Lecture 2: Swaps Nattawut Jenwittayaroje, Ph.D., CFA 01135532: - - PDF document

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Lecture 2: Swaps

Nattawut Jenwittayaroje, Ph.D., CFA NIDA Business School National Institute of Development Administration 01135532: Financial Instrument and Innovation

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Topics Covered

• The concept of a swap
• Basic characteristics of different types of swaps, based on the

underlying: interest rate and currency

• Pricing of swaps
• Strategies using swaps

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• Definition of a swap

 A swap is a transaction in which two parties agree to pay each other a

series of cash flows over a specified period of time.

• For example, a forward/futures contract can be viewed as a simple example of

a swap.

 Forward and futures contracts are commitments for one party to buy

something from another at a fixed price at a future date.

 Suppose it is March 1, 2008, and a company enters into a forward contract

to buy 100 ounces of gold for $850 per ounce in one year.

 The company can sell the gold in one year as soon as it is received. The

forward contract is, therefore, equivalent to a swap agreement where the company pays a cash flow of $85,000 on March 1, 2009, and receives a cash flow equal to 100S on the same date, where S is the market price of

• ne ounce of gold on March 1, 2009.

Introduction

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• In some cases, a party would like to make a series of purchases, instead of

a single purchase, from the other at a fixed price at various future dates.

• The party could agree to a series of forward or futures contracts, each

expiring at different dates. But it is highly likely the contracts would each have a different price.

• A better way to construct this type of strategy is to enter into a single

agreement for one party to make a series of equal payments to the other party at specific dates and receive a “good” (e.g., a payment) from the

• ther party.
• This type of transaction, specifically characterized by a series of regularly

scheduled payments, is called a swap. The parties are said to be swapping payments or assets.

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• Four types of swaps

 Interest rate swap: the two parties make a series of interest

payments to each other, with both payments in the same currency. One payment is variable, and the other payment can be fixed or

• variable. The principal on which the payments are based is not

exchanged.

 Currency swap: the parties make either fixed or variable interest

payments to each other in different currencies. There may or may not be a principal payment.

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• Four types of swaps

 Equity swap (not covered): one of the two parties makes payments

determined by the price of a stock, the value of a stock portfolio, or the level of a stock index. The other payment can be determined by another stock, portfolio, or index, or by an interest rate, or it can be fixed.

 Commodity (not covered): one set of payments is determined by

the price of a commodity, such as oil or gold. The other payment is typically fixed. The commodity swap is usually used to hedge against the price of the commodity.

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• The Figure below shows the growth in world-wide notional principal of swaps

 There has been steady growth in the use of interest rate swaps, which had

notional principal at the end of 2005 of about $173 trillion.

• Currency swaps had

notional principal at the end of 2005 of about $8.5 trillion.

• The reason that interest

rate swaps are more widely used than currency swaps is that virtually every business borrows money and is, therefore, exposed to some form of interest rate risk.

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• Basic Characteristics of swaps

 Initiation date, termination date, and the dates on which the payments are

to be made.

 No cash up front: similar to forward and futures contracts, swaps have zero

value at the start.

 Settlement date, settlement period: the day on which a payment occurs is

called the settlement date, and the period between settlement dates is called the settlement period.

 Notional principal: the interest payments are based on the multiplication of

an interest rate times a principal amount. In interest rate swaps this principal amount is never exchanged. That is why it is termed the notional principal.

 Over the counter and dealer markets: swaps are exclusively customized,

• ver-the-counter instruments. Swap dealers quotes prices and rates at

which they will enter into either side of a swap transaction.

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An Example of a “Plain Vanilla” Interest Rate Swap

Company A Company B

LIBOR 5%

• Consider a three-year swap initiated on March 1, 1998,
• Company B agrees pay to company A an interest rate of 5% per annum on a

notional principal of $100 million

• Company A agrees to pay to company B the 6-month LIBOR rate on the same

notional principal.

• Assume that the payments are to be exchanged every six months.

 This swap is represented diagrammatically in the figure below.

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What is LIBOR?

• LIBOR is the London Interbank Offer Rate.
• LIBOR is the rate of interest offered by banks on deposits from other

banks in Eurocurrency markets.

• For example, one- (three-) month LIBOR is the rate offered on one-

(three-) month deposits.

