Swaps Pricing and Strategies

1
Swaps Pricing and Strategies

• FIN 828 Lecture Notes
• Yea-Mow Chen
• Department of Finance
• San Francisco State University

2
I. Defining A Swap

• A plain vanilla interest rate swap is a
  contract that involves two parties exchanging
  their interest payments obligations (no principal
  is exchanged) of two different kinds of debt
  instruments - one bearing a fixed interest rate
  (fixed-rate payer) and the other a floating rate
  (floating-rate payer) on a periodic basis over
  the fixed time period.

3
I. Defining A Swap

• EX A 3-year 11 fixed for six-month LIBOR
  floating 10 million swap settled every six
  months requires a fixed-rate payer to pay 11
  fixed-rate interest on a notional principal of
  10 million to a floating-rate payer in exchange
  for a variable-rate interest that depends on a
  pre-specific six-month LIBOR rate on 10 million
  principal. If the suitable LIBOR rate was 10,
  the swap requires the fixed-rate-payer to pay
  550,000 ( 10m 11 0.5) to
  floating-rate-payer in exchange for receiving
  500,000 ( 10m 10 0.5) from floating-rate-
  payer.

4
I. Defining A Swap

• In real practice, only the difference is
  transacted, that is, the swap requires
  fixed-rate-payer to pay 50,000 net to floating
  rate payer. This exchange will take place every
  six months until the maturity.
• The six-month LIBOR rate that is actually used on
  a payment date is the rate prevailing six months
  earlier. This reflects the way in which interest
  is paid on LIBOR-based loans. The first exchange
  of cash flows is know with certainty when the
  contract is negotiated.

5
II. Gains From Swaps

• Typical transactions involve one party that is an
  established, highly  rated issues that prefers
  floating rate  obligations  but can  sell 
  fixed-rate debt at a relatively low  rate, 
  while  the other party is usually a lower-rated
  issuer preferring fixed-rate obligation.  This 
  arrangement allows each party to borrow  with
  the  preferred  type  of interest obligation
  usually at  a  lower overall cost of financing
  than each party could obtain on its own (to
  exploit "comparative advantage").

6
II. Gains From Swaps

• This exploitation is possible because the
  existence of different relative costs in
  different maturity markets which is connected to
  differences in the credit ratings of swap
  partners. Investors  require  lower-rated 
  borrowers  to pay relatively high risk premiums
  when borrowing at a long-term fixed rate rather
  than at a short-term floating rate.

7
II. Gains From Swaps

• Example
• The  Sallie Mae  A highly-rated institution
  prefers floating  rate debt to match short-term
  loan in  its students  loan portfolio but can
  sell fixed-rate debt at relatively low rate.
• A MSB A relatively low-rated institution
  prefers to match its long-term, fixed-rate
  mortgage portfolio with fixed-rate funds.

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II. Gains From Swaps

• ________________________________________
• Cost Fixed Rate
  Floating-Rate
• Borrowing Cost
  Borrowing Cost
• ________________________________________
• MSB 13 LIBOR1.5
• SALLIE MAE 11 LIBOR
• Quality Spread 2 1.5
• Quality Spread Difference
• or Arbitrage Opportunity 0.5
• _______________________________________

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II. Gains From Swaps

• All-in-cost computation
• __________________________________________________
  ______ MSB Sallie Mae
• __________________________________________________
  ______
• Funding Cost
• MSB issues floating L1.5
• Sallie Mae issues Fixed 11
•  Swap Payments
• MSB pays fixed to Sallie Mae 11.3 L
• Sallie Mae pays floating to MSB -L -11.3
• __________________________________________________
  ______
• All-in-cost 12.8 L - 0.3
• Comparable Cost 13.0 L
• Cost Saving 0.2 0.3
• __________________________________________________
  ______

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II. Gains From Swaps

• MSB Bank Sallie Mae
• __________________________________________________
  ____________
• Funding Cost
• MSB issues floating L1.5
• Sallie issues Fixed 11
• Swap Payments
• MSB pays fixed to Bank 11.3 -11.3
• Bank pays floating to MSB - L L
• Bank pays fixed to Sallie Mae
  11.2 -11.2
• Sallie Mae pays floating to Bank
  -L L
• __________________________________________________
  ___________
• All-in-cost 12.8 -0.1 L -0.2
• Comparable Cost 13.0 0 L
• Cost Saving 0.2 0.1 0.2
• __________________________________________________
  ____________

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III. Why Swap? Alternative Explanations

• 1. Underpriced Credit Risk or Risk Shifting
• It has been argued that credit risk is
  underpriced in floating-rate loans, which gives
  rise to the arbitrage opportunities.
• However, the arbitrage opportunities should
   disappear  as  the expansion of the swap market
  has effectively increased the demand for
   floating-rate debt by lower-rated companies and
   the  demand for fixed-rate debt by higher-rated
  companies.

