12/11/2015 Nattawoot Koowattanatianchai 1 Derivatives Analysis - - PowerPoint PPT Presentation

12/11/2015 Nattawoot Koowattanatianchai 1

12/11/2015 Nattawoot Koowattanatianchai 2

Derivatives Analysis

Nattawoot Koowattanatianchai

12/11/2015 Nattawoot Koowattanatianchai 3

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12/11/2015 Nattawoot Koowattanatianchai 4

Lecture 5

Swap contracts

Discussion topics

 Characteristics of swap

contracts

 Termination of a swap  The structure of global swap

markets

 Types of swaps

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Readings

 CFA Program Curriculum 2015 -

Level II – Volume 6: Derivatives and Portfolio Management.

 Reading 50

 Don M. Chance and Robert

Brooks, An Introduction to Derivatives and Risk Management, 9th Edition, 2013, Thomson.

 Chapter 12

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Introduction

 A swap

 An agreement between two parties to exchange a

series of future cash flows.

 One party makes payments that are determined

by a random outcome, such as an interest rate, a currency rate, an equity return or a commodity

• price. These payments are commonly referred to

as variable or floating.

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Introduction

 A swap

 The other party either makes variable or floating

payments determined by some other random factor or makes fixed payments.

 One type of swap involves both parties making

fixed payments, but the values of those payments vary due to random factors.

 Many swaps designate one party as being the

floating- (or variable-) rate payer, and the other party being the fixed-rate payer.

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Introduction

 Which party is long and

which party is short?

 Swaps in which one party

receives a floating rate and the other receives a fixed rate, the former is usually said to be “long” and the latter is said to be “short”.

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Characteristics

 A swap is basically a series of forward

contracts.

 A swap with one payment is just a forward

contract.

 Zero value at the start of the contract

 When a swap is initiated, neither party pays any

amount to the other.

 A technical exception is a currency swap, in which

each party pays the notional principal to the other, but the amounts exchanged are equivalent.

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Characteristics

 Settlement date (payment date)

 Each date on which the parties make payments.  The time between settlement dates is called the

settlement period.

 On a given settlement date when payments are

due, one party makes a payment to the other, which in turn makes a payment to the first party.

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Characteristics

 Netting

 With the exception of currency swaps, both sets of

payments are made in the same currency. Consequently, the parties typically agree to exchange only the net amount owed from one party to the other, a practice called netting.

 In currency swaps and a few other special cases,

the payments are not made in the same currency. Hence, the parties usually make separate payments without netting.

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Characteristics

 Swaps are generally settled in cash.

 It is quite rare for swaps to call for actual physical

delivery of an underlying asset.

 Termination date

 The date of the final payment. The original time to

maturity is sometimes called the “tenor” of a swap.

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Characteristics

 The swap market is almost exclusively an

• ver-the-counter market.

 Swaps are customized to the parties’ specific

needs.

 Default risk

 Over-the-counter instruments are subject to

default risk. When a series of payments is made, there is default risk potential throughout the life of the contract, depending on the financial condition

• f the two parties.

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Characteristics

 Default risk

 Example

 On a settlement date, Party A owes Party B a payment

• f $50,000 and Party B owes Party A a payment of

$12,000.

 Agreeing to net, Party A owes Party B $38,000 for that

particular payment. But it may be the case that the market value of the swap, which reflects the present value of the remaining payments, could be positive from the perspective of Party A and negative from the perspective of Party B. In that case, Party B owes Party A more for the remaining payments.

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Termination of a swap

 A swap has a termination or expiration date.

Sometimes, however, a party could want to terminate a swap before its formal expiration. This scenario is much like a party selling a bond before it matures or selling an exchange-traded option on futures contract before its expiration. With swaps, early termination can take place in several ways.

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Termination of a swap

 Possibility 1

 If a party holds a swap with a market value of

$125,000, it can settle the swap with the counterparty by having the counterparty pay it $125,000 in cash. This payment terminates the transaction for both parties.

 From the opposite perspective, a party holding a

swap with a negative market value can terminate the swap by paying the market value to the counterparty.

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Termination of a swap

 Possibility 1

 Terminating a swap in this

manner is possible only if the counterparties specify in advance that such a transaction can be made, or if they reach an agreement to do so without having specified in advance.

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Termination of a swap

 Possibility 2

 Many swaps are terminated

early by entering into a separate and offsetting swap.

