CHAPTER 25

Swaps

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 Swaps Contracts – Basic Features
 Swaps: a derivative contract that requires each party to exchange (swap) specified periodic
cash flows based on some underlying instrument (e.g., a fixed or floating rate on a bond or
note).
─ Swap can offer cash exchange with various contract maturities, timing of payments, and
different underlying securities used to determine payments.
 Commercial and investment banks act as the major dealers in the swap market.
─ Swap market dealers help keep the swap market liquid by matching counterparties and also
taking a counterparty position in the swap contract.
─ The swap dealer acts as an intermediary since the dealer incurs any costs associated with the
default of any one party by replacing the defaulting party on the same terms as the original swap
─ Swap dealers also generally guarantee swap payments over the life of the contract.

 Swaps Objective:
1. Hedge FI balance sheet risk exposures (interest, FX, and credit risks).
2. Generate off-balance sheet pay-off gains by trading in swaps.
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 Interest Rate Swaps
 Interest rate swaps (IRS): an exchange of fixed interest payments for floating interest
payments by counterparties, all denominated in the same currency.

─ Important elements of Interest-rate swaps:

1. Counterparty exchange of interest payments on Swap notional amount.
2. Types of interest payments (fixed and variable rate payments)
3. Time period over which the exchanges of interest payments continue to be made.

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 Interest Rate Swaps (IRS)

 Generally in an IRS, the Swap buyer makes fixed-rate payments and the Swap seller makes
floating-rate payments.
 IRS can be considered as a series of forward contracts on interest rates.
─ Example: A 4-year IRS with annual swap dates involves four net cash flows between the parties
to a swap is similar to four forward contracts: a 1-year, a 2-year, a 3-year, and a 4-year.

 IRS allows FI a long-term on-balance sheet hedge, sometimes for 15 years.

─ Interest rate forwards and futures reduce the need to roll over balance sheet contracts when
used for long-term hedges.

 IRS is considered the largest segment of the global swap market that also includes currency
swaps, credit swaps etc.

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 Interest Rate Swaps
 IRS is executed in two different ways:
 By an agent (broker): A bank or an investment bank acting as an agent (a third party) to
bring swap counterparties together for a fee.
1. A pure fixed-floating IRS called a plain vanilla interest swap is generally brokered by an agent.
2. The agent usually provides lines of credit to an IRS counterparty with poor credit ratings.

 By a principal: another FI (a third party) that accepts counterparty credit risk exposure in
an IRS by guaranteeing swaps cash flows.
─ The principal FI enters into two separate swap agreements; one with the swap buyer and one
with the swap seller.
─ In the event of a default of a party in an IRS, the principal replaces the defaulting party
position on the terms of the original swap contract.
─ By acting as a principal, the FI can add a credit risk premium of the defaulting party to the
simple fee charged by the broker.

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 Interest Rate Swaps - Example

 MCB balance sheet structure:

─ Liability portfolio: raised $100 million by issuing 4-year fixed notes that pay 10% coupon
rates per year.
─ Asset portfolio: invested in C&I loans that earn interest rates linked to one year LIBOR.
─ MCB duration gap: DA - kDL < 0
 MCB interest rate risk exposure (re-investment risk): variable return on asset portfolio
may be insufficient to cover the cost of fixed coupon payments liability annually if market
interest rates fall during 4 years of asset creation.

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 Interest Rate Swaps - Example

 Saving bank (SB) balance sheet structure:

─ Liability Portfolio: raised $100 million on CDs of one-year maturity that have to be rolled over
next year at current market interest rate.
─ Asset Portfolio: invested $100 million in 10% fixed-rate residential mortgages of long-term
duration.
─ SB duration gap: DA - kDL > 0
 SB interest rate risk exposure (re-financing risk): fixed interest rate returns on asset
portfolio may be insufficient to cover the variable interest cost of CDs if interest rates rise
during 4 years of liability creation.
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 Fixed-Floating-Rate Swap
 Interest swap contract:
─ SB (swap buyer) sends fixed annual interest payments of 10% on $100 million notional amount
of swap contract to MCB to fully cover the yearly fixed coupon 10% interest payments cost on
MCB medium term note.

─ MCB (swap seller) sends annual interest payments earned on its assets indexed to one-year
LIBOR (e.g. 8%) + 2% to help SB to fully cover the cost of refinancing its one-year renewable
CDs.