• LIBOR rates are determined by trading between banks and change

continuously as economic conditions change.

• LIBOR is frequently a reference rate of interest for loans in

international financial markets.

 For example, a loan with a rate of interest specified as six-month LIBOR

plus 1.5% per annum. The life of the loan is divided into six-month periods. For each period, the rate of interest is set at 1.5% per year above the six- month LIBOR rate at the beginning of the period. Interest is paid at the end

• f the period.

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• --------Millions of Dollars---------

LIBOR FLOATING FIXED Net Date Rate Cash Flow Cash Flow Cash Flow Mar.1, 1998 4.2%

• Sept. 1, 1998

4.8% +2.10 –2.50 –0.40 Mar.1, 1999 5.3% +2.40 –2.50 –0.10

• Sept. 1, 1999

5.5% +2.65 –2.50 +0.15 Mar.1, 2000 5.6% +2.75 –2.50 +0.25

• Sept. 1, 2000

5.9% +2.80 –2.50 +0.30 Mar.1, 2001 6.4% +2.95 –2.50 +0.45

An Example of a “Plain Vanilla” Interest Rate Swap

• --------Millions of Dollars---------

LIBOR FLOATING FIXED Net Date Rate Cash Flow Cash Flow Cash Flow Mar.1, 1998 4.2%

• Sept. 1, 1998

4.8% +2.10 –2.50 –0.40 Mar.1, 1999 5.3% +2.40 –2.50 –0.10

• Sept. 1, 1999

5.5% +2.65 –2.50 +0.15 Mar.1, 2000 5.6% +2.75 –2.50 +0.25

• Sept. 1, 2000

5.9% +2.80 –2.50 +0.30 Mar.1, 2001 6.4% +2.95 –2.50 +0.45

• --------Millions of Dollars---------

LIBOR FLOATING FIXED Net Date Rate Cash Flow Cash Flow Cash Flow Mar.1, 1998 4.2%

• Sept. 1, 1998

4.8% +2.10 –2.50 –0.40 Mar.1, 1999 5.3% +2.40 –2.50 –0.10

• Sept. 1, 1999

5.5% +2.65 –2.50 +0.15 Mar.1, 2000 5.6% +2.75 –2.50 +0.25

• Sept. 1, 2000

5.9% +2.80 –2.50 +0.30 Mar.1, 2001 6.4% +2.95 –2.50 +0.45

• --------Millions of Dollars---------

LIBOR FLOATING FIXED Net Date Rate Cash Flow Cash Flow Cash Flow Mar.1, 1998 4.2%

• Sept. 1, 1998

4.8% +2.10 –2.50 –0.40 Mar.1, 1999 5.3% +2.40 –2.50 –0.10

• Sept. 1, 1999

5.5% +2.65 –2.50 +0.15 Mar.1, 2000 5.6% +2.75 –2.50 +0.25

• Sept. 1, 2000

5.9% +2.80 –2.50 +0.30 Mar.1, 2001 6.4% +2.95 –2.50 +0.45

• --------Millions of Dollars---------

LIBOR FLOATING FIXED Net Date Rate Cash Flow Cash Flow Cash Flow Mar.1, 1998 4.2%

• Sept. 1, 1998

4.8% +2.10 –2.50 –0.40 Mar.1, 1999 5.3% +2.40 –2.50 –0.10

• Sept. 1, 1999

5.5% +2.65 –2.50 +0.15 Mar.1, 2000 5.6% +2.75 –2.50 +0.25

• Sept. 1, 2000

5.9% +2.80 –2.50 +0.30 Mar.1, 2001 6.4% +2.95 –2.50 +0.45

• --------Millions of Dollars---------

LIBOR FLOATING FIXED Net Date Rate Cash Flow Cash Flow Cash Flow Mar.1, 1998 4.2%

• Sept. 1, 1998

4.8% +2.10 –2.50 –0.40 Mar.1, 1999 5.3% +2.40 –2.50 –0.10

• Sept. 1, 1999

5.5% +2.65 –2.50 +0.15 Mar.1, 2000 5.6% +2.75 –2.50 +0.25

• Sept. 1, 2000

5.9% +2.80 –2.50 +0.30 Mar.1, 2001 6.4% +2.95 –2.50 +0.45 (--------Millions of Dollars--------) LIBOR FLOATING FIXED Net Date Rate Cash Flow Cash Flow Cash Flow Mar.1, 1998 4.2%

