An interest rate swap is an exchange of cash flows between two parties where party A pays a fixed rate and receives a floating rate and party B receives a fixed rate and pays the floating rate. In essence, party A and party B, known as counterparties, agree to exchange a series of cash flows in the future for a specified period of time. Since only cash follows are exchanged, principal payments are not involved.
<h4>Example 1</h4>
Assume a $100 million, three year paying fixed interest rate swap is set at 5.50% versus 6 month LIBOR (assumed at 3.50%). This transaction hedges the Treasurer against higher rates and costs nothing to enter into. However, exchanging of cash flows negatively impacts the company in the beginning as they are paying 5.50% to the counterparty and in return receiving 3.50% on the initial rate setting. Consequently, the steepness of the yield curve makes hedging with swaps very difficult for Treasurers.

The following diagram depicts an interest rate swap.

<img class="aligncenter size-full wp-image-669" title="IRS" src="https://financetrain.com/wp-content/uploads/2010/08/IRS.gif" alt="" width="537" height="431" />
<h4>Example 2</h4>
In another example, if a manufacturing firm wanted to “swap out” its floating rate debt, its all-in-cost of fixed rate debt would be quoted at 7.50% assuming the following information.
<table border="1" cellspacing="0" cellpadding="0">
<tbody>
<tr>
<td width="295" valign="top">Term of floating debt</td>
<td width="295" valign="top">5 years</td>
</tr>
<tr>
<td width="295" valign="top">5-year Treasury yield</td>
<td width="295" valign="top">5.70%</td>
</tr>
<tr>
<td width="295" valign="top">Loan spread</td>
<td width="295" valign="top">150 basis points</td>
</tr>
<tr>
<td width="295" valign="top">3-month Libor</td>
<td width="295" valign="top">3.50%</td>
</tr>
<tr>
<td width="295" valign="top">Swap spread</td>
<td width="295" valign="top">30 days</td>
</tr>
</tbody>
</table>
All in cost approximately = 5.70 + 0.30 + 1.50 = 7.50%

The manufacturing firm will now pay 7.50% over the next five years and receive a floating 3-month Libor over the same term.

How Interest Rate Swaps Work?

An interest rate swap is an exchange of cash flows between two parties where party A pays a fixed rate and receives a floating rate and party B receives a fixed rate and pays the floating rate. An interest rate swap contract has the following characteristics:
<table border="1" cellspacing="0" cellpadding="0">
<tbody>
<tr>
<td width="151" valign="top"><strong>Terms</strong></td>
<td width="439" valign="top"><strong>Definition</strong></td>
</tr>
<tr>
<td width="151" valign="top">Maturity</td>
<td width="439" valign="top">One to 10 years</td>
</tr>
<tr>
<td width="151" valign="top">Effective Date</td>
<td width="439" valign="top">Depending on market convention, up to five business days   from trade date (corporate settlement). The effective date is such that the   first fixed and the first floating payment periods are full coupon periods   (that is, no long or short first coupons).</td>
</tr>
<tr>
<td width="151" valign="top">Settlement Date</td>
<td width="439" valign="top">Effective date</td>
</tr>
<tr>
<td width="151" valign="top">All-in-cost</td>
<td width="439" valign="top">Depends on market convention, but usually semi-annual   equivalent of the internal rate of return of the fixed flows versus the   floating index flat.</td>
</tr>
<tr>
<td width="151" valign="top">Fixed Payment

Fixed Coupon</td>
<td width="439" valign="top">Current market rate</td>
</tr>
<tr>
<td width="151" valign="top">Payment Frequency</td>
<td width="439" valign="top">Either semi-annually or annually depending on market   convention</td>
</tr>
<tr>
<td width="151" valign="top">Day Count</td>
<td width="439" valign="top">Based on market convention</td>
</tr>
<tr>
<td width="151" valign="top">Pricing Date</td>
<td width="439" valign="top">Trade date</td>
</tr>
<tr>
<td width="151" valign="top">Floating Payment

