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### Subject 1. Risk/return characteristics of interest rate swap

In a plain vanilla interest rate swap:

• One counterparty agrees to pay fixed interest payments and receive floating interest payments. This counterparty is known as the pay-fixed side of the swap.

• The opposing counterparty agrees to receive fixed interest payments and pay floating interest payments. This counterparty is known as the receive-fixed side of the swap. The fixed rate the fixed-rate payer must make is called the swap-rate.

• For each payment, the interest rates are multiplied by a fraction representing the number of days in the settlement period over the number of days in a year. In some cases, it is assumed that there are 30 days in each month, and 360 days in a year. Others use exact day count in each month and 365 days in a year.

• Typically, the floating rate is set in advance and paid in arrears. That is, the floating rate is set at one settlement date, and the cash interest is paid at the next settlement date.

• Notional principal is generally not exchanged. The notional principal is the same for both parties of the swap, so it is not necessary to transfer funds from one party to another. Notional principal is only used to calculate the amount of interest payments.

• The obligations of the counterparties are offset against each other, and net payment is made by the party who owes it. Since both parties deal in a single currency, netting of payments avoids unnecessary payments.

• The convention that has evolved for quoting a swap 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 is some "spread" above the Treasury yield curve with the same term to maturity as the swap. This spread is called the swap spread.

For example, Party A might agree to pay a fixed rate of interest on \$1 million each year for five years to Party B. In return, Party B might pay a floating rate of interest on \$1 million each year for five years.

Floating rates in the international swaps market are most often set as equaling the London Interbank Offer Rate (LIBOR). This is commonly referred to as "LIBOR flat", and is a very common benchmark for interest-rate swap transactions. Recall that:

• LIBOR is the rate at which prime banks offer to pay on Eurodollar deposits available to other prime banks for a given maturity. Basically, it is viewed as the global cost of bank borrowing.

• There is not just one rate but a rate for different maturities. For example, there is a 1-month LIBOR, 3-month LIBOR, 6-month LIBOR, etc.

Interest rate swaps can be used to hedge against interest rate risk.

• If interest rates are expected to rise, a firm with floating rate debt can enter into an interest rate swap to receive floating and pay fixed. The floating interest payments received will be used to cover the firm's original floating debt. Thus, the firm's floating rate debt is converted into a fixed rate debt, which has lower cost if rates rise.

• If interest rates are expected to fall, a firm with fixed rate debt can enter into an interest rate swap to receive fixed and pay floating.

Consider the following interest rate swap agreement:

Party A: pay-fixed
Tenor: 5 years
Notional amount: \$1,000,000
Fixed rate: 8%
Floating rate:1 Year LIBOR + 1%

The swap is "determined in advance and paid in arrears." The 1 Year LIBOR rate is:

6.50% when the swap is initiated
6.75% at end of year 1
7.00% at end of year 2
7.25% at end of year 3
7.50% at end of year 4
7.75% at end of year 5

Which are the net payments of Party B?

In this swap agreement, party A has agreed to pay party B 8% fixed interest on a \$1,000,000 notional amount (\$80,000) for the next five years. In return, party B has agreed to pay party A an interest rate tied to the 1 year LIBOR rate plus 1% on a notional amount of \$1,000,000 for the next five years. Due to the fact that the swap is "determined in advance," the floating rate is determined at the beginning of the period. Thus for year one as an example, party B is obligated to pay 6.50% + 1% or 7.50% on \$1,000,000 (\$75,000).

The net payment is simply the difference between the obligations of the two counter parties. With a plain vanilla swap, net payments are typically the only transactions involving cash that actually occur.

A swap position can be interpreted as a package of forward (futures) contracts.