• Sept. 1, 1998

4.8% +2.10 –2.50 –0.40 Mar.1, 1999 5.3% +2.40 –2.50 –0.10

• Sept. 1, 1999

5.5% +2.65 –2.50 +0.15 Mar.1, 2000 5.6% +2.75 –2.50 +0.25

• Sept. 1, 2000

5.9% +2.80 –2.50 +0.30 Mar.1, 2001 6.4% +2.95 –2.50 +0.45

Table 1: Cash Flows (in $ millions) to Company B

Settled every six months

Settlement

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• The first exchange of payments would take place on Sep 1, 1998.

 B would receive from A the six-month LIBOR rate prevailing six

months prior to Sep 1, 1998 – that is, on Mar 1, 1998. Thus B would receive from A = $2.1 million (0.5x0.042x$100)

 B would pay A = $2.5million.

• The second exchange of payments would take place on Mar 1, 1999.

 B would receive from A the six-month LIBOR rate prevailing six

months prior to Mar 1, 1999 – that is, on Sep 1, 1998. Thus B would receive from A = $2.4 million (0.5x0.048x$100)

 B would pay A = $2.5million.

An Example of a “Plain Vanilla” Interest Rate Swap

See Table 1

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• In total, there are six exchanges of payment on the swap.

 The fixed payments are always $2.5 million (i.e., B would

always pay A = $2.5million).

 The floating-rate payments on a settlement date are calculated

using the six-month LIBOR rate prevailing six months before the settlement date.

 An interest rate swap is usually structured so that one side pays

the difference. E.g., on Sep 1, 1998, B would pay A = $0.40 million (= $2.1 - $2.5).

• Note that the $100 million principal is not exchanged (i.e., that’s

why it’s called notional principal), but used only for the calculation

• f interest payments.

An Example of a “Plain Vanilla” Interest Rate Swap

See Table 1

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• Characteristics of swaps

 Dealer market: swaps are exclusively customized, over-the-

counter instruments.

 Thus, the two parties are usually a dealer, which is a financial

institution that makes markets in swaps, and an end user, which is usually a customer of the dealer and might be a corporation, pension fund, hedge fund, or some other organization.

 Swap dealers quotes prices and rates at which they will enter into

either side of a swap transaction.

• For example, three year swap rate (i.e., fixed rate) is 4.985% -

5.015%

Role of Financial Intermediary

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Role of Financial Intermediary

F.I.

LIBOR LIBOR 4.985% 5.015%

Company A Company B

• Characteristics of swaps

 If neither company defaults on the swap, the financial institution

(F.I) is certain to make a profit of 3 basis points per year (or 0.03%

• f $100 million = $30,000 per year for the three year period.)

 Credit risk: like forward contracts, swaps are subject to the risk

that a given party could default.

 If one of the company defaults, the F.I. still has to honor its

agreement with the other party. The 3 bps earned is partly to compensate the F.I. for the default risk it is bearing.

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Interest Rate Swap Strategies

• Figure 12.5 is an example of converting a floating-rate loan into a fixed-rate loan
• XYZ has a one-year floating rate loan at LIBOR plus 100 bps.
• To convert the floating-rate loan into a fixed-rate loan, XYZ decided to engage

in the swap, in which XYZ pays a fixed rate of 7.5% and receives LIBOR.

• In effect, XYZ pays a fixed rate of 8.5%.

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Pricing Interest Rate Swaps

• How is the fixed rate determined?
• The fixed rate in a swap is not an arbitrary rate, but is determined from a

process called pricing the swap.

• If the principal were exchanged at the end of the swap life, its nature would

NOT be changed. Exchanging $100 million for $100 million at the end of the swap life would have no financial value to either party, shown in Table 2.

• Table 2, however, shows that the interest-rate swap can be viewed as the

exchange of a fixed-rate for a floating-rate bond.

 The cash flow in the third column are the cash flows from a long position

in a floating-rate bond.  B (A) takes a long (short) position in floating- rate bond.

 The cash flow in the fourth column are the cash flows from a short

position in a fixed-rate bond.  B (A) takes a short (long) position in fixed-rate bond.

