Interest rate swap
Encyclopedia
An interest rate swap
Swap (finance)
In finance, a swap is a derivative in which counterparties exchange certain benefits of one party's financial instrument for those of the other party's financial instrument. The benefits in question depend on the type of financial instruments involved...

is a popular and highly liquid
Market liquidity
In business, economics or investment, market liquidity is an asset's ability to be sold without causing a significant movement in the price and with minimum loss of value...

 financial derivative
Derivative (finance)
A derivative instrument is a contract between two parties that specifies conditions—in particular, dates and the resulting values of the underlying variables—under which payments, or payoffs, are to be made between the parties.Under U.S...

 instrument in which two parties agree to exchange interest rate cash flows, based on a specified notional amount from a fixed rate to a floating rate (or vice versa) or from one floating rate to another. Interest rate swaps are commonly used for both hedging
Hedge (finance)
A hedge is an investment position intended to offset potential losses that may be incurred by a companion investment.A hedge can be constructed from many types of financial instruments, including stocks, exchange-traded funds, insurance, forward contracts, swaps, options, many types of...

 and speculating
Speculation
In finance, speculation is a financial action that does not promise safety of the initial investment along with the return on the principal sum...

.

Structure

In an interest rate swap, each counterparty
Counterparty
A counterparty is a legal and financial term. It means a party to a contract. A counterparty is usually the entity with whom one negotiates on a given agreement, and the term can refer to either party or both, depending on context....

 agrees to pay either a fixed or floating rate denominated in a particular currency to the other counterparty. The fixed or floating rate is multiplied by a notional principal amount (say, USD 1 million). This notional amount is typically not exchanged between counterparties, but is used only for calculating the size of cashflows to be exchanged.

The most common interest rate swap is one where one counterparty A pays a fixed rate (the swap rate) to counterparty B, while receiving a floating rate indexed to a reference rate
Reference rate
A reference rate is a rate that determines pay-offs in a financial contract and that is outside the control of the parties to the contract. It is often some form of LIBOR rate, but it can take many forms, such as a consumer price index, a house price index or an unemployment rate...

 (such as LIBOR). By market convention, the counterparty paying the fixed rate is called the "payer" (while receiving the floating rate), and the counterparty receiving the fixed rate is called the "receiver" (while paying the floating rate).

A pays fixed rate to B (A receives variable rate)

B pays floating rate to A (B receives fixed rate)

Currently, A borrows from Market @ LIBOR +1.5%. B borrows from Market @ 8.5%.

Consider the following swap in which Party A agrees to pay Party B periodic fixed interest rate payments of 8.65%, in exchange for periodic variable interest rate payments of LIBOR + 70 bps
Basis point
A basis point is a unit equal to 1/100 of a percentage point or one part per ten thousand...

 (0.70%). Note that there is no exchange of the principal amounts and that the interest rates are on a "notional" (i.e. imaginary) principal amount. Also note that the interest payments are settled in net (e.g. Party A pays (LIBOR + 1.50%)+8.65% - (LIBOR+0.70%) = 9.45% net). The fixed rate (8.65% in this example) is referred to as the swap rate
Swap rate
Swap rate is the fixed rate that makes the market value of a given swap at initiation zero. They are the borrowing rates between financial institutions, usually with credit ratings of A/AA equivalent. Swap rates are calculated using the fixed rate leg of interest rate swaps. Swap rates form the...

.

At the point of initiation of the swap, the swap is priced so that it has a net present value
Net present value
In finance, the net present value or net present worth of a time series of cash flows, both incoming and outgoing, is defined as the sum of the present values of the individual cash flows of the same entity...

 of zero. If one party wants to pay 50 bps
Basis point
A basis point is a unit equal to 1/100 of a percentage point or one part per ten thousand...

 above the par swap rate
Swap rate
Swap rate is the fixed rate that makes the market value of a given swap at initiation zero. They are the borrowing rates between financial institutions, usually with credit ratings of A/AA equivalent. Swap rates are calculated using the fixed rate leg of interest rate swaps. Swap rates form the...