Continue with the above example. Party A has agreed to pay 8% and receive 1-year LIBOR + 1%. More specifically, party A has agreed to buy a commodity called "1-year LIBOR + 1%" for \$80,000. This is effectively a 1-year forward contract where A agrees to pay \$80,000 in exchange for delivery of 1-year LIBOR + 1%. If interest rates increase to 9%, the price of that commodity (1-year LIBOR + 1%) is higher, resulting in a gain for the fixed-rate payer, who is effectively long a 1-yar forward contract on 1-year LIBOR + 1%. The floating-rate payer is effectively short a 1-year forward contract on 1-year LIBOR + 1%. There is therefore an implicit forward contract corresponding to each exchange date.

Consequently, interest rate swaps can be viewed as a package of more basic interest rate derivatives such as forwards. The pricing of an interest rate swap will then depends on the price of a package of forward contracts with the same settlement dates in which the underlying for the forward contract is the same reference rate.

There are, however, differences between an interest rate swap and a package of forward contracts:

• Maturities for forward or futures contracts do not extend out as far as those of an interest rate swap. An interest rate swap with a term of 20 years or longer can be obtained.
• An interest rate swap is a more transactionally efficient instrument.
• Interest rate swaps provide more liquidity than forward contracts, particularly long-dated forward contracts.

The second interpretation (not required by the los) is that an interest rate swap is a package of cash market instruments.

• From the perspective of the fixed-rate payer, it is equivalent to buying a floating-rate note (with the reference rate for the note being the reference rate for the swap) and funding by issuing a fixed-rate bond (with the coupon rate for the bond being the swap rate). The par value of the floating rate note and the fixed-rate bond is the notional amount of the swap.

• For the fixed-rate receiver, a swap is equivalent to purchasing a fixed-rate bond and funding it by issuing a floating-rate note.

#### Practice Question 1

Assume that you are analyzing a plain vanilla interest rate swap with the following characteristics:

Counterparty X Counterparty Y
pay fixed rate 6% pay floating rate LIBOR + 0.5%
Swap tenor: 10 years
Notional principal: \$1,000,000
LIBOR0: 4.75%

Assume further that payments for this swap are determined in advance but paid in arrears. Which of the following is the fixed rate payment made by Counterparty X?

A. \$60,000
B. \$47,500
C. \$52,500.

(1,000,000)(.06) = 60,000

#### Practice Question 2

Assume that you are analyzing a plain vanilla interest rate swap with the following characteristics:

Counterparty X : Counterparty Y
pay fixed rate 6% : pay floating rate LIBOR + 0.5%
Swap tenor: 10 years
Notional principal: \$1,000,000
LIBOR0: 4.75%

Swap payments are determined in advance but paid in arrears. Given this information, which of the following best describes the first net payment for the swap?

A. \$7,500 from Counterparty X to Counterparty Y
B. \$7,500 from Counterparty Y to Counterparty X
C. \$12,500 from Counterparty X to Counterparty Y.

Counterparty X has agreed to pay (1,000,000)(.06) = 60,000 and Counterparty Y has agreed to pay (1,000,000)(.0475 + .005) = 52,500. The net payment, then, is from X to Y in the amount of 60,000 - 52,500 = 7,500

#### Practice Question 3

First National Bank finds itself in a situation where it is receiving fixed rate income from its loan portfolio and must pay floating rate expenses to its depositors. If interest rates rise, First National Bank will:

C. pay higher expenses to its depositors.

Since the bank's expenses to its depositors are at a floating rate, rising rates will cause these expenses to increase.

#### Practice Question 4

In an interest rate swap, the swap rate is the ______.

A. fixed rate that the fixed-rate payer agrees to pay over the life of the swap
B. reference rate (e.g., LIBOR) used to calculate the floating rate
C. floating rate that the fixed-rate receiver agrees to pay over the life of the swap
D. spread between the fixed rate and floating rate. Both parties use the spread at the end of each period to calculate the net payment

#### Practice Question 5

Suppose that an investor enters into a 5-year interest rate swap with a dealer. The notional amount is \$100 million and the reference rate is 3-month LIBOR. Payments are made quarterly. The swap rate that the investor agrees to pay is 5%. Suppose for the first floating-rate payment 3-month LIBOR is 4.4%. How much should the investor pay the dealer at the end of the first quarter?

