UNDERSTANDING YIELD SPREADS
VI. SWAP SPREADS
Another important spread measure is theswap spread.
A. Interest Rate Swap and the Swap Spread
In an interest rate swap, two parties (calledcounterparties) agree to exchange periodic interest payments. The dollar amount of the interest payments exchanged is based on a predetermined dollar principal, which is called the notional principal or notional amount. The dollar amount each counterparty pays to the other is the agreed-upon periodic interest rate times the notional principal. The only dollars exchanged between the parties are the interest payments, not the notional principal. In the most common type of swap, one party agrees to pay the other party fixed interest payments at designated dates for the life of the swap. This party is referred to as thefixed-rate payer. The fixed rate that the fixed-rate payer pays is called the swap rate. The other party, who agrees to make interest rate payments that float with some reference rate, is referred to as thefixed-rate receiver.
The reference rates used for the floating rate in an interest rate swap is one of various money market instruments: LIBOR (the most common reference rate used in swaps), Treasury bill rate, commercial paper rate, bankers’ acceptance rate, federal funds rate, and prime rate.
The convention that has evolved for quoting a swap rate is that a dealer sets the floating rate equal to the reference rate and then quotes the fixed rate that will apply. The fixed rate has a specified ‘‘spread’’ above the yield for a Treasury with the same term to maturity as the swap. This specified spread is called theswap spread. Theswap rateis the sum of the yield for a Treasury with the same maturity as the swap plus the swap spread.
To illustrate an interest rate swap in which one party pays fixed and receives floating, assume the following:
Chapter 4 Understanding Yield Spreads 93
term of swap: 5 years swap spread: 50 basis points reference rate: 3-month LIBOR notional amount: $50 million
frequency of payments: every three months
Suppose also that the 5-year Treasury rate is 5.5% at the time the swap is entered into. Then the swap rate will be 6%, found by adding the swap spread of 50 basis points to the 5-year Treasury yield of 5.5%.
This means that the fixed-rate payer agrees to pay a 6% annual rate for the next five years with payments made quarterly and receive from the fixed-rate receiver 3-month LIBOR with the payments made quarterly. Since the notional amount is $50 million, this means that every three months, the fixed-rate payer pays $750,000 (6% times $50 million divided by 4). The fixed-rate receiver pays 3-month LIBOR times $50 million divided by 4. The table below shows the payment made by the fixed-rate receiver to the fixed-rate payer for different values of 3-month LIBOR:14
If 3-month LIBOR is Annual dollar amount Quarterly payment
4% $2,000,000 $500,000
5% 2,500,000 625,000
6% 3,000,000 750,000
7% 3,500,000 875,000
8% 4,000,000 1,000,000
In practice, the payments are netted out. For example, if 3-month LIBOR is 4%, the fixed-rate receiver would receive $750,000 and pay to the fixed-rate payer $500,000. Netting the two payments, the fixed-rate payer pays the fixed-rate receiver $250,000 ($750, 000−
$500, 000).
B. Role of Interest Rate Swaps
Interest rate swaps have many important applications in fixed income portfolio management and risk management. They tie together the fixed-rate and floating-rate sectors of the bond market. As a result, investors can convert a fixed-rate asset into a floating-rate asset with an interest rate swap.
Suppose a financial institution has invested in 5-year bonds with a $50 million par value and a coupon rate of 9% and that this bond is selling at par value. Moreover, this institution borrows $50 million on a quarterly basis (to fund the purchase of the bonds) and its cost of funds is 3-month LIBOR plus 50 basis points. The ‘‘income spread’’ between its assets (i.e., 5-year bonds) and its liabilities (its funding cost) for any 3-month period depends on 3-month LIBOR. The following table shows how the annual spread varies with 3-month LIBOR:
14The amount of the payment is found by dividing the annual dollar amount by four because payments are made quarterly. In a real world application, both the fixed-rate and floating-rate payments are adjusted for the number of days in a quarter, but it is unnecessary for us to deal with this adjustment here.
Asset yield 3-month LIBOR Funding cost Annual income spread
9.00% 4.00% 4.50% 4.50%
9.00% 5.00% 5.50% 3.50%
9.00% 6.00% 6.50% 2.50%
9.00% 7.00% 7.50% 1.50%
9.00% 8.00% 8.50% 0.50%
9.00% 8.50% 9.00% 0.00%
9.00% 9.00% 9.50% −0.50%
9.00% 10.00% 10.50% −1.50%
9.00% 11.00% 11.50% −2.50%
As 3-month LIBOR increases, the income spread decreases. If 3-month LIBOR exceeds 8.5%, the income spread is negative (i.e., it costs more to borrow than is earned on the bonds in which the borrowed funds are invested).
