedded loan as being carried at fair value through earnings. Receipts and payments on the financing are not contributors to ineffectiveness, but changes in the fair value of the unpaid receivable or payable do cause ineffectiveness in earnings subject to the OCI limitations on cash flow hedges.

Slide 31



Accounting Techniques

PwC

Most Common Question Received

Facts:

• Cash flow hedge of existing variable-rate debt

• Qualifies for critical terms (perfect hypothetical), so all amounts are deferred in AOCI

• Client decides to cancel the derivative (swap or cap), because :

- It has decided to stop hedging, as it thinks rates are not going to go back up over the remaining life of the derivative;

- Or, it has refinanced or modified the debt and can no longer qualify to assess qualitatively;

- Or, its debt modification resulted in an accounting extinguishment

I stopped hedging, so I recognize all the AOCI in earnings, right?

Discussion:

Hedge was of variability in debt payments.

Debt payments remain probable or reasonably possible of occurring.

Answer:

No AOCI amounts are recognized immediately in earnings.

Recognize AOCI amounts as interest expense, as the future interest payments affect earnings

Use swaplet or yield adjustment method to recognize the frozen AOCI amounts

If the debt was refinanced to another lender, and hedge docs were of variability in debt payments to Lender A, only then release AOCI amounts and disclose.

Slide 34


FAIR VALUATION PRACTICES WITH DERIVATIVES

Timothy Woods, Mayer Hoffman McCann

36

Presentation Overview

• Most common interest rate derivatives

– Interest rate swaps

– Interest rate cap agreements

• Risk characteristics

• Pros and cons of each

• Valuation

– Interest rate swap

– Interest rate cap

– Futures contracts

– Forward contracts

– Options on futures and forward contracts

• CBIZ MHM, LLC services

• Questions

37

Interest Rate Swaps

• Most common is a plain vanilla interest rate swap in which:

– A company agrees to pay cash flows equal to interest at a pre-

determined fixed rate on a stated notional principal for a stated

period, and in return, the company receives interest at a floating

rate on the same notional principal for the same period of time.

– Company can be the fixed-rate payer and the floating rate

receiver, or vice versa.

38

Interest Rate Swaps (Cont.)

• For example:

– Company XYZ has outstanding $10 million of non-amortizing

variable rate debt, for which interest payments are due on a

quarterly basis. The note accrues interest at the three-month

London Interbank Offered Rate (LIBOR) plus 5%, and matures

via a bullet payment in five years.

– In this case, in order to hedge the company’s interest rate risk,

the company would enter into a five-year interest rate swap for a

notional amount of $10 million at a swap rate (fixed rate) of

2.60%.

39


• Example (Cont.)

– The company would pay the fixed rate of 2.6% on the $10 million

notional amount on a quarterly basis and would receive the three-month

LIBOR rate on a quarterly basis. The LIBOR received is set a quarter

prior to payment, so the payment is made three months in arrears.

Accordingly, the company knows three months in advance what the

payment will be.

– Payments are settled on a net basis, so if the three-month LIBOR is

greater than 2.6%, then the company will receive a payment.

– Therefore, the company has effectively turned its variable rate debt into

fixed-rate debt with an effective interest rate of 7.6% (2.6% fixed + 5%

spread).

40


• Example (Cont.)

– FIXED RATE PAYMENT = $10,000,000 * .026 / 4 = $65,000

– VARIABLE RATE PAYMENT = $10,000,000 * 3 MONTH LIBOR

(3.0%) or .03 / 4 = $75,000

– THEREFORE, COMPANY RECEIVES:

• $75,000 - $65,000 = $10,000 AT QUARTERLY

SETTLEMENT. THE FIXED RATE PAYMENT WILL BE

$65,000 AT EACH SETTLEMENT

• THE VARIABLE RATE PAYMENT IS THE MOVING

COMPONENT AS THE THREE MONTH LIBOR WILL

CHANGE.

41

Interest Rate Cap Agreement

• An interest rate cap is an option that provides a payoff when a

specified interest rate above a certain level (the cap rate). The

specified rate is a floating rate that is set periodically.

42

Interest Rate Caps: Terms

• Interest rate caps can be described by a “term sheet.”

