### Alfred Mukunya

```Swaps and
Derivative Valuations
November 2012
presented by:
Alfred Mukunya
Director
Summary of Presentation
•
Introduction to Interest Rate Swaps
•
Swap Pricing and Valuation
•
New Developments in Valuations (OIS curve discounting)
•
GASB 53 & 64
•
ASC 820 Fair Value
•
•
Appendix A: Case Studies & Suggested Accounting
Appendix B: Barclays OIS Paper
PFM Asset Management LLC: May, 2012
2
Introduction to
Interest Rate Swaps
Interest Rate Swaps in General
•
•
•
•
An interest rate swap is a contract between two parties (“counterparties”) to
exchange interest rate payments at specified dates in the future.
The interest rate payments for a given counterparty equal the product of an
interest rate (swap rate) and a principal amount.
Usually, the swap rate for one counterparty is a fixed rate, while the swap
rate for the other counterparty is a variable rate.
The principal amount by which the swap rates are multiplied is “notional”.
That is, principal payments are not swapped, paid or exchanged; the
notional principal amount is only an arithmetic device to calculate swap
payments.
Counterparty
A
Fixed Payments
(Fixed interest rate X
notional principal amount)
Counterparty
B
Floating Payments
(Variable interest rate X
notional principal amount)
PFM Asset Management LLC: May, 2012
4
Floating-To-Fixed Swap (“Synthetic Fixed”)
•
A floating-to-fixed interest rate swap allows an issuer to effectively convert all or a portion of its
variable (floating) rate debt to a “synthetic” fixed rate
•
The issuer becomes a “fixed rate payor”, receiving a floating rate payment from a counterparty
and paying a predetermined fixed rate
•
To the extent the variable rate received by the issuer offsets the variable rate paid by the issuer to
bondholders, the issuer’s debt cost equals the fixed swap rate plus any ancillary fees
Fixed Swap Rate
Swap
Counterparty
Issuer
Variable Bond Rate
Bondholders
PFM Asset Management LLC: May, 2012
Floating Swap Rate
30-Yr Synthetic Fixed Example
Pay Fixed Swap Rate:
2.65%
Rec Floating Swap Rate: (SIFMA)
Pay VRDB Rate: SIFMA
Pay Liquidity/Remarketing:
0.75%
Net:
3.40%
Ancillary Fees:
Remarketing
Liquidity
5
Swap Pricing and Valuation
Market Rates
•
There is an actively traded inter-dealer broker market for interest rate swaps
PFM Asset Management LLC: May, 2012
7
Swap Pricing - Approach to Market Value
•
Fixed swap rate is the breakeven rate that sets the present value of the
fixed payments equal to the present value of the expected floating, e.g.
LIBOR payments
– Expected floating payments are calculated using implied forward rates which can
be derived from exchange traded Eurodollar futures
•
Price or value of a swap = present value of fixed leg - present value of
floating leg
•
Price of an “at the market” swap = 0
•
An “off market” swap has value to one party and requires an up-front cash
payment to compensate for “off-market” rate
•
Additional features, such as embedded caps, floors and swaptions, can be
decomposed and independently valued.
PFM Asset Management LLC: May, 2012
8
Swap Termination Calculation Methodology
•
For a plain-vanilla interest rate swap:
– The existing swap is compared to a hypothetical at-market “mirror offset” swap with
identical terms
• Floating leg re-valued to next reset date (value equals zero if calculated on a rate reset
date)
• Fixed leg value equals PV of difference between the fixed payments on the old and mirror
swap
– All discounting normally done at dealer’s (taxable) cost of capital
Existing Swap
Mirror Offset Swap
New Fixed Rate
Old Fixed Rate
Issuer
Swap Dealer
Floating Rate
PFM Asset Management LLC: May, 2012
Issuer
Floating Rate
9
A Sample Swap Valuation
•
The issuer would be required to pay \$1,903,864 to terminate this swap
Scenario: 8 years ago an issuer entered into a 10-year Pay Fixed swap
Notional Amount: \$100,000,000
Existing Fixed Rate Paid by Issuer: 5.00%
