Interest Rate and Currency Swaps

Read Chapter 7

Outline

• Interest Rate SWAPS
• Comparative Advantage
• Bootstrapping
• Valuing an Interest-Rate 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 6-month 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

• 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 variable-rate 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 variable-rate 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 fixed-rate loan into variable-rate 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
      • Pays 5.3%
      • Receives LIBOR
    • Convert fixed-interest 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 variable-interest 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
  • Net cash flows matter

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%

• 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 5-year rates
  • The LIBOR−0.2% and LIBOR+0.2% rates available in the floating rate market are six-month rates
  • Boeing Corp's fixed rate depends on the spread above LIBOR it borrows at in the future
• The Nature of Swap Rates
  • Six-month LIBOR is a short-term AA borrowing rate
  • The 5-year swap rate has a risk corresponding to the situation where 10 six-month 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 5-year 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 floating-rate rate bond is worth par
    • The swap is worth zero
    • The fixed-rate 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
    • 6-month 4.2%
    • 12-month 4.4%
    • 18-month 4.6%
  • Two-year swap rate is 6% and pays semi-annually
  • The 2-year LIBOR/swap rate, R, is 5.979%

Valuing an Interest-Rate SWAP

• Interest-rate 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 six-month LIBOR
    • 6-month LIBOR on last payment date was 3.1%, semi-annual compounding
  • Pay 4%, semi-annual compounding, on a principal of $10 million
  • Remaining life is 1.5 years
  • LIBOR rates for 6-month, 12-month and 18-month 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 semi-annual compounding, 3.96%
    • 12 to 18 month period: Forward rate is 4.4%, continuous
      • In semi-annual compounding, 4.35%
• The table show the payoffs
  • Floating rate – just divide the semi-annual rates by 2
  • Holder receives floating and pays fixed

• Method 2 - Valuating as if interest-rate 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

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
    • Called notional
  • 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

• 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

• 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

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

• Other Currency Swaps
  • Fixed-for-floating: equivalent to a fixed-for-fixed currency swap plus a fixed for floating interest rate swap
  • Floating-for-floating: equivalent to a fixed-for-fixed currency swap plus two floating interest rate swaps

Overnight Indexed Swaps

• Overnight Indexed Swaps
  • Fixed rate for Overnight Indexed SWAPS (OIS)
    • Usually for three months
  • 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 fixed-rate payer pays to the floating-rate receiver
• If fixed rate is less than variable rate, then the fixed-rate 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
        • Geometric of average
      • 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 LIBOR-OIS 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

• At Time 0, a swap is worth zero to a company
  • 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
  • LIBOR-in-arrears swap
  • Accrual swap
  • Equity swap
  • Cross currency interest rate swap
  • Floating-for-floating currency swap
  • Diff swap
  • Commodity swap
  • Variance swap