Interest Rate and Currency Swaps
Read Chapter 7
Outline
 Interest Rate SWAPS
 Comparative Advantage
 Bootstrapping
 Valuing an InterestRate SWAP
 Currency SWAP
 Overnight Indexed Swaps
 Other SWAP Types
Interest Rate SWAPS
 A swap is where two parties agree to exchange cash flows at specified future times according to certain specified rules
 An example
 Microsoft enters an agreement to receive 6month LIBOR and pay a fixed rate of 4% per annum every 6 months for 3 years on a notional principal of $100 million
 Notional principal – parties do not exchange principal; only to calculate interest payments
 Called "Plain vanilla"  just like plain ole vanilla ice cream
 We do not consider the day count conventions such as 360, actual, etc.
 The previous LIBOR rate determines the current floating rate
 Microsoft's cash flows below
Date 
Libor Floating Rate (%) 
Floating Cash Flow
($ million) 
Fixed Cash Flow
($ million) 
Net Cash Flow
($ million) 
Feb 10, 2014 
3.50 



Aug 10, 2014 
3.80 
+1.75 
–2.00 
–0.25 
Feb 10, 2015 
4.00 
+1.90 
–2.00 
–0.10 
Aug 10, 2015 
3.80 
+2.00 
–2.00 
–0.00 
Feb 10, 2016 
4.05 
+1.90 
–2.00 
–0.10 
Aug 10, 2016 
4.20 
+2.025 
–2.00 
+0.025 
Feb 10, 2017 
4.30 
+2.10 
–2.00 
+0.10 
 Using an interest rate swap
 Convert a liability from
 Fixed rate to floating rate
 Floating rate to fixed rate
 Convert an investment from
 Fixed rate to floating rate
 Floating rate to fixed rate
 Example  Microsoft
 Microsoft could have a variablerate loan
 Microsoft can convert it to a fixed rate loan
 Enter a swap and receive floating
 The floating cancels the cash flows if Microsoft has another variablerate loan
 Pay fixed
 Microsoft must believe interest rates will rise
 Swap does not eliminate the original loans
 Swap changes the cash flows
 SWAP
 Ford borrows LIBOR + 0.2% from a bank
 Enters a SWAP
 Pays 5.5% fixed rate
 Receives LIBOR
 Convert a variable rate loan into a fixed loan
 Ford borrowing cost = LIBOR + 0.2%+ 5.5% – LIBOR = 5.7%
 Ford comes out ahead on the swap if a bank would charge more than 5.7% on a fixed loan
 Ford believes interest rates will rise
 GM borrows at 6.0% fixed from a bank
 Enters a SWAP
 Receives 5.5% fixed
 Pays LIBOR
 Convert fixedrate loan into variablerate loan
 GM borrowing cost = 6.0% + LIBOR – 5.5% = LIBOR + 0.5%
 GM comes out ahead on the swap if a bank would charge a greater rate of LIBOR +0.5% on a variable rate loan
 GM believes interest rates will fall
 Financial institution sets up the SWAP
 Financial institution
 For fixed loans:
 Receives 5.6% and pays 5.4%
 Profit = 5.6% – 5.4% = 0.2%
 For variable loans:
 Receives and pays LIBOR
 Profit = LIBOR – LIBOR = 0%
 Financial institution shares in the gains of a SWAP
 Investment SWAP
 Ford receives 5.0% fixed
 Could enter a SWAP
 Convert fixedinterest earning asset into variable
 Net investment = 5% + LIBOR – 5.3% = LIBOR – 0.3%
 Ford does better SWAP if it were offered a lower investment rate than LIBOR – 0.3%
 Ford believes interest rates will rise
 GM receives LIBOR – 0.5%
 Could enter a SWAP
 Pays LIBOR
 Receives 5.3% fixed
 Convert variableinterest earning asset into fixed
 Net investment = LIBOR – 0.5% – LIBOR + 5.3% = 4.8%
 GM does better with SWAP then if it were offered a rate lower than 4.8%
 GM believes interest rate must fall
 Intermediary
 Profits from fixed leg and earns zero on bottom leg
 profit = 5.4% – 5.2% = 0.2%
 Intermediary can earn a loss on one of the legs
Comparative Advantage
 Airbus Corp wants to borrow floating
 Airbus Corp borrows fixed
 Boeing Corp wants to borrow fixed
 Boeing Corp borrows floating
 Parties can gain by entering a swap
 They pay less interest rate than if borrow from bank using rates in the table
 Comparative Advantage – companies borrow from the low cost source and exchange (swap) payments
 Gain from Fixed: 6.3% – 5.0% = 1.30%
 Gain from Floating: LIBOR + 0.2% – (LIBOR – 0.2%) = 0.4%
 Total gain: 1.30% – 0.4% = 0.9%
 Companies and bank can divide 0.9% among themselves
 Give each company an equal benefit of 0.45%