Current Market Fixed Rate for 2-year swap: 4.00%
Period
Fixed
Payments @
5.00%
Fixed
Payments @
4.00%
1
2
3
4
2,500,000
2,500,000
2,500,000
2,500,000
2,000,000
2,000,000
2,000,000
2,000,000
PFM Asset Management LLC: May, 2012
Difference
Present
Value
-500,000
-490,196
-500,000
-480,584
-500,000
-471,161
-500,000
-461,923
Swap value = (1,903,864)
10
Swap Termination Matrix
•
A swap termination matrix can be used for sensitivity analysis
Swap Term (Years):
Notional Amount:
Contract Swap Rate:
Payment Frequency:
Issuer Pays:
10.0
\$ 100,000,000
5.00%
2
Fixed
TERMINATION PAYMENT AMOUNT
Remaining Term of Swap
(in Years)
PFM Asset Management LLC: May, 2012
Change in Swap Rate
10
9
8
7
6
5
4
3
2
1
-1.00%
(\$8,175,717)
(\$7,496,016)
(\$6,788,855)
(\$6,053,124)
(\$5,287,671)
(\$4,491,293)
(\$3,662,741)
(\$2,800,715)
(\$1,903,864)
(\$970,780)
-0.50%
(\$3,990,928)
(\$3,666,915)
(\$3,328,158)
(\$2,973,985)
(\$2,603,695)
(\$2,216,554)
(\$1,811,796)
(\$1,388,619)
(\$946,185)
(\$483,617)
0.00%
\$0
\$0
\$0
\$0
\$0
\$0
\$0
\$0
\$0
\$0
0.50%
\$3,806,813
\$3,512,192
\$3,201,143
\$2,872,752
\$2,526,051
\$2,160,019
\$1,773,579
\$1,365,592
\$934,857
\$480,106
1.00%
\$7,438,737
\$6,876,757
\$6,280,551
\$5,648,037
\$4,977,002
\$4,265,101
\$3,509,846
\$2,708,596
\$1,858,549
\$956,735
11
Mechanics of Fuel Price Swap
•
•
•
Hedger is normally a “fixed rate (price) payer” on swap
Floating index typically used in energy hedging is published price from an
industry trade publication, e.g. Platt’s Oilgram
Can specify physical or cash settlement on contract
– Physical settlement exposes hedger to force majeure events
Fixed Price \$/gal
Hedger
Counterparty
ULS Diesel Index Price
\$/gal
Variable Price
\$/gal
Diesel Fuel
Supplier
PFM Asset Management LLC: May, 2012
12
New Developments in
Valuations (OIS curve
discounting)
New Developments in Valuations/Modeling
From a major bank:
[Counterparty] will value OTC derivative
transactions using rates to discount
expected
cash
flows
under
the
transactions reflecting the terms of any
CSA (considering factors such as the yield
of the eligible assets which may be posted
as collateral, rather than a standard
discount curve based upon LIBOR, and
‘projection’ curves derived from market
standard instruments). 
PFM Asset Management LLC: May, 2012
14
Swap Discount Curves — New and Old
3.00
as of May 15, 2012
2.50
Overnight Index Swap
USD LIBOR Swap
2.00
1.50
1.00
0.50
0.00
1M
3M
6M
PFM Asset Management LLC: May, 2012
9M
12 M
2 Yr
3 Yr
4 Yr
5 Yr
7 Yr
10 Yr 12 Yr 15 Yr 20 Yr 25 Yr 30 Yr 40 Yr 50 Yr
15
New Developments in Valuations/Modeling
•
USD LIBOR Curve vs. Overnight Index Swap (OIS) Curves — \$100MM 20
year swap
LIBOR Discounting
OIS Discounting
Impact: (\$24.60MM) vs. (\$25.17MM) = (\$0.57MM)
Rate Equivalent: 3.5 basis points (0.035%)
PFM Asset Management LLC: May, 2012
16
GASB 53 & 64
Market Environment During GASB 53 Implementation
•
20 Year USD-LIBOR from 2000 to Present
PFM Asset Management LLC: May, 2012
18
Low Rates Persist — Compared to Initial Transactions
•
20 Year TaxExempt Rate
2001 to Present
– Level of
interest rates
are key drivers
of Fair Value
– Most borrowers
hedge against
rising interest
rates
– Results in
relatively large
liabilities
PFM Asset Management LLC: May, 2012
19
GASB 53 Summary Review
The following are the three core concepts of GASB 53:
1. Report the fair value of a derivative on the statement of net assets
(balance sheet).
2. All hedges must be evaluated for effectiveness
(methods outlined in the Statement, applied in stepladder fashion).
3. Recognize changes in the fair value - of the derivative either:
a) on the balance sheet or statement of net assets,
as deferred inflows or deferred outflows
if the derivative passes its effectiveness test; OR
b) as investment revenue/loss (i.e., gain or loss through statement of
revenues, expenses, changes in fund net assets, as appropriate) if the
derivative fails, or is not a hedge.
