INTERNATIONAL FINANCE
Saikrishnaind
IF_UNIT7_SwapXCCY.pdf
Swaps Unit 7
International Finance
• Any corporate is sensitive to the movement of interest rates. If you are paying interest an increase in interest rates may increase your cost of borrowing, whilst if you are borrowing a decrease in interest rates may reduce your overall return (and vice versa).
• 2 counterparties agree to a contractual arrangement wherein they agree to exchange cash flows at periodic intervals
• 2 main types of interest rate swaps: – Single currency interest rate swap: Plain vanilla – Currency Swap: Exchange of liabilities in different currencies
• Cross currency interest rate swap: Combine an interest rate and a Currency Swap
Definition
• An agreement between two parties to exchange cash flows in the future.
• The agreement specifies the dates that the cash flows are to be paid and the way that they are to be calculated.
• A forward contract is an example of a simple swap. With a forward contract, the result is an exchange of cash flows at a single given date in the future.
• In the case of a swap the cash flows occur at several dates in the future. In other words, you can think of a swap as a portfolio of forward contracts.
Swaps
• Currency Swaps – fixed for fixed – fixed for floating – floating for floating – amortizing
• Interest Rate Swaps – Fixed for floating – Fixed for fixed – zero-for floating – floating for floating
• For a swap to be possible, a QSD must exist. Beyond that, creativity is the only limit.
Types
• The most commonly used swap agreement is an exchange of cash flows based upon a fixed and floating rate.
• Often referred to a “plain vanilla” swap, the agreement consists of one party paying a fixed interest rate on a notional principal amount in exchange for the other party paying a floating rate on the same notional principal amount for a set period of time.
• In this case the currency of the agreement is the same for both parties.
• The term notional principal implies that the principal itself is not exchanged. If it was exchanged at the end of the swap, the exact same cash flows would result.
Mechanics
• Interest Rate Swaps: Exchange of fixed-rate payments for floating-rate payments
• Cross-Currency Swaps: Combination of Interest rate and Currency swap
• Credit Default Swaps: Exchange of premium payments for default protection
Introduction
• Popular with bankers, corporate treasurers, and portfolio managers who need to manage interest rate risk
• A swap enables you to alter the level of risk without disrupting the underlying portfolio
• Plain Vanilla or Generic Interest Rate Swap involves the exchange of fixed-rate payments for floating-rate payments.
Interest rate swaps
• The most common type of interest rate swap is the fixed for floating rate swap – One party makes a fixed interest rate payment to another party making
a floating interest rate payment – Only the net payment is made (difference check) – 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.
Interest rate swaps
• Fixed rate payer: Pays 3% annually • Floating Rate payer: Pays 3 months LIBOR + 2% every quarter • Notional: 100 MM EUR • Start date: 1/3/2021 • Effective date fixed leg: 1/3 • Effective date floating date: 1/3, 1/6, 1/9 and 1/12 • Maturity: 1/3/2026
Plain vanilla interest rate example
• It allows to create a synthetic floating or fixed position liability or asset – A synthetic fixed rate payment
• A bond issuer pays floating coupons under the bond issued to bondholders. • It fears that rates may go up, to the cost of liabilities may increase • It decides to enter into a IRS where it pays a fixed coupon and receives a
floating coupon • In fact their liabilitiy exposed to a floating rate has been converted into a net
fixed payment – Under the bond = - floating coupon (payment) – Under the IRS = + floating coupon (receives) - Fixed leg (pays) – Net = Fixed leg
Interest rate swaps basic use (1)
• It allows to create a synthetic floating or fixed position liability or asset – A synthetic floating rate payment
• A bond issuer pays fixed coupons under the bond issued to bondholders. • It fears that rates may go down, so the bondholder fears may not benefit of
the lower rates • It decides to enter into a IRS where it pays a floating coupon and receives a
fixed coupon • In fact their liabilitiy exposed to a floating rate has been converted into a net
fixed payment – Under the bond = - fixed coupon (payment) – Under the IRS = + Fixed coupon (receives) – Floating leg (pays) – Net = Floating leg
Interest rate swaps basic use (2)
• Typically, the floating interest rate is linked to a market rate such as LIBOR or T-bill rates
• The swap market is standardized partly by the International Swaps and Derivatives Association (ISDA) – ISDA provisions are master agreements – Confirmation
• A confirmation is the legal agreement underlying a swap and is signed by representatives.
