## Transcript

Interest Rate Swaps
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Interest Rate Swaps: Origin
Today there exist an interest rate swap market where trillions of dollars (in notional principal) of swaps of fixed-rate loans for floating-rate loans occur each year.
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Interest Rate Swaps: Origin
The market primarily consist of financial institutions and corporations who use the swap market to hedge more efficiently their liabilities and assets. Many institutions create synthetic fixed- or floating-rate assets or liabilities with better rates than the rates obtained on direct liabilities and assets.
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Interest Rate Swaps: Definition
Definition: A swap is an exchange of cash flows, CFs. It is a legal arrangement between two parties to exchange specific payments.
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Interest Rate Swaps: Types
There are four types of swaps:
1. Interest Rate Swaps: Exchange of fixed-rate payments for floating-rate payments Currency Swaps: Exchange of liabilities in different currencies Cross-Currency Swaps: Combination of Interest rate and Currency swap Credit Default Swaps: Exchange of premium payments for default protection
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2.
3.
4.
Plain Vanilla Interest Rate Swaps
Definition Plain Vanilla or Generic Interest Rate Swap involves the exchange of fixed-rate payments for floating-rate payments.
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Plain Vanilla Interest Rate Swaps: Terms
1. Parties to a swap are called counterparties. There are two parties: Fixed-Rate Payer Floating-Rate Payer 1. Rates: Fixed rate is usually a T-note rate plus basis points. Floating rate is a benchmark rate: LIBOR.
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Plain Vanilla Interest Rate Swaps: Terms 3. Reset Frequency: Semiannual 4. Principal: No exchange of principal 5. Notional Principal (NP): Interest is applied to a notional principal; the NP is used for calculating the swap payments.
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Plain Vanilla Interest Rate Swaps: Terms 6. Maturity ranges between 3 and 10 years. 7. Dates: Payments are made in arrears on a semiannual basis: Effective Date is the date interest begins to accrue Payment Date is the date interest payments are made
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Plain Vanilla Interest Rate Swaps: Terms 8. Net Settlement Basis: The counterparty owing the greater amount pays the difference between what is owed and what is received—only the interest differential is paid. 9. Documentation: Most swaps use document forms suggested by the International Swap Dealer Association (ISDA) or the British Banker’s Association. The ISDA publishes a book of definitions and terms to help standardize swap contracts.
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Web Site
For information on the International Swap and Derivative Association and size of the markets go to www.isda.org
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Swap Terminology
Note: Fixed-rate payer can also be called the floating-rate receiver and is often referred to as having bought the swap or having a long position. Floating-rate payer can also be referred to as the fixed-rate receiver and is referred to as having sold the swap and being short.
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Plain Vanilla Interest Rate Swap: Example Example: Fixed-rate payer pays 5.5% every six months Floating-rate payer pays LIBOR every six months Notional Principal = $10 million Effective Dates are 3/1 and 9/1 for the next three years
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Plain Vanilla Interest Rate Swap: Example
1 Effective Dates 1 LIBOR 1 1 1 1 Floating-Rate Fixed-Rate Net Interest Received Net Interest Received Payer's Payment* Payer's Payment** by Fixed-Rate Payer by Floating-Rate Payer Column 1 Column 1 Column 1 Column 1 $11111 ,1 $11111 ,1 $11111 ,1 $11111 ,1 $11111 ,1 $11111 ,1 $22222 ,2 $11111 ,1 $11111 ,1 $11111 ,1 $11111 ,1 $11111 ,1 -$11 , 111 -$11 , 111 $1 $11 , 111 $11 , 111 $11 , 111 $11 , 111 $11 , 111 $1 -$11 , 111 -$11 , 111 -$11 , 111
11 1 / /Y 11 1 . 1 11 1 / /Y 11 1 . 1 11 1 / /Y 11 1 . 1 11 1 / /Y 11 1 . 1 11 1 / /Y 11 1 . 1 11 1 / /Y 11 1 . 1 11 1 / /Y * (LIBOR/ 1 11 , 111 )($ , 111 ) ** (. 111 11 , 111 /1 )($ , 111 )
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Interest Rate Swap: Point
Points:
If LIBOR > 5.5%, then fixed payer receives the interest differential. If LIBOR < 5.5%, then floating payer receives the interest differential.
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Interest Rate Swaps’ Fundamental Use One of the important uses of swaps is in creating a synthetic fixed- or floating-rate liability or asset that yields a better rate than a conventional or direct one:
Synthetic fixed-rate loans and investments Synthetic floating-rate loans and investments
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A synthetic fixed-rate loan is formed by combining a floating-rate loan with a fixedrate payer’s position Conventional FloatingRate Loan Swap: Fixed-Rate Payer Position Swap: Fixed-Rate Payer Position Synthetic Fixed Rate Pay Floating Rate Pay Fixed Rate Receive Floating Rate
Pay Fixed Rate
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Synthetic Fixed-Rate Loan
Example: A synthetic fixed-rate loan formed with 2-year, $10,000,000 floating-rate loan with rates set equal to the LIBOR on 3/1 and 9/1 combined with a fixed-rate payer’s position on the swap just analyzed.
