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## Interest Rate Swaps

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**Interest Rate Swaps: Origin**• Today there exist an interest rate swap market where trillions of dollars (in notional principal) of swaps of fixed-rate loans for floating-rate loans occur each year.**Interest Rate Swaps: Origin**• The market primarily consist of financial institutions and corporations who use the swap market to hedge more efficiently their liabilities and assets. • Many institutions create synthetic fixed- or floating-rate assets or liabilities with better rates than the rates obtained on direct liabilities and assets.**Interest Rate Swaps: Definition**Definition: • A swap is an exchange of cash flows, CFs. • It is a legal arrangement between two parties to exchange specific payments.**Interest Rate Swaps: Types**• There are four types of swaps: • Interest Rate Swaps: Exchange of fixed-rate payments for floating-rate payments • Currency Swaps: Exchange of liabilities in different currencies • Cross-Currency Swaps: Combination of Interest rate and Currency swap • Credit Default Swaps: Exchange of premium payments for default protection**Plain Vanilla Interest Rate Swaps**Definition • Plain Vanilla or Generic Interest Rate Swap involves the exchange of fixed-rate payments for floating-rate payments.**Plain Vanilla Interest Rate Swaps: Terms**• Parties to a swap are called counterparties. There are two parties: • Fixed-Rate Payer • Floating-Rate Payer • Rates: • Fixed rate is usually a T-note rate plus basis points. • Floating rate is a benchmark rate: LIBOR.**Plain Vanilla Interest Rate Swaps: Terms**• Reset Frequency: Semiannual • Principal: No exchange of principal • Notional Principal (NP): Interest is applied to a notional principal; the NP is used for calculating the swap payments.**Plain Vanilla Interest Rate Swaps: Terms**• Maturity ranges between 3 and 10 years. • Dates: Payments are made in arrears on a semiannual basis: • Effective Date is the date interest begins to accrue • Payment Date is the date interest payments are made**Plain Vanilla Interest Rate Swaps: Terms**• Net Settlement Basis: The counterparty owing the greater amount pays the difference between what is owed and what is received—only the interest differential is paid. • Documentation: Most swaps use document forms suggested by the International Swap Dealer Association (ISDA) or the British Banker’s Association. The ISDA publishes a book of definitions and terms to help standardize swap contracts.**Web Site**• For information on the International Swap and Derivative Association and size of the markets go to www.isda.org**Swap Terminology**Note: • Fixed-rate payer can also be called the floating-rate receiver and is often referred to as having bought the swap or having a long position. • Floating-rate payer can also be referred to as the fixed-rate receiver and is referred to as having sold the swap and being short.**Plain Vanilla Interest Rate Swap: Example**Example: • Fixed-rate payer pays 5.5% every six months • Floating-rate payer pays LIBOR every six months • Notional Principal = $10 million • Effective Dates are 3/1 and 9/1 for the next three years**Interest Rate Swap: Point**Points: • If LIBOR > 5.5%, then fixed payer receives the interest differential. • If LIBOR < 5.5%, then floating payer receives the interest differential.**Interest Rate Swaps’ Fundamental Use**• One of the important uses of swaps is in creating a synthetic fixed- or floating-rate liability or asset that yields a better rate than a conventional or direct one: • Synthetic fixed-rate loans and investments • Synthetic floating-rate loans and investments**Conventional Floating-Rate Loan**Swap: Fixed-Rate Payer Position Swap: Fixed-Rate Payer Position Synthetic Fixed Rate Pay Floating Rate Pay Fixed Rate Receive Floating Rate Pay Fixed Rate A synthetic fixed-rate loan is formed by combining a floating-rate loan with a fixed-rate payer’s position**Synthetic Fixed-Rate Loan**Example: • A synthetic fixed-rate loan formed with 2-year, $10,000,000 floating-rate loan with rates set equal to the LIBOR on 3/1 and 9/1 combined with a fixed-rate payer’s position on the swap just analyzed.**Conventional Fixed-Rate Loan**Swap: Floating-Rate Payer Position Swap: Floating-Rate Payer Position Synthetic Floating Rate Pay Fixed Rate Pay Floating Rate Receive Fixed Rate Pay Floating Rate A synthetic floating-rate loan is formed by combining a fixed-rate loan with a floating-rate payer’s position.