An%20Economic%20Analysis%20of%20Interest%20Rate%20Swaps

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An Economic Analysis of Interest Rate Swaps

• Member
• R94723046 ???
• R94723043 ???
• R94723052 ???

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Agenda

• Introduction
• The basic interest rate swap
• Many uses of interest rate swap
• The valuation of swaps

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I. Introduction
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Introduction

• Based on the principle of comparative advantage
• A useful tool of active liability management and
  for hedging against interest rate risk.

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History background Of IRS

• Since late 1970s
• Significant increase in both the levels and
  the volatilities of market interest rates.
• Influence
• Business firms and financial institutions
  face higher interest-rate risks.

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History background Of IRS (contd)

• Since the early 1980s
• One of the most popular vehicles utilized to
  hedge against interest rate risk.
• Reason
• Simple technique and easy to execute

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II. The basic irs
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The basic interest rate swap

• Definition
• An agreement between two parties to exchange
  a series of interest rate payment.
• Calculation of CF
• The cash flow is calculated at a fixed or
  floating rate on the notional principal.
• Ex. fixed-rate payer v.s. floating-rate payer
• Voluntary market transactions

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Reasons for IRS

• Both parties obtain economic benefits
• National and international money
  
• and capital market imperfections
• comparative advantages among
• different borrowers in these
• markets

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Reasons for IRS (contd)
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Gaps in Balance Sheet

• U.S. financial institutions
• Assets -fixed rate of interestlong maturities
• (mortgage and consumer installment loans)
• Liabilities-short maturities
• (money market deposit accounts and
  variable-rate certificates of deposit)
• v.s. European financial institutions
• Assets with relatively short maturities and
  liabilities with relatively long maturities

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Gaps in Balance Sheet (contd)

• differences in inter-firm asset/liability
  composition represent opposite kinds of gaps in
  balance sheet.
• interest rate swaps provide an economic mechanism
  whereby both financial institutions can benefit
  from a reduction in their respective
  balance-sheep gaps and a decrease of exposure to
  interest-rate risk.

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III. Uses of IRS
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Uses of IRS

• Gap management
• Lower fixed-rate cost
• Restructure debt mix
• Manage basis risk

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A. Using IRS in gap management

• What is gap management?
• Duration gap
• If there exists a duration gap, it means the
  organization will benefit or suffer if
  interest rate changes
• In order to prevent from loss of net value
• DA A DD D DE E (dollar duration)
  
• In order to sustain the debt ratio
• DA DD

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A. Using IRS in gap management (contd)

• Sallie Mae (student loan marketing association )
• floating rate student loans
• medium-term fixed rate cost
• have to shorten the duration of its
  liabilities

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B. Using IRS to Lower Fixed-Rate Cost

• A useful tool for lowering a companys cost of
  long-term fixed interest rate borrowing,
  especially for a company with low credit rating.
• The quality spread is narrower in the
  floating-rate market than in the fixed-rate
  market.

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B. Using IRS to Lower Fixed-Rate Cost (contd)

• Example

Floating Rate Fixed Rate
Aaa Corp. T-Bill0.25 11.5
Baa Corp. T-Bill0.5 13
Quality Speard 0.25 1.5
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B. Using IRS to Lower Fixed-Rate Cost (contd)
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B. Using IRS to Lower Fixed-Rate Cost (contd)
Net Cost Original Cost Cost Saving
Aaa Corp. T-Bill - 0.5 T-Bill 0.25 0.75
Baa Corp. 12.5 13 0.5
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C. Using IRS to Restructure Debt Mix

• A useful tool for active liability management.
• For example, a firm with too many high-coupon
  fixed-rate liabilities may
• (1) Refinancing
• - Drawbacks high cost / restrictions
• (2) IRS

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C. Using IRS to Restructure Debt Mix (contd)

• A company has a 50 million of noncallable debt
  with a fixed-rate of 14
• What will happen if the company enter into the
  following IRS agreement ?
• - Pay floating rate prime rate 50bp
• - Receive fixed rate 13

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C. Using IRS to Restructure Debt Mix (contd)

• December 1, 1985
• Prime rate 9.5 Floating rate
  10
• The result of IRS
• Financing cost
• Fixed rate of 14 Net floating
  rate of 11
• - An economic gain of 3

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D. Using IRS to Manage Basis Risk

• A useful tool for manage the basis risk in the
  B/S.
• The B/S of a bank
• - Asset yield LIBOR 0.75
• - Liability cost T-Bill 0.25

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D. Using IRS to Manage Basis Risk (contd)
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D. Using IRS to Manage Basis Risk (contd)

• After into an IRS, the bank has
• - Asset yield LIBOR 0.75
• - Liability cost LIBOR - 0.75
• (1) Transforming T-Bill-rate-based
• liability into LIBOR-based one
• (2) Locking in a positive spread of
• 150bp

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IV. The Valuation Of IRS
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B. Simple Comparison of Alternative Swap

• The choice between two interest rate swaps with
  different floating-rate indices should be based
  on the same economic criterion.
• The economic decision rules for choosing between
  alternative swaps are the minimization of the
  present value of interest costs, or equivalently,
  the one that results in the largest value.

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B. Simple Comparison of Alternative Swap

• Compare the partial ex post performance of two
  swaps completed in August, 1982.
• -10-year Treasury Bond rate 0.75
• against 6-month LIBOR rate
• -10-year Treasury Bond rate -0.80
• against 6-month T-Bill rate
• 
  
• The floating rate difference was 158 basis points
  and the fixed rate difference was 155 basis
  point. So they were comparable.