– Maturity (for example, five years)

– Notional amount (usually set equal to borrowed amount)

– Strike price (sometimes called the protection level)

– Frequency (how many payments per year)

• Payments per year times maturity tells you how many caplets

– Basis (how you’re going to count days)

– Underlying rate (usually LIBOR of some maturity)

43

Interest Rate Cap

• For example:

– Company XYZ has outstanding $10 million of non-amortizing variable-rate debt,

for which interest payments are due on a quarterly basis. The note accrues

interest at the three-month LIBOR plus 5%, and matures via a bullet payment in

five years.

– In this case, in order to hedge the company’s interest rate risk, the company

would purchase a five-year interest rate cap agreement for a notional amount of

$10 million, which has a cap rate of 2.6% (for example) and designated

maturities of three months. For purposes of this example, the purchase price is

$200,000 for the interest rate cap agreement.

– Therefore, given that the company purchased an interest rate cap agreement

with a term of five years and quarterly settlements, the interest rate cap

agreement is comprised of 20 individual cap agreements (“caplets”) that are

settled on a quarterly basis. As with the interest rate swap, the cap rate is set

three months prior to settlement and as such, the settlement amount is known

three months in advance.

44

Interest Rate Cap (Cont.)

• For example (Cont.):

– With an interest rate cap, the company that purchased the cap

agreement will only receive a payment if the three-month LIBOR closes

above the cap rate. At no time will the company be required to pay

additional funds at any of the caplet settlements.

– For example, if the three-month LIBOR rate closes at 3%, the company

will receive a payment equal to (3% - 2.6%) *10,000,000 / 4 = $10,000.

– Therefore, the company has ensured that the effective rate of its debt

will not go above 7.6% (LIBOR of 2.6%, the cap rate, plus the 5%

margin on the underlying debt). However, the company’s effective rate

can go as low as the market will take it, which as we will see is not the

situation with the interest rate swap.

45

Risk Characteristics

• Risk characteristics of interest rate swaps

– As we discussed before, the swap rate is the fixed rate of

interest that the receiver (variable-rate payer) demands in

exchange for the uncertainty of having to pay the short-term

three-month LIBOR (floating rate) over the term of the swap.

– Therefore, at the time that the interest rate swap is entered, the

total present value of the fixed-rate payments to be received

(made) is equal to the expected value of the variable-rate

payments to be made (received). As such, at the date the swap

is entered, the value of the swap is $0, which is why there is no

purchase price for the swap (without commissions).

46

Risk Characteristics (Cont.)

• Interest rate swaps involve two primary risks: 1) Interest rate risk and 2) credit, or

counterparty, risk.

• Interest rate risk

– When a company enters into an interest rate swap for purposes of risk

management, it is stating that it is comfortable with the effective interest rate that

has been set as a result of entering into the swap.

– Therefore, because actual interest rate movements do not always match

expectations, from the stand-alone viewpoint of the swap only, swaps entail

interest rate risk. For example, the variable rate receiver will profit if interest rates

rise and will lose if interest rates fall, and vice versa for the fixed rate receiver.

– However, when viewed in conjunction with the cash flows of the underlying debt

being hedged, the variable rate receiver has effectively locked in the hedged

interest rate at the time the swap was entered into, as the any fluctuations in the

variable rate being received will be offset by the variable rate being paid on the

underlying debt. The company is effectively left with the fixed rate + the margin

on the underlying debt.

47


• While we will get into the accounting for interest rate swaps later in the webinar, it is

important to note that interest rate swaps are “marked to market” at each reporting

date; that is, they are recorded at estimated fair value, with the change either being

reported in earnings or through other comprehensive income. Therefore, depending

upon whether the company designates the interest rate swap as a hedge under ASC

815 as an investment, the change in fair value could have a material effect on the

company’s earnings, even though the company has effectively locked in the same

interest rate over the period of the interest rate swap.

• For example, if the company has not designated hedge accounting and as the

variable rate payer under an interest rate swap, interest rates drop by a large amount,

the value of the interest rate swap will be significantly decreased such that the

company will need to record the change in fair value through earnings. However, the

company does not get an offset to the drop in fair value of the swap by reducing the

value of its debt. Therefore, companies must keep this in mind before they enter into

interest rate swaps and determine whether hedge accounting will be utilized (note

there are specific and stringent criteria to qualify for hedge accounting).

