Derivatives

DERIVATIVES: FUTURES, OPTIONS AND SWAPS

A derivative is a financial instrument whose value depends on or is derived from the value of

some other financial instruments, called underlying asset. Some common examples of

underlying assets are stocks, bonds, wheat, snowfall, and stock market indices. A simple

example of derivative is a contractual agreement between two investors that obligates one to

make a payment to the other, depending on the movement in the interest rates over the next year.

This type of derivative is called an interest rate futures contract. This is different from purchasing

a bond because, while a fall in bond price is profitable for a derivative investment, it is not

desirable for a bond investment. Second, in derivative transactions, one partys loss is the other

partys gain. Risk can be bought and sold using derivatives. Thus, the purpose of derivative is to

transfer risk from one person or firm to another.

Derivatives may be divided into three major categories: forwards and futures, options and swaps.

Forwards and Futures they are the simplest derivative instruments. A forward or forward

contract is an agreement between a buyer and a seller to exchange a commodity or financial

instrument for a specified amount of cash on a pre-arranged future date. It is a private agreement

between two parties, usually two financial institutions or between a financial institution and one

of its clients. And since, it is customized, it is very difficult to resell.

Forward contracts on foreign exchanges are very popular. The following table shows quotes on

the exchanges between the British pound (GBP) and US dollar that might be made by a large

bank on July 20, 2007. If the treasurer of a US corporation knows that the corporation will pay

1 million in 6 months and wants to hedge against exchange rate moves, the treasurer can buy 1

million 6-month forward at an exchange rate of 2.0489.

Spot and forward quotes for the USD/GBP exchange rate, July 20, 2007

Bid Offer

Spot 2.0558 2.0562

1-month forward 2.0547 2.0552



Following the contract the corporation is obligated to buy 1 million for US$ 2,048,900. If the

spot exchange rate rose to 2.1 at the end of 6 months, the contract would be worth $51,100 to the

corporation. If the spot exchange rate fell to 1.9 at the end of 6 months, the forward contract

would have a negative value of $ 148900. In general the pay off from a long position in a

forward contract on one unit of an asset is ST K, where ST is the spot price and K is the delivery

price at the maturity of the contract. Similarly the pay off from a short position is K ST. They

are shown in the following figures.

Pay offs from a forward contract: a ) long position, b) short position

Payoff Payoff

0 K ST 0 K ST

a) Long Position b) Short Position

A future or futures contract is a forward contract that has been standardized and sold through an

organized exchange. It specifies that the seller who has the short position will deliver some

quantity of a commodity or financial instrument to the buyer who has the long position on a

specific date, called the settlement or delivery date for a predetermined price. In order to ensure

that both the buyer and the seller meet their obligations, each makes an agreement with a

clearing corporation. The clearing corporation operates like a large insurance company

guaranteeing that they will meet their obligations. It is the counterparty to both sides of

transactions. If you hedge billions of dollars worth of bets through derivatives offered by another

firm, and that firm then goes insolvent, you suddenly have a serious exposure problem, which

can ripple through the financial system. A central clearinghouse aims to change the system from

one which is vulnerable to the loss of any big player to one which isn't. The arrangement reduces

the risk the buyers and the sellers face.

The clearing corporation requires both parties to a futures contract to place a deposit with the

corporation. This practice is called posting margin in a margin account. It also posts daily gains

and losses on the contract to the margin accounts of the parties involved. This process is called

marking to market.

The investor is entitled to withdraw any balance in margin account in excess of the initial

margin. To ensure that the initial margin account never becomes negative a maintenance margin,

somewhat lower than the initial margin is set. If the balance in the margin account falls below the

maintenance margin, the investor gets a margin call to top up the margin account to the initial

margin level the next day. The extra funds deposited are known as variation margin. If the

investor does not provide variation margin, the broker closes out the position. The following

table illustrates the operations of a margin account. Assume that on June 5 an investor buys two

December gold futures contracts (each contract is of 100 ounces) at a price of $600 per ounce.

The initial margin is $2000 per contract and the minimum margin is $3000 in total. The margin

accounts transactions on the basis of daily settlement prices are listed below.