 Example

 Suppose a corporation is engaged

in a swap to make fixed payments

• f 5% and receive floating

payments based on Libor, with the payments made each 15 January and 15 July.

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Termination of a swap

 Possibility 2

 Example

 Three years remain on the

• swap. That corporation can
• ffset the swap by entering

into an entirely new swap in which it makes payments based on Libor and receives a fixed rate with the payments made each 15 January and 15 July for three years.

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Termination of a swap

 Possibility 2

 Example

 The swap fixed rate is determined by market conditions

at the time the swap is initiated. Thus, the fixed rate on the new swap is not likely to match the fixed rate on the

• ld swap, but the effect of this transaction is simply to

have the floating payments offset; the fixed payments will net out to a known amount. Hence the risk associated with the floating rate is eliminated. The default risk, however, is not eliminated because both swaps remain in effect.

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Termination of a swap

 Possibility 3

 Another way to terminate a swap early is sell the

swap to another counterparty.

 Example

 Suppose a corporation holds a swap worth $75,000. If it

can obtain the counterparty’s permission, it can find another party to take over its payments. In effect, it sells the swap for $75,000 to that party.

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Termination of a swap

 Possibility 4

 A final way to terminate a

swap early is by using a

• swaption. This instrument is

an option to enter into a swap at terms that are established in advance. Thus, a party could use a swaption to enter into an

• ffsetting swap.

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Global swap markets

 Much like the global forward and over-the-

counter options markets, the global swap market is made up of dealers, which are banks and investment banking firms.

 Dealers make markets in swaps, quoting bid

and as prices and rates, thereby offering to take either side of a swap transaction.

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Global swap markets

 Upon taking a position in a swap, the dealer

generally offsets the risk by making transactions in other markets.

 The counterparties to swaps are either end

users or other dealers.

 End users are often corporations with risk

management problems (exposing to risks from interest rates, exchange rates, stock prices, or commodity prices) that can be solved by engaging in a swap.

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Global swap markets

 The end user contacts a dealer that makes a

market in swaps. The two engage in a transaction, at which point the dealer assumes some risk from the end user. The dealer then usually lays off the risk by engaging in a transaction with another party. That transaction could be something as simple as a futures contract, or it could be an

• ver-the-counter transaction with another

dealer.

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Type of swaps

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Types of swap contracts Currency swaps Interest rate swaps Equity swaps Commodity and

• ther types of

swaps

Currency swaps

 In a currency swap, each party makes

interest payments to the other in different currencies.

 Example

 The US retailer Target Corporation (NYSE: TGT)

does not have an established presence in Europe. It has decided to begin opening a few stores in Germany and needs €9 million to fund construction and initial operations.

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Currency swaps

 Example

 TGT would like to issue a fixed-rate euro-

denominated bond with face value of €9 million, but the company is not very well known in Europe. European investment bankers have given it a quote for such a bond. Deutsche Bank, AG (NYSE: DB), however, tells TGT that it should issue the bond in dollars and use a swap to convert it to euros.

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Currency swaps

 Example

 Suppose TGT issues a five-year US$10 million

bond at a rate of 6%. It then enters into a swap with DB in which DB will make payments to TGT in US dollars at a fixed rate of 5.5% and TGT will make payments to DB in euros at a fixed rate of 4.9% each 15 March and 15 September for five

• years. The payments are based on a notional

principal of 10 million in dollars and 9 million in euros.

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Currency swaps

 Example

 We assume the swap starts on 15 September of

the current year. The swap specifies that the two parties exchange the notional principal at the start

• f the swap and at the end. Because the

payments are made in different currencies, netting is not practical, so each party makes its respective

• payments. We shall assume 180 days between

payment dates. In practice, exact day counts are usually used, leading to different fixed payment amounts in different periods.

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Currency swaps

 Example

 The swap is composed of the following

transactions:

 15 September:  DB pays TGT €9 million, and  TGT pays DB $10 million.  Each 15 March and 15 September for five years:  DB pays TGT 0.055(180/360)$10 million = $275,000, and  TGT pays DB 0.049(180/360)€9 million = €220,500

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Currency swaps

 Example

 The swap is composed of the following

transactions:

 15 September five years after initiation:  DB pays TGT $10 million €9 million, and  TGT pays DB €9 million.

 The TGT-DB transaction looks just like TGT is

issuing a bond with face value of €9 million and that bond is purchased by DB. TGT converts the €9 million to $10 million and buys a dollar- denominated bond issued by DB.