**Synthetic Floating-Rate Loans**Example: • A synthetic floating-rate loan formed with a 3-year, $10,000,000, 5% fixed-rate loan combined with the floating-rate payer’s position on the swap just analyzed.**Swaps as Bond Positions**• Swaps can be viewed as a combination of a fixed-rate bond and flexible-rate note (FRN). • A fixed-rate payer position is equivalent to • Buying a FRN paying the LIBOR and • Shorting a fixed-rate bond at the swap’s fixed rate. • From the previous example, the fixed-rate payer’s swap’s CFs can be replicated by: • Selling at par a 3-year bond, paying a 5.5% fixed rate and a principal of $10,000,000 (semiannual payments) and • Purchasing a 3-year, $10,000,000 FRN with the rate reset every six months at the LIBOR.**Swaps as Bond Positions**• A floating-rate payer position is equivalent to • Shorting a FRN at the LIBOR and • Buying a fixed-rate bond at the swap fixed rate • From the previous example, the floating-rate payer’s swap’s CFs can be replicated by: • Selling a 3-year, $10,000,000 FRN paying the LIBOR and • Purchasing 3-year, $10,000,000, 5.5% fixed-rate bond at par**Swaps as Eurodollar Futures Positions**• A swap can also be viewed as a series of Eurodollar futures contracts. • Consider a short position in a Eurodollar strip in which the short holder agrees to sell 10 Eurodollar deposits at the CME‑index price of 94.5 (or discount yield of RD = 5.5%) with • Each of the contracts having a face value of $1,000,000 and maturity of 6 months • The expirations on the strip being March 1st and September 1st for a period of two and half years**Swaps as Eurodollar Futures Positions**• With the index at 94.5, the contract price on one Eurodollar futures contract is $972,500: • The next slide shows the cash flows at the expiration dates from closing the 10 short Eurodollar contracts at the same assumed LIBOR used in the previous swap example, with the Eurodollar settlement index being 100 − LIBOR.**Swaps as Eurodollar Futures Positions**• Comparing the fixed-rate payer's net receipts shown in Column 5 of the first exhibit (Slide 14) with the cash flows from the short positions on the Eurodollar strip shown in Slide 27, one can see that the two positions yield the same numbers.**Swaps as Eurodollar Futures Positions**• Note there are some differences between the Eurodollar strip and the swap: • First, a 6‑month differential occurs between the swap payment and the futures payments. This time differential is a result of the interest payments on the swap being determined by the LIBOR at the beginning of the period, whereas the futures position's profit is based on the LIBOR at the end of its period. • Second, the futures contract is on a Eurodollar deposit with a maturity of 6 months instead of the standard 3 months.**Swaps as Eurodollar Futures Positions**• Credit Risk: On a futures contract, the parties transfer credit risk to the exchange. The exchange then manages the risk by requiring margin accounts. Swaps, on the other hand, are exposed to credit risk. • Marketability: Swaps are not traded on an exchange like futures and therefore are not as liquid as futures.**Swaps as Eurodollar Futures Positions**• Standardization: Swaps are more flexible in design than futures that are standardized. • Cash Flow Timing: CFs on swaps are based on the LIBOR 6 months earlier; CFs on futures are based on the current LIBOR.**Swap Market Structure**• Swap Banks: The market for swaps is organized through a group of brokers and dealers collectively referred to as swap banks. • As brokers, swap banks try to match counterparties. • As dealers, swap banks take temporary positions as fixed or floating players; often hedging their positions with positions in Eurodollar futures contracts or with spot fixed-rate and floating-rate bond positions.**Swap Market Structure**• Brokered Swaps: • The first interest rate swaps were very customized deals between counterparties with the parties often negotiating and transacting directly between themselves.**Swap Market Structure**• Brokered Swaps: • The financial institutions role in a brokered swap was to bring the parties together and to provide information; their continuing role in the swap after it was established was minimal; they received a fee for facilitating the swap. • Note: • The financial institution does not assume any credit risk with a brokered swap. • The counterparties assume the credit risk and must make their own assessment of default potential.