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 Realized Cash Flows on 4-Years Interest Rate Swaps ($ millions)
 The SB payments of fixed interest to the MCB = 10% x $100 million
 The MCB payments of variable interest to the SB = (LIBOR + 2%) x $100 million
 SB’s net gains from the swap in years 1 and 2 are $1 million per year.
o SB’s net gains from the swap offsets the increased cost of refinancing its CDs when the interest rate
on short-term CDs are higher in year 1 and 2.
 The MCB net gains from the swap in year 3 is $1 million and year 4 is $2 million.
o The positive cash flow from the swap in years 3 and 4 offsets the decline in MCB variable returns on
asset portfolio when floating interest rates on MCB loan investment fall in years 3 and 4.

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 Interest Rate Swaps – Swaps Financing Costs

 Swap buyer (SB) makes fixed interest rate payments on swap settlement dates.
─ Fixed-rate payer FI (Swap buyer) seeks to transform the variable-rate liabilities into fixed-rate
liabilities to better match the fixed returns earned on its assets.
 Swap seller (MCB) makes variable rate interest payments on swap settlement dates.
─ Variable-rate payer FI (Swap seller) seeks to turn its fixed rate liabilities into variable rate
liabilities to better match the variable returns on its assets.

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 Interest Rate Swaps and Basis Risk

 SB basis risk, two possible sources:

─ First, CD rates do not exactly match the movements of LIBOR rates over time, since the former
are determined in the domestic (U.S.) money market and the latter in the Eurodollar market.
─ Second, the credit risk premium on SB CD may increase over time; thus, +2% adds-on to LIBOR
from MCB may be insufficient to fully hedge SB cost of funds (liability).

 No basis risk for MCB.

─ Annual 10% interest payments MCB receives from SB at the end of each year allow MCB to meet
the promised 10% coupon rate payments to its liability holders regardless of the return it
receives on its variable-rate assets.

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 Special Types of Interest Rate Swaps
 An off-market swap: a customized swap contract where one party pays an upfront fee to
the other party to relax certain terms of the swap agreement.
─ Terms of swaps include the use of special interest rates and indexes (other than LIBOR), and
swap notional values can be allowed either to decrease or to increase over a swap contract’s
life.
 Inverse floater Swap (IFS): A swap contract designed to lower the cost of borrowing on
government bonds to various government agencies.
─ Figure: A govt. agency issues borrowing notes (worth $100 million) to investors with a coupon
rate (inverse floating coupon) = 7% - LIBOR (spread liability).

─ Inverse floating coupon feature: When market rates fall and LIBOR gets low it causes spread
liability to rise, investor gains, and govt. agency borrowing cost increases.

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 Special cases of Swaps

 Hedging government agency interest rate risks with IFS: The agency converts this spread
liability (7% - LIBOR ) into a LIBOR liability at IFS expiry LIBOR rate by entering into a swap
contract with an FI dealer by paying an upfront swap fee.
 With IFS, the cost of $100 million note issue (debt) to the govt. agency is converted into
LIBOR plus any fees relating to the swap agreement with the FI dealer.

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 Macro-hedging with Swaps

1. An FI balance sheet equity is exposed to losses due to RISE in interest rates when:
a) FI duration gap is positive, i.e., DA - kDL > 0.
b) FI fund fixed-rate assets with floating-rate liabilities
 FI Interest risk exposure: FI variable rate liabilities mature earlier than fixed-rate assets
and FI faces a risk of rising interest costs when such liability is refinanced.

2. An FI balance sheet equity is exposed to losses due to FALL in interest rates when:
a) FI duration gap is negative, i.e., DA - kDL < 0.
b) FI fund floating rate assets with fixed-rate liabilities.
 FI Interest risk exposure: FI variable rate assets mature earlier than fixed-rate liabilities
and FI faces a risk of falling interest return when such assets are reinvested.

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 Macro-hedging with IRS
 Assume that an FI (savings bank) has a positive duration gap so that it has positive net worth
exposure to rising interest rates:

 Suppose FI chooses to hedge by buying a 10-year interest rate swaps.

─ FI pays fixed-rate annual coupon payments on underlying 10-year T-bond every year.
─ FI receives variable-rate coupon payments on underlying 1-year T-bond where coupons are
repriced to LIBOR every year.