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Synthetic Fixed-Rate Loan
1 Effective Dates 1 LIBOR 1 Swap Floating-Rate Payer's Payment* 1 Swap Fixed-Rate Payer's Payment** 1 Swap Net Interest Received by Fixed-Rate Payer Column 1− Column 1 -$11 ,111 -$11 ,111 $1 $11 , 111 $11 , 111 $11 , 111 1 Loan Interest Paid on Floating-Rate Loan* 1 1 Synthetic Loan Synthetic Loan Payment on Swap Effective and Loan Annualized Rate*** Column 1− Column 1 $11111 ,1 $11111 ,1 $11111 ,1 $11111 ,1 $11111 ,1 $11111 ,1 11 1 . 1 11 1 . 1 11 1 . 1 11 1 . 1 11 1 . 1 11 1 . 1
11 1 / /Y 11 1 . 1 11 1 / /Y 11 1 . 1 $11111 ,1 11 1 / /Y 11 1 . 1 $11111 ,1 11 1 / /Y 22 2 . 2 $11111 ,1 11 1 / /Y 11 1 . 1 $11111 ,1 11 1 / /Y 11 1 . 1 $11111 ,1 11 1 / /Y $11111 ,1 * (LIBOR/ 1 11 ,111 )($ ,111 ) ** (. 111 11 ,111 /1 )($ ,111 ) *** 1(Payment on Swap and Loan)/$11 ,111 , 111
$22222 ,2 $11111 ,1 $11111 ,1 $11111 ,1 $11111 ,1 $11111 ,1
$11111 ,1 $11111 ,1 $11111 ,1 $11111 ,1 $11111 ,1 $11111 ,1
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A synthetic floating-rate loan is formed by combining a fixed-rate loan with a floating-rate payer’s position. Conventional Fixed-Rate Loan Swap: Floating-Rate Payer Position Swap: Floating-Rate Payer Position Pay Fixed Rate Pay Floating Rate Receive Fixed Rate
Synthetic Floating Rate
Pay Floating Rate
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Synthetic Floating-Rate Loans
Example: A synthetic floating-rate loan formed with a 3-year, $10,000,000, 5% fixed-rate loan combined with the floating-rate payer’s position on the swap just analyzed.
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Synthetic Floating-Rate Loans
1 Effective Dates 1 LIBOR 1 Swap Floating-Rate Payer's Payment* 1 Swap Fixed-Rate Payer's Payment** 1 Swap Net Interest Received by Floating-Rate Payer Column 1− Column 1 $11 , 111 $11 , 111 $1 -$11 , 111 -$11 , 111 -$11 , 111 1 Loan Interest Paid on 1 Fixed-Rate Loan % 1 Synthetic Loan Payment on Swap and Loan Column 1− Column 1 $11111 ,1 $11111 ,1 $11111 ,1 $11111 ,1 $11111 ,1 $11111 ,1 1 Synthetic Loan Effective Annualized Rate***
1 /Y1 /1 11 .11 1 /Y1 /1 11 .11 $11111 ,1 1 /Y1 /1 11 .11 $11111 ,1 1 /Y1 /1 22 .22 $11111 ,1 1 /Y1 /1 11 .11 $11111 ,1 1 /Y1 /1 11 .11 $11111 ,1 1 /Y1 /1 $11111 ,1 * (LIBOR/ 1 11 , 111 )($ , 111 ) ** (. 111 11 , 111 /1 )($ , 111 ) *** 1 (Payment on Swap and Loan)/$ 11 , 111 , 111
$22222 ,2 $11111 ,1 $11111 ,1 $11111 ,1 $11111 ,1 $11111 ,1
$11111 ,1 $11111 ,1 $11111 ,1 $11111 ,1 $11111 ,1 $11111 ,1
11 .11 11 .11 11 .11 11 .11 11 .11 11 .11
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Swaps as Bond Positions
Swaps can be viewed as a combination of a fixed-rate bond and flexible-rate note (FRN). A fixed-rate payer position is equivalent to
1. Buying a FRN paying the LIBOR and 2. Shorting a fixed-rate bond at the swap’s fixed rate.
From the previous example, the fixed-rate payer’s swap’s CFs can be replicated by:
1. Selling at par a 3-year bond, paying a 5.5% fixed rate and a principal of $10,000,000 (semiannual payments) and 2. Purchasing a 3-year, $10,000,000 FRN with the rate reset every six months at the LIBOR.
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Swaps as Bond Positions
A floating-rate payer position is equivalent to
1. Shorting a FRN at the LIBOR and 2. Buying a fixed-rate bond at the swap fixed rate
From the previous example, the floating-rate payer’s swap’s CFs can be replicated by:
1. Selling a 3-year, $10,000,000 FRN paying the LIBOR and 2. Purchasing 3-year, $10,000,000, 5.5% fixed-rate bond at par
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Swaps as Eurodollar Futures Positions
A swap can also be viewed as a series of Eurodollar futures contracts. Consider a short position in a Eurodollar strip in which the short holder agrees to sell 10 Eurodollar deposits at the CME‑ index price of 94.5 (or discount yield of RD = 5.5%) with
Each of the contracts having a face value of $1,000,000 and maturity of 6 months The expirations on the strip being March 1st and September 1st for a period of two and half years
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Swaps as Eurodollar Futures Positions
With the index at 94.5, the contract price on one Eurodollar futures contract is $972,500:
1 .1 2 / 1) 11− (1 )(22 11 f1 = ,11 1) 1,11 ($1 1,11 = $11 1 11 1
The next slide shows the cash flows at the expiration dates from closing the 10 short Eurodollar contracts at the same assumed LIBOR used in the previous swap example, with the Eurodollar settlement index being 100 − LIBOR.
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Swaps as Eurodollar Futures Positions
1 Closing Dates 11 1 / /Y 11 1 / /Y 11 1 / /Y 11 1 / /Y 11 1 / /Y 1 LIBOR % 11 . 1 11 . 1 11 . 1 11 . 1 11 . 1 1 1 Cash Flow*
fT
$22222 ,2 $11111 ,1 $11111 ,1 $11111 ,1 $11111 ,1
1[f1− fT ] 1
-$11 , 111 $1 $11 , 111 $11 , 111 $11 , 111
*f1= 111 ,111
1− 2 / 1) 11 (LIBOR%)(2211 fT = ,11 1) ($1 1,11 11 1
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Swaps as Eurodollar Futures Positions
Comparing the fixed-rate payer's net receipts shown in Column 5 of the first exhibit (Slide 14) with the cash flows from the short positions on the Eurodollar strip shown in Slide 27, one can see that the two positions yield the same numbers.
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Swaps as Eurodollar Futures Positions
Note there are some differences between the Eurodollar strip and the swap: 1. First, a 6‑ month differential occurs between the swap payment and the futures payments. This time differential is a result of the interest payments on the swap being determined by the LIBOR at the beginning of the period, whereas the futures position's profit is based on the LIBOR at the end of its period. 2. Second, the futures contract is on a Eurodollar deposit with a maturity of 6 months instead of the standard 3 months.