Floating Index</td>
<td width="439" valign="top">Certain money market indices</td>
</tr>
<tr>
<td width="151" valign="top">Spread</td>
<td width="439" valign="top">None</td>
</tr>
<tr>
<td width="151" valign="top">Determination Source</td>
<td width="439" valign="top">A publicly quoted source</td>
</tr>
<tr>
<td width="151" valign="top">Payment Frequency</td>
<td width="439" valign="top">Term of the floating index</td>
</tr>
<tr>
<td width="151" valign="top">Day Count</td>
<td width="439" valign="top">Based on market convention</td>
</tr>
<tr>
<td width="151" valign="top">Reset Frequency</td>
<td width="439" valign="top">Term of the floating index</td>
</tr>
<tr>
<td width="151" valign="top">First Coupon</td>
<td width="439" valign="top">Current market rate of the index</td>
</tr>
<tr>
<td width="151" valign="top">Premium or Discount</td>
<td width="439" valign="top">None</td>
</tr>
</tbody>
</table>

Details of an Interest Rate Swap Contract

The unifying theory of interest rate risk management rests upon the basis that all hedging instruments (swaps, caps, floors, collars) can be created directly or synthetically from each other.

The relationship between option contracts and swap transactions operates at an important level.

<strong><em>The Relationship between Option Contracts and Interest Rate Swaps</em></strong>

&nbsp;

A call option can be replicated by continuously adjusting or dynamically managing a portfolio of securities on the underlying asset and cash. As the price of the asset rises, the call option equivalent portfolio would contain an increasing proportion of the assets .As the financial price of the asset decreases, the call option equivalent portfolio would reduce the holding of the assets.

More directly, options may have a direct relationship to interest rate swaps insofar as an interest rate swap can be characterized as a portfolio of purchased and sold options. Swap instruments, such as caps, floors and collars are in effect a series of option contracts.

The following will demonstrate the synthetic concept using simple mathematics.

A seller can provide an interest rate cap directly or synthetically.

Synthetically:

<strong> A cap =  Purchase floor + Swap (pay fixed rate &amp; receive floating rate)</strong>

A quick look at the cap payoff rate will bear this relationship out. Suppose a 10% cap was sold directly. At an 11% reset, the cap would make a payment of 11%-10% =1%

At 9% reset, the cap would make no payment.

Alternatively, suppose the cap provider created the cap synthetically by purchasing a 10% floor and swapping cash flows. This synthetic 10% cap would have the following payoff rate:

At an 11% reset, the floor would be worth zero (no payment made) and the swap would pay a fixed 10% and receive a floating 11% for a net gain of 1%.

At a 9% reset, the floor would be worth  1% (a payment of11%-10% would be made) and the swap would pay a fixed 10% and receive a floating for a net result of 1%-1% =0.

Comparing the two payoff’s results in the following matrix:
<table border="1" cellspacing="0" cellpadding="0">
<tbody>
<tr>
<td valign="top" width="197"><strong>Type of Cap</strong></td>
<td valign="top" width="197"><strong>Reset at 9% </strong></td>
<td valign="top" width="197"><strong>Reset at 11%</strong></td>
</tr>
<tr>
<td valign="top" width="197">Direct</td>
<td valign="top" width="197">0%</td>
<td valign="top" width="197">1%</td>
</tr>
<tr>
<td valign="top" width="197">Synthetic</td>
<td valign="top" width="197">0%</td>
<td valign="top" width="197">1%</td>
</tr>
</tbody>
</table>
The results are identical and show that the provider of the floor has more than one way to sell this option.

A fixed /floating swap can be provided directly or synthetically by the seller.

Synthetically:

<strong>A swap = Purchase cap and sell floor at same strike prices</strong>

Using the same numbers from the previous example, the two payoff’s result in the following matrix:
<table border="1" cellspacing="0" cellpadding="0">
<tbody>
<tr>
<td valign="top" width="197"><strong>Type of Cap</strong></td>
<td valign="top" width="197"><strong>Reset at 11% </strong></td>
<td valign="top" width="197"><strong>Reset at 9%</strong></td>
</tr>
<tr>
<td valign="top" width="197">Direct</td>
<td valign="top" width="197">1%</td>
<td valign="top" width="197">-1%</td>
</tr>
<tr>
<td valign="top" width="197">Synthetic</td>
<td valign="top" width="197">1%</td>
<td valign="top" width="197">-1%</td>
</tr>
</tbody>
</table>

Synthetic Relationship Between Swaps and Derivatives 

In this lesson, we will look at a few examples of how corporations and financial institutions use interest rate swaps.