This financial institution has a mismatch between its assets and its liabilities. An interest rate swap can be used to hedge this mismatch. For example, suppose the manager of this financial institution enters into a 5-year swap with a $50 million notional amount in which it agrees to pay a fixed rate (i.e., to be the fixed-rate payer) in exchange for 3-month LIBOR. Suppose further that the swap rate is 6%. Then the annual income spread taking into account the swap payments is as follows for different values of 3-month LIBOR:
Asset 3-month Funding Fixed rate 3-month LIBOR Annual
yield LIBOR cost paid in swap rec. in swap income spread
9.00% 4.00% 4.50% 6.00% 4.00% 2.50%
9.00% 5.00% 5.50% 6.00% 5.00% 2.50%
9.00% 6.00% 6.50% 6.00% 6.00% 2.50%
9.00% 7.00% 7.50% 6.00% 7.00% 2.50%
9.00% 8.00% 8.50% 6.00% 8.00% 2.50%
9.00% 8.50% 9.00% 6.00% 8.50% 2.50%
9.00% 9.00% 9.50% 6.00% 9.00% 2.50%
9.00% 10.00% 10.50% 6.00% 10.00% 2.50%
9.00% 11.00% 11.50% 6.00% 11.00% 2.50%
Assuming the bond does not default and is not called, the financial institution has locked in a spread of 250 basis points.
Effectively, the financial institution using this interest rate swap converted a fixed-rate asset into a floating-rate asset. The reference rate for the synthetic floating-rate asset is 3-month LIBOR and the liabilities are in terms of 3-month LIBOR. Alternatively, the financial institution could have converted its liabilities to a fixed-rate by entering into a 5-year $50 million notional amount swap by being the fixed-rate payer and the results would have been the same.
This simple illustration shows the critical importance of an interest rate swap. Investors and issuers with a mismatch of assets and liabilities can use an interest rate swap to better match assets and liabilities, thereby reducing their risk.
Chapter 4 Understanding Yield Spreads 95
C. Determinants of the Swap Spread
Market participants throughout the world view the swap spread as the appropriate spread measure for valuation and relative value analysis. Here we discuss the determinants of the swap spread.
We know that
swap rate=Treasury rate+swap spread
where Treasury rate is equal to the yield on a Treasury with the same maturity as the swap.
Since the parties are swapping the future reference rate for the swap rate, then:
reference rate=Treasury rate+swap spread Solving for the swap spread we have:
swap spread=reference rate−Treasury rate
Since the most common reference rate is LIBOR, we can substitute this into the above formula getting:
swap spread=LIBOR−Treasury rate
Thus, the swap spread is a spread of the global cost of short-term borrowing over the Treasury rate.
EXHIBIT 8 Three-Year Trailing Correlation Between Swap Spreads and Credit Spreads (AA, A, and BB): June 1992 to December 2001
1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0
1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0
Correlation Coefficient
AA A BBB
Jun-92 Mar-93 Dec-93 Sep-94 Jun-95 Mar-96 Dec-96 Sep-97 Jun-98 Mar-99 Dec-99 Sep-00 Jun-01
Source: Lehman Brothers Fixed Income Research,Global Fixed Income Strategy ‘‘Playbook,’’ January 2002.
EXHIBIT 9 January and December 2001 Swap Spread Curves for Germany, Japan, U.K., and U.S.
Germany Japan U.K. U.S.
2-Year 5-Year 10-Year 30-Year 2-Year 5-Year 10-Year 30-Year 2-Year 5-Year 10-Year 30-Year 2-Year 5-Year 10-Year 30-Year
Jan-01 23 40 54 45 8 10 14 29 40 64 83 91 63 82 81 73
Dec-01 22 28 28 14 3 (2) (1) 8 36 45 52 42 46 76 77 72
Source: Lehman Brothers Fixed Income Research,Global Fixed Income Strategy ‘‘Playbook,’’January 2002.
EXHIBIT 10 Daily 5-Year Swap Spreads in Germany and the United States: 2001 bp
100 90 80 70 60 50 40 30 20
bp Germany 100 U.S.
90 80 70 60 50 40 30 20
Dec-00 Feb-01 Apr-01 Jan-01 Aug-01 Oct-01 Dec-01
Source: Lehman Brothers Fixed Income Research,Global Fixed Income Strategy ‘‘Playbook,’’January 2002.
The swap spread primarily reflects the credit spreads in the corporate bond market.15 Studies have found a high correlation between swap spreads and credit spreads in various sectors of the fixed income market. This can be seen in Exhibit 8 (on the previous page) which shows the 3-year trailing correlation from June 1992 to December 2001 between swap spreads and AA, A, and BBB credit spreads. Note from the exhibit that the highest correlation is with AA credit spreads.
D. Swap Spread Curve
A swap spread curve shows the relationship between the swap rate and swap maturity. A swap spread curve is available by country. The swap spread is the amount added to the yield of the respective country’s government bond with the same maturity as the maturity of the swap. Exhibit 9 shows the swap spread curves for Germany, Japan, the U.K., and the U.S. for January 2001 and December 2001. The swap spreads move together. For example, Exhibit 10 shows the daily 5-year swap spreads from December 2000 to December 2001 for the U.S. and Germany.
15We say primarily because there are also technical factors that affect the swap spread. For a discussion of these factors, see Richard Gordon, ‘‘The Truth about Swap Spreads,’’ in Frank J. Fabozzi (ed.), Professional Perspectives on Fixed Income Portfolio Management: Volume 1(New Hope, PA: Frank J.
Fabozzi Associates, 2000), pp. 97–104.