• International Swap and Derivatives Association (ISDA) in New York. • The confirmation specifies that the following business day convention is to
be used and that the US calendar determines which days are business days and which are holiday.
Regulation
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.
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.
Comparative Advantage
bp50bp100SpreadCredit Floatingbp25LIBOR%5.8XYZ Fixedbp75LIBOR%5.9ABC
preferenceRateFloatingRateFixed
+ +
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.
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.
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.
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 XYZ %5.8RateFixed =
LIBORRateFloating =
BankSwap %5.8RateFixed =
LIBORRateFloating =
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%:
%5.9RateLoanDirect
%25.9%75.%5.8Pay LIBORLIBORceiveReSwap %5.8Fixed%5.8PaySwap
%75.LIBOR%75LIBORPayFRN LoanRateFixedSynthetics'ABC
=
-=+ += -=
--=+ -
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.
%25.LIBORLoanFloatingDirectonRate
LIBORLIBORPay %5.8RateFixed%5.8ceiveReSwap
LIBORLIBORPaySwap %5.8fixed%5.8PayLoan
LoanRateFloatingSynthetics'XYZ
+=
-= += -= -=
-
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.
2. The total arbitrage gain available to each party depends on the comparative advantage.
3. 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.
4. If each party has an absolute advantage in one market, then the arbitrage gain is equal to the sum of the comparative advantages.
Trading swaps
24
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.
25
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 – 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.
26
Swap Market Price Quotes
Swap Maturity Treasury Yield Bid Swap Spread (BP) Ask Swap Spread (BP) Fixed Swap Rate Spread Swap Rate 2 year 4.98% 67 74 5.65% - 5.72% 5.69% 3 year 5.17% 72 76 5.89% - 5.93% 5.91% 4 year 5.38% 69 74 6.07% - 6.12% 6.10% 5 year 5.50% 70 76 6.20% - 6.26% 6.23%
Swap Rate = (Bid Rate + Ask Rate)/2
Swap Bank Quote Offerings Example:
27
Swap Market Price Quotes Example of Swap Quote and Terms 5-Year Swap
Swap Agreement: 1. Initiation Date = June 10, Y1 2. Maturity Date = June 10, Y6 3. Effective Dates: 6/10 and 12/10 4. NP = $20,000,000 5. Fixed-Rate Payer: Pay = 6.26% (semiannual)/ receive LIBOR 6. Floating-Rate Payer: Pay LIBOR/Receive 6.20% (semiannual) 7. LIBOR determined in advance and paid in arrears
AParty BParty %26.6RateFixed =
LIBORRateFloating =
BankSwap %20.6RateFixed =
LIBORRateFloating =
28
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:
NP 365 Daysof.No
)RateFixed(
:PaymentSettlementRateFixed
úû ù
êë é
-
NP 360 Daysof.No
)LIBOR(
:PaymentSettlementRateFloating
úû ù
êë é
-
29
Swap Market Price Quotes
Cash Flow for Fixed-Rate Payer paying 6.26%
Fixed-Rate Payers Position Settlement Date Number of Days LIBOR Fixed Payment Floating Payment Fixed Net Payment
6/10/Y1 5.50% 12/10/Y1 183 5.75% $627,715.07 $559,166.67 $68,548.40 6/10/Y2 182 6.00% $624,284.93 $581,388.89 $42,896.04 12/10/Y2 183 6.25% $627,715.07 $610,000.00 $17,715.07 6/10/Y3 182 6.50% $624,284.93 $631,944.44 -$7,659.51 12/10/Y3 183 6.75% $627,715.07 $660,833.33 -$33,118.26 6/10/Y4 182 $624,284.93 $682,500.00 -$58,215.07
Fixed Payment = (.0626)(no. of days/365)($20,000,000) Floating Payment = LIBOR(no. of days/360)($20,000,000)
30
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%.