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Swaps as Eurodollar Futures Positions
3. Credit Risk: On a futures contract, the parties transfer credit risk to the exchange. The exchange then manages the risk by requiring margin accounts. Swaps, on the other hand, are exposed to credit risk. Marketability: Swaps are not traded on an exchange like futures and therefore are not as liquid as futures.
4.
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Swaps as Eurodollar Futures Positions
5. Standardization: Swaps are more flexible in design than futures that are standardized. 6. Cash Flow Timing: CFs on swaps are based on the LIBOR 6 months earlier; CFs on futures are based on the current LIBOR.
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Swap Market Structure
Swap Banks: The market for swaps is organized through a group of brokers and dealers collectively referred to as swap banks. As brokers, swap banks try to match counterparties. As dealers, swap banks take temporary positions as fixed or floating players; often hedging their positions with positions in Eurodollar futures contracts or with spot fixed-rate and floating-rate bond positions.
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Swap Market Structure
Brokered Swaps: • The first interest rate swaps were very customized deals between counterparties with the parties often negotiating and transacting directly between themselves.
Fixed − Rate Payer
Party A
Party B
Floating − Rate Payer
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Swap Market Structure
Brokered Swaps:
• The financial institutions role in a brokered swap was to bring the parties together and to provide information; their continuing role in the swap after it was established was minimal; they received a fee for facilitating the swap. • Note:
The financial institution does not assume any credit risk with a brokered swap. The counterparties assume the credit risk and must make their own assessment of default potential.
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Swap Market Structure
Dealers Swaps: One of the problems with brokered swaps is that it requires each party to have knowledge of the other party’s risk profile. This problem led to more financial institutions taking positions as dealers in a swap—acting as market makers.
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Swap Market Structure
Dealers Swaps:
• With dealer swaps, the swap bank acts as swap dealer making commitments to enter a swap as a counterparty before the other end party has been located. In this market, the end parties contract separately with the swap bank, who acts as a counterparty to each.
Floating − Rate Payer Floating − Rate Payer
Party A
Swap Bank
Fixed − Rate Payer
Party B
Fixed − Rate Payer
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Swap Market Structure
Dealers Swaps: Features
Acting as swap dealers, financial institutions serve an intermediary function. The end parties assume the credit risk of the financial institution instead of that of the other end party. Small or no swap fee. The swap dealer’s compensation comes from a markup on the bid-ask spread extended to the end parties. The spread is reflected on the fixed rate side.
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Swap Market Structure
Dealers Swaps: Features
Because the financial institution is exposed to default risk, the bid-ask spread should reflect that risk. Because the swap dealer often makes commitments to one party before locating the other, it is exposed to interest rate movements.
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Swap Market Structure
Dealers Swaps: Features Warehousing: To minimize its exposure to market risk, the swap dealer can hedge her swap position by taking a position in a Eurodollar futures, Tbond, FRN, or spot Eurodollar contract. This practice is referred to as warehousing.
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Swap Market Structure
Dealers Swaps: Features Size Problem: Swap dealers often match a swap agreement with multiple counterparties. For example, a fixed for floating swap between a swap dealer and Party A with a notional principal of $50,000,000 might be matched with two floating for fixed swaps with notional principals of $25,000,000 each.
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Swap Market Structure
Floating − Rate Payer
Party B NP = $1m 1
Fixed − Rate Payer
Floating − Rate Payer
Party A NP = $1m 1
Swap Bank
Fixed − Rate Payer
Floating − Rate Payer
Fixed − Rate Payer
Party C NP = $1m 1
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Swap Market Structure
Dealers Swaps: Features Running a Dynamic Book: Any swap commitment can be effectively hedged through a portfolio of alternative positions—other swaps, spot positions in T-notes and FRNs, and futures positions. This approach to swap market management is referred to as running a dynamic book.
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Swap Market Price Quotes
By convention, the floating rate is quoted flat without basis point adjustments; e.g., LIBOR flat. The fixed rate is quoted in terms of the on-the-run (newly issued) T-note or T-bond YTM and swap spread.
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Swap Market Price Quotes
Swap spread: Swap dealers usually quote two different swap spreads
1. One for deals in which they pay the fixed rate 2. One in which they receive the fixed rate
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Swap Market Price Quotes
Swap Spread: 80/86 dealer buys at 80bp over T-note yield and sells at 86 over T-note yield. That is, the dealer will
Take the fixed payer’s position at a fixed rate equal to 80 BP over the T-note yield and Take the floating payer’s position, receiving 86 bp above the T-note yield.
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Swap Market Price Quotes
Swap Bank Quote Offerings Example:
Swap Maturity 1year 1year 1year 1year Treasury Yield 11 .1 % 22 .2 % 11 .1 % 11 .1 % Bid Swap Spread (BP) 1 1 1 1 1 1 1 1 Ask Swap Spread (BP) 1 1 1 1 1 1 1 1 Fixed Swap Rate Spread 1 1 -1 1 .1 % .1 % 1 1 -1 1 .1 % .1 % 2 2 -2 2 .2 % .2 % 1 1 -1 1 .1 % .1 % Swap Rate 11 .1 % 11 .1 % 11 .1 % 11 .1 %
Swap Rate = (Bid Rate + Ask Rate)/2
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Swap Market Price Quotes Example of Swap Quote and Terms
5-Year Swap
Party A
1. 2. 3. 4. 5. 6. 7.