48


• Credit, or counterparty, risk

– Swaps are also subject to the counterparty’s credit risk: The

chance that the other party in the contract will default on its

responsibility. Although this risk is very low – banks that deal in

LIBOR and interest rate swaps generally have very high credit

ratings of double-A or above – it is still higher than that of a risk-

free U.S. Treasury bond.

49

Risk Characteristics: Caps

• Interest rate caps are option products and as such, share certain

common characteristics with all options.

– An upfront premium is required to purchase a cap.

– The value of a cap depends upon the variability of interest rates

(that is, the projected volatility of interest rates over the life of the

cap).

– The longer the maturity of the cap, the more expensive.

– A cap provides “insurance” against higher interest rates.

– The farther out of the money a cap is (that is, the higher the cap

rate), the cheaper it will be.

50

Risk Characteristics: Caps (Cont.)

• As stated before, the only value at risk with an interest rate cap is

the premium paid for the cap agreement.

• The value of the interest rate cap agreement will increase with

increases in interest rates, and will decrease with decreases in

interest rates.

• All other aspects of the value of the interest rate cap are the same

as for other types of options.

– Increase in interest rate volatility increases the value of the interest rate

cap

– Increase in term, increases the value of the interest rate cap

– Increase in cap rate, decreases the value of the interest rate cap

– And vice versa

51

Pros And Cons: Interest Rate Swaps

Pros

• No up-front cash outlay

• Effective hedging vehicle

• Locks in an effective rate

Cons

• No upside participation (no gain from decline or rise in interest rates)

• Mark-to-market accounting can have large effect on net income.

• Credit, non-performance risk

52

Pros And Cons: Interest Rate Caps

Pros

• Effective interest rate risk hedging vehicle with participation in gains

from decrease in interest rates

• Can only lose premium paid; cannot go to below zero (re: no liability

treatment)

• Caps interest rate

Cons

• Up-front cash outlay

• Mark-to-market accounting can have large effect on net income,

although losses only to the extent premium paid.

• Credit, non-performance risk

53

Valuation

• ASC 820 provides a fair value hierarchy under which among other

items, derivatives, must be measured and disclosed.

• Given that interest rate swaps and caps into which your companies

will enter will not be able to be valued by obtaining market quotes,

the fair values must be estimated via cash flow and option pricing

models.

• Typically, your banker will provide a statement of the fair value of

these instruments. However, if the value is considered material in

relation to your financial statements, your auditors will need to audit

it, and it is rare that the banker will provide them access to their

pricing models as they are typically deemed to be proprietary.

54

Valuation (Cont.)

• Therefore, in the situation of a non-publicly traded entity, the auditor

maybe able to estimate the value of the interest rate swap and/or

cap for the company, in the context of auditing the confirmation

received from the bank. However, auditors cannot derive the

valuation assumptions for management.


56

Valuation: Interest Rate Swaps

• Interest rate swaps are valued by taking the net present value of the

estimated cash flows over the life of the swap.

• Given that the fixed rate payments are known, the variable rate

payments must be estimated.

– The future variable rate payments can be estimated by extracting

the forward rates for the variable rate, and using these as our

estimates of the variable rate that will be in effect at settlement.

– By definition, a forward interest rate is the interest rate for a

future period of time that is implied by the interest rates

prevailing in the market today.

57

Valuation: Forward Rates

• Forward rates: Example

– Forward rates are derived from the current rates in the market; for

example:

– Three-month LIBOR = 2%

– Six-month LIBOR = 4%

– The implied three-month LIBOR rate from the 4th – 6th month is 6%.

– This is because if an investor can invest $1,000 for three months @ 2%

and can invest for six months @ 4% then the sum of the three month

periods must be equivalent to the six-month return of 4%.

– Therefore, the investor earns $20 for the six months at 4% and earns $5

for the three months at 2%. So, he must earn $15 for the second three

months, which is equivalent to a rate of 6%.