Fixed 
Floating 
Airbus Corp 
5.0% 
6month LIBOR – 0.2% 
Boeing 
6.3% 
6month LIBOR + 0.2% 
 Boeing Corp borrows LIBOR + 0.2% from bank
 Enters SWAP
 Pays 5.65% fixed
 Receives LIBOR
 Net Interest: LIBOR – (LIBOR + 0.2%) – 5.65% = –5.85%
 Boeing lowers borrowing cost by 0.45% via the SWAP
 The bank would charge 6.3%
 Airbus Corp pays 5.0% fixed to bank
 Enters SWAP
 Pays LIBOR
 Receives 5.65%
 Net Interest: 5.65% – 5.0% – LIBOR = 0.65% – LIBOR = – (LIBOR – 0.65)
 Airbus lowers borrowing costs by 0.45% via the SWAP
 The bank would charge LIBOR – 0.2%
 Allow a bank to earn 0.30% on SWAP
 That leaves 0.6% for the companies
 Each company can benefit by 0.3%
 Verify each company receives a benefit of 0.3% while the bank earns 0.3%
 Requires trial and error to balance interest rates

Criticism of the Comparative Advantage Argument
 The 5.0% and 6.3% rates available to Airbus Corp and Boeing Corp in fixed rate markets are 5year rates
 The LIBOR−0.2% and LIBOR+0.2% rates available in the floating rate market are sixmonth rates
 Boeing Corp's fixed rate depends on the spread above LIBOR it borrows at in the future
 The Nature of Swap Rates
 Sixmonth LIBOR is a shortterm AA borrowing rate
 The 5year swap rate has a risk corresponding to the situation where 10 sixmonth loans are made to AA borrowers at LIBOR
 This is because the lender can enter into a swap where income from the LIBOR loans is exchanged for the 5year swap rate
Bootstrapping
 Bootstrap the LIBOR/Swap Zero Curve when using LIBOR discounting
 Consider a new swap where the fixed rate is the swap rate
 When principals are added to both sides on the final payment date the swap is the exchange of a fixed rate bond for a floating rate bond
 The floatingrate rate bond is worth par.
 The swap is worth zero.
 The fixedrate bond must therefore also be worth par
 This shows that swap rates define par yield bonds that can be used to bootstrap the LIBOR (or LIBOR/swap) zero curve
 Example
 The LIBOR/swap rates with continuous compounding are
 6month 4.2%
 12month 4.4%
 18month 4.6%
 Twoyear swap rate is 6% and pays semiannually
 The 2year LIBOR/swap rate, R, is 5.979%
Valuing an InterestRate SWAP
 Interestrate SWAP
 Initially interest rate swaps are worth close to zero
 At later times they can be valued as a portfolio of forward rate agreements (FRAs)
 Example
 Receive sixmonth LIBOR
 6month LIBOR on last payment date was 3.1%, semiannual compounding
 Pay 4%, semiannual compounding, on a principal of $10 million
 Remaining life is 1.5 years
 LIBOR rates for 6month, 12month and 18month are 3.0%, 3.5%, and 3.8%, continuous compounding
 Method 1 – Use forward rates
 Each exchange of payments in an interest rate swap is an FRA – fixed for variable
 We value the FRAs assuming the forward rates are good forecasts of future rates
 The forward rates can be calculated directly from the LIBOR/swap zero curve
 Calculate Forward Rates
 6 to 12 month period: Forward rate is 4.0%, continuous
 In semiannual compounding, 3.96%
 12 to 18 month period: Forward rate is 4.4%, continuous
 In semiannual compounding, 4.35%
 The table show the payoffs
 Floating rate – just divide the semiannual rates by 2
 Holder receives floating and pays fixed
Time 
Pay Fixed cash flow 
Receive Floating cash flow 
Net Cash Flow 
Discount factor 
PV 
0.5 
0.2 
+0.1550 
0.0450 
0.9851 
0.0443 
1.0 
0.2 
+0.2020 
+0.0020 
0.9656 
+0.0019 
1.5 
0.2 
+0.2224 
+0.0224 
0.9446 
+0.0212 
Total 