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Currency swaps

 Example

 TGT, having issued a bond denominated in euros,

accordingly makes interest payments to DB in

• euros. DB, appropriately, makes interest

payments in dollars to TGT. At the end, they each pay off the face values of the bond they have

• issued. Note that neither TGT nor DB actually

issues or purchases a bond. They exchange only a series of cash flows that replicated the issuance and purchase of these bonds.

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Currency swaps

 15 September

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Ne Net effect fect: TGT T has the €9 m million n to begin its expansion sion.

TGT DB DB

€9 million

• n

$10 million

• n

$10 million

• n

TGT bondholder ndholders

Currency swaps

 Each 15 March and 15 September

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Ne Net effect: fect: TGT’s interest rest payment nts s consist ist of €220,50 ,500 0 and $25,000 000.

TGT DB DB

$275,000 5,000 €220,500 0,500 $300,000 0,000 (6 percent ent)

TGT bondholder ndholders

Currency swaps

 15 September, five years later

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Ne Net effect: fect: TGT T pays off f its bondholders lders and term rminates nates its swa wap.

TGT DB DB

$10 million

• n

€9 million

• n

$10 million

• n

TGT bondholder ndholders

Currency swaps

 Example

 On the interest payment dates, the swap

generates $275,000 of the $300,000 in interest TGT needs to pay its bondholders. In turn, TGT makes interest payments in euros. Still, small dollar interest payments are necessary because TGT cannot issue a dollar bond at the swap rate.

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Currency swaps

 Example

 TGT has effectively issued a dollar-denominated

bond and converted it to a euro-denominated

• bond. In all likelihood, it can save on interest

expense by funding its need for euros in this way, because TGT is better known in the US than in

• Europe. Its swap dealer, DB, knows TGT well and

also obviously has a strong presence in Europe. Thus, DB can pass on its advantage in euro bond markets to TGT. TGT, however, has to assume a remote possibility of DB defaulting.

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Currency swaps

 Example

 Suppose instead that TGT preferred to borrow in

euros at a floating rate. It then would have specified that the swap required it to make payments to DB at a floating rate. Had TGT preferred to issue the dollar denominated bond at a floating rate, it would have specified that DB pays it dollars at a floating rate.

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Currency swaps

 Example

 Although TGT and DB exchanged notional

principal, some scenarios exist in which the notional principals are not exchanged. For example, suppose many years later, TGT is generating €10 million in cash semiannually and converting it back to dollars on 15 January and 15

• July. It might then wish to lock in the conversion

rate by entering into a currency swap that would require it to pay a dealer €10 million and receive a fixed amount of dollars.

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Currency swaps

 Example

 If the euro fixed rate were 5%, a notional principal

• f €400 million would generate a payment of

0.05(180/360) €400 million = €10 million. If the exchange rate is, for example, $0.85, the equivalent dollar notional principal would be $340

• million. If the dollar fixed rate is 6%, TGT would

receive 0.06(180/360)$340 million = $10.2 million. These payments would occur twice a year for the life of the swap.

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Currency swaps

 Example

 TGT might then lock in the conversion rate by

entering into a currency swap with notional principal amounts that would allow it to receive a fixed amount of dollars on 15 January and 15

• July. There would be no reason to specify an

exchange of notional principal.

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Currency swaps

 Example

 There are four types of currency swap. Using the

• riginal TGT-DB swap as an example, the

semiannual payments would be:

 Swap A  TGT pays euros at a fixed rate; DB pays dollars at a fixed

rate.

 Swap B  TGT pays euros at a fixed rate; DB pays dollars at a

floating rate.

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Currency swaps

 Example

 There are four types of currency swap. Using the

• riginal TGT-DB swap as an example, the

semiannual payments would be:

 Swap C  TGT pays euros at a floating rate rate; DB pays dollars at a

floating rate rate.

 Swap D  TGT pays euros at a floating rate rate; DB pays dollars at a

fixed rate.

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Currency swaps

 Example

 Or, reversing the flow, TGT could be the payer of

dollars and DB could be the payer of euros:

 Swap E  TGT pays dollars at a fixed rate; DB pays euros at a fixed

rate.

 Swap F  TGT pays dollars at a fixed rate; DB pays euros at a

floating rate.