Day Futures price Daily gain

(loss)

Cumulative

gain (loss)

Margin

account

balance

Margin call

600 4000

June 5 597 (600) (600) 3400

June 6 596.1 (180) (780) 3220

June 9 598.2 420 (360) 3640

June 10 597.1 (220) (580) 3420

June 11 596.7 (80) (660) 3340

June 12 595.4 (260) (920) 3080

June 13 593.3 (420) (1340) 2660 1340

June 16 593.6 60 (1280) 4060

June 17 591.8 (360) (1640) 3700

June 18 592.7 180 (1460) 3880

June 19 587 (1140) (2600) 2740 1260

June 20 587 0 (2600) 4000

June 23 588.1 220 (2380) 4220

June 24 588.7 120 (2260) 4340

June 25 591.0 460 (1800) 4780

June 26 592.3 260 (1540) 4060

Transfer of risk using forwards and futures contract is accomplished through hedging and

speculation. The above example of an importing firm receiving 1 million in 6-months and

buying a futures contract was of hedging. Similarly, if an exporting firm knows that it is going to

receive 30 million after 3 months then it can hedge its foreign exchange risk by getting into a

forward contract to lock in the US dollars to be realized for the sterling. Note that a company

might do better or worse if it chooses to hedge than if it chooses not to hedge.

In futures contract a seller or short position benefits from a price fall while the buyer at the long

position benefits from a rise in price. Suppose a govt. security dealer wants to insure against

decline in the value of an inventory of bonds. Now, he would hedge against this by investing in

another financial instrument that delivers a high pay-off when bond prices fall. A futures contract

can guarantee the price at which the bonds would be sold. The buyer might be a pension fund

manager who plans to purchase bonds in the future but want to insure against possible price

increases. Again buying a futures contract fixes the price that the fund will need to pay. Thus,

both sides use futures contract as a hedge. Similarly, farmers, mining companies, oil drillers, all

these sellers use futures contract to stabilize the revenue they receive when they sell. In contrast,

millers, jewellers, and oil distributors want to buy futures to take long position to reduce risk

arising from fluctuations in the cost of essential inputs.

Speculators try to make profit by betting on price movements. Sellers of futures bet that prices

will fall while buyers bet that prices will rise. Futures contract are popular tools for speculation

because they are cheap. An investor needs only a relatively small amount of investment the

margin to purchase a futures contract that is worth a great deal. Margin requirements of 10

percent or less are common. For example consider a speculator who thinks that GBP will

strengthen in the next 2 months against USD. He has two options: either to buy 250000 in the

spot market and sell later at a higher price or take a long position in futures contract on sterling.

If the current exchange rate 2.0470 dollars per sterling and the futures price is 2.0410

dollar/pound and it increases to 2.1000 after 2 months then the speculator makes a profit of

$14750. The spot market alternative leads to a profit of $13250. On the other hand, if the

exchange rate falls to 2.0000 dollars/pound the loss from a futures contract would be $10250

while the loss from the spot market alternative would be $11750. The futures market is highly

leveraged. Therefore, the interest earned or paid actually makes the losses or profits from both

alternatives same. But the first alternative requires an upfront investment of $511750 while the

second alternative requires a small amount that needs to be posted in the margin account. Thus,

with a relatively small initial outlay, the investor is able to take a large speculative position.

The practice of buying and selling financial instruments in order to benefit from temporary price

differences is called arbitrage and the people who are engaged in it are called arbitrageurs. If for

example, the price of a bond is higher in one market than in another, an arbitrageur can buy at

the low price and sell in the market with high price. The increase in the demand in the low-price

market will drive the price up there while an increase in the supply in the high-price market will

lower the price. This process will continue until prices are equal in both the markets. As long as

there are arbitrageurs, the price of a bond futures contract on the day it is settled will be same as

the market price of the bond, called the spot price. Therefore, on the settlement date the price of

a futures contract must equal the spot price of the underlying asset. But arbitrage takes place

because the prices were not same before the settlement date. Here is how it is done.