Floating Rate = LIBOR
Swap Bank
Floating Rate = LIBOR
Party B
Fixed Rate = 1 1 .1%
Fixed Rate = 1 2 .2%
Swap Agreement:
Initiation Date = June 10, Y1 Maturity Date = June 10, Y6 Effective Dates: 6/10 and 12/10 NP = $20,000,000 Fixed-Rate Payer: Pay = 6.26% (semiannual)/ receive LIBOR Floating-Rate Payer: Pay LIBOR/Receive 6.20% (semiannual) LIBOR determined in advance and paid in arrears
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Swap Market Price Quotes
Note: The fixed and floating rates are not directly comparable. The T-note assumes a 365-day basis and the LIBOR assumes 360. The rates need to be prorated to the actual number of days that have elapsed between settlement dates to determine the actual payments. Formulas:
Fixed − Rate Settlement Payment : No. of Days (Fixed Rate ) NP 11 1 Floating − Rate Settlement Payment : No. of Days (LIBOR ) NP 22 2
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Swap Market Price Quotes
Cash Flow for Fixed-Rate Payer paying 6.26%
Settlement Date 11 /Y1 / 1 2/ 2 2 22 /Y 11 /Y1 / 1 1/ 1 1 11 /Y 11 /Y1 / 1 1/ 1 1 11 /Y 11 /Y1 / 1 Fixed-Rate Payers Position Number of Days LIBOR Fixed Payment Floating Payment 11 % . 1 22 2 22 % . 2 $111111 ,1 .1 $222222 , 2 .2 11 1 11 % . 1 $111111 ,1 .1 $111111 , 1 .1 11 1 11 % . 1 $111111 ,1 .1 $111111 , 1 .1 11 1 11 % . 1 $111111 ,1 .1 $111111 , 1 .1 11 1 11 % . 1 $111111 ,1 .1 $111111 , 1 .1 11 1 $111111 ,1 .1 $111111 , 1 .1 Fixed Payment = (. 1111 of days/ 11111 , 111 )(no. )($ , 111 ) Floating Payment = LIBOR(no. of days/ 111 , 11111 )($ 11 , 1 ) Fixed Net Payment $22 . 22 , 222 $11 . 11 , 111 $11 . 11 , 111 -$11111 , .1 -$11 . 11 , 111 -$11 . 11 , 111
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Opening Position: Swap Execution
Suppose a corporate treasurer wants to fix the rate on its floating-rate debt by taking a fixed-rate payer’s position on a 2-year swap with a NP of $50,000,000. The treasurer would call a swap trader at a bank for a quote on a fixed-rate payer position. Suppose the treasurer agrees to the fixed position at 100 bp above the current 2-year T-note, currently trading at 5.26%.
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Opening Position: Swap Execution
All terms of the swap, except the fixed rate, are mutually agreed to. Example:
1. 2. 3. 4. 5. 6. 7. Swap bank will pay 6-month LIBOR Corporation will pay T-note rate (approximately 5.26% ) + 100bp Settlement dates are set Interest paid in arrears NP = $50,000,000 Net payments U.S. laws govern the transaction
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Opening Position: Swap Execution
The swap bank could then hedge the swap by calling the bank’s bond trader for an exact quote on the T-note rate. To hedge its floating position, the swap bank might tell the bond trader to: Sell $50,000,000 of 2-year T-notes Invest the proceed from the T-note sale in a 2-year FRN paying LIBOR. Note: Alternatively, the trader might hedge with Eurodollar futures.
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Opening Position: Swap Execution
The T-note rate plus the 100 bp will determine the actual rate on the swap. If 2-year notes were at 5.26%, then the corporation’s fixed rate on the swap would then be set at 6.26%. The swap trader may eventually close the bond positions as other floating-rate swaps are created.
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Closing Swap Positions
Prior to maturity, swap positions can be closed by selling the swap to a swap dealer or another party. If the swap is closed by selling it to a dealer, the dealer pays or receives an upfront fee to or from the swap holder for assuming the holder’s position. Alternatively, the swap holder could also hedge his position by taking an opposite position in a current swap or possibly by hedging the position for the remainder of the maturity period with a futures or spot bond position.
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Closing Swap Positions
Example: A fixed-rate payer who unexpectedly sees interest rates decreasing and, as a result, wants to change his position, could do so by: Selling the swap to a dealer Taking a floating-rate payer's position in a new swap contract Going long in an appropriate futures contract; this strategy might be advantages if there is only a short period of time left on the swap.
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Closing Swap Positions
If the fixed-payer swap holder decides to hedge his position by taking an opposite position on a new swap, the new swap position would require a payment of the LIBOR that would cancel out the receipt of the LIBOR on the first swap. The difference in the positions would therefore be equal to the difference in the higher fixed interest that is paid on the first swap and the lower fixed interest rate received on the offsetting swap.
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Closing Swap Positions
Example: Suppose in our first illustrative swap example (3-year, 5.5%/LIBOR swap), a decline in interest rates occurs 1 year after the initiation of the swap, causing the fixed-rate payer to want to close his position. To this end, suppose the fixed-rate payer offsets his position by entering a new 2‑ year swap as a floating-rate payer in which he agrees to pay the LIBOR for a 5% fixed rate. The two positions would result in a fixed payment of $25,000 semiannually for two years ((.0025)NP).
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Closing Swap Positions
Offsetting Swap Positions Original Swap: Fixed Payer’s Position Original Swap: Fixed Payer’s Position Pay 5.5% Receive LIBOR − 5.5% +LIBOR −LIBOR +5%
Offsetting Swap: Floating Payer’s Position Pay LIBOR Offsetting Swap: Floating Payer’s Position Receive 5.0%
Pay 0.5% (annual) −0.5% Pay 0.25% (annual) (semiannually) −0.25% (semiannually
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Closing Swap Positions
Instead of hedging the position, the fixed-rate payer is more likely to close his position by simply selling it to a swap dealer. In acquiring a fixed position at 5.5%, the swap dealer would have to take a floating-payer’s position to hedge the acquired fixed position. If the fixed rate on a new 2-year swap were at 5%, the dealer would likewise lose $25,000 semiannually for 2 years from the two swap positions given a NP of $10,000,000.
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Closing Swap Positions
Thus, the price the swap bank would charge the fixed payer for buying his swap would be at least equal to the present value of $25,000 for the next four semiannual periods. Given a discount rate of 5%, the swap bank would charge the fixed payer at least $94,049 for buying his swap.
Fix V1
− $1,11 11 = ∑ = − $1,11 11 t + 2 )) t =1(1 (.2 / 1
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1
Closing Swap Positions
In contrast, if rates had increased, the fixed payer would be able to sell the swap to a dealer at a premium. Example:
If the fixed rate on a new swap were 6%, a swap dealer would realized a semiannual return of $25,000 for the next two years by buying the 5.5%/LIBOR swap and hedging it with a floating position on a 2-year 6%/LIBOR swap. Given a 6% discount rate, the dealer would pay the fixed payer a maximum of $92,927 for his 5.5%/LIBOR swap.