0.0212 
 Method 2  Valuating as if interestrate SWAP were bonds
 Easier method
 The fixed rate bond is discounted as a normal cash flow
 We act if we pay the principal in the end, $10 million
 The floating rate bond is valued by noting that it is worth as if paid in full during the next payment date
 We do not know the future interest rates
 We act if we receive the principal, $10 million
 We calculate the present value for the next payment
Time 
Pay fixed cash flow 
Receive variable cash flow 
Discount factor 
PV Fixed 
PV Variable 
0.5 
0.2000 
+10.1550 
0.9851 
0.1970 
+10.0038 
1.0 
0.2000 

0.9656 
0.1931 

1.5 
10.2000 

0.9446 
9.6349 

Total 



10.0250 
+10.0038 
Swap value = 10.0038 − 10.0250 = 0.0212 million
Currency Swap
 Exchange of Principal
 For an interest rate swap, the parties do not exchange the principal
 For a currency swap, the parties exchange the principal at the beginning and the end of the swap
 One party needs one currency while the other party needs the other currency
 Typical Uses
 Convert a liability in one currency to a liability in another currency
 Convert an investment in one currency to an investment in another currency
 Example
 A company agrees to pay 7% on a euro principal of €20,000,000 & receive 5% on a US$ principal of $10,000,000 every year for 5 years
 Table below shows cash flows
Date 
Dollar Cash Flows (millions) 
Euro cash flow (millions) 
May 1, 2012 
–10.00 
+20.00 
May 1, 2013 
+0.50 
–1.40 
May 1, 2014 
+0.50 
–1.40 
May 1, 2015 
+0.50 
–1.40 
May 1, 2016 
+0.50 
–1.40 
May 1, 2017 
+10.50 
–21.40 
 Comparative Advantage
 Could originate from taxes
 Boeing wants to borrow Euros
 Airbus wants to borrow USD
 Cost after adjusting for the differential impact of taxes

USD 
Euros 
Boeing 
6.0% 
8.5% 
Airbus 
7.5% 
9.0% 
 Two methods to value currency swaps
 Value cash flows as two bonds that pay in different currencies
 Use exchange rate to convert to same currency
 Calculate the currency forward rates
 Currency forward contains the exchange rate
 Example
 Current exchange rate is 1.50 USD per Euro
 All Euro LIBOR/swap rates are 5%
 All USD LIBOR/swap rates are 7%
 Fixed payments are made annually
 6% is paid in dollars
 7% is received in euros
 Principals are $30 million and €20 million
 Swap will last for 3 more years
 First Method – Treat cash flows as if they are bonds
 Table shows the calculations
Time 
Cash Flows ($) 
PV ($) 
Cash flows (€) 
PV (€) 
1 
1.8 
1.6783 
+1.4 
1.3317 
2 
1.8 
1.5648 
+1.4 
1.2668 
3 
1.8 
1.4591 
+1.4 
1.2050 
3 
30.0 
24.3175 
+20.0 
17.2142 
Total 