First, the arbitrageur borrows at the current market interest rate. Then with the funds, the

arbitrageur buys a bond and sells a bond futures contract. The arbitrageur has to pay interest on

the loan and at the same time bond would yield interest income. They generally cancel out and

this position costs nothing to initiate. If the market price is below the futures contract price, the

bond will yield a risk-free profit. So the investor will continue to engage in the transactions

needed to generate it. This implies, continue to buy bonds, driving the price up and sell futures,

forcing the price down, until the prices converge and no further profit is available.

For example, consider a stock which is traded in both NY stock exchange as well as London

stock exchange. Suppose, that the stock price is $200 in NY while 100 in London while the

exchange rate is 2.0300 dollars/pound. An arbitrageur can simultaneously buy 100 shares of the

stock in NY and sell them in London and make a risk-free profit of 100 [($2.03100) - $200] =

$300; we assume away any transaction costs. However, for large investment banks transaction

costs are very low and thus, they find arbitrage opportunity very attractive. But as explained

above arbitrage opportunities do not last long.

Options like futures, options are also agreement between two parties, an option writer, and an

option holder. Option writers incur obligations while option holders obtain rights. There are two

basic options: puts and calls.

A call option is the right to buy or call away a given quantity of underlying asset at a

predetermined price, called the strike price or exercise price, on or before a specific date. The

writer of the call option must sell the shares if and when the holder chooses to use the call option.

The holders of the call are not obligated to buy the shares; rather they have the option to buy and

will do so if it is beneficial. For example, a January 2008 call option on 100 shares of IBM stock

at a strike price of 90 gives the option holder to buy 100 shares of IBM for Rs 90 a piece prior to

the third Friday of January 2008. When the IBM stock exceeds the option strike price of 90, say

Rs 95, the option holder can call away the 100 shares from the option writer for Rs 90 per share

and reap Rs 5 per share profit. Whenever the price of the stock is above the strike price of the

call option, exercising the call option is profitable for the holder and the option is said to be in

the money. If price of stock equal the strike price, the option is said to be at the money and when

the strike price exceeds the market price of the underlying asset, the option is termed out of

money.

A put option gives the holder the right but not the obligation to sell the underlying asset at a

predetermined price on or before a fixed date. The holder can put the asset in the hands of the

option writer. Again the writer is obliged to buy the shares should the holder choose to sell them.

Continuing with the previous example, the right to sell 100 IBM stocks with strike price of Rs 90

per share becomes profitable when the market price of IBM stocks fall below Rs 90. For

instance, a stock price of Rs 80 would give a profit of Rs 10 per share. The put option is in the

money when the options strike price above the market price. And it is out of money when strike

price is below the market price. Just like futures contracts, a clearing corporation guarantees the

obligations embodied in the option those of the option writer. And the option writer is required

to post margin. Since option holders incur no obligation, they are not required to post margin.

There are four types of participants in options markets:

1. Buyers of calls

2. Sellers of calls

3. Buyers of puts

4. Sellers of puts

There are two types of calls and puts: American and European. American options can be

exercised on any date from the time they are written till they expire. Therefore, during the

holding period an American option holder can i) continue to hold the option, ii) sell the option to

someone else or iii) exercise the option. But European options can be exercised only on the day

of expiration. Therefore, during the holding period, the option holders can either hold them or

sell them. Most of the options that are traded in the markets are American.

Consider an example. Suppose an investor instructs a broker to buy one April call option contract

on Intel with a strike price of $20. The broker will relay these instructions to a trader who will

then find another trader who wants to sell one April call contract on Intel with a strike price of

$20. Suppose the call price is $1.65. This is the price for an option to buy one share. In the US an

option contract is a contract to buy or sell 100 shares. Therefore, the investor must arrange for

$165 to be remitted to the exchange through the broker and the exchange will arrange for this

amount to be passed on to the party on the other side of the transaction. If the price of Intel

shares does not rise above $20 per share before the expiration date the option is not exercised

and the investor looses $165. But if the share price rises to say $30, then the investor makes a

gain of $1000 - $165 = $835.

An alternative trade for the investor would be to purchase one April put option contract with a

strike price of $17.5. If the put price is $0.725 then it costs $72.5 to the investor. If Intel share

price stays above $17.5 then the option is not exercised and the investor looses $72.5. If the stock

price falls to $15 net profit to the investor is $250 - $72.5 = $177.5.