V
Fix 1
$2,11 21 = ∑ = $1,11 11 t + 1 )) t =1(1 (.1 / 1
1
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Swap Valuation
At origination, most plain vanilla swaps have an economic value of zero. This means that neither counterparty is required to pay the other to induce that party into the agreement. An economic value of zero requires that the swap’s underlying bond positions trade at par—par value swap. If this were not the case, then one of the counterparties would need to compensate the other. In this case, the economic value of the swap is not zero. Such a swap is referred to as an off-market swap.
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Swap Valuation
Whereas most plain vanilla swaps are originally par value swaps with economic values of zero, as we previously noted, their economic values change over time as rates change. That is, existing swaps become off-market swaps as rates change.
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Swap Valuation
In the preceding example, the fixed-payer’s position on the 5.5%/LIBOR swap had a value of −$94,049 one year later when the fixed-rate on new 2-year par value swaps was 5%; that is, the holder of the fixed position would have to pay the swap bank at least $94,049 to assume the swap. On the other hand, the fixed-payer’s position on the 5.5%/LIBOR swap had a value of $92,927 when the fixed-rate on the new 2-year par value swap was 6%; that is, the holder of the fixed position would have receive $92,927 from the swap bank.
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Swap Valuation
Just the opposite values apply to the floating position. Continuing with our illustrative example, if the fixed rate on new 2year par value swaps were at 5%, then a swap bank who assumed a floating position on a 5.5%/LIBOR swap and then hedged it with a fixed position on a current 2-year 5.5%/LIBOR swap would gain $25,000 semiannually over the next two year. As a result, the swap bank would be willing to pay $94,049 for the floating position. Thus, the floating position on the 5.5% swap would have a value of $94,049:
V
Fl 1
$1,11 11 = ∑ = $1,11 11 t + 2 )) t =1(1 (.2 / 1
1
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Swap Valuation
Offsetting Swap Positions Original Swap: Floating Payer’s Position Original Swap: Floating Payer’s Position Offsetting Swap: Fixed Payer’s Position Offsetting Swap: Fixed Payer’s Position Pay LIBOR Receive 5.5% Pay 5% Receive LIBOR Receive 0.5% (annual) −LIBOR +5.5% −5% +LIBOR 0.5% (annual)
Fl V1 =
$1,11 11 11 ∑ (1 (.2 / 1 t = $1,11 2 )) t =1 +
1
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Swap Valuation
If the fixed rate on new 2-year par value swaps were at 6%, then a swap bank assuming the floating position on a 5.5%/LIBOR swap and hedging it with a fixed position on a current 2-year 6%/LIBOR swap would lose $25,000 semiannually over the next year. As a result, the swap bank would charge $92,927 for assuming the floating position. Thus, the floating position on the 5.5% swap would have a negative value of $92,927:
Fl V1
=
− $2,11 21 11 ∑ (1 (.1 / 1 t = − $1,11 1 )) t =1 +
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1
Swap Valuation
Offsetting Swap Positions Original Swap: Floating Payer’s Position Original Swap: Floating Payer’s Position Offsetting Swap: Fixed Payer’s Position Offsetting Swap: Fixed Payer’s Position Pay LIBOR Receive 5.5% Pay 6% Receive LIBOR Pay 0.5% (annual) −LIBOR +5.5% − 6% +LIBOR − 0.5% (annual)
Fl V1
− $2,11 21 = ∑ = − $1,11 11 t + 1 )) t =1(1 (.1 / 1
1
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Swap Valuation
In general, the value of an existing swap is equal to the value of replacing the swap—replacement swap.
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Swap Valuation
Chapter 17
Formally, the values of the fixed and floating swap positions are:
SV
fix
M K P − KS = ∑ NP P t + t =1(1 K )
M KS − K P SV fl = ∑ NP P t + t =1(1 K )
KS = Fixed rate on the existing swap KP = Fixed rate on current par-value swap SVfix = Swap value of the fixed position on the existing swap SVfl = Swap value of the floating position on the existing swap
where:
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Swap Valuation
Note that these values are obtained by discounting the net cash flows at the current YTM (KP). As a result, this approach to valuing off-market swaps is often referred to as the YTM approach.
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Swap Valuation
The equilibrium price of a bond is obtained not by discounting the bond’s cash flows by a common discount rate, but rather by discounting each of the bond’s cash flows by their appropriate spot rates—the rate on a zero-coupon bond. Valuing bonds by using spot rates instead of a common YTM ensures that there are no arbitrage opportunities from buying bonds and stripping them or buying zero-coupon bonds and bundling them.
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Swap Valuation
The argument for pricing bonds in terms of spot rates also applies to the valuation of off-market swaps. Similar to bond valuation, the equilibrium value of a swap is obtained by discounting each of the swap’s cash flows by their appropriate spot rates. The valuation of swaps using spot rates is referred to as the zero-coupon approach.
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Comparative Advantage
Swaps are often used by corporations and financial institutions to take advantage of arbitrage opportunities resulting from capital-market inefficiencies. To see this consider the following case.
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Comparative Advantage
Case:
ABC Inc. is a large conglomerate that is working on raising $300,000,000 with a 5-year loan to finance the acquisition of a communications company. Based on a BBB credit rating on its debt, ABC can borrow 5-year funds at either
A 9.5% fixed – the 9% rate represents a spread of 250 bp over a 5-year T-note yield Or A floating rate set equal to LIBOR + 75
ABC prefers a fixed-rate loan.
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Comparative Advantage
Suppose: The treasurer of ABC contacts his investment banker for suggestions on how to obtain a lower rate. The investment banker knows the XYZ Development Company is looking for 5-year funding to finance its $300,000,000 shopping mall development. Given its AA credit rating, XYZ could borrow for 5 years at either
A fixed rate of 8.5% (150 bp over T-note) Or A floating rate set equal to the LIBOR + 25 bp
The XYZ company prefers a floating-rate loan.