, the other party has to pay approximately 50 bps over LIBOR to compensate for this.

Types

Being OTC
Over-the-counter (finance)
Within the derivatives markets, many products are traded through exchanges. An exchange has the benefit of facilitating liquidity and also mitigates all credit risk concerning the default of a member of the exchange. Products traded on the exchange must be well standardised to transparent trading....

 instruments, interest rate swaps can come in a huge number of varieties and can be structured to meet the specific needs of the counterparties. For example, the legs of the swap can be in the same currency or in different currencies. The notional of the swap could be amortized over time. The reset dates of the floating rate could be non-regular, etc. However, in the interbank market, just a few, standardized types are traded. They are listed below.

Fixed-for-floating rate swap, same currency

Party B pays/receives fixed interest in currency A to receive/pay floating rate in currency A indexed to X on a notional amount N for a term of T years. For example, you pay fixed 5.32% monthly to receive USD 1M Libor monthly on a notional USD 1 million for 3 years. The party that pays fixed and receives floating coupon rates is said to be long the interest swap because it is expressed as a bond convention (as prices fall, yields rise). The party interested to pay fixed and receive floating is bullish on interest rate and so long his position and thus, buy floating rate. Interest rate swaps are simply the exchange of one set of cash flows for another.

Fixed-for-floating swaps in same currency are used to convert a fixed rate asset/liability to a floating rate asset/liability or vice versa. For example, if a company has a fixed rate USD 10 million loan at 5.3% paid monthly and a floating rate investment of USD 10 million that returns USD 1M Libor +25 bps monthly, it may enter into a fixed-for-floating swap. In this swap, the company would pay a floating rate of USD 1M Libor+25 bps and receive a 5.5% fixed rate, locking in 20bps profit.

Fixed-for-floating rate swap, different currencies

Party P pays/receives fixed interest in currency A to receive/pay floating rate in currency B indeed to X on a notional N at an initial exchange rate of FX for a tenure of T years. For example, you pay fixed 5.32% on the USD notional 10 million quarterly to receive JPY 3M (TIBOR) monthly on a JPY notional 1.2 billion (at an initial exchange rate of USD/JPY 120) for 3 years.
For nondeliverable swaps, the USD equivalent of JPY interest will be paid/received (according to the FX rate on the FX fixing date for the interest payment day). No initial exchange of the notional amount occurs unless the Fx fixing date and the swap start date fall in the future.

Fixed-for-floating swaps in different currencies are used to convert a fixed rate asset/liability in one currency to a floating rate asset/liability in a different currency, or vice versa. For example, if a company has a fixed rate USD 10 million loan at 5.3% paid monthly and a floating rate investment of JPY 1.2 billion that returns JPY 1M Libor +50 bps monthly, and wants to lock in the profit in USD as they expect the JPY 1M Libor to go down or USDJPY to go up (JPY depreciate against USD), then they may enter into a Fixed-Floating swap in different currency where the company pays floating JPY 1M Libor+50 bps and receives 5.6% fixed rate, locking in 30bps profit against the interest rate and the fx exposure.

Floating-for-floating rate swap, same currency

Party P pays/receives floating interest in currency A Indexed to X to receive/pay floating rate in currency A indexed to Y on a notional N for a tenure of T years. For example, you pay JPY 1M LIBOR monthly to receive JPY 1M TIBOR monthly on a notional JPY 1 billion for 3 years.

Floating-for-floating rate swaps are used to hedge against or speculate on the spread between the two indexes widening or narrowing. For example, if a company has a floating rate loan at JPY 1M LIBOR and the company has an investment that returns JPY 1M TIBOR + 30 bps and currently the JPY 1M TIBOR = JPY 1M LIBOR + 10bps. At the moment, this company has a net profit of 40 bps. If the company thinks JPY 1M TIBOR is going to come down (relative to the LIBOR) or JPY 1M LIBOR is going to increase in the future (relative to the TIBOR) and wants to insulate from this risk, they can enter into a float-float swap in same currency where they pay, say, JPY TIBOR + 30 bps and receive JPY LIBOR + 35 bps. With this, they have effectively locked in a 35 bps profit instead of running with a current 40 bps gain and index risk. The 5 bps difference (w.r.t. the current rate difference) comes from the swap cost which includes the market expectations of the future rate difference between these two indices and the bid/offer spread which is the swap commission for the swap dealer.