Functions: options transfer risk from the buyer to the seller. So, they can be used for both

hedging and speculation. Lets take hedging first. A hedger buys insurance. For someone who

wants to purchase an asset such as a bond or a stock in future, a call option ensures that the cost

of buying the asset wont rise. For someone who plans to sell the asset in the future, a put option

ensures that the price at which the asset can be sold will not go down. To understand the

correspondence between insurance and options, consider the example of auto insurance. An

automobile owner pays insurance premium and obtains the right to file a claim in the event of an

accident. If the terms of the policy are met the insurance company is obligated to pay the claim.

If there is no accident, then no claim and no payment, the premium paid is lost. Here, the

insurance company has sold an American call option to a car owner where the underlying asset is

the car and the strike price is zero.

Options can be used for speculation as well. If you believe that interest rates are going to fall

over the next few months, then there are three ways to bet on this possibility. First, purchase

bonds and wait for a price rise and second, buy a futures contract. However, if interest rates rise

then the losses from both the strategies will be very high. The third option is to buy a call option.

If you are right and interest rate falls then the value of the call option will rise. But if you are

wrong and interest rates rise then call will expire and your loss will be limited to the price you

paid for it. This bet is highly leveraged and limited in its potential loss. In a similar fashion

purchasing a put option allows the investor to bet that the price will fall. Again, if the investor is

wrong, all that is lost is the price paid for the option. However, there are situations where a profit

from a call option is much higher than trading in the spot market and alternatively the losses are

also much higher if the spot price becomes unfavourable.

Suppose the current stock price is $20 and a 2-month call option is selling for $1 at a strike price

of $22.5. Assume that the speculator is willing to invest $2000. He can either purchase 100

shares or 2000 call options. Now if the stock price goes up to $27 then from the first option the

speculator makes a profit of $700 while from the second option the profit becomes $9000 -

$2000 = $7000. Similarly, if the price falls to $15 then the loss from the first option is $500

while from the second option is $2000 because the speculator wont exercise the option.

Now the question is who writes options? An option writer can take a large loss. Nevertheless,

there are people who are willing to take the risk for a fee. They are simply speculators. A second

group of people who are willing to write options are insured against any losses that may arise.

They are primarily dealers who engage in the regular purchase and sale of underlying assets.

These people or institutions are called the market makers. Market makers both own the

underlying asset so that they can deliver it and are willing to buy the underlying asset so that they

have it ready to sell to someone else. Since they own the underlying asset, writing a call option

that obligates them to sell it at a fixed price is not that risky, rather it fetch them a fee.

Options are very versatile and can be bought and sold in many combinations. For example the

purchase of an at the money call and simultaneous sale of an at the money put gives the exact

same payoff pattern as the purchase of a futures contract. If the price of the underlying asset rises

the calls value increases while the put remains worthless. If the price falls the put holder gains

while the call is out of the money. Finally, options allow investors to bet that prices will be

volatile. Buy a put and the call at the same strike price, and you have a bet that pays off only if

the underlying asset price moves up or down significantly.

Pricing options: intrinsic value and the time value

An option price has two parts. The first is the value of option if it is exercised immediately,

referred to as the intrinsic value and the second is the fee paid for the options potential benefits

called the time value of the option to emphasize its relationship to the time of the options

expiration. Therefore, option price = intrinsic value + time value of the option.

Consider the example of an at-the-money European call option on the stock of a corporation that

expires in one month. Since the call option is at-the-money, the strike and the current price are

the same, say $100. Since it is an European call, it cannot be exercised now and hence, the

intrinsic value is zero. Therefore, the call option has only time value. Assume that over the next

month, the price of the stock will either rise or fall by $10 with equal probability. The option is

worth something only if the price goes up otherwise it will not be exercised. Thus, for a call

option we need to concern with the upside when the price of the stock increases. The expected

pay off is the probability times the pay off which is 100.5 = 5. This is the time value of the

option. If the price is expected to fall or rise by $20, then the expected pay off become $10.

Therefore, with the increase in the stock price volatility, the time value of option increases.