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III. Why Swap? Alternative Explanations

• Jan Loeys suggests that the quality spread is the
   result  of risk  being shifted from the lenders
  to the shareholders. To  the extent  that lenders
  have the right to refuse to roll over  debt, more
  default risk is shifted from the lenders to the
  shareholders as the maturity of the debt
  decrease. With this explanation, the "gains"
   from a swap would instead be transfers from  the
   shareholders of the lower-rated firm to the
  shareholders of the  higher-rated firm.

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III. Why Swap? Alternative Explanations

• 2. Information Asymmetries
• Arak, Estrella,  Goodman, and Silver argue  that
   the  "issue short term - swap to fixed"
  combination would be preferred if the firm
• has information that would lead it to expect its
  own  credit spread  to be lower in the future
  than the market  expectation changes in its
  credit spread than  is the market
• expects higher risk-free interest rates than does
  the market
• is more risk-averse to changes in the risk-free
  rate than is the market.

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III. Why Swap? Alternative Explanations

• 3. Differential Prepayment Options
• Borrowing  fixed directly has a put option on
   interest  rates (prepayment),  while the "borrow
  floating - swap to  fixed"  does not.  Thus the
  lower-rated firm can borrow at a fixed  rate
   more cheaply by swapping from floating because
  the firm in effect  has sold an interest rate
  option. At least a portion of the  funding cost
   "savings"  obtained by the lower-rated firm come
   from  the premium on this option.

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III. Why Swap? Alternative Explanations

• 4. Tax and Regulatory Arbitrage
• In  the less-regulated Eurodollar market, the
  costs  of  issue could  be  considerably less
  than in the U.S. However,  not  all firms  have
   direct  access to the Eurodollar  market.  The
   swap contract  provides  firms with access and
  permits more  firms  to take advantage of this
  regulatory arbitrage.

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IV. VALUATION OF INTEREST RATE SWAPS

• 1.  Indication Pricing Schedule
• __________________________________________________
  ______
• Bank Pays Bank Receives
  Current
• Maturity Fixed Rate Fixed Rate TN Rate
• __________________________________________________
  ______
• 2 yrs 2 yr TN 30 bps 2 yr TN 38
  bps 7.52
• 3 3 yr TN 35 bps 3 yr TN 44
  bps 7.71
• 4 4 yr TN 38 bps 4 yr TN 48 bps
  7.83
• 5 5 yr TN 44 bps 5 yr TN
  54 bps 7.90
• 6 6 yr TN 48 bps 6 yr TN 60
  bps 7.94
• 7 7 yr TN 50 bps 7 yr TN 63 bps
  7.97
• 10 10 yr TN 60 bps 10 yr TN
  75 bps 7.99
• __________________________________________________
  ______

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IV. VALUATION OF INTEREST RATE SWAPS

• 2A. Pricing an At-Market Swap
• The  cash flows from an interest rate swap where
  the  party  pays fixed is equivalent to the cash
  flows of a portfolio of two  loan contracts,
   where borrowing is at a T-period fixed rate,
   lending is at a floating rate.
• The  loans  are both  zero-expected-NPV
   projects.  Consequently, since  the swap is
  nothing more than a long and a short  position in
   loans,  the  expected  NPV of the swap must
   also  be  zero.

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IV. VALUATION OF INTEREST RATE SWAPS

• Hence, if the actual or expected floating-rate
  payments at time 1, 2, 3,  ...., T can be
  determined and if the  term  structure  of
  interest  rate is known, the NPV of the swap can
  be set equal  to zero, and we can solve for the
  fixed rate.