Floating-for-floating rate swaps are also seen where both sides reference the same index, but on different payment dates, or use different business day conventions. This can be vital for asset-liability management. An example would be swapping 3M LIBOR being paid with prior non-business day convention, quarterly on JAJO (i.e. Jan, Apr, Jul, Oct) 30, into FMAN (i.e. Feb, May, Aug, Nov) 28 modified following・

Floating-for-floating rate swap, different currencies

Party P pays/receives floating interest in currency A indexed to X to receive/pay floating rate in currency B indexed to Y on a notional N at an initial exchange rate of FX for a tenure of T years. For example, you pay floating USD 1M LIBOR on the USD notional 10 million quarterly to receive JPY 3M TIBOR monthly on a JPY notional 1.2 billion (at an initial exchange rate of USDJPY 120) for 4 years.

To explain the use of this type of swap, consider a US company operating in Japan. To fund their Japanese growth, they need JPY 10 billion. The easiest option for the company is to issue debt in Japan. As the company might be new in the Japanese market without a well known reputation among the Japanese investors, this can be an expensive option. Added on top of this, the company might not have appropriate debt issuance program in Japan and they might lack sophisticated treasury operation in Japan. To overcome the above problems, it can issue USD debt and convert to JPY in the FX market. Although this option solves the first problem, it introduces two new risks to the company:
  • FX risk. If this USDJPY spot goes up at the maturity of the debt, then when the company converts the JPY to USD to pay back its matured debt, it receives less USD and suffers a loss.
  • USD and JPY interest rate risk
    Interest rate risk
    Interest rate risk is the risk borne by an interest-bearing asset, such as a loan or a bond, due to variability of interest rates. In general, as rates rise, the price of a fixed rate bond will fall, and vice versa...

    . If the JPY rates come down, the return on the investment in Japan might go down and this introduces an interest rate risk component.


The first exposure in the above can be hedged using long dated FX forward contract
Forward contract
In finance, a forward contract or simply a forward is a non-standardized contract between two parties to buy or sell an asset at a specified future time at a price agreed today. This is in contrast to a spot contract, which is an agreement to buy or sell an asset today. It costs nothing to enter a...

s but this introduces a new risk where the implied rate from the FX spot and the FX forward is a fixed rate but the JPY investment returns a floating rate. Although there are several alternatives to hedge both the exposures effectively without introducing new risks, the easiest and the most cost effective alternative would be to use a floating-for-floating swap in different currencies. In this, the company raises USD by issuing USD Debt and swaps it to JPY. It receives USD floating rate (so matching the interest payments on the USD Debt) and pays JPY floating rate matching the returns on the JPY investment.

Fixed-for-fixed rate swap, different currencies

Party P pays/receives fixed interest in currency A to receive/pay fixed rate in currency B for a term of T years. For example, you pay JPY 1.6% on a JPY notional of 1.2 billion and receive USD 5.36% on the USD equivalent notional of 10 million at an initial exchange rate of USDJPY 120.

Other variations

A number of other variations are possible, although far less common. Mostly tweaks are made to ensure that a bond is hedged "perfectly", so that all the interest payments received are exactly offset by the swap. This can lead to swaps where principal is paid on one or more legs, rather than just interest (for example to hedge a coupon strip), or where the balance of the swap is automatically adjusted to match that of a prepaying bond (such as RMBS Residential mortgage-backed security
Residential mortgage-backed security
Residential mortgage-backed securities are a type of bond commonly issued in American security markets. They are a type of mortgage-backed security which are backed by mortgages on residential rather than commercial real estate.-Origins:...

)

Uses

Interest rate swaps were originally created to allow multi-national companies to evade exchange controls. Today, interest rate swaps are used to hedge against or speculate on changes in interest rates.