Since the option can be either exercised or expire worthless, the intrinsic value depends on what

the holder receives if the option is exercised. The intrinsic value is the difference between the

price of the underlying asset and the strike price. If the option is at-the-money or out-of-money

then it does not have any intrinsic value or intrinsic value is equal to zero. Analogously, the

intrinsic value of a put option equals the strike price minus the market price of the underlying

asset or zero whichever is greater.

At expiration the value of an option equals its intrinsic value. Prior to expiration the potential

benefit is represented by the options time value. The longer the time to expiration, the bigger the

likely pay off. In the last example, consider what happens if the option expires in three months

and the stock price has an equal probability of rising or falling $10 each month. The following

table shows the eight possible payoff at the end of three months. And the expected payoff is

30 1

8+ 10

3

8= 7.5.

Months Possible outcomes

1 2 3 4 5 6 7 8

1st +10 +10 +10 +10 -10 -10 -10 -10

2nd +10 -10 -10 +10 +10 -10 -10 +10

3rd +10 +10 -10 -10 +10 +10 -10 -10

Payoffs 30 10 -10 10 10 -10 -30 -10

The likelihood that an option will pay off depends on the volatility or standard deviation of the

price of the underlying asset. If there is no volatility of a stock price, i.e. the price is fixed, then

no one is going to pay for the option since it will never pay off. If some variability is added to the

price, then there is some chance that the price will rise and the option will be in the money.

Moreover, regardless of how far the price of an option fall, the holder of a call option cannot lose

more than the price paid for the option. Alternatively, whenever the price rises higher, the call

options value increases. Therefore, increased volatility has no cost to the option holder, only

benefits. As mentioned earlier options provide insurance. The bigger the risk being insured, the

more valuable is the insurance and the higher the price investors will pay.

Consider examples of two sets of calls and puts of IBM stocks at a given price. The first set of

options in Panel A of the following table will have same expiration date but different strike

prices while the second set in Panel B will have same strike price but different expiration dates.

The following are observed by studying the tables:

At a given price of the underlying asset and time to expiration, the higher the strike price

of a call option, the lower its intrinsic value and the less expensive the option.

At a given price of the underlying asset and time to expiration, the higher the strike price

of a put option the higher the intrinsic value and the more expensive is the option.

The closer the strike price to the current price, the larger the options time value.

Deep in-the-money options have lower time value, because such an option is very likely

to expire in-the-money. Therefore, buying such an option is much like buying the stock

itself.

The longer the time to expiration at a given strike price the higher the option price.

Prices of IBM Puts and Calls, Feb 20, 2007, IBM Stock Price at close = 99.35

A. April Expiration

Strike Price Calls Puts

Call Price Intrinsic

Value

Time

Value

Put Price Intrinsic

Value

Time

Value

80 20.20 19.35 0.85 - 0 -

90 10.40 9.35 1.05 0.20 0 0.20

95 5.80 4.35 1.45 0.75 0 0.75

100 2.55 0 2.55 2.35 0.65 1.70

105 0.75 0 0.75 5.80 5.65 0.15

110 0.15 0 0.15 - 10.65 -

B. Strike Price of 95 Expiration month Calls Puts

April 5.80 4.35 1.45 0.75 0 0.75

July 7.70 4.35 3.35 1.75 0 1.75

October 9.4 4.35 5.05 2.6 0 2.60

Swaps a swap is an agreement between two companies to exchange cash flows in future. The

agreement defines the dates of cash flows and the way in which they are to be calculated.

Usually, the calculation of cash flows involves the future value of an interest rate, an exchange

rate or other market variable. The most common type of swap is a plain vanilla interest rate

swap. In this a company agrees to pay cash flows at a predetermined fixed interest rate on a

notional principal for a number of years. In return, it receives interest at a floating rate on the

same notional principal for the same period of time.

The principal involved is called notional principal or notional because this principal is used to

only calculate interest payment that needs to be exchanged. It is actually never paid or received

by any of the parties involved in a swap. Now consider an example. Consider a 3-year swap that

has been initiated between Microsoft and Intel on March 5, 2010. Suppose, Microsoft agrees to

pay Intel an interest rate of 5 percent per annum on a notional principal of $100 million and in

return Intel agrees to pay Microsoft the 6-month LIBOR (London Interbank Offered Rate) on the

same principal.