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Pricing Interest Rate Swaps

Settlement Date LIBOR Rate (%) Floating Cash Flow Received ($mil) Fixed Cash Flow Paid ($mil) Net Cash Flow ($mil) Mar 1, 1998 4.20 Sep 1, 1998 4.80 +2.10

• 2.50
• 0.40

Mar 1, 1999 5.30 +2.40

• 2.50
• 0.10

Sep 1, 1999 5.50 +2.65

• 2.50

+0.15 Mar 1, 2000 5.60 +2.75

• 2.50

+0.25 Sep 1, 2000 5.90 +2.80

• 2.50

+0.30 Mar 1, 2001 6.40 +102.95

• 102.50

+0.45

Table 2: Cash Flows (in $ millions) to Company B if the principal is exchanged

long position in a floating-rate bond short position in a fixed-rate bond

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Pricing Interest Rate Swaps

• Like forward/futures pricing, a swap has zero value at the
• start. The fixed rate is set so that the present value of the

stream of fixed payments is the same as the present value

• f the stream of floating payments at the start of the

transaction.

• The obligations of one party have the same value as the
• bligations of the other at the start of the swap transaction.

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Pricing Interest Rate Swaps

• To understand interest rate swap pricing, it is necessary to know how to price a

floating-rate bond.

• A floating-rate bond is one in which the coupons change at specific dates with

the market rate of interest. Typically the coupon is set at the beginning of the interest payment period, interest then accrues at that rate, and the interest is paid at the end of the period. The coupon is then reset for the next period. The coupon is usually linked with a specific market rate, such as LIBOR.

• The price of a LIBOR zero coupon bond at time 0 for maturity of ti days is

 L0(t1) represent the LIBOR rate at time 0 for maturity of t1 days.  B0(t1) is the price of a $1 discount (zero coupon) bond based on the rate

L0(t1). Thus, B0(t1) can be viewed as present value factors and used to discount future payments.

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• Consider a one-year floating-rate bond, with interest paid quarterly at

LIBOR, assuming 90 days in each quarter.

• At time 0, 90-day LIBOR is denoted as L0(90). At day 90, 90-day

LIBOR is L90(90). L180(90) is therefore the 90-day LIBOR prevailing at day 180. Finally, L270(90) is therefore the 90-day LIBOR prevailing at day 270.

• The party buying this floating-rate bond receives the payments shown

in the Figure 12.3, with q representing the factor (days/360) = 90/360.

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• First, note the payment at the maturity date, day 360, of the principal

plus the interest of L270(90) (90/360).

• Denote the value of this floating rate bond on day 270 as FLRB270,

which can be obtained as

• Hence, the value of the floating-rate bond on day 270 is its par value
• f 1.
• Step back to day 180 and determine the value of the floating-rate
• bond. Continuing this procedure back to day 0 shows that the value
• f the floating-rate bond at any payment date, as well as on the

initiation date, is its par value (i.e., 1).

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Pricing Interest Rate Swaps

• By adding the notional principals at the end, we can separate the cash flow

streams of an interest rate swap into those of a fixed-rate bond and a floating- rate bond. See Figure 12.4.

• It is now apparent that a pay-fixed, receive-floating swap is equivalent to

issuing a fixed-rate bond and using the proceeds to purchase a floating-rate bond.

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Pricing Interest Rate Swaps

• The value of a fixed-rate bond with a coupon of R (q = days/360):
• The value of a floating-rate bond

 At time 0, or a payment date

• The value of the swap (pay fixed, receive floating) is, therefore,

This VS is based on a NP of 1. For any other NP, just multiply VS by the NP.

The value of a pay- fixed, receive-floating interest rate swap is found as the value of a floating-rate bond minus the value of a fixed-rate bond.

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Pricing Interest Rate Swaps

• To price the swap at the start, set VS value to zero and solve for R
• Pricing a swap means to find the fixed rate on the swap at the start of the
• transaction. The fixed rate is obtained by finding the fixed payment that sets

the market value of the swap to zero at the start.

• This fixed rate is quoted as a spread over the rate on a Treasury security of

equivalent maturity. Such spread is referred to as the swap spread, which reflects the general level of credit risk in the global economy.

R is the fixed rate

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• Table 12.2 is an example of the computation of a

fixed-rate in a swap.