<strong>GAP Management</strong>

This example represents a financial institution, a bank, that is “lengthening the maturity,” “fixing” the interest rate, on its funding base in order to better match the funding costs with the fixed rate yield from its assets, say loans or investments.

In the example, the effective fixed rate debt cost is now 11 + 1/8%.

<img class="aligncenter size-full wp-image-1032" title="IRS1" src="https://financetrain.com/wp-content/uploads/2010/09/IRS1.png" alt="" width="614" height="442" />

<strong>Liability Management</strong>

In this example, a synthetic floating rate note, i.e., floating rate debt, could be created by converting a long-term liability (for example, term deposits of a bank or fixed rate debt of a corporation or bank) to a floating rate.

The issuer in this example had borrowed term funds at a 13% fixed rate and transformed them to an effective floating rate cost of treasuries plus 1.

<img class="aligncenter size-full wp-image-1033" title="IRS2" src="https://financetrain.com/wp-content/uploads/2010/09/IRS2.png" alt="" width="613" height="312" />

<strong>Asset Management - 1</strong>

Fixed rate assets (such as fixed income bonds, private placements, mortgage loans or mortgage backed securities) can be converted to floating rates using a swap.

In the example, a pool of mortgages with a weighted average coupon (WAC) of 10.5% has been converted to yield LIBOR + ¼ %.

<strong><img class="aligncenter size-full wp-image-1034" title="IRS3" src="https://financetrain.com/wp-content/uploads/2010/09/IRS3.png" alt="" width="611" height="355" />
</strong>

<strong>Asset Management- 2</strong>

To fix the rate on variable rate assets, perhaps to match available long-term funding, floating rate assets (such as domestic or foreign floating rate notes, adjustable rate mortgages, floating rate preferred stock or CD’s) can be converted to fixed rate assets using swaps.

In the example, the investment in variable rate CD’s has been transformed into a 12% fixed rate investment.

<img class="aligncenter size-full wp-image-1035" title="IRS4" src="https://financetrain.com/wp-content/uploads/2010/09/IRS4.png" alt="" width="618" height="352" />

As you can see, one of the advantages of swaps is that you can obtain the best available funding, whatever the maturity, when market conditions are favourable and the opportunity is right. These funds can then be swapped into the desired maturity or interest rate structure.

Hedging Using Interest Rate Swaps

Currency swaps are foreign exchange contracts in which two parties agree to exchange the principal and interest of a loan in one currency with the principal and interest of an equivalent loan in another currency.

The motive behind a currency swap is to enable each party to gain exposure to another currency at a more competitive rate. A currency swap deal will be driven by comparative advantage.

For example, assume that a US Company wants to do some business in India, and at the same time an Indian company is looking at taking a loan in the US. Both the businesses could find it difficult to get competitive financing. The Indian banks may offer a loan to a US company at 11%, while they may be willing to offer the same loan to an Indian company at a lower rate, say 7%. Similarly, it will be cheaper for a US Company to take a loan in the US compared to the Indian Company.

In the international market, the financing is expensive for both these companies; however, they have a cost advantage in their domestic markets.  The following table presents a hypothetical scenario:
<table border="1" cellspacing="0" cellpadding="0">
<tbody>
<tr>
<td valign="top" width="213">&nbsp;</td>
<td valign="top" width="213">US Company</td>
<td valign="top" width="213">Indian Company</td>
</tr>
<tr>
<td valign="top" width="213">Finance cost in US</td>
<td valign="top" width="213">6%</td>
<td valign="top" width="213">10%</td>
</tr>
<tr>
<td valign="top" width="213">Finance Cost in India</td>
<td valign="top" width="213">11%</td>
<td valign="top" width="213">7%</td>
</tr>
</tbody>
</table>
There is a clear comparative advantage if these two companies borrow in their home countries and exchange the cash flows.

Assume that both the companies have an equivalent loan requirement of $10million, and the current exchange rate is USD/INR 45.

The US Company will borrow $10million from a US bank at 6%. The Indian Company will borrow INR450mn from an Indian bank at 7%.