Speculation

Interest rate swaps are also used speculatively by hedge funds or other investors who expect a change in interest rates or the relationships between them. Traditionally, fixed income investors who expected rates to fall would purchase cash bonds, whose value increased as rates fell. Today, investors with a similar view could enter a floating-for-fixed interest rate swap; as rates fall, investors would pay a lower floating rate in exchange for the same fixed rate.

Interest rate swaps are also very popular due to the arbitrage
Arbitrage
In economics and finance, arbitrage is the practice of taking advantage of a price difference between two or more markets: striking a combination of matching deals that capitalize upon the imbalance, the profit being the difference between the market prices...

 opportunities they provide. Due to varying levels of creditworthiness in companies, there is often a positive quality spread differential
Quality Spread Differential
Quality Spread Differential arises during an interest rate swap in which two parties of different levels of creditworthiness experience different levels of interest rates of debt obligations...

 which allows both parties to benefit from an interest rate swap.

The interest rate swap market is closely linked to the Eurodollar
Eurodollar
Eurodollars are time deposits denominated in U.S. dollars at banks outside the United States, and thus are not under the jurisdiction of the Federal Reserve. Consequently, such deposits are subject to much less regulation than similar deposits within the U.S., allowing for higher margins. The term...

 futures market which trades at the Chicago Mercantile Exchange
Chicago Mercantile Exchange
The Chicago Mercantile Exchange is an American financial and commodity derivative exchange based in Chicago. The CME was founded in 1898 as the Chicago Butter and Egg Board. Originally, the exchange was a non-profit organization...

.

British local authorities

In June 1988 the Audit Commission
Audit Commission
The Audit Commission is a public corporation in the United Kingdom.The Commission’s primary objective is to improve economy, efficiency and effectiveness in local government, housing and the health service, directly through the audit and inspection process and also through value for money...

 was tipped off by someone working on the swaps desk of Goldman Sachs
Goldman Sachs
The Goldman Sachs Group, Inc. is an American multinational bulge bracket investment banking and securities firm that engages in global investment banking, securities, investment management, and other financial services primarily with institutional clients...

 that the London Borough of Hammersmith and Fulham
London Borough of Hammersmith and Fulham
The London Borough of Hammersmith and Fulham is a London borough in West London, and forms part of Inner London. Traversed by the east-west main roads of the A4 Great West Road and the A40 Westway, many international corporations have offices in the borough....

 had a massive exposure to interest rate swaps. When the commission contacted the council, the chief executive told them not to worry as "everybody knows that interest rates are going to fall"; the treasurer thought the interest rate swaps were a 'nice little earner'. The controller of the commission, Howard Davies realised that the council had put all of its positions on interest rates going down; he sent a team in to investigate.

By January 1989 the commission obtained legal opinions from two Queen's Counsel
Queen's Counsel
Queen's Counsel , known as King's Counsel during the reign of a male sovereign, are lawyers appointed by letters patent to be one of Her [or His] Majesty's Counsel learned in the law...

. Although they did not agree, the commission preferred the opinion which made it ultra vires
Ultra vires
Ultra vires is a Latin phrase meaning literally "beyond the powers", although its standard legal translation and substitute is "beyond power". If an act requires legal authority and it is done with such authority, it is...

for councils to engage in interest rate swaps. Moreover interest rates had gone up from 8% to 15%. The auditor and the commission then went to court and had the contracts declared illegal (appeals all the way up to the House of Lords
Judicial functions of the House of Lords
The House of Lords, in addition to having a legislative function, historically also had a judicial function. It functioned as a court of first instance for the trials of peers, for impeachment cases, and as a court of last resort within the United Kingdom. In the latter case the House's...

 failed); the five banks involved lost millions of pounds. Many other local authorities had been engaging in interest rate swaps in the 1980s, although Hammersmith was unusual in betting all one way.

Valuation and pricing

The present value of a plain vanilla (i.e. fixed rate for floating rate) swap can easily be computed using standard methods of determining the present value
Present value
Present value, also known as present discounted value, is the value on a given date of a future payment or series of future payments, discounted to reflect the time value of money and other factors such as investment risk...