The government must also provide a summary of activity through the reporting
period
PFM Asset Management LLC: May, 2012
20
Primary Issuer Concerns of GASB 53
(in order of importance)
New asset/liability effect on bond covenant ratios
Potential investment revenue/loss effect on bond covenant
ratios
Potential Board, Investor, Press impact of recording
new liabilities/losses
Potential of recording large loss upon losing effectiveness
PFM Asset Management LLC: May, 2012
21
What are the Pros and Cons?
Pros
Cons
Consistent Critical Terms
Easy to implement
No flexibility for other types of swaps
Relatively easy to implement;
Uses observed bond and swap data
Could fall out of range in differing rate
environments
Conceptually easy to implement –just
Unpredictable and subjective if hedging
and hedged rates do not move significantly,
and in tandem.
Favorite among ASC 815;
Has worked well historically
Relatively harder to implement;
Needs statistical knowledge
Flexible, as long as one can justify
Too much subjectivity, and need to
document procedure
Quantitative Methods
Synthetic Instruments
Dollar Offset
Regression Analysis
Other Quantitative Methods
PFM Asset Management LLC: May, 2012
22
How to Account for an Effective Hedge (Journal
Entries)?
•
When a derivative is an effective hedge and its value goes up by
\$1,000,000
Date
Account Titles
Debit
June 30, 20XX
Swap
1,000,000
Deferred Inflow
•
Credit
1,000,000
When a derivative is an effective hedge and its value goes down by
\$1,000,000
Date
Account Titles
Debit
June 30, 20XX
Deferred Outflow
1,000,000
Swap
PFM Asset Management LLC: May, 2012
Credit
1,000,000
23
What Happens to an Ineffective Hedge (Journal
Entries)?
•
When a derivative is an ineffective hedge and its value goes up by
\$1,000,000
Date
Account Titles
Debit
June 30, 20XX
Swap
1,000,000
Investment Revenue
•
Credit
1,000,000
When a derivative is an ineffective hedge and its value goes down by
\$1,000,000
Date
Account Titles
Debit
June 30, 20XX
Investment Loss
1,000,000
Swap
PFM Asset Management LLC: May, 2012
Credit
1,000,000
24
2. Refundings and Restructurings 2008 through 2011
– Timeline Linking Market and Accounting Events
Bear
Stearns
Collapse
GASB 53
Implementation
for most Issuers:
Lehman
Bankruptcy
GASB 53
Effective,
periods after
9/15/08
6/15/2009
20 Year LIBOR
Swap Rate: 3.59%
6/30/09
6/30/10
GASB 64
Effective,
periods after
6/15/2011
3/08
Market
Events
Fiscal Year Ending 6/30/08
GASB 53
Release
20 Year
LIBOR
Swap Rate:
5.81%
6/08
6/30/07
20 Year
LIBOR
Swap Rate:
2.80%
6/30/11
GASB 53
In effect:
GASB 64
Release
7/1/2010
6/11
12/31/2008
Hedges
Hedge &
Hedged
Item
Events
A.
B.
C.
D.
Fixed Payer Swaps
Forward Swaps
Swaptions
Basis Swaps
A.
B.
C.
D.
Auction Rate Security (ARS)
Anticipated Issuance
Fixed Rate Bond
Defaults result in swap
assignments from one
counterparty to another.
Swaption exercises;
Swap Modifications from SIFMA to 67% of LIBOR;
Swaps paired to other bonds;
Terminations.
Hedged Items
PFM Asset Management LLC: May, 2012
Conversion/Reissuance from
ARS to Variable Rate Demand
Bond (VRDB) , or bank notes.
Refunding Bonds issued;
Refunding Bonds not issued;
Fixed Rate Bonds issued;
Anticipated Bonds not issued.
25
GASB 64 in Effect, Fair Value Measurements Coming Up
20 Year
LIBOR
Swap Rate:
3.94%
6/30/11
20 Year
LIBOR Swap
Rate: 2.60%
20 Year
LIBOR Swap
Rate: 2.50%
Fair Value
Measurement
Formed
20 Year
LIBOR Swap
Rate: 2.91%
20 Year
LIBOR Swap
Rate:
2.3655%
9/30/11
12/31/11
2/12
3/31/12
6/30/12
9/30/11
GASB 64
In effect:
12/31/11
3/31/12
T
o
d
a
y
Fiscal Year Ending 6/30/12
Fair Value Measurement
Exposure Draft Expected
11/12
7/1/2011
PFM Asset Management LLC: May, 2012
26
Credit Support
Credit Support
Function
PFM Asset Management LLC: May, 2012
Credit Support
pulldown
for access
to more
detail.