– This is the logic behind forward rates and how they are determined from

the yield curve for the underlying base rate

58

Valuation: Interest Rate Swaps – No CVA

Example

1 2 3 4 5 6 7 8 9 10 11

Swap Rate: 2.60% Annualized Period Present

3 Month LIBOR 3 Month LIBOR Payer Receiver Value of

Total Period Notional Forward Forward Fixed Floating Net Discount Net

Date Days Days Principal Rate Rate Cash Flow Cash Flow Cash Flow Factor Cash Flow

12/31/2012 $10,000,000

3/31/2013 90.00 90.00 $10,000,000 2.0000% 0.5000% ($64,110) $50,000 ($14,110) 0.99502 ($14,039)

6/30/2013 181.00 91.00 $10,000,000 2.2500% 0.5625% ($64,822) $56,250 ($8,572) 0.98946 ($8,482)

9/30/2013 273.00 92.00 $10,000,000 2.5000% 0.6250% ($65,534) $62,500 ($3,034) 0.98331 ($2,984)

12/31/2013 365.00 92.00 $10,000,000 2.7500% 0.6875% ($65,534) $68,750 $3,216 0.97660 $3,141

($22,364)

Therefore, based upon the following swap terms:

Notional Amount: $10,000,000

Swap Rate: 2.60%

Fixed Rate Payer: XYZ Company & Floating Rate Receiver

Floating Rate Payer: ABC Bank & Fixed Rate Receiver

Settlement: Every 3 months

Floating Rate: 3 month LIBOR

Maturity: 12/31/2013

The value of the interest rate swap to XYZ Company is as follows: ($22,364)

Which would be recorded as follows as of 12/31/12, assuming

hedge accounting has not been elected: Unrealized loss - derivatives $22,364

ST Derivative Liability $22,364

59

Valuation: Counterparty Valuation Adjustment

As stated before, over-the-counter derivatives (not actively traded)

must have the counterparty valuation adjustment (CVA) factored into

fair valuation estimate of the derivative. With interest rate swaps, the

CVA is representative of the credit risk of the counterparty. For

interest rate swaps, as there are 2 parties, there are 2 CVA factors: 1

for the bank and 1 for the counterparty (although for swaps with

projected net cash flows that are either all outflows or all inflows, the

CVA for the party paying the cash flows is the only applicable CVA).

The CVA is the rate that represents the credit risk of the counterparty

and is added to the risk free rate to calculate the applicable discount

factor for each projected net cash flow over the life of the interest

rate swap.

60

Valuation: Interest Rate Swaps – With CVA

Example

1 2 3 4 5 6 7 8 9 10 11

Swap Rate: 2.60%

CVA XYZ Co 2.00% Fixed payer Annualized Period Present

CVA ABC Bank 1.00% Floating payer 3 Month LIBOR 3 Month LIBOR Payer Receiver Value of

Total Period Notional Forward Forward Fixed Floating Net Discount Net

Date Days Days Principal Rate Rate Cash Flow Cash Flow Cash Flow Factor Cash Flow

12/31/2012 $10,000,000

3/31/2013 90.00 90.00 $10,000,000 2.0000% 0.5000% ($64,110) $50,000 ($14,110) 0.99038 ($13,974)

6/30/2013 181.00 91.00 $10,000,000 2.2500% 0.5625% ($64,822) $56,250 ($8,572) 0.97957 ($8,397)

9/30/2013 273.00 92.00 $10,000,000 2.5000% 0.6250% ($65,534) $62,500 ($3,034) 0.96761 ($2,936)

12/31/2013 365.00 92.00 $10,000,000 2.7500% 0.6875% ($65,534) $68,750 $3,216 0.96386 $3,100

($22,207)

Therefore, based upon the following swap terms: Valuation w/o CVA factor ($22,364)

CVA $157

Notional Amount: $10,000,000

Swap Rate: 2.60%

Fixed Rate Payer: XYZ Company & Floating Rate Receiver

Floating Rate Payer: ABC Bank & Fixed Rate Receiver

Settlement: Every 3 months

Floating Rate: 3 month LIBOR

Maturity: 12/31/2013

The value of the interest rate swap to XYZ Company is as follows: ($22,207)

Which would be recorded as follows as of 12/31/12, assuming

hedge accounting has not been elected: Unrealized loss - derivatives $22,207

ST Derivative Liability $22,207

61

Valuation: Interest Rate Cap

• Given that interest rate caps are options, we must use an option

pricing model to estimate the fair value thereof.