31
Opening Position: Swap Execution • All terms of the swap, except the fixed rate,
are mutually agreed to. • Example:
1. Swap bank will pay 6-month LIBOR 2. Corporation will pay T-note rate
(approximately 5.26% ) + 100bp 3. Settlement dates are set 4. Interest paid in arrears 5. NP = $50,000,000 6. Net payments 7. U.S. laws govern the transaction
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.
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.
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.
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.
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.
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).
Closing Swap Positions
Offsetting Swap Positions Original Swap: Fixed Payer’s Position Original Swap: Fixed Payer’s Position
Offsetting Swap: Floating Payer’s Position Offsetting Swap: Floating Payer’s Position
Pay 5.5% Receive LIBOR
Pay LIBOR Receive 5.0%
− 5.5% +LIBOR
−LIBOR +5%
Pay 0.5% (annual) Pay 0.25% (semiannually)
−0.5% (annual) −0.25% (semiannually
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.
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 $94,049 for buying his swap.
å =
-= + -
= 4
1t t
Fix 0 049,94$))2/05(.1(
000,25$ V
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 $92,927 for his 5.5%/LIBOR swap.
å =
= +
= 4
1t t
Fix 0 927,92$))2/06(.1(
000,25$ V
Swap valuation
• To value a swap, this can be seen as either: – A long position in one bond (fixed/floating) combined with a short
position in another bond (floating/fixed) or – A portfolio of forward rate agreements. – A pair of option contracts
Valuation of Interest Rate swap
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.
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, $10,000,000, 5.5% fixed-rate bond at par
Swap Valuation
å =
= +
= 4
1t t
Fl 0 049,94$))2/05(.1(
000,25$ V
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
−LIBOR +5.5%
−5% +LIBOR
Receive 0.5% (annual) 0.5% (annual)
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 $92,927:
å =
-= + -
= 4
1t t
Fl 0 927,92$))2/06(.1(
000,25$ V
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
−LIBOR +5.5%
− 6% +LIBOR
Pay 0.5% (annual) − 0.5% (annual)
å =
-= + -
= 4
1t t
Fl 0 927,92$))2/06(.1(
000,25$ V
Swap Valuation
• Formally, the values of the fixed and floating swap positions are:
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
NP )K1( KK
SV M
1t tP
SP fix
ú û
ù ê ë
é
+ -
= å =
NP )K1(
KK SV
M
1t tP
PS fl
ú û
ù ê ë
é + -
= å =
where:
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.
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.
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
Swaps as Eurodollar Futures Positions • With the index at 94.5, the contract price on one
Eurodollar futures contract is $972,500:
• The next slide shows the cash flows at the expiration dates from closing the 10 short Eurodollar contracts at the same assumed LIBOR used in the previous swap example, with the Eurodollar settlement index being 100 − LIBOR.
500,972$)000,000,1($ 100
)360/180)(5.5(100 f0 =úû
ù êë é -=
Swaps as Eurodollar Futures Positions 1 2 3 4
Closing Dates LIBOR % fT Cash Flow* 10[f0 − fT ]
9/1/Y1 5.00 $975,000 -$25,000 3/1/Y2 5.50 $972,500 $0 9/1/Y2 6.00 $970,000 $25,000 3/1/Y3 6.50 $967,500 $50,000 9/1/Y3 7.00 $965,000 $75,000
*f0 = 972,500
)000,000,1($ 100
)360/180%)(LIBOR(100 fT úû
ù êë é -
=
55
Swaps as A Pair of Option Contracts
• Assume a firm buys a cap and writes a floor, both with a 5% striking price
• At the next payment date, the firm will – Receive a check if the benchmark rate is above 5% – Remit a check if the benchmark rate is below 5%
• The cash flows of the two options are identical to the cash flows associated with a 5% fixed rate swap – If the floating rate is above the fixed rate, the party paying the fixed rate
receives a check – If the floating rate is below the fixed rate, the party paying the floating
rate receives a check
56
Swaps as A Pair of Option Contracts (cont’d)
• Cap-floor-swap parity
5% + =
5% 5%
Write floor Buy cap Long swap
Duration of Swaps
• A plain vanilla swap can be valued as a portfolio of two bonds, therefore the duration of the swap should equal the duration of the bond portfolio.