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Currency Swaps

• A currency swap is a swap in which the two parties agree to

exchange a series of interest payments in different currencies. Either or both sets of payments can be fixed or floating.

• In a currency swap, there are two notional principals, one in

each of the two currencies.

• The notional principal can be exchanged at the beginning and

at the end of the swap life. In addition, currency swap payments are typically not netted, because they are in different currencies.

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Structure of a Typical Currency Swap

• Example 1: Advanced Technology (ADV) enters into currency swap with

Global Swaps dealer, Inc. (GSI). Assume the current exchange rate is 33baht/USD. Under the currency swap, ADV will pay Thai Baht at 4.35% based

• n NP of Bt 33 million semiannually for two years. GSI will pay US dollars at

6.1% based on NP of $ 1 million semiannually for two years. Notional principals will be exchanged. At the initiation date of the swap

 ADV pays GSI $1 million  GSI pays ADV Bt33 million

Semiannually for two years

 ADV pays GSI 0.0435(180/360) Bt33,000,000 = Bt717,750  GSI pays ADV 0.061(180/360) $1,000,000 = $30,500

At the termination date of the swap

 ADV pays GSI Bt33 million  GSI pays ADV $1 million

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• Note that the series of cash flows looks like ADV has issued a ThaiBaht-denominated

bond for 33 million Baht, taken the funds, and purchased a USdollar-denominated bond for $1 million.

• Since swaps have zero value at the start, the exchange rate at the time the swap is

initiated is Bt33 per $USdollar (Bt33 million in exchange for $1 million).

• At the end of the swap life, however, the exchange rate will certainly be different from
• 33. Thus, the exchange rate risk gives rise to gains and losses for the two parties,

which is an important factor in determining the value of the currency swap.

ADV receives ADV pays

$1,000,000 $1,000,000 + $30,500 = $1,030,500 $30,500 Bt717,750 Bt33,000,000 Bt717,750 Bt717,750 $30,500 $30,500 Bt33,000,000 + Bt 717,750 = Bt33,717,750 30

• Currency swaps are

primarily used to convert a loan in one currency into a loan into another currency.

• A typical case is a firm

borrowing in one currency and wanting to borrow in another. See Figure 12.8 for ADV- GSI example.

Currency Swap Strategies

GSI GSI GSI

GSI

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Pricing Currency Swaps

• To determine the value of a currency swap, first find the PVs
• f the two streams of cash flows, with both expressed in a

common currency. Subtracting the value of the outflow stream from the value of the inflow stream gives rise to the value of the currency swap.

• Let dollar notional principal be NP$. Then Thai Baht notional

principal is NPBt = S0 (i.e., spot or current exchange rate) for every dollar notional principal. Here Thai Baht notional principal will be Bt33,000,000. With S0 = 33, NP$ = $1,000,000.

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Pricing Currency Swaps

• For fixed payments, we use the fixed rate on plain vanilla swaps

in that currency, R$ or RBt.

 Determine the fixed rate in dollars that will make the PV of

the fixed payments equal the notional principal of $1.

 Determine the fixed rate in Baht that will make the PV of the

fixed payments equal the notional principal of NPBt = S0.

• For the floating side of a currency swap, no pricing is required

 For each currency, the PV of the floating-rate side is always

the notional principal in that currency.

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33 Baht rate

The fixed rate on a Baht plain vanilla interest rate swap would be

RBt

B0Bt(180) B0Bt(360) B0Bt(540) B0Bt(720)

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Pricing Currency Swaps

• The current exchange rate is Bt33 per US dollar.
• Since the PV of the dollar payments at 6.1% per $1 notional principal is $1, the

PV of the dollar payments at 6.1% for a notional principal of $1 million would be $1 million.

• The PV of the Baht payments at 4.35% for a notional principal of Bt 1 is Bt 1.

So the PV of the Baht payments at 4.35% for a notional principal of Bt 33 million would be Bt 33 million.

• Converting Bt 33 million to dollars gives $33,000,000/33 = $1,000,000, which

is the dollar notional principal.

• In summary, these four streams of cash flows are equal

 PV of dollar-fixed at 6.1% of $ 1 million  PV of dollar-floating rate of $ 1 million  PV of Baht-fixed at 4.35% of Bt 33 million  PV of Baht-floating rate of Bt 33 million