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Currency swaps

 Example

 Or, reversing the flow, TGT could be the payer of

dollars and DB could be the payer of euros:

 Swap G  TGT pays dollars at a floating rate rate; DB pays euros at a

floating rate rate.

 Swap H  TGT pays dollars at a floating rate rate; DB pays euros at a

fixed rate.

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Currency swaps

 Example

 Suppose we combine Swap A with Swap H. With

TGT paying euros at a fixed rate and DB paying euros at a fixed rate, the euro payments wash out and the net effect is:

 Swap I  TGT pays dollars at a floating rate; DB pays dollars at a

fixed rate.

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Currency swaps

 Example

 Suppose we combine Swap B with Swap E.

Similarly, the euro payments again wash out, and the net effect is:

 Swap J  TGT pays dollars at a fixed rate; DB pays dollars at a

floating rate.

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Currency swaps

 Example

 Suppose we combine Swap C with Swap F.

Likewise, the euro floating payments wash out, and the net effect is:

 Swap K  TGT pays dollars at a fixed rate; DB pays dollars at a

floating rate.

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Currency swaps

 Example

 Lastly, suppose we combine Swap D with Swap

• G. Again, the euro floating payments wash out,

and the net effect is:

 Swap L  TGT pays dollars at a floating rate; DB pays dollars at a

fixed rate.

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Currency swaps

 Example

 Of course, the net results of I and L are

equivalent, and the net results of J and K are

• equivalent. Combinations of currency swaps

eliminate the currency flows and leave us with transactions in only one currency. A swap in which both sets of interest payments are made in the same currency is an interest rate swap.

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Interest rate swaps

 An interest rate swap is a currency swap in

which both currencies are the same. Because we are paying in the same currency, there is no need to exchange notional principals at the beginning and at the end of an interest rate swap.

 Interest rate swaps evolved into their own

• market. In fact, the interest rate swap market

is much bigger than the currency swap market.

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Interest rate swaps

 A plain vanilla swap

 An interest rate swap in which one party pays a

fixed rate and the other pays a floating rate, with both sets of payments in the same currency.

 Because we are paying in the same currency, the

interest payments can be, and nearly always are,

• netted. If one party owes $X and the other owes

$Y, the party owing the greater amount pays the net difference, which greatly reduces the credit risk.

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Interest rate swaps

 A plain vanilla swap

 Having both parties pay a fixed rate does not

make sense. The two streams of payments would be identical in that case. So in an interest rate swap, either one side always pays fixed and the

• ther side pays floating, or both sides paying

floating, but never do both sides pay fixed.

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Interest rate swaps

 Example

 Suppose that on 15 December, General Electric

Company (NYSE: GE) borrows money for one year from a bank such as Bank of America (NYSE: BAC). The loan is for $25 million and specifies that GE will make interest payments on a quarterly basis on the 15th of March, June, September, and December for one year at the rate of Libor plus 25 basis points. At the end of the year, it will pay back the principal. Libor is

• bserved at the beginning of each quarter.

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Interest rate swaps

 Example

 GE believes that it is getting a good rate, but

fearing a rise in interest rates, it would prefer a fixed-rate loan. It can easily convert the floating- rate loan to a fixed-rate loan by engaging in a swap.

 Suppose it approaches JP Morgan Chase (NYSE:

JPM), a large dealer bank, and requests a quote

• n a swap to pay a fixed rate and receive Libor,

with payments on the dates of its loan payments.

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Interest rate swaps

 Example

 JPM prices the swap (a procedure we will not

cover in this course) and quotes a fixed rate of 6.2%. The fixed payments will be made based on a day count of 90/365, and the floating payments will be made based on 90/360. Current Libor is 5.9%. Therefore, the first fixed payment, which GE makes to JPM, is $25,000,000(0.062)(90/365) = $382,192. This is also the amount of each remaining fixed payments.

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Interest rate swaps

 Example

 The first floating payment (known on the 15th of

December and paid on the 15th of March), which JPM makes to GE, is $25,00,000(0.059)(90/360) = $368,750. The remaining floating payments will not be known until later.

 It would appeared as if GE had issued a fixed-rate

bond (with a principal of $25 million) and JPM had issued a floating-rate bond (with a principal of $25 million), and each purchased the bond of the

• ther.

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Interest rate swaps

 Example

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Ne Net effect fect: GE E pays 6.2% % + 25 bps = 6.45% % fixed. ed.