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IV. VALUATION OF INTEREST RATE SWAPS

• EX  GI  wishes to enter into a swap in which GI
   will  pay  cash flows based on a floating rate
  and receive cash flows based on  a fixed rate. A
  quote from a bank 
• Notional Principal Amount 100
• Maturity
  one year
• Floating Index
  6-month LIBOR
• Fixed Coupon
  ______________
• Payment Frequency
  Semiannual
• Day Count
  30/360
• Suppose now the yield curve shows that interest
  rate on six-month ECD  is  8 percent and 10
  percent on one-year ECD.  What  is  the
  appropriate fixed rate? (Answer 9.70)

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IV. VALUATION OF INTEREST RATE SWAPS

• Solution
• The first floating-rate inflow is the six-month
  LIBOR in effect at the contract origination, 8.
  Hence at the six-month settlement, the bank
  expects to receive
• R1 100 8(180/360) 4.00
• To determine the expected floating-rate inflow at
  the one-year settlement, extract the six-month
  rate is six months
• (1 r12) 1 r 6 (1/2) 1 6r 12
  (1/2)
• with r 6 8, r 12 10, we have 6 r 12
  11.5.

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IV. VALUATION OF INTEREST RATE SWAPS

• Therefore, R2 100 1/2 11.5 5.75.
•  
• At the origination, the expected NPV of this
  at-market swap must be zero
•  (4.00 - R1)/(1 8/2) (5.75 - R2)/1.10 0,
•  we thus have
• R1 R2 4.85,
• which implies the appropriate fixed rate to be
  9.70.

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IV. VALUATION OF INTEREST RATE SWAPS

• B. Marking the Swap to Market
•  
• Once  a swap has been contracted, its value
  (after origination) depends on what  happens to
  the market price on which the swap is based.
•  
• EX (GI example continued) If the LIBOR yield
  curve shifted up by 1, what is the value of the
  swap to the bank?

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IV. VALUATION OF INTEREST RATE SWAPS

• Solution
•  
• With the new term structure, the forward rate is
  (1 11) (1 9/2) (1 6 r 12 /2) gives
  12.4 for 6 r 12. The value of the swap to the
  bank has risen from zero at origination to 0.42
•  
• (4.00 - 4.850/(1 9/2) (6.22 - 4.85)/(1
  11/2) 0.42

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IV. VALUATION OF INTEREST RATE SWAPS

• C. Pricing Off-Market-Swaps
• When the fixed rate paid by a party is higher
  than the prevailing market  fixed rate, then at
  contract origination, a payment  will have  to be
  made from the floating-rate payer to  the
  fixed-rate payer.
• The  size of the initial payment from the
  floating-rate payer  to the fixed-rate payer is
  determined by the difference between  the market
   value  of a bond that carries the  above-market
   interest rate and the notional principal of the
  swap.

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IV. VALUATION OF INTEREST RATE SWAPS

• EX (A Delayed LIBOR Reset Swap)
• In  a delayed reset or in arrears swap, the rate
  paid at month  6 is  the six-month rate in effect
  at month 6 and the rate paid  in month 12 is the
  six-month rate in effect at month 12.
• For  the example above, if the swap is on a
  delayed  LIBOR  reset basis,  then  at the
  origination, the rate the  bank  expects  to
  receive at month 6 is not the six-month spot rate
  at origination, i.e.,  8,  but  the forward rate
  of 11.5.  Likewise,  the  rate expects to
  receive at month 12 is not the six-month rate in
   six months, but the six-month rate in 12 months.
  Assume this is 13.

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IV. VALUATION OF INTEREST RATE SWAPS

• To determine the appropriate fixed rate for the
  bank to pay,
•  
• (5.75 - R) 6.50 - R
• ---------------- --------------
  0.
• (1 8/2) 1 10
•  
• Thus R is 6.11 or fixed rate is 12.22.

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IV. VALUATION OF INTEREST RATE SWAPS

• 3. Pricing Interest Rate Swaps
• A. Relationship To Bond Prices
• Consider  a  swap  contract for a financial
   institution  to  pay floating  rate of LIBOR to
  company B in exchange for 10.0  fixed on a
  notional principal of 10m. This is the same as
• a. B has lent the financial institution 10m at
  the 6-month LIBOR rate
• b. The financial institution has lent B 10m at a
  fixed rate of 10 per annum.

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IV. VALUATION OF INTEREST RATE SWAPS

• The  value  of the swap is therefore the
  difference  between  the values of two bonds
• V B1- B2
• where V the value of the swap
• B1 the value of the fixed rate
  bond
• B2 the value of the floating rate
  bond
• Q notional principal
• k coupon payment on fixed rate
  bond
• k the floating rate payment to be
  made
• at time t1
• ri risk-free interest rate at ti.

