Title: An%20Economic%20Analysis%20of%20Interest%20Rate%20Swaps
1An Economic Analysis of Interest Rate Swaps
- Member
- R94723046 ???
- R94723043 ???
- R94723052 ???
2Agenda
- Introduction
- The basic interest rate swap
- Many uses of interest rate swap
- The valuation of swaps
3I. Introduction
4Introduction
- Based on the principle of comparative advantage
- A useful tool of active liability management and
for hedging against interest rate risk.
5History 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.
6History 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
7II. The basic irs
8 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
9Reasons for IRS
- Both parties obtain economic benefits
- National and international money
- and capital market imperfections
-
- comparative advantages among
- different borrowers in these
- markets
-
10Reasons for IRS (contd)
11Gaps 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 -
12Gaps 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.
13III. Uses of IRS
14Uses of IRS
- Gap management
- Lower fixed-rate cost
- Restructure debt mix
- Manage basis risk
15A. 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
-
-
16A. 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 -
17B. 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.
18B. Using IRS to Lower Fixed-Rate Cost (contd)
Floating Rate Fixed Rate
Aaa Corp. T-Bill0.25 11.5
Baa Corp. T-Bill0.5 13
Quality Speard 0.25 1.5
19B. Using IRS to Lower Fixed-Rate Cost (contd)
20B. 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
21C. 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
22C. 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
23C. 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
24D. 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
25D. Using IRS to Manage Basis Risk (contd)
26D. 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
27IV. The Valuation Of IRS
28B. 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.
29B. 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.
30The comparison of LIBOR and T-Bill
31The valuation Procedure
- The valuation of IRS
- In a fair transaction principle, the value
of IRS is initially worth zero. - The valuation of CRS
32The 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
33The 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?
34The 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
35The 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.
36The 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
37The 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
38Supplement Valuation of currency swaps
- Decomposing a currency swap into
- (1) Two bonds
- (2) A series of forward contracts
39Decomposition 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)
40Decomposition 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?
41Decomposition 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
42Decomposition 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.
43Decomposition 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
44Decomposition 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
45Conclusion
- 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.