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 Macro-hedging with IRS
 ∆S: change in the market value of swap when the interest rate rise depends on the relative
interest sensitivity of 10-year bonds to 1-year bonds (D10 − D1).
─ As long as Dfixed > Dfloat , when interest rates rise the market value of fixed-rate payments will fall
by more than the market value of floating-rate payments and fixed-rate payer gains.
─ Assuming ∆S +∆E = 0 represents that the gain on interest swap fully offsets the loss in net worth
on the balance sheet when interest rates rise:

─ Solving for NS: Optimal notional value of swap contracts

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 Macro-hedging with IRS
 Suppose: DA = 5 years, DL = 3 years, ΔR = 0.01 (from 10% to 11%), k = 0.9, A = $100 million
ΔE = - [5 - (0.9)(3)] $100 (0.01/1.10) = - $2.091 million
 Suppose, FI chooses to hedge NW loss with 10-year interest rate swaps.
─ Assume, the duration of a current 10-year fixed-rate T-bond is 7 years while the duration of a
floating-rate 1-year T-bond that is repriced annually is 1 year.
 Optimal notional value of swap contracts FI must buy:

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 Macro-hedging with IRS - Payoffs

 The loss of $2.09 million in NW is exactly offset by a gain on the IRS hedge.
 If FI is engaged in a longer-term swap (15 years or more), the notional value of swap
would fall.
 Longer-term swaps contracts, however, have greater risk of counterparty default (credit
risk)

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 Currency Swaps: Fixed-Fixed

 Fixed-Fixed Currency Positions at fixed spot ER of $2/£1:

─ U.S. FI financed fixed-rate dollars denominated assets at an annual rate of return of 11% with
£50 million CDs liability at an annual cost of 10%.
─ U.K. FI financed fixed rate pound-denominated assets at an annual rate of return of 11% with
$100 million medium-term notes liability at an annual cost of 10%.

─ Assumption: both balance sheets are not exposed to interest rate risks and credit risks.
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 Currency Swaps: Fixed-Fixed

 These two FIs are exposed to opposing foreign currency risks.

 Foreign currency risk exposure at a time zero spot ER of $2/£1:

─ U.S. FI FX risk: if the dollar depreciates against the pound over the next four years, it will be
more costly for the U.S. FI to cover annual coupon and principal repayment on its 4-year pound-
denominated CDs (liability) from dollars-denominated asset cash flows.
─ U.K. FI FX risk: if the pound depreciates against the dollar, it will be more expensive for UK FI to
cover annual coupon and principal payments on its 4-year dollar-denominated notes (liability)
from pound-denominated asset cash flows.
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 Currency Swaps: Fixed-Fixed
 Both FI can enter into a currency swap contract by agreeing on a fixed exchange rate for the
respective cash flows at the beginning of each of the payment periods.
─ The U.K. FI sends annual payments in pounds to cover the coupon and principal repayments of the
U.S. FI pound note issue, and the U.S. FI sends annual dollar payments to the U.K. FI to cover the
interest and principal repayments on its dollar note issue.

 USFI $ cash outflow on SWAP settlement dates:

o U.S. FI sends dollar interest payments (10% x $100m) at the end of each year (swap settlement date)
to cover U.K. FI interest cost on dollar CD.
o On the last settlement date (end of year 4), USFI sends interest payments (10% x $100m) plus $100m
in principal to cover UK FI principal repayments as well.
 UKFI £ cash outflow on SWAP settlement dates:
─ U.K. FI sends £ interest payments (10% x £50m) at the end of each year (swap settlement date) to
cover U.S. FI interest payments cost of £ note issues.
─ On the last settlement date (end of year 4), UKFI sends interest (10% x £50m) plus £50m in principle
to cover U.S. FI principal repayments as well.
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 Currency Swaps: Fixed-Fixed

 With Swap, both FI effectively obtain financing at 10% to cover liability cost in
foreign currency while also hedging the liability portfolio against exchange rate risk.

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 Fixed-Fixed Currency Swaps: Limitations
1. The same rate of costs of both liabilities is not a necessary requirement for the fixed-
fixed currency swap agreement.
2. Fixed ER is not required for Fixed-Fixed currency swap agreements.
3. If the spot ER during the life of the swap contract is different from the swap ER agreed
to ($2/£1), a new swap might be entered into at an ER more favorable to one party.
─ If the dollar were to appreciate against the pound over the life of the swap, the agreement
would become more costly for the U.S. FI.
─ If the pound were to appreciate against dollars, the U.K. FI would find the agreement
increasingly costly over the swap’s life.

