International Fixed Income

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International Fixed Income

• Topic 7ASWAPS

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Outline

• Description of a Swap
• Motivation for Swaps
• Graphical Analysis
• Valuation and Interest Rate Sensitivity
• Credit Risk
• Currency Swaps

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I. Description

• An interest rate swap is a contract which commits
  two counterparties to exchange, over an agreed
  period, two streams of interest payments, each
  calculated using a different interest rate index,
  but applied to a common notional principal amount.

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Plain Vanilla Swap

• A plain vanilla or generic swap is a
  fixed-for-floating swap with
• constant notional principal
• constant fixed interest rate
• floating interest rate such as 6-month LIBOR
  (London Interbank Offer Rate), a Treasury bill
  rate, Prime rate, Fed Funds,...
• semi-annual payments of fixed and floating.
• The swap rate quoted is the fixed rate.

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Swap Jargon

• The fixed-rate payer is
• paying fixed and receiving floating
• long the swap
• short the bond market

• The floating-rate payer is
• paying floating and receiving fixed
• short the swap
• long the bond market

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Importance of Swaps Market
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II. Motivation for Swaps

• Risk Taking
• Arbitrage due to market imperfections?
• Risk Management
• Hedging interest rate risks
• Financing
• Low transaction costs
• Off-balance sheet

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Example Using swaps to take advantage of market
imperfections?

• Company A has an AAA credit rating
• Borrows fixed at 10 or at LIBOR20bp
• Company B has a BBB credit rating
• Borrows at 11.20 or at LIBOR75bp
• Their spreads allow for swap market arbitrage
• A borrows fixed and swaps to pay LIBOR with
  dealer, while B borrows floating, and swaps to
  pay fixed 10.20 with dealer.

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Example continued...
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Example continued...

• Is this really arbitrage?
• The conventional wisdom is that B is reducing its
  borrowing costs and sharing some of the savings
  with A.
• On the other hand, if B is achieving the floating
  debt by rolling over short term debt, which has a
  lower spread than long term debt, then B is at
  risk if its credit quality deteriorates.

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Example Mortgage Lending Institution

• Typically invests in fixed-rate assets
  (mortgages) funded by liabilities on which it
  pays a floating rate (deposits).
• How can the bank hedge its interest rate risk?
• Go long a swap
• It pays fixed and receives floating
• It funds the fixed from its mortgage payments,
  and uses the floating to pay its deposits.
• Why? It makes money from the business side, not
  in taking interest rate risk.

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Hedging Interest Rate Risk
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III. Graphical Analysis
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3 ways to view the cash flow from a swap - 1
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2 - short a fixed, long a floater
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3 - a portfolio of forward contracts
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Swaps as a portfolio of forward contracts

• The 2-year (annual reset) swap is like a
  portfolio of 4 forwards of maturities .5-2 years.
• Since swaps have a present value of zero, the
  portfolio is also PV zero.
• However, because the obligated payment is fixed
  each period with the swap, the fixed swap rate
  will not equal the time-zero forward rates unless
  the term structure is flat.
• Thus, each individual forward embedded in the
  swap will not have the usual zero present value,
  only their sum will.
• If the term structure is upward (downward)
  sloping, then the payer of fixed initially
  expects to have losses (gain) before eventual
  gains (losses).

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IV. Valuation Interest Rate Sensitivity

• Three Components
• Distribution of Cash Flows
• Valuation of Swap
• Interest Rate Sensitivity of Swap
• Illustration using an example of a 2-year swap of
  fixed against 6-month Libor.

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A. Cash Flow Rule

• Every six months until maturity, the party who is
  long the swap receives the 6-month rate set
  6-months earlier minus a fixed rate k.
• If the notional amount of the swap is N and the
  maturity is T, the time t cash flow to this party
  for t 0.5, 1, 1.5, ..., T can be written as

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Example Cash Flows to Long Position in 5.5
2-Year Swap with 100 Notional Amount
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B. Valuation

• As shown earlier, the cash flows from a swap are
  equivalent to a long position in a floater
  (indexed to Libor) minus a fixed-rate bond (with
  rate k).
• The difference between the coupons of the two
  notes equals the swap payment, and the difference
  between their principal payments is zero.
• Thus, default risk aside, the value of a swap is
  just the difference between the value of the
  floater and the fixed rate bond

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Valuation continued...