29.0197 

21.0176 
Value ($) = $29.0197 + 21.0176€ x 1.5 $/€ = $2.507 million
 Second Method  Use currency forwards to value SWAP
 Calculate the currency forward rates by using interest rates
 Equation is below
 t is the year
 Multiply the Euro cash flow by the currency forward to convert to US$
 Use the U.S. interest rate to discount
Time 
Pay cash flow ($) 
Receive cash flow (€) 
Currency Forward ($ per €) 
Receive cash flow ($) 
Net Cash Flow ($) 
Present value ($) 
1 
1.8 
+1.4 
1.5303 
2.1424 
0.3424 
0.3193 
2 
1.8 
+1.4 
1.5612 
2.1857 
0.3857 
0.3353 
3 
1.8 
+1.4 
1.5928 
2.2299 
0.4299 
0.3484 
3 
30.0 
+20.0 
1.5928 
31.8551 
1.8551 
1.5037 
Total 





2.507 
 Other Currency Swaps
 Fixedforfloating: equivalent to a fixedforfixed currency swap plus a fixed for floating interest rate swap
 Floatingforfloating: equivalent to a fixedforfixed currency swap plus two floating interest rate swaps
Overnight Indexed Swaps
 Overnight Indexed Swaps
 Fixed rate for Overnight Indexed SWAPS (OIS)
 Variable interest rate
 Geometric average of overnight interest rates during period
 Geometric average
 Rolling over daily, i.e. compounding daily, (1 + i_{1}) (1 + i_{2}) (1 + i_{3})∙∙∙ (1 + i_{n})
 Geometric average
 If fixed rate exceeds variable rate, the fixedrate payer pays to the floatingrate receiver
 If fixed rate is less than variable rate, then the fixedrate payer receives difference.
 No exchange for principle
 On maturity, calculate the geometric rate
 Loser pays the winner the difference
 If OIS rate = LIBOR rate?
 A bank can
 Borrow $100 million in the overnight market (variable)
 Roll forward for 3 months
 Pay federal funds rate – U.S. banks lend to other banks overnight
 Enter a SWAP
 Receive variable rate for OIS
 Pay fixed rate of OIS for 3 months
 Lend the funds to another bank at LIBOR for 3 months
 Note: Bank is borrowing at a variable rate and lending at a fixe rate.
 The SWAP connects the two, so bank does not get squeezed if interest rate changes
 The excess of LIBOR over the OIS rate is the LIBOROIS spread.
 It is usually about 10 basis points but spiked at an all time high of 364 basis points in October 2008
 2008 Global Financial Crisis
 Valuation of Swaps Using OIS discounting
 Zero rates are bootstrapped from OIS rates
 This is similar to the way the LIBOR/swap zero curve is produced
 Forward LIBOR rates are then calculated so that so that swaps entered into at the current swap rate are worth zero
 The swap is valued by assuming that forward LIBOR is realized and discounting at the OIS rate
 There is no simple way of valuing the swap in terms of bonds
Other SWAP Types
 A swap is worth zero to a company initially
 At a future time its value is liable to be either positive or negative
 The company has credit risk exposure only when its value is positive
 Some swaps are more likely to lead to credit risk exposure than others
 What is the situation if early forward rates have a positive value?
 What is the situation when the early forward rates have a negative value?
 Credit Default Swaps:
 Start with a notional principal (e.g. $100 million) and maturity (e.g. 5 yrs)
 Buyer pays a fixed rate (e.g. 150 bp) on the notional principal (the CDS spread)
 Buyer is buying insurance on a security such as bonds
 If the security drops in value, the buyer can exercise CDS
 Investment banks wrote trillions of dollars of CDS
 One the factors that amplified the 2008 Global Financial Crisis
 Total face value of bonds bought equals notional principal
 Other Types of Swaps
 Amortizing/ step up
 Compounding swap
 Constant maturity swap
 LIBORinarrears swap
 Accrual swap
 Equity swap
 Cross currency interest rate swap
 Floatingforfloating currency swap
 Diff swap
 Commodity swap
 Variance swap

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