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 Currency Swaps: Fixed-Floating
Asset Liability
Panel A: C.A.FI
$100 million £50 million
C.A. Loans (LIBOR+2%) in dollars U.K. GIC (4-year, fixed) in pound, 10%

Panel B: U.K.FI
£50 million $100 million
U.K. Loans (4-year, fixed) in pounds, 10% C.A. notes (LIBOR+2%) in dollars

 Fixed-Floating Currency Positions at fixed spot ER of $2/£1:

─ C.A. FI financed variable-rate dollars denominated assets at a rate of return of (LIBOR+2%)
with £50 million 4-year GIC liability at an annual cost of 10%.
─ U.K. FI financed fixed rate 4-year pound-denominated assets at at a rate of return of 10%
with $100 million short-term notes liability at a cost of LIBOR+2%.

 Assumption: both balance sheets are not exposed to interest rate risks and credit risks.
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 Currency Swaps: Fixed-Floating
Asset Liability
Panel A: C.A.FI
$100 million £50 million
C.A. Loans (LIBOR+2%) in dollars U.K. GIC (4-year, fixed) in pound, 10%

Panel B: U.K.FI
£50 million $100 million
U.K. Loans (4-year, fixed) in pounds, 10% C.A. notes (LIBOR+2%) in dollars

 Foreign currency risk exposure at spot ER of $2/£1:

─ C.A.FI FX risk: If dollar interest rates (LIBOR) on the assets fall and the dollar depreciates
against the pound, the C.A. FI may face a problem in covering its promised year-end fixed-
coupon and principal payments on the pound-denominated liability.

─ U.K. FI FX risk: If dollar interest rates (LIBOR) on the liability rise and the pound depreciates
against the dollar, U.K. FI will find it more difficult to cover its promised year-end coupon
and principal payments on its dollar-denominated liability.
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 Currency Swaps: Fixed-Floating

 Fixed-Floating currency swaps end of each year at swap ER of $2/£1.

─ C.A.FI sends floating interest and principal payments in dollars to cover the U.K. FI’s floating
rate dollar notes costs (interest + principal).
─ U.K. FI sends fixed interest and principal payments in pounds to cover fixed cost of the C.A.FI’s
pound-denominated GIC (interest + principal).
 Table ($ in millions): The swaps results in a net payment of $2 million by C.A. FI to the U.K.
FI over 4-years of the fixed-floating currency swap.

C.A. C.A.

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 Credit Default Swaps (CDS)
 CDS buyers are mostly commercial banks seeking to protect balance sheet credit risks.
 CDS sellers are mostly insurance companies.
How does CDS work?
 The CDS buyer makes periodic payments (every quarter, six months, or year) to the CDS
seller until the end of the life of the swap or until the credit event specified in the contract
occurs.
 In the event of loan default, settlement of the CDS involves either physical delivery of the
bonds or loans or a cash payment, as specified in the CDS contract.
─ CDS contract specifies deliverables as bonds, loans, or cash in the event of a default.
─ Holding the underlying security at the time of a CDS contract is not considered a requirement.
─ Therefore, the notional value of CDS contracts in recent years has exceeded the total value of
the outstanding debt instruments.
 In 2008-09, due to significant loan defaults, many credit swap sellers (AIG) could not pay
the promised obligation on credit default swaps (CDS), and buyers of credit swaps (banks)
were exposed to significantly higher credit risks. 27
 Credit Swap: Total Return Swap
 U.S. FI lend $100 million to a Brazilian firm at a fixed loan rate of 10%.
─ Assumption: any change in the value of Br. Govt. U.S.$ denominated bonds due to any adverse
political and economic events in Brazil will also change the credit quality of the Brazilian
borrowing firm (perfect credit risk correlation).
─ If borrower credit risk increases unexpectedly over the life of the loan, lender FI NW would fall
due to a borrower’s inability to service the loan in full (loss in the market value of the loan).
 Use of total return swap to hedge lender-FI credit risk:
─ Under the total return Swap contract lender FI agrees to swap annual fixed interest rate of 12% (f
= 12%) + any change in the market price of the Brazilian govt. dollar bond (=PT – P0 / P0) and
would receive in return a floating payment (e.g., LIBOR) from the counterparty to the swap at the
end of the swap contract.