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IV. VALUATION OF INTEREST RATE SWAPS

• Since  B1  is the present value of the fixed rate
   bond's  future cash flows,
• n
• B1 ? k e -ri ti Q e-rntn .
• i1
• The  floating rate of interest that is of
  equivalent risk to  the risk must be the floating
  rate of interest underlying the swap.

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IV. VALUATION OF INTEREST RATE SWAPS

• We can  therefore use the floating rate
  underlying the swap to  discount the cash flows
  of the floating rate bond. Immediately after a
  payment date the value of the floating rate bond,
  B2, is always its  face  value, Q.
• Between payment dates, we can use  the  fact that
  B2 will equal Q immediately after the next
  payment date. In notation, the time until the
  next payment date is t1, so that
•  
• B2 Q e-r1 t1 k e-r1 t1

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IV. VALUATION OF INTEREST RATE SWAPS

• EX Suppose that under the terms of a swap, a
  financial  institution  has  agreed to pay
  6-month LIBOR and receive 8  per  annum (with
  semiannual compounding) on a 100m notional
  principal.  The swap has a remaining life of 1.25
  years. The relevant fixed rates of  interest with
  continuous compounding for 3-month, 9-month, and
  15-month maturities are 10.0, 10.50, and 11.0,
  respectively. The 6-month LIBOR rate at the last
  payment date  was  10.2.

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IV. VALUATION OF INTEREST RATE SWAPS

• In this case,
•   k 4m and k 5.1m, so that
•  
• B1 4m e-0.250.1 4m e-0.750.105
• 104m e1.250.11
•   98.4m
•  
• B2 5.1m e-0.250.1 100m e-0.250.1
•   102.51m
•  Hence V B1 - B2 -4.27m.

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IV. VALUATION OF INTEREST RATE SWAPS

• B. Relationship To Forward Contracts
• An interest rate  swap  can  be decomposed into a
  series of forward contracts.
• Suppose  that  Ri is the forward interest rate
   for  the  6-month period  prior  to  a payment
  date i (i?2). The value  of  a  long forward
  contract on an asset is the PV of the amount by
  which the current forward price exceeds the
  delivery price. Thus the value of  the forward
  contract corresponding to the payment  number  i
  (i?2)  for the party receiving fixed and paying
  floating  can  be shown to be
• (k - 0.5 RiQ) e-ri ti.

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IV. VALUATION OF INTEREST RATE SWAPS

• The  exchange  that  will take place on the
   first  payment  date involves a payment K and
  receipt of k. The value of this is
• (k - k) e-r1 t1 .
•  
• The total value of the swap is therefore
• n
• (k - k)e-r1 t1 ? (k -
  0.5RiQ)e-ri ti
• i2

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IV. VALUATION OF INTEREST RATE SWAPS

• EX Consider the previous example
•  
• k 4m, k 5.1m Q
  100m
• r1 0.10 r2 0.105
  r3 0.11
• t1 0.25 t2 0.75
  t2 1.25
•  
• R2 (r2t2 - r1t1) / (t2 - t1)
  0.1075
• R3 (r3t3 - r2t2) / (t3 - t2)
  0.1210

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IV. VALUATION OF INTEREST RATE SWAPS

• Converted to semiannual compounding
•   R2 0.1104
• R3 0.1210
•  The value of the swap is therefore
•   (4m - 5.1m)e-01.0.25
•       (4.0m - 0.50.1104100m)e-0.105
  0.75
•   (4.0m - 0.50.1210100m)e-0.11
  1.25
•   -4.27m

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V. Returns and Risks of Swaps to End Users

• On the positive side
• 1.  Interest rate swaps primarily allow
  institutions to manage interest  rate  risk  by
  swapping for  preferred  interest payment
  obligations.
• 2.  Swaps  also provide institutions with
  vehicles  to  obtain cheaper  financing by
  exploiting  arbitrage  opportunities across
  financial markets.
• 3.  Swaps  allow institutions to gain access to
  debt  markets that otherwise would be
  unattainable or too costly.
• 4.  Relative  to other alternative risk
  management,  swaps are more flexible and
  costless.