• Since it is standard to set the initial value of
  the swap to zero, this means the swap rate is the
  fixed rate that sets the floater equal to the
  fixed-rate bond.
• Thus, the swap rate is chosen such that

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Example

• What is the value of a 5.5 plain, vanilla
  interest rate 2-year swap
• assuming the current zero curve is 5.54, 5.45,
  5.47 and 5.5 for the 6 mth through 2 year
  zeroes (cocnistent with previous classes), that
  is, discount factors of .973, .9746, .9222 and
  ,8972, respectively.
• The 2-year swap with fixed rate 5.5 is worth
  -0.0019 per 100 notional amount
• The 2-yr 5.5 bond is worth 100.0019
• The floater is worth 100 (see below)
• swap value 100 - 100.0019

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Review Floaters

• A floating rate note (FRN) is a bond with a
  coupon that is adjusted periodically to a
  benchmark interest rate, or indexed to this rate
  (e.g., LIBOR)
• Consider a semi-annual coupon floating rate note,
  with the coupon indexed to the 6-month interest
  rate. Each coupon date, the coupon paid is equal
  to the par value of the note times one-half the
  6-month rate quoted 6 months earlier, at the
  beginning of the coupon period. The note pays par
  value at maturity.
• Valuation (See next two pages)
• What is the duration of a floater?
• The note is always worth par on the next coupon
  date with certainty. So a floater is equivalent
  to a zero that matures on the next coupon date
  with face value equal to the par value of the
  floater plus the current coupon.The duration of
  the floater is therefore equal to the duration of
  a zero maturing on the next coupon date. Their
  convexities are the same, too.

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Calculating the Swap Rate

• The swap rate is the fixed rate that sets the
  swap's value equal to zero.
• If the swap is fixed-against-LIBOR, then the swap
  rate should be above the Treasury rate.
• Why?
• Because LIBOR is appropriate for A-rated banks
  and the default risk on swaps is much lower it
  must be the case that the fixed rate should
  reflect the default-free rate plus the LIBOR
  spread (TED spread).

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Swap rate continued...

• For each maturity T, the swap rate k(T) is the
  coupon rate that sets the fixed-rate component
  equal to the floater. With no default risk, the
  floater's value is par plus the present value of
  the spread over Treasuries. Denote s as the
  spread, and d as the discount factors then for a
  semi-annual swap, we have

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Example

• Assume a spread of zero, so that we are working
  off treasuries, then
• The 2-year swap with fixed rate 5.5 is worth
  -0.0019 (per 100 notional amount).
• To make the swap worth exactly zero, the swap
  rate must be set equal to the par rate for 2 year
  maturity
• 2-year par rate 2(1-0.897166)/
  (0.9730470.9476490.9222420.897166) 5.499

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The Swap Curve

• Recall that the swap curve relates the generic
  swap rate to the maturity of the swap. (It refers
  to dealer rates for fixed-against-six month
  Libor).
• The swap spread is the spread between the swap
  rate and a U.S. Treasury of similar maturity.
• This curve generally coincides with what a dealer
  would pay/receive in a swap with a AAA (or AA)
  party.
• The variation in the swap spread across
  maturities is empirically related to
• demand/supply factors (price pressure)
• credit spreads in the corporate bond market

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April 1,2000Swap Curve Treasury Curve
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January 1,2000Swap Curve Treasury Curve
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Swap Spreads (1997-2000)
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C. Interest Rate Sensitivity

• The dollar duration (or, the price value of a
  basis point DV01) and the dollar convexity of
  the swap respectively is simply the dollar
  duration and dollar convexity of a floating rate
  note minus the fixed-rate bond.
• Since a floater faces only interest rate risk
  between reset dates, the duration then is
  primarily that of the underlying fixed-rate bond.
• Note that the surprising charateristic here is
  that a swap has no principal amount at stake
  (i.e., it's a levered position in the underlying
  bond).
• A long position in a swap has, therefore,
  negative duration, as it is primarily a negative
  position in a long-term fixed rate bond.
• Increasing (decreasing) interest rates increase
  (decrease) the swap's value.

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Example
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V. Credit Risk

• The swap curve generally indicates what a dealer
  would pay/receive in a swap with a AAA (or AA)
  counterparty. However, spreads for lower quality
  counterparties are about the same.
• How important is credit risk?
  Many regulators argue that
  credit risk is underpriced in the swaps market,
  e.g., swap spreads much lower than corporate
  credit spreads. However, swaps have many special
  features, which substantially reduce their credit
  risk.

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Are the concerns warranted?

• Loan
• Full principal at risk
• Full interest payments at risk
• Defaults always matter
• Covenants apply

• Swap
• No principal at risk
• Only a spread payment is at risk
• Default matters only if in the money
• Long maturity contracts often have rating-related
  unwind/settlement triggers and advanced credit
  enhancement collateralization features

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Characteristics of SwapsCredit Risk Issues 1

• Although the cash flows of long a floater, short
  a fixed-rate bond are equal to a swap note that
  only the difference between their coupons are at
  risk.
• Thus, the capital at risk is of a much smaller
  magnitude than the underlying fixed income
  market.