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 Credit Swap: Total Return Swap

 P0: Brazilian govt $ bond priced at par (P0 =$100) at the beginning of the swap contract
period (time zero).
 PT: market price of Brazilian govt $ bond at the end of the swap settlement period (end of
year 1).
─ A fall in the Brazilian govt. bond price in the secondary market to $90 could be due to an increase
in political and economic uncertainty in Brazil that could be directly correlated with the credit risk
of the Brazilian borrowing firm.

 Swap buyer (Lender FI ) payment = agreed annual fixed-rate payment + changes in the
market value of Brazilian government debt (dollar-denominated bond).
 Swap seller payment = spot variable market rate payment of interest (e.g., one-year LIBOR
rate) at the end of the year.
 Notional value of Swap = $100 million (loan par value)

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 Credit Swap: Total Return Swap
 P0 = $100 and PT = $90, Brazilian govt. bond price in the secondary market fell to $90 due to an
increase in political and economic uncertainty in Brazil.
─ Swap buyer interest payments = 12% – 10% (= 90 – 100/100) = 2%
─ Swap seller interest payments = 11% (agreed floating rate payment such as 1-year LIBOR)
─ FI lender (swap buyer) net profit on the swap = 11% - 2% = 9% times the notional amount of the swap
contract.

 Lender-FI will offset some of the Brazilian loan loss with a gain from the total return swap if
borrower credit risk deteriorates along with the Brazilian economy.
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 Credit Swap: Total Return Swap

 Total return swap does not completely hedge lender credit risk if basis risk is
present, for two reasons:
1. The Brazilian firm’s US dollar loan might not be perfectly correlated with Brazilian country
risk reflected in the price of the Brazilian govt. bonds.
2. If LIBOR rate changes, the net cash flows to FI lender (swap buyer) on total return swap will
change, even though the credit risks of the underlying loans have not changed.

 Total return swap Interest rate risk: total return swap is subject to interest rate risk if
the LIBOR rate also changes at the end of the swap contract.

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 Credit Swaps - Pure Credit Swap
 Pure credit swap: A swap by which an FI (lender) receives the par value of the loan on default
in return for paying a periodic swap fee.
 In a pure credit swap a lender FI (swap buyer) will send a fixed fee/payment (like an insurance
premium) to the other FI (swap seller) at the end of each swap period.
─ If the lender-FI loan does not default, lender FI will receive nothing back from the counterparty FI
(swap seller).
─ In the case of loan default, the swap seller payment to the swap buyer = par value of the original
loan (P0) - the secondary market value of the defaulted loan (PT).
 Swap seller payment to the swap buyer in the event of loan default = P0 ($100) – PT ($40) = $60

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 Swaps Vs other Derivatives

1. Swaps can be viewed as a series of forward contracts with different maturity dates.
2. Swaps are marked to market at payment exchange dates while forward contracts are
settled only upon maturity.
3. Swaps have a longer maturity than any other derivative and enable FI to hedge longer-
term positions at the lowest costs.
4. Swap and options dealers can significantly reduce the credit risk exposure and
information and monitoring costs of the swap contract as opposed to the credit risk
exposure of forward contracts.
 However, in the event of an extreme amount of defaults by one counterparty that a swap
dealer cannot honor, both parties in a swap contract are exposed to credit risk.
5. Transaction costs are highest for the options contracts (premium), next for the swaps
contract (dealer fee), and finally for the forward and future (no upfront payment).

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 Trading in Swaps and credit risk exposure (2008–2012)
 As of June 30, 2008, AIG had written $441 billion worth of swaps on corporate bonds (CDS)
and mortgage-backed securities.
─ When mortgage-backed securities started going bad, AIG suffered massive write-downs
 Lehman Brothers wrote billions of dollars of CDS contracts that were insured by AIG saw a
fall in value when mortgages underlying these contracts fell drastically in value.
─ Lehman Brothers and AIG failed on promised payments to CDS buyers (swap buyers) that led to
a decrease in CDS buyer profits and a significant increase in exposure to financial risk.
 A default of AIG on CDS means every FI CDS buyer from AIG would have suffered huge losses
causing them their own credit problems.
─ 2012: J.P. Morgan lost $5 billion in trading on CDS contracts.
─ Losses on credit swaps led to the failure/near failure of some of the largest FIs (e.g., Lehman
Brothers, Washington Mutual, and Merrill Lynch).

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