 (PV) of the fixed leg and the floating leg.

The value of the fixed leg is given by the present value of the fixed coupon payments known at the start of the swap, i.e.


where C is the swap rate, M is the number of fixed payments, P is the notional amount, ti is the number of days in period i, Ti is the basis according to the day count convention
Day count convention
In finance, a day count convention determines how interest accrues over time for a variety of investments, including bonds, notes, loans, mortgages, medium-term notes, swaps, and forward rate agreements . This determines the amount transferred on interest payment dates, and also the calculation of...

 and dfi is the discount factor.

Similarly, the value of the floating leg is given by the present value of the floating coupon payments determined at the agreed dates of each payment. However, at the start of the swap, only the actual payment rates of the fixed leg are known in the future, whereas the forward rates (derived from the yield curve
Yield curve
In finance, the yield curve is the relation between the interest rate and the time to maturity, known as the "term", of the debt for a given borrower in a given currency. For example, the U.S. dollar interest rates paid on U.S...

) are used to approximate the floating rates. Each variable rate payment is calculated based on the forward rate for each respective payment date. Using these interest rates leads to a series of cash flows. Each cash flow is discounted by the zero-coupon rate for the date of the payment; this is also sourced from the yield curve
Yield curve
In finance, the yield curve is the relation between the interest rate and the time to maturity, known as the "term", of the debt for a given borrower in a given currency. For example, the U.S. dollar interest rates paid on U.S...

 data available from the market. Zero-coupon rates are used because these rates are for bonds which pay only one cash flow. The interest rate swap is therefore treated like a series of zero-coupon bonds. Thus, the value of the floating leg is given by the following:


where N is the number of floating payments, fj is the forward rate, P is the notional amount, tj is the number of days in period j, Tj is the basis according to the day count convention
Day count convention
In finance, a day count convention determines how interest accrues over time for a variety of investments, including bonds, notes, loans, mortgages, medium-term notes, swaps, and forward rate agreements . This determines the amount transferred on interest payment dates, and also the calculation of...

 and dfj is the discount factor. The discount factor always starts with 1. The discount factor is found as follows:
[Discount factor in the previous period]/[1 + (Forward rate of the floating underlying asset in the previous period × Number of days in period/360)].


(Depending on the currency, the denominator is 365 instead of 360; e.g. for GBP.)

The fixed rate offered in the swap is the rate which values the fixed rates payments at the same PV as the variable rate payments using today's forward rates, i.e.:


Therefore, at the time the contract is entered into, there is no advantage to either party, i.e.,


Thus, the swap requires no upfront payment from either party.

During the life of the swap, the same valuation technique is used, but since, over time, the forward rates change, the PV of the variable-rate part of the swap will deviate from the unchangeable fixed-rate side of the swap. Therefore, the swap will be an asset to one party and a liability to the other. The way these changes in value are reported is the subject of IAS 39 for jurisdictions following IFRS
International Financial Reporting Standards
International Financial Reporting Standards are principles-based standards, interpretations and the framework adopted by the International Accounting Standards Board ....

, and FAS 133 for U.S. GAAP. Swaps are marked to market by debt security traders to visualize their inventory at a certain time.

Risks

Interest rate swaps expose users to interest rate risk and credit risk.
  • Market Risk: A typical swap consists of two legs, one fixed, the other floating. The risks of these two component will naturally differ. Newcomers to market finance may think that the risky component is the floating leg, since the underlying interest rate floats, and hence, is unknown. This first impression is wrong. The risky component is in fact the fixed leg and it is very easy to see why this is so.


The discussion of pricing interest rate swaps illustrated an important point. Regardless of what happens to future Libor rates, the value of a rolling deposit or FRN always equals the notional amount N at the reset dates. Between the reset dates this value may be different than N, but the discrepancy cannot be very large since the δ will be 3 or 6 months. Interest rate fluctuations have minimal effect on the values of fixed instruments with such maturities. In other words, the value of the floating leg changes
very little during the life of a swap.