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Comparative Advantage
Fixed Rate ABC 1% .1 XYZ 1% .1 Credit Spread 11 1 bp Floating Rate LIBOR + 1 bp 1 LIBOR + 1 bp 1 1 bp 1 preference Fixed Floating
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Comparative Advantage
The Investment banker realizes there is a comparative advantage.
XYZ has an absolute advantage in both the fixed and floating market because of its lower quality rating, but it has a relative advantage in the fixed market where it gets 100 bp less than ABC. ABC has a relative advantage (or relatively less disadvantage) in the floating-rate market where it only pays 50 bp more than XYZ.
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Comparative Advantage
Thus, it appears that investors/lenders in the fixed-rate market assess the difference between the two creditors to be worth 100 bp, whereas investors/lenders in the floating-rate market assess the difference to be 50 bp. Arbitrage opportunities exist whenever comparative advantage exist. In this case, each firm can borrow in the market where it has a comparative advantage and then swap loans or have the investment banker set up a swap.
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Comparative Advantage
Note: The swap won’t work if the two companies pass their respective costs. That is: ABC swaps floating rate at LIBOR + 75bp for 9.5% fixed XYZ swaps 8.5% fixed for floating at LIBOR + 25bp Typically, the companies divide the differences in credit risk, with the most creditworthy company taking the most savings.
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Comparative Advantage
Given total savings of 50 bp (100 bp on fixed – 50bp float), suppose the investment banker arranges an 8.5%/LIBOR swap with a NP of $300,000,000 in which ABC takes the fixed-rate position and XYZ takes the floating-rate payer position.
ABC
Floating Rate = LIBOR
Swap Bank
Floating Rate = LIBOR
XYZ
Fixed Rate = 1 % .1
Fixed Rate = 1 % .1
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Comparative Advantage
ABC would issue a $300,000,000 FRN paying LIBOR + 75bp—the FRN combined with the fixed-rate swap would give ABC a synthetic fixed-rate loan paying 9.25%:
ABC' s Synthetic Fixed − Rate Loan FRN Swap Swap Pay LIBOR + 1% 1 Pay 1 % Fixed .1 Re ceive LIBOR Pay 1 % + .1% .1 1 Direct Loan Rate = 1 % .1
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= − LIBOR − .1% 1 = −1 % .1 = + LIBOR = −1 1 . 1%
Comparative Advantage
XYZ would issue a $300,000,000, 8.5% fixed-rate bond —this fixed-rate loan combined with the floating-rate swap would give XYZ a synthetic floating-rate loan paying LIBOR.
XYZ' s Synthetic Floating − Rate Loan Loan Swap Swap Pay 1 % fixed .1 = −1% .1 Pay LIBOR = − LIBOR Re ceive 1 % Fixed Rate = + 1 % .1 .1 Pay LIBOR = − LIBOR
Rate on Direct Floating Loan = LIBOR + .1% 1
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Comparative Advantage
Points:
1. For a swap to provide arbitrage opportunities, at least one of the counterparties must have a comparative advantage in one market. The total arbitrage gain available to each party depends on the comparative advantage. If one party has an absolute advantage in both markets, then the arbitrage gain is the difference in the comparative advantages in each market – the above case. If each party has an absolute advantage in one market, then the arbitrage gain is equal to the sum of the comparative advantages.
2.
3.
4.
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Hidden Option
The comparative advantage argument has often been cited as the explanation for the growth in the swap market. This argument, though, is often questioned on the grounds that the mere use of swaps should over time reduce the credit interest rate differentials in the fixed and flexible markets, taking away the advantages from forming synthetic positions.
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Hidden Option
With observed credit spreads and continuing use of swaps to create synthetic positions, some scholars have argued that the comparative advantage that is apparently extant is actually a hidden option embedded in the floating-rate debt position that proponents of the comparative advantage argument fail to include.
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Hidden Option
Scholars argue that the credit spreads that exit are due to the nature of contracts available to firms in fixed and floating markets. In the floating market, the lender usually has the opportunity to review the floating rate each period and increase the spread over the LIBOR if the borrower’s creditworthiness has deteriorated. This option, though, does not exist in the fixed market.
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Hidden Option
In the preceding example, the lower quality ABC Company is able to get a synthetic fixed rate at 9.5% (.25% less than the direct loan). However, using the hidden option argument, this 9.5% rate is only realized if ABC can maintain its creditworthiness and continue to borrow at a floating rate that is 100 bp above LIBOR. If its credit ratings were to subsequently decline and it had to pay 150 bp above the LIBOR, then its synthetic fixed rate would increase.
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Hidden Option
Studies have shown that the likelihood of default increases faster over time for lower quality companies than it does for higher quality. In our example, this would mean that the ABC Company’s credit spread is more likely to rise than the XYZ Company’s spread and that its expected borrowing rate is greater than the 9.5% synthetic rate. As for the higher quality XYZ Company, its lower synthetic floating rate of LIBOR does not take into account the additional return necessary to compensate the company for bearing the risk of a default by the ABC Company. If it borrowed floating funds directly, the XYZ Company would not be bearing this risk.
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Swap Applications In general, swaps can be used in three ways: 1. Arbitrage 2. Hedging 3. Speculation
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Arbitrage
In the above case, the differences in credit spreads among markets made it possible for the corporations to obtain better rates with synthetic positions than with direct. This example represents an arbitrage use of swaps.
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Arbitrage
In general, the presence of comparative advantage makes it possible to create not only synthetic loans with lower rates than direct, but also synthetic investments with rates exceeding those from direct investments. To illustrate this, four cases showing how swaps can be used to create synthetic fixed-rate and floating-rate loans and investments are presented below.
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Swap Applications – Arbitrage: Synthetic Fixed-Rate Loan
Suppose a company is planning on borrowing $20,000,000 for 5 years at a fixed-rate.