**Swap Market Structure**Dealers Swaps: • One of the problems with brokered swaps is that it requires each party to have knowledge of the other party’s risk profile. • This problem led to more financial institutions taking positions as dealers in a swap—acting as market makers.**Swap Market Structure**• Dealers Swaps: • With dealer swaps, the swap bank acts as swap dealer making commitments to enter a swap as a counterparty before the other end party has been located. In this market, the end parties contract separately with the swap bank, who acts as a counterparty to each.**Swap Market Structure**• Dealers Swaps: Features • Acting as swap dealers, financial institutions serve an intermediary function. • The end parties assume the credit risk of the financial institution instead of that of the other end party. • Small or no swap fee. • The swap dealer’s compensation comes from a markup on the bid-ask spread extended to the end parties. The spread is reflected on the fixed rate side.**Swap Market Structure**• Dealers Swaps: Features • Because the financial institution is exposed to default risk, the bid-ask spread should reflect that risk. • Because the swap dealer often makes commitments to one party before locating the other, it is exposed to interest rate movements.**Swap Market Structure**• Dealers Swaps: Features • Warehousing: To minimize its exposure to market risk, the swap dealer can hedge her swap position by taking a position in a Eurodollar futures, T-bond, FRN, or spot Eurodollar contract. • This practice is referred to as warehousing.**Swap Market Structure**• Dealers Swaps: Features • Size Problem: Swap dealers often match a swap agreement with multiple counterparties. • For example, a fixed for floating swap between a swap dealer and Party A with a notional principal of $50,000,000 might be matched with two floating for fixed swaps with notional principals of $25,000,000 each.**Swap Market Structure**• Dealers Swaps: Features • Running a Dynamic Book: Any swap commitment can be effectively hedged through a portfolio of alternative positions—other swaps, spot positions in T-notes and FRNs, and futures positions. • This approach to swap market management is referred to as running a dynamic book.**Swap Market Price Quotes**• By convention, the floating rate is quoted flat without basis point adjustments; e.g., LIBOR flat. • The fixed rate is quoted in terms of the on-the-run (newly issued) T-note or T-bond YTM and swap spread.**Swap Market Price Quotes**• Swap spread: Swap dealers usually quote two different swap spreads • One for deals in which they pay the fixed rate • One in which they receive the fixed rate**Swap Market Price Quotes**• Swap Spread: • 80/86 dealer buys at 80bp over T-note yield and sells at 86 over T-note yield. • That is, the dealer will • Take the fixed payer’s position at a fixed rate equal to 80 BP over the T-note yield and • Take the floating payer’s position, receiving 86 bp above the T-note yield.**Swap Market Price Quotes**Swap Bank Quote Offerings Example: Swap Rate = (Bid Rate + Ask Rate)/2**Swap Market Price Quotes**Example of Swap Quote and Terms 5-Year Swap Swap Agreement: • Initiation Date = June 10, Y1 • Maturity Date = June 10, Y6 • Effective Dates: 6/10 and 12/10 • NP = $20,000,000 • Fixed-Rate Payer: Pay = 6.26% (semiannual)/ receive LIBOR • Floating-Rate Payer: Pay LIBOR/Receive 6.20% (semiannual) • LIBOR determined in advance and paid in arrears**Swap Market Price Quotes**Note: • The fixed and floating rates are not directly comparable. The T-note assumes a 365-day basis and the LIBOR assumes 360. • The rates need to be prorated to the actual number of days that have elapsed between settlement dates to determine the actual payments. • Formulas:**Swap Market Price Quotes**Cash Flow for Fixed-Rate Payer paying 6.26%**Opening Position: Swap Execution**• Suppose a corporate treasurer wants to fix the rate on its floating-rate debt by taking a fixed-rate payer’s position on a 2-year swap with a NP of $50,000,000. • The treasurer would call a swap trader at a bank for a quote on a fixed-rate payer position. • Suppose the treasurer agrees to the fixed position at 100 bp above the current 2-year T-note, currently trading at 5.26%.