The swap transaction will take place as follows:
<ol>
	<li>After borrowing from their local banks, both the companies will exchange the principals at the beginning of the arrangement.</li>
	<li>As per the prescribed payment schedule (quarterly, semi-annually, or yearly), both the companies will exchange the interest payment on their loans.</li>
	<li>At the end of the swap agreement, the companies will re-exchange the principals.</li>
</ol>
<img class="aligncenter size-full wp-image-3083" title="Currency Swap" src="https://financetrain.com/wp-content/uploads/2011/10/SH05.gif" alt="" width="642" height="349" />Note that this example assumes a simplified scenario. In a real transaction, there will be a swap dealer who facilitates this swap deal. To pay commissions to the dealer, the interest rates will become slightly higher. If the spread is assumed to be 20bps, the actual interest rate will be 6.2% and 7.2%.

What are Foreign Currency Swaps?

A basis swap is a type of swap in which two parties exchange the interest payments based on two floating rates.

<a href="https://financetrain.com/what-are-foreign-currency-swaps/">Currency swaps</a> are a type of basis swaps, except that the basis swaps involve only one currency. Similarly, we can say that an <a href="https://financetrain.com/how-interest-rate-swaps-work/">interest rate swap</a> with two floating rates is a basis swap.

The basis swaps are used to hedge the interest rate risk arising from the borrowing and lending at two different floating rates.

For example a bank might be lending at an interest rate tied to Libor but itself borrows at Constant Maturity Treasury rate. The hedge the interest rate risk, it may enter into a basis swap to pay at LIBOR rate and receive at Constant Maturity Treasury rate.

The pricing of basis swaps is similar to currency swaps, except that there is no exchange rate involved.

There are also cross-currency basis swaps, in which two streams of money market floating rates of two different currencies are exchanged. The cross-currency basis swaps may or may not involve exchange of notional at the beginning and end of the swap.

What are Basis Swaps?

Volatility <a title="How Interest Rate Swaps Work?" href="https://financetrain.com/how-interest-rate-swaps-work/">swaps</a> (also known as variance swaps) are <a title="Exchange-traded versus Over-the-counter (OTC) Derivatives" href="https://financetrain.com/exchange-traded-versus-over-the-counter-otc-derivatives/">over-the-counter derivatives</a> that used to hedge against the volatility risk of the underlying instruments. The underlying in this case could be foreign exchange rates, interest rates, or stock market indices.

The volatility swap will have floating volatility as one leg and fixed volatility as the other leg.

The floating leg will pay based on the volatility of the price change of the underlying asset. For example, it could be the variance of the daily log-normal returns.

The fixed leg will make a fixed payment decided at the time of entering into the swap.

The volatility swaps are usually settled in cash as the net payoff being the difference between the fixed and floating legs.

One of the most important applications of volatility swaps is in volatility trading as an alternative to using <a title="What are Options?" href="https://financetrain.com/what-are-options/">options</a> for speculating in volatility. Variance swaps provide pure exposure to the volatility of the underlying price. This is not the case with call and put options which may carry directional risk (<a title="Option Greeks: Delta" href="https://financetrain.com/option-greeks-delta/">delta</a>), and will require constant delta hedging. The profit and loss from a variance swap depends directly on the difference between realized and implied volatility.

What are Volatility Swaps?

A swap is an agreement between two parties where they agree to exchange the cash flows on different assets for a specified period of time. For example, in a vanilla <a href="https://financetrain.com/how-interest-rate-swaps-work/">interest rate swap</a>, two parties agree to exchange the interest obligations on their loans. One party pays interest based on a floating interest rate while the other pays a fixed rate. Swaps have a fixed maturity and naturally expire once the maturity reaches. However, the parties involved in a swap transaction may also terminate the contract before its expiry. Let’s look at the different ways in which a swap can be terminated.

<strong>1. By Mutual Agreement or as per Contract Details</strong>

When a swap contract is initiated it has zero value. However, as time passes and circumstances change, the swap will be more valuable to one party than the other party. This value is called the market value. If both parties mutually decide to go for swap termination, they can do so by exchange this market value. For example, if one party holding the swap has a positive market value of $100,000, then the swap can be settled if the other party pays $100,000 to the party with positive value. To be able to settle a swap in this way either both parties should agree or there should be a provision for this in the swap agreement.