A. \$1.1 million.
B. \$1.25 million.
C. \$0.15 million.

The fixed-rate payment each quarter is (\$100 million x 0.05/4) = \$1.25 million. The first quarter floating-rate payment is (\$100 million x 0.044/4) = \$1.1 million.

The net payment is simply the difference between the two payments: the investor should pay 1.25 - 1.1 = \$0.15 million to the dealer.

#### Practice Question 6

A fixed-rate payer in a swap transaction has a position similar to

A. buying a package of interest rate forward contracts.
B. buying a package of interest rate futures contracts and financing the purchase at a floating rate, where the floating rate is the reference rate for the swap.
C. selling a package of interest rate forward contracts and buying a fixed-rate bond.

There are two ways that a swap position can be interpreted: 1. a package of forward (futures) contracts, and 2. a package of cash flows from buying and selling cash market instruments.

Note that the second interpretation is not required in the study guide.

There is a similarity between the risk/return relationship for an interest rate swap and a forward (futures) contract. For example, if interest rates increase, the long forward (futures) position gains, and the fixed-rate payer also gains.

#### Practice Question 7

A fixed-rate payer in an interest rate swap is said to be ______.

A. long the bond market.
B. short the bond market.
C. long the swap market.

Both an investor who is short the bond market and a fixed-rate payer in an interest rate swap gain when interest rates increase.

#### Practice Question 8

National Financial Corporation has a large number of outstanding bonds with floating coupon rates. This means that National Financial is making periodic interest payments based on a floating rate of interest. If interest rates rise:

A. National Financial will have smaller interest payments.
B. National Financial will have larger interest payments.
C. National Financial's interest payments will be unaffected.

Since the company's bond payments are based on a floating rate, rising interest rates will cause these payments to increase.

#### Practice Question 9

Assume that you are analyzing a plain vanilla interest rate swap with the following characteristics:

Counterparty X : Counterparty Y
pay fixed rate 6% : pay floating rate LIBOR + 0.5%
Swap tenor: 10 years
Notional principal: \$1,000,000
LIBOR0: 4.75%

Swap payments are determined in advance but paid in arrears. Given this information, which of the following best describes the first net payment for the swap?

A. \$7,500 from Counterparty X to Counterparty Y.
B. \$7,500 from Counterparty Y to Counterparty X.
C. \$12,500 from Counterparty X to Counterparty Y.

Counterparty X has agreed to pay (1,000,000)(.06) = 60,000 and Counterparty Y has agreed to pay (1,000,000)(.0475 + .005) = 52,500. The net payment, then, is from X to Y in the amount of 60,000 - 52,500 = 7,500.

#### Practice Question 10

Suppose that an investor enters into a 4-year interest rate swap with a dealer. The notional amount is \$100 million and the reference rate is 6-month LIBOR. Payments are made semi-annually. The swap rate that the investor agrees to pay is 6%. Suppose for the first floating-rate payment 6-month LIBOR is 5%. At the end of the first six-month period, which of the following is true?

A. The investor pays \$1 million to the dealer.
B. The investor pays \$0.5 million to the dealer.
C. The dealer pays \$0.5 million to the investor.

The fixed-rate payment each period (6-month) is (\$100 million x 0.06/2) = \$3 million.

The floating-rate payment at the end of the first period is (\$100 million x 0.05/2) = \$2.5 million.

The net payment is simply the difference between the two payments: the investor should pay 3 - 2.5 = \$0.5 million to the dealer.

#### Practice Question 11

A floating-rate payer in a swap transaction has a position similar to

A. selling a package of interest rate futures contracts.
B. buying a package of interest rate futures contracts and financing the purchase at a floating rate, where the floating rate is the reference rate for the swap.
C. selling a package of interest rate forward contracts and buying a fixed-rate bond.