Alternatives: 1. Issue 5-year 10%, fixed rate bond paying coupons on a semiannual basis
Or
2. Create a synthetic fixed-rate bond by issuing a 5year FRN paying LIBOR plus 100 bp combined with a fixed rate payer’s position
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Swap Applications – Arbitrage: Synthetic Fixed-Rate Loan A synthetic fixed-rate loan formed with a 5-year, 9%/LIBOR swap with NP of $20,000,000 and a 5-year, FRN paying LIBOR plus 100 bp is equivalent to 10% fixed rate loan.
Synthetic Fixed − Rate Loan FRN Pay LIBOR + 1 % Swap Pay 1 Fixed % Swap Re ceive LIBOR Pay 1 + 1 % % Direct Loan Rate = 1% 1 = − LIBOR −1 % = −1 % = + LIBOR = − 1% 1
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Swap Applications – Arbitrage: Synthetic Fixed-Rate Loan
The synthetic fixed-rate bond will be cheaper if the synthetic fixed rate can be formed with a swap with a fixed rate less than 9%—the fixed rate on direct loan (10%) minus the 100 bp on the FRN. For example, if the company could obtain an 8%/LIBOR swap, then the company would be able to create a synthetic 9% fixed-rate loan by issuing the FRN at LIBOR plus 100 bp and taking the fixed payer’s position on the swap:
Synthetic Fixed − Rate Loan FRN Swap Swap Pay LIBOR + 1 % Pay 1 Fixed % Re ceive LIBOR Pay 1 + 1 % % Direct Loan Rate = 1% 1
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= − LIBOR −1 % = −1 % = + LIBOR = −1 %
Arbitrage Example: Synthetic Floating-Rate Loan Bank with an AA rating has made a 5-year, $20,000,000 loan that is reset every six months at the LIBOR plus bp. The bank could finance this by Selling CDs every 6 months at the LIBOR
Or
Create a synthetic floating-rate loan by selling a 5-year fixed note and taking a floating-rate payer’s position on a swap.
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Arbitrage Example: Synthetic Floating-Rate Loan The synthetic floating-rate loan will be equivalent to the direct floating-rate loan paying LIBOR if the swap has a fixed rate that is equal to the 9% fixed rate on the note:
Synthetic Floating − Rate Loan Loan Pay 1 fixed % = −1 % Swap Pay LIBOR = − LIBOR Swap Re ceive 1 Fixed Rate = + 1 % % Pay LIBOR = − LIBOR Rate on Direct Floating Loan = LIBOR
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Arbitrage Example: Synthetic Floating-Rate Loan
Given the bank can borrow at a 9% fixed rate for 5 years, the synthetic floating-rate loan will be cheaper than the direct floating-rate loan at LIBOR if the swap has a fixed rate that is greater than 9%. Example: A synthetic floating-rate loan formed with a 9.5%/LIBOR swap is 50 bp less than the direct floating rate:
Synthetic Floating − Rate Loan Loan Pay 1 fixed % = Swap Pay LIBOR = Swap Re ceive 1 % Fixed Rate = .1 Pay LIBOR − .1 % = −1 % − LIBOR +1% .1 − (LIBOR − .1 %)
Rate on Direct Floating − Rate Loan = LIBOR
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Arbitrage Example: Synthetic Fixed-Rate Investment
Swaps can also be used to augment investment return. Example:
A trust fund that is looking to invest $20,000,000 for 5 years in a high quality fixed-income security. Alternatives: Invest in a high quality, 5-year 6% fixed coupon bond selling at par Or Buy a 5-year FRN paying the LIBOR + bp and take a floatingrate payer position on a swap.
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Arbitrage Example: Synthetic Fixed-Rate Investment
If the fixed rate on the swap is greater than the rate on the direct investment (6%) minus the bp on the FRN, then the synthetic fixed-rate loan will yield a higher return than the T-note.
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Arbitrage Example: Synthetic Fixed-Rate Investment
Example: A synthetic fixed rate investment formed with an investment in a 5-year FRN paying LIBOR plus 100 bp and a 6%/LIBOR swap yields a 7% rate compared to a 6% rate from the direct investment.
Synthetic Fixed − Rate Investment FRN Swap Swap Re ceive LIBOR + 1 % Pay LIBOR Re ceive 1 Fixed Rate % Re ceive 1 Fixed Rate % = = = = LIBOR + 1 % − LIBOR +1 % 1 %
Rate on Direct Fixed Rate Investment = 1 %
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Arbitrage Example: Synthetic Floating-Rate Investment
Example: Investment Fund is looking to invest $20,000,000 for 5 years in a FRN. Alternatives:
Invest in a high quality, five-year FRN paying LIBOR plus 50 bp Or Invest in a 5-year fixed-rate bond and take a fixed-rate payer position
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Arbitrage Example: Synthetic Floating-Rate Investment
If the fixed rate on the swap plus the bp on the direct FRN investment is less than the rate on fixed-rate bond, then the synthetic floating-rate investment will yield a higher return than the FRN. Example: A synthetic floating-rate investment formed with an investment in a 5-year, 7% fixed-rate bond and a fixed-rate payer’s position on a 6%/LIBOR swap 50 bp more than the direct investment.
Synthetic FRN Fixed − Rate Bond Swap Swap Re ceive 1 % Re ceive LIBOR Pay 1 Fixed Rate % Re ceive LIBOR + 1 % = = = = +1 % + LIBOR −1 % LIBOR + 1 %
Rate on Direct FRN = LIBOR + .1 %
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Swap Applications—Hedging Cases
Hedging applications of swaps are often done to minimized the market risk of positions currently exposed to interest rate risk.
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Swap Applications—Hedging Cases
Hedging Example 1:
Suppose a company has financed its capital budget with floating-rate loans set equal to the LIBOR plus bps. Suppose that the company’s revenues have been closely tied to short-term interest rates in the past, but fundamental changes have occurred making revenues more stable; in addition, also suppose that short-term rates have increased. To avoid CF problems and higher interest payments, the company would now like its debt to pay fixed rates instead of variable.
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Swap Applications—Hedging
Hedging Example 1:
One alternative would be to refund the floating-rate debt with fixed-rate debt. This, though, would require the cost of issuing new debt (underwriting, registration, etc.), as well as calling the current FRN or buying the FRN in the market. Problem: Very costly.