<strong>2. By Entering into an Offsetting Swap   </strong>

A swap can also be terminated indirectly by entering into a similar swap agreement that offsets the original contract. For example, let’s say we have a swap contract where we pay fixed (5%) and receive floating (LIBOR). Now we can terminate this contract, by entering into a new swap agreement with same or different counterparty where we pay floating (LIBOR) and receive fixed. The fixed rate in the new contract will be decided based on the current market conditions but the floating rates will offset. However, this method will not eliminate the default risk.

<strong>3. By Selling the Swap</strong>

A swap can also be terminated by selling it to another counterparty. If one party wants to exit the swap contract, and the swap is worth $100,000, it can take consent from its counterparty and place another counterparty in its own place to make the swap payments. In effect, the swap is sold for $100,000.

<strong>4. By Using a Swaption</strong>

The swap can also be terminated by using <a href="https://financetrain.com/swaptions-and-their-valuation/">swaptions</a>. A swaption provides option holder the option to enter into a swap. A party can use a swaption to enter into an offsetting swap.

Swap Termination

In an equity swap, two parties agree to exchange a set of future cash flows periodically for s specified period of time. Once leg of the equity swap is pegged to a floating rate such as LIBOR or is set as a fixed rate. The cash flows on the other leg are linked to the returns from a stock or a stock index. The leg linked to the stock or the stock index is referred to as the equity leg of the swap.

Let’s take an example to understand the various aspects of an equity swap. Let’s say an asset manager who manages a fund called Alpha Fund follows a passive <a href="https://financetrain.com/short-term-investment-strategies/">investment strategy</a> and his portfolio tracks the S&amp;P 500 Total Returns Index. The asset manager can enter into an equity swap contract with a counterparty say Goldman Sachs with the following terms:

<strong>Notional Principal:</strong> $100 million

<strong>Alpha Fund pays:</strong> Total returns on the S&amp;P 500 Index

<strong>Goldman Sachs pays:</strong> Fixed 6%

Payments to be made at the end of every six months, that is, 30<sup>th</sup> June and 31<sup>st</sup> December

The swap has a maturity of 3 years.

Let’s see how the cash flows turn out in the first year. At the beginning, the S&amp;P Total Return Index was at 2500 level, on 30<sup>th</sup> June it was 2600, and on 31<sup>st</sup> December it was at 2570. Let’s look at the cash flows in both the legs of the transaction.
<table border="1" cellspacing="0" cellpadding="0">
<tbody>
<tr>
<td valign="top" width="147"><b> </b></td>
<td valign="top" width="247"><b>Alpha Pays</b></td>
<td valign="top" width="198"><b>Goldman Pays</b></td>
</tr>
<tr>
<td valign="top" width="147">30<sup>th</sup> June</td>
<td valign="top" width="247">Return on index = 2600/2500 = 4%

&nbsp;

= 100,000,000*0.04

= $4,000,000</td>
<td valign="top" width="198">&nbsp;

=100,000,000 * 182/365 * 6%

=$2,991,780</td>
</tr>
<tr>
<td valign="top" width="147">31<sup>st</sup> December</td>
<td valign="top" width="247">Return on index = 2570/2600 = -1.154%

&nbsp;

Alpha pays nothing.</td>
<td valign="top" width="198">Fixed payment

=100,000,000 * 183/365 * 6%

=$3,008,219

&nbsp;

Floating payment

= 100,000,000*0.01154

= $1,154,000

&nbsp;

<strong>Total payment</strong>

= $3,008,219+$1,154,000

=$4,162,219</td>
</tr>
</tbody>
</table>
&nbsp;

Let’s make a few observations from the above table:
<ol>
	<li>If the index returns are positive, Alpha Fund pays index returns to Goldman and Goldman pays fixed rate to Alpha.</li>
	<li>If the index returns are negative, Alpha pays nothing and Goldman pays the fixed rate plus any loss on the index returns. It’s as if Alpha sold out its positions in stocks and had a fixed rate position instead.</li>
	<li>The fixed payments are calculated on actual/365 basis.</li>
	<li>The amount of payment is not known till the last day of the payment.</li>
	<li>The net effect of the swap is that a position in an equity portfolio has been converted into a fixed income position.</li>
</ol>
An equity swap can be of three types: the first leg will be a fixed rate, a floating rate or an equity or index return, while the other let will always be an equity or index return. So, an equity swap can have both the legs as returns from two different equities or equity indexes.

Equity Swap Example

Swaps

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COURSE

Swaps

Lessons

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