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The comparison of LIBOR and T-Bill
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The valuation Procedure

• The valuation of IRS
• In a fair transaction principle, the value
  of IRS is initially worth zero.
• The valuation of CRS

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The valuation of IRS

• IRS can be viewed as buying and selling the bond
  with different interest rate at the same time.
• Bfix Value of fixed-rate bond underlying the
  swap
• Bfl Value of floating-rate bond underlying
  the swap
• ti Time when ith papements are
  exchanged(1?i?n)
• LNational principal in swap agreement
• ri LIBOR zero rate for a maturity ti
• kFixed payment made on each payment date
• kFloating payment made on a next date

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The valuation of IRS (contd)

• Example
• 1.Pay six-month LIBOR and receive 8 per annum
  (with semiannual compounding)
• 2. A national principal of 100 million.
• 3.The Swap has a remaining life of 1.25 years.
• 4.LIBOR rates with continuous compounding for
  3-month, 9-month, and 15-month maturities are
  10, 10.5,and 11, respectively.
• 5.The 6-month LIBOR rate at the last payment date
  was 10.2.
• What is the value of IRS for FI?

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The valuation of IRS (contd)

• (unit million)
• K 4
• K 5.1
• Bfix 4e-0.10.25 4e-0.1050.75
  104e-0.111.25
• 98.24
• Bfl (100 5.1)e-0.10.25 102.51
• Vswap 98.24 - 102.51 -4.27

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The valuation of IRS (contd)

• IRS also can be seen as a portfolio of
  forward-rate agreements.
• V swap sum of the value of all forward
  contracts
• The procedure is as followed
• 1.Caculate forward rates for each of the LIBOR
  rates will equal the forward rates.
• 2.Caculate swap cash flow on the assumption that
  the LIBOR rates will equal the forward rates.
• 3.Set the swap value equal to the present value
  of these cash flows.

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The valuation of IRS (contd)
First CF exchanging Interest for six months at a rates of 8 per annum will be exchanged for interest at a rate of 10.2 per annum for six months. The value of the exchange to FI is 0.5 100 (0.08-0.102)e-0.10.25 -1.07
Second CF exchanging Calculate the forward rate corresponding to the period between 3 and 9 months. (0.105 0.75 - 0.10 0.25)/0.5 0.1075 10.75 per annum with continuous compounding 11.044 per annum with semiannual compounding.
Second CF exchanging The value of the FRA corresponding to the exchange in 9 months is 0.5 100 (0.08-0.11044)e-0.1050.75 -1.41
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The valuation of IRS (contd)
Third CF exchanging Calculate the forward rate corresponding to the period between 9 and 15 months. (0.11 1.25 - 0.105 0.75)/0.5 0.1175 11.75 per annum with continuous compounding 12.102 per annum with semiannual compounding
Third CF exchanging The value of the FRA corresponding to the exchange in 15 months is 0.5 100 (0.08-0.12102)e-0.111.25 -1.79
The total value of swap The total value of swap -1.07 - 1.41 - 1.79 -4.27
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Supplement Valuation of currency swaps

• Decomposing a currency swap into
• (1) Two bonds
• (2) A series of forward contracts

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Decomposition into bonds

• The value in U.S. dollars of a swap where dollars
  are received and a foreign currency is paid
• Vswap BD - S0BF
• BD the value of the U.S. dollar bond
• BF the value of the foreign bond
• S0 the current spot exchange rate (/F)

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Decomposition into bonds (contd)

• Example
• A company enters into a 3-yr currency swap
  where
• (1) Receive 5 in yen / ?1,200 million
• (2) Pay 8 in dollars / 10 million
• (3) Japanese rate 4 / U.S. rate 9
• (4) Current exchange rate ?110 1
• Whats the value of the swap for the
  company?

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Decomposition into bonds (contd)

• BD 0.8e-0.091 0.8e-0.092 10.8e-0.093
  
• 9.644 million dollars
• BF 60e-0.041 60e-0.042 1,260e-0.043
  
• 1,230.55 million yen
• The value of the swap
• 1,230.55/110 9.644
• 1.543 million

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Decomposition into forwards

• Each of the exchanges can be view as a forward
  contract.
• The value of a forward contract
• the forward price of the underlying
• asset is realized.

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Decomposition into forwards (contd)

• Followed the above example
• S0 1/110 0.009091 / yen
• F1 0.009091e(0.09-0.04)1 0.009557
• F2 0.009091e(0.09-0.04)2 0.010047
• F3 0.009091e(0.09-0.04)3 0.010562

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Decomposition into forwards (contd)

• The values of the forward contracts in 1yr, 2yr
  and 3yr are
• (600.009557-0.8)e-0.091 -0.2071
• (600.010047-0.8)e-0.092 -0.1647
• (12600.010562-10.8)e-0.093 1.9147
• Total value of the swap
• 1.9147-0.2071-0.1647 1.543 million

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Conclusion

• IRS transactions are based upon a simple economic
  principle of comparative advantage.
• Using swaps, financial managers can readily
  transform the economic characteristics of their
  liabilities.
• IRS are more effective than financial futures and
  options in hedging against the interest rate risk
  for horizons beyond two or three years.