27
ASC 820 Fair Value
The New Accounting Standards Codification (ASC)
•
The Financial Accounting Standards Board (FASB) Accounting
Standards Codification (ASC) has changed the structure and hierarchy
of accounting standards. FASB ASC disassembled and reassembled
thousands of accounting pronouncements (Statements, Issues, etc.) to
organize them under approximately 90 topics, and Accounting
•
FASB issued the last Statement No. 168 in June 2009 establishing
FASB ASC as the source of authoritative US accounting and reporting
standards for nongovernmental entities. This is effective for periods
ending after September 15, 2009.
•
FAS 157 is now known as FASB ASC 820 or ASC 820.
PFM Asset Management LLC: May, 2012
29
ASC 820 Reporting Requirements
Example level disclosure:
Level 1
Common stocks - Consumer
durable goods
Common stocks - Consumer
nondurable goods
\$
Level 2
1,086,000 \$
Level 3
-
\$
Total
-
\$
1,086,000
3,280,000 \$
3,435,000
155,000
-
921,000
-
-
\$
921,000
Convertible bonds
-
5,400,000
-
\$
5,400,000
Swaps
-
2,710,000
-
\$
2,710,000
U.S. government obligations
-
3,475,000
-
\$
3,475,000
Repurchase agreements
-
500,000
-
\$
500,000
3,280,000 \$
17,527,000
Common stocks - Other industries
TOTAL
PFM Asset Management LLC: May, 2012
\$
2,162,000 \$
12,085,000 \$
30 30
ASC 820 and ASU No. 2010-06 Summary:
Fair Value Definition
• Fair value shall reflect the nonperformance risk of the client
counterparty relating to that liability
• Fair value shall reflect the nonperformance risk of the bank counterparty
relating to that asset
Fair Value Hierarchy based on Valuation Technique/Input
• Inputs to generate the valuation are classified into three different Levels
– Level 1 – Quoted prices
– Level 2 – Observable inputs
– Level 3 – Unobservable inputs
•
Disclosure is made of the Level within which the Fair Value falls
•
PFM will help compute Fair Value Measurements for any
Asset/Liability requiring compliance with ASC 820 .
PFM Asset Management LLC: May, 2012
31
ASC 820 Outline of Methodology
•
Determine nonperformance risk free valuation
– Old definition of fair value, e.g. using a mid LIBOR curve
•
Absent nonperformance risk, determine whether asset or liability
•
Absent nonperformance risk, determine which counterparty is at risk of
nonperformance
•
Create a counterparty specific discounting curve based on:
– A: Relevant, Observable (Level 2) industry, sector, geographic curves, e.g. Fair
Market Curves on Bloomberg, or Thomson Financial.
– B: Unobservable (Level 3) client specific curve adjustments – if necessary
•
Compute a risk adjusted valuation using the counterparty specific
discounting curve
•
The difference between the nonperformance risk free valuation and risk
•
In the simplest case, this is the Credit Value Adjustment (CVA) to apply to
the nonperformance risk free valuation to get the Fair Value under ASC 820
PFM Asset Management LLC: May, 2012
32
Appendix A:
Case Studies &
Suggested Accounting
Case Studies - Outline
1. Refunding and Restructuring
•
•
•
Changes in Hedging Item
Changes in Hedged Item
Imputed Borrowings
2. GASB 64 Update
3. Swaption Bifurcation -Trifurcation (contains all aspects of GASB 53)
•
•
•
Investment
Borrowing
Hedge
PFM Asset Management LLC: May, 2012
34
Refundings (Hedged Item Events) and
Restructurings (Hedging Item Events)
Situation:
FY ending June 2010 - Off-market SIFMA swap with up front amount received at inception.
- booked as a hybrid instrument consisting of a borrowing and an at-the-market SIFMA
swap as of June 30, 2010.
During FY ending June 2011 floating leg of the swap is amended from SIFMA to 67% of USD
LIBOR resulting in a lower fixed rate for the rest of the life of the swap. No cash changes
hands.