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V. Returns and Risks of Swaps to End Users

• On the negative side
• 1.Swaps are not standardized contracts, which lead
  s to several problems
• a. Negotiating a mutually agreeable swap contract
  involved time, energy, and resources.
• b. A secondary market is not available, at a
  result, it is difficult  and costly to "back out"
  of a swap agreement if the need arises.
• 2.  Swaps holders are exposed to default risk. 
  A default  on one  party  exposes the other party
  to interest rate  risk and possible lose of
  funds.

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VI. Risks For Banks In Intermediating Swaps

• 1. As a Broker in the early stages, commercial
  banks and investment  banking  firms found in
  their client bases  those  entities that needed
  swaps to accomplish funding or investing
   objectives, and they matched the two entities.
• 2. As a Guarantor To reduce the risk of
  default, many early swap transactions required
  that the lower credit-rated entity obtain a
  guarantee from a highly rated commercial bank.
• 3.  As a Dealer Advanced in quantitative
  techniques and  futures products  for  hedging
  complex positions such as swaps  made  the
  protection of large inventory positions feasible.

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VI. Risks For Banks In Intermediating Swaps

• Regulators Concern
• a.  Pricing Risk
• Pricing risk occurs from banks "warehousing -
  swaps  - from arranging a swap contract with one
  end-user without  having arranged at offsetting
  swap  with  another end-user.  Until an
  offsetting swap is arranged,  the  bank has an
  open swap position and is vulnerable to an 
  adverse change is swap prices.
•  b. Credit Risk
• A bank with perfectly matched swaps does not
  expose to price risk. If interest rates change,
  the value of  one swap will fall while the value
  of the other  rises an equal amount.  But if one
  of the end-user defaults, the  bank  loses the
  hedging value of the offsetting  swap and may
  suffer a capital loss.

41
VI. Risks For Banks In Intermediating Swaps

• c. As a way to exploit deposit insurance
  subsidies
• The swaps market may offer banks some
  opportunities for exploitation of the deposit
  insurance system. Specifically, banks can leave
  their swaps unhedged and thereby speculate on
  interest rate movements, or they can engage in
  swaps with unusually risky counterparties.
  Regulators have recognized the risk inherent in
  swaps and have taken it into account in the new
  risk-based capital requirements for banks. They
  reduce incentives for risk-taking through swaps
  by including swaps in the calculation of
  risk-adjusted assets. The requirements state
  that half of the sum of (1) 0.5 percent of the
  notional principal of a swap with a life of more
  than one year and (2) the market value of the
  swap, if it is positive, is to be included in
  risk-adjusted assets. Thus, investment in a swap
  requires some commitment of capital, and this
  reduces the risk of bank failures because capital
  acts as a cushion against losses.

42
VI. Risks For Banks In Intermediating Swaps

• d. Systematic Risk to the Financial System
• The capital requirement also reduces the
  possibility of a destabilizing disruption to the
  financial markets as a result of systemic risk
  from swaps because swaps dealers tend to have
  numerous swaps deals with each of the other
  dealers, a problem at one bank could be
  transmitted to other banks and ultimately cause
  multiple failures.

43
VII. SWAP APPLICATIONS

• 1. Minimizing Financing Costs
• A  U.S. Co. - wants to borrow an  amount of US
  100 million for seven years. Having issued
  bonds  heavily in  the recent past, US Co. would
  have to borrow at a  relatively unattractive
   rate in the U.S.market. On the other hand, it
  could  obtain  favorable terms on a private
   placement  issue  in Dutch marks where, for a
  variety of reasons, there is a  strong demand
   for US Co.'s paper. In this environment, US Co.
  will  be wise to issue DM-denominated seven-year
  bonds and arrange a currency swap with a
  financial intermediary to exchange DM and U.S.
  dollar cash flows.

44
VII. SWAP APPLICATIONS

• DM 190m US100 million
• Private Placement Investor Issuer U.S. Company
  swap Counterparty
• DM 190 million
•  
• Each year
• DM 6.5 DM 6.5
• Investor U.S. Company
  Swap Counterparty
• US9.5
•  
• At Maturity
• DM 190 m DM 190 million
• Investor U.S. Company Swap
  Counterparty
• US 100 million

45
VII. SWAP APPLICATIONS

• 2. Synthetic Asset Creation
• Synthetic assets are created through a
  combination of a bond  and a swap. A common
  structure is a bond denominated in a non-dollar
  currency  and a currency swap. For example, a
  U.S.  dollar-based investor  wants an attractive
  spread over six-month LIBOR,  which is  the rate
  at which it can fund its investments. For this,
   it can  purchase a dollar denominated
  floating-rate note  (FRN)  or, alternatively,  it
   can purchase a yen-denominated  bond  coupled
  with a currency swap (fixed yen vs. six-month
  LIBOR).