Aside: LIBOR (or ICE LIBOR) is the worlds most widely-used benchmark for short-term

interest rates. It serves as the primary indicator for the average rate at which banks that

contribute to the determination of LIBOR may obtain short-term loans in the London interbank

market. Currently there are 11 to 18 contributor banks for five major currencies (US$,

EUR, GBP, JPY, CHF), giving rates for seven different maturities. A total of 35 rates are posted

every business day (number of currencies x number of different maturities) with the 3-month

U.S. dollar rate being the most common one (usually referred to as the current LIBOR rate).

(From investopedia.com)

The first exchange would take place after 6-months on September 5, 2010 where Microsoft

would pay Intel $ 2.5 million. If the 6-month LIBOR rate prevailing 6-month prior to September

5, 2010 was 4.2% then Intel would pay Microsoft 0.5 0.042 1000000 = $2.1 million. The

second exchange would take place again after 6 months on March 5, 2011, where Microsoft

would again pay $2.5 million to Intel. If the LIBOR rate on September 5, 2010 was 4.8% then

Intel would pay Microsoft $2.4 million. An interest rate is swap is generally structured so that

one side remits the difference between the two payments to the other side. For instance, in this

example Microsoft would pay Intel $0.4 million on September 5, 2010 and again $0.1 million on

March 05, 2011. In total there will be six exchanges on the swap with a fixed payment of $ 2.5

million from Microsoft. The floating rate payments on a payment date are calculated using the 6-

month LIBOR rate prevailing 6-months before the payment date.

If the notional principal is actually transacted between the two companies then it is not going to

make any difference in the cash flows calculated. Therefore, this transaction can also be seen as

exchange of bonds between the two companies. Here Microsoft buys floating rate bonds from

Intel while Intel buys fixed rate bonds from Microsoft. So, Microsoft takes a long position in

floating rate bonds and takes a short position in fixed rate bonds while the reverse is true for

Intel.

Swap could be used to transform liability. For instance, Microsoft could use the swap to

transform a floating-rate loan into a fixed-rate loan. Suppose, Microsoft has borrowed $100

million dollars at LIBOR plus 10 basis point or LIBOR plus 0.1 percent. After Microsoft has

entered the swap, it has the following three sets of cash flows:

1. It pays LIBOR plus 0.1 to its outside lenders

2. It receives LIBOR under the terms of the swap

3. It pays 5 percent under the swap

These three sets of cash flows net out to an interest payment of 5.1 percent. Thus, the swap has

the effect of transferring borrowings at a floating rate to borrowing at a fixed rate. Alternatively

for Intel the swap can transform a fixed rate loan into a floating rate loan. Suppose, Intel has a 3-

year $100 million loan outstanding on which it pays 5.2%. Because of the swap it also has three

sets of cash flows:

1. It pays 5.2% to its outside lenders

2. It pays LIBOR under the terms of the swap

3. It receives 5% under the terms of swap.

These three sets of cash flows net out to an interest rate payment of LIBOR plus 0.2 percent.

Thus, Intel transforms borrowing at a fixed rate into borrowing at a floating rate.

Swap could also be used to transform the nature of an asset. For instance, if Microsoft owns

bonds worth $100 million which will provide interest at 4.7% per annum over the next three

years then getting into the swap would render the asset to be floating rate asset with interest

received LIBOR minus 0.3 percent following the same arguments as presented above, i.e.

1. It receives 4.7% on the bonds

2. It receives LIBOR under the terms of the swap

3. It pays 5% under the terms of swap.

Similarly for Intel the swap could have the effect of transforming an asset earning a floating rate

of interest into an asset earning a fixed rate of interest. Suppose, Intel has an investment of $100

million that yields LIBOR minus 20 basis points. After the swap, the sets of cash flows are,

1. It receives LIBOR minus 20 basis points

2. 2. It pays LIBOR under the terms of the swap

3. It receives 5% under the terms of the swap

Therefore, it receives a net interest inflow of 4.8%.