• The duration can be either positive or negative depending on the side of the swap
• Duration of Receive Fixed Swap = – Duration of Underlying coupon bond
- Duration of underlying floating Rate Bond >0
• Duration of Pay Fixed Swap = – Duration of underlying floating Rate Bond
- Duration of Underlying coupon bond <0
Example
• Consider a swap with a semiannual fixed rate of 7% and a floating rate that resets each six months.
• The duration of the fixed rate side (assuming a 100 notional principal) is 5.65139 years
Duration of Receive Fixed Swap =5.65139-0.5=5.15369
Duration of Pay Fixed Swap =0.5-5.65139=-5.15369
Calculating Duration
• Duration of floating rate security is equal to the time between resetting of the rate.
• Therefore the duration of the swap actually depends upon the duration of the fixed rate side.
• Receive Fixed rate swaps will then usually lengthen the duration of an existing position while pay fixed swaps will shorten the duration of an existing position.
Basic Duration
iasset ofDuration Macaulay Da Assets All of ValueMarket
Asset wwhere
DawDA PortfolioAsset of
Duration Weighted$
i
i i
i
N
1i i
=
=
== å =
jLiability ofDuration Macaulay Dl sLiabilitie All of ValueMarket
Asset wwhere
DlwDL PortfolioLiability of Duration Weighted$
j
j j
j
N
1j j
=
=
== å =
Swap Applications
Swap Applications
• In general, swaps can be used in three ways:
1. Arbitrage 2. Hedging 3. Speculation
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.
Swap Applications—Hedging Cases
• Hedging applications of swaps are often done to minimized the market risk of positions currently exposed to interest rate risk.
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.
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.
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.
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.
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.
Currency swaps
• In a currency swap, two parties – Exchange currencies at the prevailing exchange rate – Then make periodic interest payments to each other based on a
predetermined pair of interest rates, and – Re-exchange the original currencies at the conclusion of the swap
Currency Swaps
Currency Swaps
• The primary purpose of a currency swap is to transform a loan denominated in one currency into a loan denominated in another currency.
• In a currency swap, a principal must be specified in each currency and the principal amounts are exchanged at the beginning and end of the life of the swap.
• The principal amounts are approximately equal given the exchange rate at the beginning of the swap.
A simple example
Assume that company A pays a fixed rate of 11% in sterling and receives a fixed interest rate of 8% in dollars.
Let interest payments be made once a year and the principal amounts be $15 million and L10 Million
Company A Dollar Cash Sterling Cash Flow (millions) Flow (millions)
2/1/1999 -15.00 +10.00 2/1/2000 +1.20 -1.10 2/1/2001 +1.20 -1.10 2/1/2002 +1.20 -1.10 2/1/2003 +1.20 -1.10 2/1/2004 +16.20 -11.10
Intuition
• Suppose A could issue bonds in the US for 8% interest, the swap allows it to use the 15 million to actually borrow 10million sterling at 11% (A can invest L 10M @ 11% but is afraid that $ will strength it wants US denominated investment)
Comparative Advantage Again
• The argument for this is very similar to the comparative advantage argument presented earlier for interest rate swaps.
• It is likely that the domestic firm has an advantage in borrowing in its home country.
Example using comparative advantage
Dollars AUD (Australian $) Company A 5% 12.6% Company B 7% 13.0% 2% difference in $US .4% difference in AUD
The strategy
• Company A borrows dollars at 5% per annum • Company B borrows AUD at 13% per annum They enter into a swap Result Since the spread between the two companies is different for each firm
there is the ability of each firm to benefit from the swap. We would expect the gain to both parties to be 2 - 0.4 = 1.6% (the differences in the spreads).