46
VII. SWAP APPLICATIONS

• Purchase Euroyen bond Yen 15,000
• Yen 15,000 Investor Swap Counterparty
• US 100
•  
• Each year
• LIBOR 22bp semiannual
• Euroyen bond Investor Swap Counterparty
• Yen 5,5 annual Yen 15,000 principal
•  At maturity
• US 100 return of initial investment
• Euroyen bond Investor Swap Counterparty
• Yen 15,000 principal
• Yen 15,000 principal

47
VII. SWAP APPLICATIONS

• 3. Asset-Liability Management
• Swaps can also be used in an overall portfolio or
  a balance sheet of  assets and liabilities to
  alter an institution's exposure  to interest
   rate or currency movement. Entering into  an
   interest rate  or currency  swap will result in
  one becoming longer or shorter the bond market,
  or longer or shorter a currency. This may  be
   done to reduce or eliminate interest rate or
  currency exposure, or to take a view without
  having to actually buy or short a bond, which
  could be difficult.

48
VII. SWAP APPLICATIONS

• For  example,  a bank in Singapore has a
  portfolio  of  Eurobonds that are largely funded
  with short-term Eurodollar deposits. The average
  maturity of the Eurobonds is 3.5 years. While
  the bank's asset-liability manager is pleased
  with the spread they have been making, he is now
  afraid that rates may soon rise.
•  

49
VII. SWAP APPLICATIONS

• Rather  than sell off his carefully selected
  Eurobond  portfolio, he  arranges to enter into a
  3.5 year interest rate swap  to  receive
  three-month LIBOR and pay a fixed rate. He is
  now approximately hedged against interest rate
  increases, since he  is  receiving  fixed  (on
  the bonds) and paying fixed  (on the  swap).
  Later on, if his view changes, he may cancel the
  swap in part  or in whole. Thus can he use the
  swap as a tool in  asset-liability management.

50
VII. SWAP APPLICATIONS

• 4. Hedging Future Liabilities - Forward Swaps
• Swaps may also be done on a forward basis, with
  interest beginning to  accrue  as of a date from
  one week to several  years  in  the future.
• EX A corporation has outstanding high coupon
  debt that is callable  in two years. The
  corporation thinks that  current  interest rate
   levels are attractive and would like to lock in
   today  the cost of refunding its debt on the
  call date. The corporate  could enter  into a
  forward swap in which it will pay a fixed rate
   and receive a floating rate.

51
VIII. INTEREST RAE SWAPS AND FINANCIAL
INTERMEDIARIES SOME EXERCISES

• 1. Interest  Rate  Swap Between a Savings and
  Loan  Association  and Foreign Commercial Bank
• Swap Term 50 million for five year
• Savings and Loan (negative GAP)
• Agrees to make semiannual interest payments to
  bank at  fixed rate of 12 per year
• Agrees to pay underwriter costs associated with
  bank  issuing 50 million in fixed-rate
  Eurobonds
• Issues 50 million in floating-rate debt at LIBOR
  2.0

52
VIII. INTEREST RAE SWAPS AND FINANCIAL
INTERMEDIARIES SOME EXERCISES

• Foreign Commercial Bank (Positive GAP)
• Agrees  to make semiannual interest payments to
   the  SLA  at floating rate equal to 6-month
  LIBOR
• Issues 50 million in 5-year Eurobonds at a fixed
  12 rate
• Intermediary
• Guarantees performance by each party to
  transaction
• Receives up-front fee of 1/4 of of 50  million
   (125,000) for arranging swap and providing
  guarantee
• Every six months it calculates obligated interest
  payments and remits difference to appropriate
  party

53
VIII. INTEREST RAE SWAPS AND FINANCIAL
INTERMEDIARIES SOME EXERCISES

• Hypothetical Payments between Swap Parties First
  30 Months
•  
• Time Fixed-Rate LIBOR Average
  Floating-Rate Net
• Frame SLA Payment (Annual)
  Bank Payment Payment
• __________________________________________________
  ______
• 6 months 3m 10.0 2.500m 0.500m
•  
• 1 year 3m 11.5 2.875m 0.125m
•  
• 18 months 3m 12.5 3.125m -0.125m
•  
• 2 years 3m 13.0 3.250m -0.250m
•  
• 30 months 3m 12.0 3.000m 0
• __________________________________________________
  _____
• 0 month 125,000 10.0  