Suggested treatment: new hybrid instrument accounted for as:
a)
b)
Termination of at-the-market SIFMA swap
•
Clear out associated deferral account
New imputed borrowing of fair value of terminated at-the-market SIFMA swap
•
c)
New at-the-market 67% of LIBOR swap
•
d)
To be amortized over the life of the new at-the-market 67% of LIBOR swap
Amended swap terminates the old
Old borrowing of upfront amount received at inception of original transaction
•
Continues to be amortized over remaining life
PFM Asset Management LLC: May, 2012
35
Refundings (Hedged Item Events) and
Restructurings (Hedging Item Events)
Situation:
During FY ending June 2012, Bank Counterparty seeking to exit municipal derivatives business
agrees with issuer to novate a swap transaction to another Bank Counterparty.
Suggested treatment:
a)
b)
Viewed by the Board as a termination that changes a government’s financial position,
therefore
•
Clear out associated deferral account
•
Gain/Loss is recognized in Statement of Activities
New off-market swap, with Imputed At-the-Market Swap, and Fixed Rate Imputed
Debt.
•
The above market portion of the swap is an imputed borrowing
•
Government could have paid off the fair value of swap by a borrowing
PFM Asset Management LLC: May, 2012
36
Swaptions
Background - The Bite at the Apple:
– Municipal bond issuers often have the right to call and refund fixed-rate bonds
at par (face), typically 10 years after issuance of the debt.
– The right to call tax-exempt debt is restricted by the call date and the Treasury
rules for tax-exempt debt.
• Advance refundings are possible but restricted by tax law to one per bond issue.
• Funds must be escrowed to the call date and costs may impact efficiency.
– Ability to refund bonds has been described as a “bite at the apple” to signify
the one-time only decision.
– Traditionally, an issuer would wait until the call date, call the bonds and issue
new refunding bonds at lower interest rates.
– Benefit of a traditional refunding is recognized through lower interest cost over
time.
PFM Asset Management LLC: May, 2012
37
Swaptions
Synthetic (as opposed to Traditional) Refunding:
– Issuer possesses the right (option) to call their outstanding fixed-rate bonds.
– The option increases in value as rates fall.
– Swaption sale allows the Issuer to synthetically forward refund the Bonds to lock
in savings based on prevailing market conditions.
• Intrinsic value – the amount by which the fixed rate commitment (strike) of the option
exceeds the prevailing interest rate (at-the-money) and
• Time value of the option – the amount above the intrinsic value which a banker will
pay the issuer based on the probability the option will increase more in value between
the premium payment date and maturity of the option.
– Swaption sale monetizes the option embedded in the callable bonds.
• Prior to a current refunding
• Swaption is structured to mirror the optional redemption features of the Bonds.
PFM Asset Management LLC: May, 2012
38
Swaption Accounting
Illustration 11 – Hybrid Instrument Bifurcation
– Embedded Derivative Instrument
• Time Value
• Goes to zero at maturity of the swaption
• Will change depending on prevailing rates
– Borrowing
• Instrinsic Value, carried at Historical Cost
– Rates fell significantly since inception of most swaptions
– Differences interpreting definitions in the Standard, and how to compute the
components based on the definitions resulted in material differences of opinion in
what to book.
– For example:
• Does the Embedded Derivative Instrument value result from subtracting the prevailing
intrinsic value?
• Or the historical borrowing?
• Is it only the time value?
• What about the large increases/decreases in the fair value of the entire swaption?
PFM Asset Management LLC: May, 2012
39
Swaption Accounting
Swaption Trifurcation
– Embedded Derivative Instrument
• Time Value.
• Goes to zero at maturity of the swaption.
• Will change depending on prevailing rates.
– Borrowing
• Instrinsic Value, carried at Historical Cost.
– At-the-Money Swap
• Originally at zero cost.
• Reflects the original intent of the Issuer to refund in the future.
• The prevailing at-the-money swap rate at inception is the beneficial fixed rate the issuer
has locked in upon selling the swaption.
PFM Asset Management LLC: May, 2012
40
Appendix B:
Barclays OIS Paper
This material is based on information obtained from sources generally believed to be reliable and available to the
public, however PFM Asset Management LLC cannot guarantee its accuracy, completeness or suitability. This material
is for general information purposes only and is not intended to provide specific advice or a specific recommendation.
All statements as to what will or may happen under certain circumstances are based on assumptions, some but not all
of which are noted in the presentation. Assumptions may or may not be proven correct as actual events occur, and
results may depend on events outside of your or our control. Changes in assumptions may have a material effect on
results. Past performance does not necessarily reflect and is not a guaranty of future results. The information
contained in this presentation is not an offer to purchase or sell any securities.
PFM Asset Management LLC: May, 2012
42
```