Swap Diagram
Co A FI Co B
A pays 11.9% AUD instead of 12.6% AUD B pays 6.3% $US instead of 7% $US
The FI makes .2%
5% AUD 13%
6.3%
AUD 11.9%
5%
AUD 13%
Valuation of Currency Swaps
• Using Bond Techniques • Assuming there is no default risk the currency swap can be
decomposed into a position in two bonds, just like an interest rate swap.
• In the example above the company is long a sterling bond and short a dollar bond. The value of the swap would then be the value of the two bonds adjusted for the spot exchange rate.
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Pricing A Currency Swap
• To value a currency swap: – Solve for the equilibrium fixed rate on a plain vanilla interest rate swap
for each of the two countries • Determine the relevant spot rates over the tenor of the swap • Determine the relevant implied forward rates
– Find the equilibrium swap price for an interest rate swap in both countries
Swap variations
• Deferred swap: In a deferred swap (forward start swap), the cash flows do not begin until sometime after the initiation of the swap agreement – If the swap begins now, the deferred swap is called a spot start swap
• Floating for floating swap (basis swap): In a floating for floating swap, both parties pay a floating rate, but with different benchmark indices
• Amortizing swap: In an amortizing swap, the notional value declines over time according to some schedule
• Accreting swap: In an accreting swap, the notional value increases through time according to some schedule
• Yield curve swap: Both parties pay floating but based off of different maturities. Is similar to a basis swap since the effective result is based on the spread between the two rates. A steepening curve thus benefits the payer of the shorter maturity rate.
Basic Swap Variations
Beyond Plain Vanilla
• You can combine amortizing and accreting swaps to allow the notional principal to both increase and decrease. – Seasonal Swap -- Increase and decrease of notional principal based of f
of designated plan
– Roller Coaster Swap -- notional principal first increases the amortizes to zero.
Off Market Swap
• The interest rate is set at a rate above market value. • For example the fixed rate may pay 9% when the yield curve implies
it should pay 8%. • The PV of the extra payments is transferred as a one time fee at the
beginning of the swap (thus keeping the initial value equal to zero)
Swaption
• An option on a swap that specifies the tenor, notional principal fixed rate and floating rate
• Price is usually set a a % of notional principal • Receiver swaption
– The holder has the right to enter into a swap as the fixed – rate receiver • Payer swaption
– The holder has the right to enter into a particular swap as the fixed rate payer.
Swaption as call (or put) Options
• Receiver swaption – similar to a call option on a bond. The owner receives a fixed payment (like a coupon payment) and pays a floating rate (the exercise price)
• Payer swaption – if exercised the owner is paying a stream similar to the issue of a bond.
In-the-Money Swaptions
• A receiver swaption is in the money if interest rates fall. The owner is paying a lower fixed rate in exchange for the fixed rate specified in the contract.
• Similarly a payer swaption is generally in the money if interest rates increase since the owner will receive a higher floating rate.
• The owner of the receiver swaption should exercise if the fixed rate on the swap underlying the swaption is greater than the market fixed rate on a similar swap. In this case the swap is paying a higher rate than that which is available in the market.
Example
• Assume the firm has previously issued a 9% coupon bond that makes semiannual payments and matures in 7 years with a face value of $150 Million.
• The bond has a call option for one year from today.
Example continued
• The firm can sell a European Receiver swaption with an expiration in one year. The swaption terms are for semiannual payments at a fixed rate of 9% in exchange for floating payments at LIBOR.
• The firm receives a premium for the swaption equal to a fixed percentage of the $150 Million notional value (equal to the value of the call option).
• The firm can keep the premium but has a potential obligation in one year if the counter party exercises the swap.
Example Continued
• In one year the fixed rate for this swap is 11% • The option will expire worthless since the owner can earn a fixed
11% on a similar swap. • The firm gets to keep the premium.
Example Continued
• If in one year the fixed rate of interest on a similar swap is 7% the owner will exercise the swap since it calls for a 9% fixed rate.
• The firm can call the bond since rates have decreased. It can finance the call by issuing a floating rate note at LIBOR for the term of the swap.
• The floating rate side of the swap pays for the note and the firm is still paying the original 9% fixed, but it has also received the premium on the swaption