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Characteristics of SwapsCredit Risk Issues 2

• Rational default occurs only when the swap's
  value is negative.
• In our example, this happens only when interest
  rates have fallen (from the perspective of being
  long the swap), thus reducing the incidence of
  default.
• This also highlights the importance of the term
  structure of interest rates, as displayed by
  thinking of swaps as a portfolio of forwards.

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Characteristics of SwapsCredit Risk Issues 3

• Credit Enhancement Vehicles
• The most "matured" setting can be found on
  organized exchanges
• The OTC market provides a variety of standard
  (ISDA master agreement) and new
  (asset/counterparty-specific) additions

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Credit Enhancement (Exchanges)

• Options and futures margin requirements
• margin serves as a collateral
• Daily mark-to-market and possible liquidation of
  a position
• margin is proportional to avg. vol
• margin may be related to the nature of the trade
  (hedging or speculative)
• Position limits vis-a-vis each counterparty helps
  diversify default risk
• Cross-clearing agreements

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Credit Enhancement (OTC Derivatives)

• Netting Arrangements
• bilateral close-out is now standard in the ISDA
  master swap agreement
• Position Limits
• RM group monitors the "exposure profile" for each
  counterparty
• each trade is considered for its portfolio effect
• Margins and Collateral
• common to require dynamic margining
• Derivative Product Companies
• dynamically capitalized
• AAA-rated SPVs
• Often a requirement for sovereigns
• Recouponing
• periodic change of coupon payment to bring the
  transaction to market
• Credit Triggers
• if a counterparty falls below investment grade,
  the other counterparty may require an immediate
  cash settlement (of questionable effectiveness)
• common for long-dated swaps

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VI. Currency Swaps

• A contract by which two counterparties exchange,
  over an agreed period, two streams of interest
  payments in different currencies and, at the end
  of the period, the corresponding principal
  amounts at an exchange rate agreed at the start
  of the contract.
• Different from an interest rate swap in that
• the interest and principal are denominated in
  different currencies
• exchange of principal at maturity

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Currency Swapfixed/fixed /DM
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Other types of currency swaps

• Cross-Currency Coupon Swap
• Fixed-against-floating counterparty A pays fixed
  DM interest and principal in exchange for
  floating interest and principal at maturity
• Cross-Currency Basis Swap
• Floating-against-floating counterparty A pays
  floating DM interest and principal in exchange
  for floating interest and principal at
  maturity.

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Interest Rate and Cross-Currency SwapsNotional
Principal, Trillions , 1995
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Currency Swap Pricing

• We can think of a currency swap as an exchange of
  notes, one denominated in each currency
• Price of swap price of DM note - price of
  note
• For the fixed/fixed swap here, it can be written
  as Price of swap price of fixed rate DM bond -
  price of fixed rate bond
• The interest rate sensitivity of the swap,
  however, is different. To see this note that the
  change in the swap's value can be approximated by
• DSwapDp-sDpDm-pDmDs, where s is the exchange
  rate ( per DM)
• The duration of the swap then depends on the
  interest rate sensitivity of three factors US
  rates, German rates, and the exchange rate. Since
  the exchange rate is roughly 8 times more
  variable than the underlying interest rates, much
  of a swap's risk comes from currency changes.

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Comparison of Currency Swaps and Forwards

• Currency Swaps
• Involves exchange of interest and principal
  amounts of currencies
• Exchange of principal takes place at an exchnage
  rate agreed at start of swap, usually the spot
  rate
• E.G., exchange streams of dollar and DM payments,
  and principal amounts at maturity at current spot
  rate.

• Forwards
• Only principal amounts at maturity
• Exchange of principal takes place at the forward
  exchange rate (at start of swap)
• E.G., transaction takes place at forward rate F
  agreed at start of swap,i.e., simple exchange of
  principal amount at maturity

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VII. Other Types of Swaps

• Amortizing and Accreting Swaps
• Notional declines (increases) through time
• Step Up/Down Swaps
• Coupon starts low (high) then steps up (down)
• Basis Swaps
• Exchange of two floating rates, e.g., T-bill rate
  versus LIBOR
• CMT Swaps
• Floating rate is tied to a long-treasury yield

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LTCM Example Reviewed European credit spreads

• Swap spreads represent the spread between future
  LIBOR (bank offer rates) and future T-bills.
  During the 1996-1997 period, UK swap spreads
  began to rise relative to German swap spreads. In
  other words, UK swaps (relative to their
  treasuries) were cheap compared to German swaps
  (relative to their treasuries).
• LTCM went long UK swap spreads and short German
  swap spreads, betting they would eventually
  converge.

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Swap Spreads UK Germany
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Swap Spreads UK Germany