54
VIII. INTEREST RAE SWAPS AND FINANCIAL
INTERMEDIARIES SOME EXERCISES

• 2. A regional bank holding company recently
  bought 100 million package of mortgages from the
  RTC. The  holding  company  will establish a new
  subsidiary to manage this package. This
   subsidiary will be financed by selling its own
  90-day commercial  paper. Market conditions
  dictate this arrangement although the management
  realizes the subsidiary is burdened with high
  interest  rate risk  because the average duration
  of the mortgages is  7  years. The bank decides
  to arrange a swap for the subsidiary.

55
VIII. INTEREST RAE SWAPS AND FINANCIAL
INTERMEDIARIES SOME EXERCISES

• a Does this subsidiary want to buy floating-rate
  payments or fixed-rate payments in the swap
  market?
• b. The subsidiary will pay 9 percent interest on
  its commercial paper. This rate will vary with
  the Fed funds rate and be recalculated  as Fed
  funds plus 1 percent. If forced to  issue longer
  term bonds the subsidiary would have to pay 12
  percent. A swap partner has been located. The
  partner can raise  variable-rate funds for itself
  at Fed funds plus 0.4 percent and it can  sell
  bonds at 10 percent. Does the situation exist for
   a successful swap?

56
VIII. INTEREST RAE SWAPS AND FINANCIAL
INTERMEDIARIES SOME EXERCISES

• c. Would a better swap result with a partner
  that could raise variable-rate funds at the Fed
  funds rate and sell bonds at 11 percent? Why or
  Why not?
• d. Describe one swap arrangement that would be
  satisfactory to the  subsidiary, the swap pattern
  described in part b and  the intermediary.

57
VIII. INTEREST RAE SWAPS AND FINANCIAL
INTERMEDIARIES SOME EXERCISES

• 3. Under the terms of an interest rate swap a
  financial  institution has agreed to pay 10 per
  annum and to receive 3-month LIBOR in  return on
  a notional principal of 100 million with
   payments being exchanged every 3 months. The
  swap has a remaining life  of 14  months. The
  average of the bid and ask fixed  rate  currently
  being swapped for 3-month LIBOR is 12 per annum
  for all  maturities.  The 3-month LIBOR rate one
  month ago was 11.8 per  annum. All  rates  are
  compounded quarterly. What is the  value  of  the
  swap?
•  

58
VIII. INTEREST RAE SWAPS AND FINANCIAL
INTERMEDIARIES SOME EXERCISES

• 4.  (On-Market Forward Swap) Suppose two years
  ago a  corporation issued 100 million in seven
  year 12 coupon bonds at par  value. Assume  also
  that the bonds pay coupons semi-annually, the
   issue was  originally  callable  at par in four
  years,  and  two  years remain in the call
  protection period.
• Now  suppose that an on-market, 100 million
   notional  principal forward  swap  is available
  such that the corporation  could  pay 10.25 and
  receive six-month LIBOR for three years, starting
   two years from now.

59
VIII. INTEREST RAE SWAPS AND FINANCIAL
INTERMEDIARIES SOME EXERCISES

• If  interest rates are denoted as TBS for
  three-year fixed  rate cost of funds, TSS for
  the fixed rate on a three-year swap,  and
  LIBORCS  for  the three-year floating rate note.
   On  the  call date,  if  Treasury yields are
  allowed to range from  9  to  12 (while bond
  credit and swap spreads are assumed to remain
   fixed, and  in equilibrium, at BS0.75,
  CS0.25, and  SS0.50),  Show the  forward swap
  hedging results. A Table is provided below  for
  your references

60
VIII. INTEREST RAE SWAPS AND FINANCIAL
INTERMEDIARIES SOME EXERCISES

• --------------------------------------------------
  ----------------------------------
• Treasury Yield (T) 9 10 11
  12
• --------------------------------------------------
  ----------------------------------
• Refunding 9.75 10.75 11.75
  12.75
• Fixed Rate
• (TBS)
• Decision
• Value of the
• Call Option
• Swap
• Fixed Rate
• (TSS)
•  Gain on Forward Swap
•  Total Gain
•  Present Value
• --------------------------------------------------
  ----------------------------------