Usually two non-financial companies do not get into contract directly, rather they each deal with

a financial intermediary and most of they do not know that the financial intermediary is into an

offsetting deal with another company. The financial intermediary acts as counterparty and earns

a fee for this which is generally 0.03 to 0.04 percent on a pair of offsetting transactions. If it is

0.03% then Microsoft will be paying 5.015% interest and Intel will receive 4.985% from

Microsoft under the swap. The financial intermediary makes a profit of $30,000 each year. If one

company defaults, the financial institution still has to honour its agreement with the other

company.

It is unlikely that two companies will contact a financial institution at the same time and would

take opposite position in exactly the same swap. Here large financial institutions acting as a

market maker agree to enter into a swap without having an offsetting swap with another

company. This is often referred to as warehousing swaps. The following table shows the quotes

for plain vanilla US dollar swaps posted by a market maker. The bid-offer spread is 3 to 4 basis

points while the average of the bid and offer fixed rates is known as the swap rate.

Maturity (years) Bid p.a. Offer p.a. Swap rate p.a.

2 6.03 6.06 6.045

3 6.21 6.24 6.225

4 6.35 6.39 6.370

5 6.47 6.51 6.490

7 6.65 6.68 6.665

10 6.83 6.87 6.850

The comparative advantage argument an explanation commonly put forward to explain the

popularity of swaps concerns comparative advantage. Some companies might have a

comparative advantage when borrowing from floating rate markets while some others may have

an advantage in borrowing from fixed-rate market. To obtain a new loan, it makes sense for a

company to go to the market where it has a comparative advantage. As a result the company may

borrow fixed when it wants floating or vice versa. Then swap is used to transform a fixed-rate

loan into a floating rate loan and vice versa. For example, consider 2 companies AAA and BBB

having credit rating AAA and BBB, respectively. They face the following borrowing rates in the

fixed and floating markets:

Fixed rate Floating rate

AAA 4.0% 6-month LIBOR 0.1%

BBB 5.2% 6-month LIBOR + 0.6%

So, the company with BBB rating faces a 1.2% higher interest rate in the fixed market while in

the floating market it pays only 0.7% higher than company AAA. Therefore, AAA has a

comparative advantage in fixed rate market while BBB has a comparative advantage in the

floating rate market. BBB will choose to borrow from the floating rate market though it wanted

to borrow from the fixed rate market. So, it has an incentive to get into a swap. Similarly, AAA

may also get into swap where it would pay floating rate (say LIBOR) and receive fixed rate (say

4.35%). Then the cash flows AAA would have are,

1. It pays 4% p.a. to outside lenders

2. It receives 4.35% p.a. from BBB

3. It pays LIBOR to BBC

Therefore, the net effect is AAA pays LIBOR minus 0.35 percent p.a. to BBB which is 0.25%

less than what it would pay by directly borrowing from the floating rate market. Similarly for

BBB the cash flows are,

1. It pays LIBOR plus 0.6 percent to outside lenders

2. It receives LIBOR from AAA corporation

3. It pays 4.35% per annum to AAA corporation.

The net effect is it pays 4.95% p.a. This is 0.25% p.a. less than what it would pay in the fixed

rate market. In the presence of a financial intermediary making a profit of 0.04% p.a. the

borrowing rates from AAA and BBB would be LIBOR minus 0.33% and 4.97%, respectively.

Currency swap currency swap in its simplest form involves exchanging principal and interest

payments in one currency for interest and principal payments in another currency. Consider a 5-

year currency swap agreement between an US company (USC) and a British company (BC) on

Feb 1, 2012. Suppose, that USC pays a fixed interest rate of 5% in sterling and receives a fixed

interest rate of 6% in dollars once in a year and the principal amounts are $18 million and 10

million. This implies that at the outset USC pays $18 million and receives 10 million and at the

end of the life of the swap, USC pays 10 million to BC and BC pays $18 million to USC. Each

year during the life of the swap contract, USC receives $1.08 million and pays 0.5 million. This

is termed as a fixed-for-fixed currency swap because the interest rates on both currencies are

fixed.

There are other types of swaps as well like fixed-for-floating currency swaps and floating-for-

floating currency swaps. Additionally, there is equity swap where the total returns (dividends

plus capital gains) realized on an equity index is exchanged for either a fixed or floating rate of

interest. Equity swaps can be used by portfolio managers to convert return from a fixed or

floating investments to the returns from investing in an equity index and vice versa.

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