On the other hand the fixed leg of a swap is equivalent to a coupon bond and fluctuations of the swap
rate may have major effects on the value of the future fixed payments.
  • Credit risk on the swap comes into play if the swap is in the money or not. If one of the parties is in the money
    In the Money
    In the Money is a comedy film starring The Bowery Boys. The film was released on February 16, 1958 by Allied Artists Pictures and is the forty-eighth and final film in the series. It was directed by William Beaudine and written by Al Martin and Elwood Ullman.-Plot summary:Sach is hired to take...

    , then that party faces credit risk of possible default by another party.

Market size

The Bank for International Settlements
Bank for International Settlements
The Bank for International Settlements is an intergovernmental organization of central banks which "fosters international monetary and financial cooperation and serves as a bank for central banks." It is not accountable to any national government...

 reports that interest rate swaps are the largest component of the global OTC
Over-the-counter (finance)
Within the derivatives markets, many products are traded through exchanges. An exchange has the benefit of facilitating liquidity and also mitigates all credit risk concerning the default of a member of the exchange. Products traded on the exchange must be well standardised to transparent trading....

 derivative
Derivative (finance)
A derivative instrument is a contract between two parties that specifies conditions—in particular, dates and the resulting values of the underlying variables—under which payments, or payoffs, are to be made between the parties.Under U.S...

 market. The notional amount
Notional amount
The notional amount on a financial instrument is the nominal or face amount that is used to calculate payments made on that instrument...

 outstanding as of June 2009 in OTC interest rate swaps was $342 trillion, up from $310 trillion in Dec 2007. The gross market value was $13.9 trillion in June 2009, up from $6.2 trillion in Dec 2007.

Interest rate swaps can now be traded as an Index through the FTSE MTIRS Index
FTSE MTIRS Index
Clive connorsThe FTSE MTIRS Indices are designed to accurately move in direct correlation to OTC Interest Rate Swaps market with a total of 45 indices covering the USD curve from 2 years to 30 years including spreads and butterflies. FTSE MTIRS Indices account for changes to both fixed and floating...

.

See also

  • Swap rate
    Swap rate
    Swap rate is the fixed rate that makes the market value of a given swap at initiation zero. They are the borrowing rates between financial institutions, usually with credit ratings of A/AA equivalent. Swap rates are calculated using the fixed rate leg of interest rate swaps. Swap rates form the...

  • Interest rate cap and floor
    Interest rate cap and floor
    An interest rate cap is a derivative in which the buyer receives payments at the end of each period in which the interest rate exceeds the agreed strike price...

  • Equity swap
    Equity swap
    An equity swap is a financial derivative contract where a set of future cash flows are agreed to be exchanged between two counterparties at set dates in the future. The two cash flows are usually referred to as "legs" of the swap; one of these "legs" is usually pegged to a floating rate such as...

  • Total return swap
    Total return swap
    Total return swap, or TRS , or total rate of return swap, or TRORS, is a financial contract that transfers both the credit risk and market risk of an underlying asset.- Contract definition :...

  • Inflation derivatives
    Inflation derivatives
    In finance, inflation derivative refers to an over-the-counter and exchange-traded derivative that is used to transfer inflation risk from one counterparty to another...

  • Eurodollar
    Eurodollar
    Eurodollars are time deposits denominated in U.S. dollars at banks outside the United States, and thus are not under the jurisdiction of the Federal Reserve. Consequently, such deposits are subject to much less regulation than similar deposits within the U.S., allowing for higher margins. The term...

  • Constant maturity swap
    Constant maturity swap
    A constant maturity swap, also known as a CMS, is a swap that allows the purchaser to fix the duration of received flows on a swap.The floating leg of an interest rate swap typically resets against a published index...

  • FTSE MTIRS Index
    FTSE MTIRS Index
    Clive connorsThe FTSE MTIRS Indices are designed to accurately move in direct correlation to OTC Interest Rate Swaps market with a total of 45 indices covering the USD curve from 2 years to 30 years including spreads and butterflies. FTSE MTIRS Indices account for changes to both fixed and floating...


External links

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