• The most widely used option pricing model for interest rate caps is a

derivation of the Black Scholes option pricing model, called the

Black option pricing model.

62

Valuation: Interest Rate Caps (Cont.)

• While going through the math that is behind the valuation of an

interest rate cap using the Black Model is beyond the scope of this

webinar, we will touch upon the variables that must be

input/estimated for the Black Model.

63


flag = "caplet" for pricing European call options on interest rates

X = option strike price (e.g. 2.6%)

ndays = the number of days in the protection period ( = life of option)

basis = the number of days used in the forward market for quoting interest rates

( e.g., 360 days or 365 days)

ep = length of the exposure period (also called the reset period), measured in

years (e.g., 0.5 yrs, or 2.75 yrs, etc.)

z = the continously compounded zero coupon rate over the exposure period

f = the forward rate over the protection (or reset period) period

Vol = volatility of the forward interest rate

Exposure Period

t=0 t= 6

Protection Period

t = 1 year

f = z=

Life of

64


1 2 3 4 5 6 7 8 9 10 11 12 13 14

X ndays basis ep z f Vol

Notional: $10,000,000 # of Days # of Days (Reset zero Forward Volatility

Base Rate: 3 month LIBOR Option In In Fwrd Period) Rate for Rate for 3 mn LIBOR Value

Life of Strike Protection Market Exposure Exposure Protection Forward Caplet of

Period From To Days Caplet Price Period Quotes Period (yrs) Period (yrs) Period (yrs) Rate Price Caplet

31-Dec-12 31-Mar-13 90.00 0.3 2.60% 90.0 360.0 2.00% 60.00%

1 1-Apr-13 30-Jun-13 90.00 0.5 2.60% 90.0 360.0 0.3 2.25% 2.25% 60.00% 0.0003628 $3,628

2 1-Jul-13 30-Sep-13 91.00 0.8 2.60% 91.0 360.0 0.5 2.38% 2.50% 60.00% 0.0009437 $9,437

3 1-Oct-13 31-Dec-13 91.00 1.0 2.60% 91.0 360.0 0.8 2.50% 2.75% 60.00% 0.0015457 $15,457

$28,522

Therefore, in this example, the Company has purchased an interest rate cap for a period

of 1 year, with 3 remaining settlements. The notional amount is $10,000,000 and the cap rate is 2.60%.

Given the forward rate curve as of 12/31/12 (hypothetical not actual), and an estimated volatiltiy

of the 3 month LIBOR of 60%, the total value of the entire interest rate cap agreement is $28,522

Exposure Periodt= t= 6 mosPro t = 1 z= .07

65

Interest Rate Caps: Volatility

• As we can see from the example, the most important variables that

are input into the Black model are as follows:

• Forward curve: Three-month LIBOR – obtained from observed

market rates as of the valuation date

• Volatility for the underlying, in this case the three-month LIBOR rate:

Volatility is an estimate which, as with any estimates, needs to be

that amount that we most expect to occur in the future. This can be

obtained from historical data representing the actual volatility that

has occurred over a period consistent with the term of the interest

rate cap agreement. Or, volatility can be estimated using the implied

volatility in the valuations of similar actively traded instruments.

66

Futures Contracts

• Futures contracts are actively traded instruments in the marketplace

on certain regulated exchanges.

• Futures contracts allow the buyer (seller) to purchase (sell) a stated

notional amount of a certain commodity, currency, financial

instrument, etc. … at a stated price over a designated period of time.

• Futures contracts may be entered and exited at anytime during the

life of the futures contract, provided that the buyer (seller) is willing

to accept a net settlement of the value of the futures contract and

not physical settlement (receipt of the actual underlying).

• The prices of futures contracts are based on the current spot price

and can be estimated from the spot price using the risk-free rate, the

dividend or stated interest rate on the underlying (if any), costs of

storage and convenience cost.

67

Futures Contracts (Cont.)