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Swap Applications—Hedging
Hedging Example 1:
Another alternative would be to hedge the floating-rate debt with short Eurodollar futures contracts (strip), put options on Eurodollar futures, or an interest rate call. Problem: Standardization of futures and options creates hedging risk.
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Swap Applications—Hedging
Hedging Example 1:
Third alternative would be to combine the floating-rate debt with a fixed-rate payer’s position on a swap to create a synthetic fixed -rate debt. Advantage: Less expensive and more efficient than issuing new debt and can be structured to create a better hedge than exchange options and futures.
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Swap Applications—Hedging
Hedging Example 2:
Suppose a company’s current long-term debt consist primarily of fixed-rate bonds, paying relatively high rates. Suppose interest rates have started to decrease.
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Swap Applications—Hedging
Hedging Example 2:
One alternative would be to refund the fixed-rate debt with floating-rate debt. This, though, would require the cost of issuing FRN (underwriting, registration, etc.), as well as calling the current fixed rate bonds or buying them in the market if they are not callable Problem: Very costly.
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Swap Applications—Hedging
Hedging Example 2:
Another alternative would be to hedge the fixed-rate debt with long Eurodollar futures contracts (strip), put options on Eurodollar futures, or an interest rate call. Problem: Standardization of futures and options creates hedging risk.
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Swap Applications—Hedging
Hedging Example 2:
Third alternative would be to combine the fixed-rate debt with a floating-rate payer’s position on a swap to create synthetic floating-rate debt. Advantage: Less expensive and more efficient than issuing new debt and can be structured to create a better hedge than exchange options and futures.
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Swap Applications—Speculation
Swaps can be used to speculate on short-term interest rate.
Speculators who want to profit on short-term rates increasing can take a fixed-rate payer’s position— alternative to a short Eurodollar futures strip. Speculators who want to profit on short-term rates decreasing can take a floating-rate payer’s position— alternative to a long Eurodollar futures strip.
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Swap Applications—Changing a Fixed-Income Fund’s Interest Rate Exposure For financial and non-financial corporations, speculative positions often take the form of the company changing the exposure of its balance sheet to interest rate changes. For example, suppose a fixed income bond fund with a portfolio measured against a bond index wanted to increase the duration of its portfolio relative to the index’s duration based on an expectation of lower interest rate across all maturities. The fund could do this by selling its short-term Treasuries and buying longer-tern ones or by taking long positions in Treasury futures. With swaps, the fund could also change in portfolio’s duration by taking a floating-rate payer’s position on a swap.
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Swap Applications—Changing a Fixed-Income Fund’s Interest Rate Exposure If they take a floating-rate position and rates were to decrease as expected, then not only would the value of the company’s bond portfolio increase but the company would also profit from the swap. On the other hand, if rates were to increase, then the company would see decreases in the value of its bond portfolio, as well as losses from its swap positions. By adding swaps, though, the fund has effectively increased its interest rate exposure by increasing its duration.
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Swap Applications—Changing a Fixed-Income Fund’s Interest Rate Exposure Instead of increasing its portfolio’s duration, the fund may want to reduce or minimized the bond portfolio’s interest rate exposure based on an expectation of higher interest rate. In this case, the fund could effectively shorten the duration of its bond fund by taking a fixed-rate payer’s position on a swap. If rates were to later increase, then the decline in the value of the company’s bond portfolio would be offset by the cash inflows realized from the fixed-payer’s position on the swap.
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Credit Risk
As noted, swaps have less credit risk than the equivalent fixed and floating bond positions. Credit Risk: Swaps fall under contract law and not security law. Consider a party holding a portfolio consisting of a short FRN and a long fixed-rate bond. If the issuer of the fixed-rate bond defaults, the party still has to meet its obligations on the FRN. On a swap, if the other party defaults, the party in question no longer has to meet her obligation. Swaps therefore have less credit risk than combinations of equivalent bond positions.
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Credit Risk
The mechanism for default on a swap is governed by the swap contract, with many patterned after ISDA documents.
When a default does occur, the non-defaulting party often has the right to give up to a 20-day notice that a particular date will be the termination date. This gives the parties time to determine a settlement amount.
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Credit Risk
Suppose the fixed payer on a 9.5%/LIBOR swap with NP of $10,000,000 runs into severe financial problems and defaults on the swap agreement when there are 3 years and 6 payments remaining. Question: How much would the fixed-payer lose as a result of the default? Answer: Depends on the value of an existing swap, which depends on the terms of a replacement swap.
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Credit Risk
Suppose a current three-year swap calls for an exchange of 9% fixed for LIBOR. By taking a floating position on the 9%/LIBOR swap, the floating payer would be receiving only $450,000 each period instead of $475,000 on the defaulted swap. Thus, the default represents a loss of $25,000 for three years and six periods. Using 9% as the discount rate, the present value of this loss is $128,947:
1 (1.111 − $1,11 11 − / 1) PV = ∑ = − $1,11 1 1 1,11 = − $11 1 t .11 1 + 1 )) t =1(1 (.1 / 1
1
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Credit Risk
Thus, given a replacement fixed swap rate of 9%, the actual credit risk exposure is $128,947 (this is also the economic value of the original swap). If the replacement fixed swap rate had been 10%, then the floating payer would have had a positive economic value of $126,892.
1 (1.1) 1 $1,11 11 − / 1 PV = ∑ = $1,11 1 1 1,11 = $11 1 t .1 1 t =11 (.1 / 1 ( + 1 ))
1
The increase in rates has made the swap an asset instead of a liability.
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Credit Risk
The example illustrates that two events are necessary for default loss on a swap: Actual default on the agreement Adverse change in rates Credit risk on a swap is therefore a function of the joint likelihood of financial distress and adverse interest rate movements.
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Credit Risk
The negotiated fixed rate on a swap usually includes an adjustment for the difference in credit risk between the parties. A less risky firm (which could be the swap bank acting as dealer) will pay a lower fixed rate or receive a higher fixed rate the riskier the counterparty. In addition to rate adjustments, credit risk is also managed by requiring the posting of collateral or requiring maintenance margins.
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