• Therefore, using the following formulae, the value of a futures

contract can be derived from the current spot price of the underlying

and compared to the actual future price to identify any opportunities

in the marketplace:

Futures prices with:

T = Time to maturity

S = Current Spot price of Underlying

r = risk free rate for T

I = Known income provided by underlying

q = Known convenience income or yield

c = costs of carrying the commodity

e = 2.71828

^ = to the power of

F = Se^rT Provides no income

F = (S - I)e^rT Provides income with present value = I

F = Se^(r-q)T Provides yield = to q%

F = Se^(r+c)T Cost to maintain = c%

68

Futures Contracts (Cont.)

EXAMPLE – value of futures contract

Futures prices with: VARIABLES FOR CONTRACT

T = Time to maturity 1

S = Current Spot price of Underlying $1,578.00 GOLD - 1 oz

r = risk free rate for T 0.13%

I = Known income provided by underlying 0

q = Known convenience income or yield 0

c = costs of carrying the commodity 0

e = 2.71828 2.71828

^ = to the power of

ACTUAL per CME $1,588.00

F = Se^rT Provides no income $1,580.05 = 1580*(2.71828)^(.0013*1)

F = (S - I)e^rT Provides income with present value = I

F = Se^(r-q)T Provides yield = to q%

F = Se^(r+c)T Cost to maintain (storage) = c%

69

Forward Contracts

• Therefore, although forward contracts may impose explicit times for settlement (e.g.,

at the maturity of the contract), the formula for calculating the value of a forward

contract is the same as the formula for calculating the value of a futures contract,

except for one difference – CREDIT RISK.

• Given that futures contracts are traded on organized exchanges, the requirement for

initial and maintenance margin limits the credit risk associated with these contracts,

and as such credit risk is generally not considered in the valuation of futures

contracts.

• However, assuming that a forward contract meets the definition of a derivative, and if

the underlying is consistent with the underlying of an actively traded futures contract,

it is likely that this is the case, the holder of the forward contract must take into

account the credit risk of the counterparty, when determining the value of the forward

contract. That is, the CVA must be added to r when discounting the value of the

contract.

– NOTE: You must take into account the presence of credit enhancements when

valuing the contract. E.g,. collateral, letters of credit, guarantees, master netting

arrangements, etc.

70

Options On Futures And

Forward Contracts • Options on Futures and Forward contracts have the same properties as options on any financial asset (e.g.

stocks) and can, provided that the options are European, that is, they can only be exercised at maturity of the

contract (or at a certain date) be valued using the Black Scholes Option Pricing Model (or a derivation thereof, the

Black model).

• Therefore, a European call and put option can be valued using the following formulae:

Black Scholes Option Pricing Model for Futures Contracts:

EXAMPLE:

c = e^-rT[F*N(d1) - K*N(d2)] call = $1.05

p = e^-rT[K*N(-d2) - F*N(-d1)] put = $3.35

where

N(d) N(-d)

d1 =[ln(F/K) + σ^2*T/2] / σ*SQRT(T) 0.072169 N(d1) = 0.528766 0.471234

d2 =[ln(F/K) - σ^2*T/2] / σ*SQRT(T) = d1 - σ*SQRT(T) -0.07217 N(d2) = 0.471234 0.528766

EXAMPLE: PUT - CALL PARITY, requires that:

European call and put option on an oil futures contract c + Ke^-rT = p + Fe^-rt

T = 0.333333 Time to expiration

F = 60 Current Futures price We can use put-call parity to find

K = 60 Exercise price mispriced options in the market.

r = 0.09 Risk free rate

σ = 0.25 Volatility of Oil Futures Contract

e = 2.71828

71

Options On Futures

And Forward Contracts (Cont.)

• We can also calculate the values of options on futures contracts

using lattice based models (binomial and trinomial models) and

simulation. However, this is beyond the scope of this webinar.

72

Interest Rate Swaps:

Current Market Rate • Given the decrease in interest rates experienced over the past year,

the current index for swap rates is very low from a historical

perspective.

• Current swap rate (www.federalreserve.gov) 4/5/13 – fixed for three-

month LIBOR

– 1 yr = .32%

– 2 yr = .37%

– 3 yr = .48%

– 4 yr = .65%

– 5 yr = .87%

– 7 yr = 1.33%

– 10 yr = 1.87%

http://www.federalreserve.gov/

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