GE GE JPM

Float ating ng payment ments Libor

• r

Fixed ed paymen ents at 6.2% 6.2% Interes est payments ments at Libor

• r + 2

25 bps

Bank nk of Amer erica ica

Interest rate swaps

 Example

 JPM is engaged in a swap to pay Libor and

receive 6.2%. It is exposed to the risk of Libor

• increasing. It would, therefore, probably engage in

some other type of transaction to offset this risk.

 One transaction commonly used in this situation is to

sell Eurodollar futures.

 Bank of America is also exposed to Libor, but in

the banking industry, floating-rate loans are often made because funding that the bank obtained to make the loan was probably already at Libor.

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Interest rate swaps

 Example

 It is possible but unlikely that GE could get a

fixed-rate loan at a better rate. The swap involves some credit risk: the possibility, however small, that JPM will default. In return for assuming that risk, GE in all likelihood would get a better rate than it would if it borrowed at a fixed rate. JPM is effectively a wholesaler of risk, using its powerful position as one of the world’s leading banks to facilitate the buying and selling of risk for companies such as GE.

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Equity swaps

 It should be apparent by

now that a swap requires at least one variable rate or price underlying it. So far, that rate has been an interest rate or an exchange rate. In an equity swap, the variable rate is the return on a stock or stock index.

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Equity swaps

 Distinguishing features

 The party making the fixed-rate payment could

also have to make a variable payment based on the equity return.

 The payment is not known until the end of the

settlement period, at which time the return on the stock is known. In an interest rate or currency swap, the floating interest rate is set at the beginning of the period. Therefore, one always knows the amount of the upcoming floating interest payment.

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Equity swaps

 Example 1

 Suppose the end user pays the equity payment

and receives the fixed payment, i.e., it pays the dealer the return on the S&P 500 Index, and the dealer pays the end user a fixed rate.

 If the S&P 500 increases, the return is positive and the

end user pays that return to the dealer. If the S&P 500 goes down, its return is obviously negative. In that case, the end user would pay the dealer the negative return on the S&P 500, which means that it would receive that return from the dealer. So, the dealer could end up making both a fixed-rate payment and an equity payment.

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Equity swaps

 Example 2

 Suppose that the Vanguard Asset Allocation Fund

(NASDAQ: VAAPX) is authorized to use swaps. On the last day of December, it would like to sell $100 million in US large-cap equities and invest the proceeds at a fixed rate. It believes that a swap allowing it to pay the total return on the S&P 500, while receiving a fixed rate, would achieve this objective. It would like to hold this position for

• ne year, with payments made on the last day of

March, June, September, and December.

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Equity swaps

 Example 2

 VAAPX enters into such a swap with Morgan

Stanley (NYSE: MWD). Specifically, the swap covers a notional principal of $100 millions and calls for VAAPX to pay MWD the return on the S&P 500 Total Return Index and for MWD to pay VPAAPX a fixed rate on the last day of March, June, September, and December for one year. MWD prices the swap at a fixed rate of 6.5%. The fixed payments will be made using an actual day count/365 days convention.

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Equity swaps

 Example 2

 Fixed payments

 31 March: $100,000,000(0.065)(90/365) = $1,602,740  30 June: $100,000,000(0.065)(9/365) = $1,620,548  30 September: $100,000,000(0.065)(92/365) =

$1,638,356

 31 December: $100,000,000(0.065)(92/365) =

$1,638,356

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Equity swaps

 Example 2

 Suppose that on the day the swap is initiated, 31

December, the S&P 500 Total Return Index is at 3,517.76. Now suppose that on 31 March, the index is at 3,579.12.

 The return on the index is 3,579.12/3,517.76 – 1 =

0.0174 or 1.74%.

 The equity payment that VAAPX would make to MWD

would be $100,000,000(0.0174) = $1,740,000. This amount would not be known until 31 March, and only the difference between this amount and the fixed payment would be paid.

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Equity swaps

 Example 2

 Suppose that on 30 June, the index declines to

3,452.78.

 The return for the second quarter would be

3,452.78/3,579.12 – 1 = -0.0353 or -3.53%. This amount represents a loss of 3.53%, requiring a payment of $100,000,000(0.0353) = $3,530,000.

 MWD would make a payment to VAAPX. In addition,

MWD would also owe VAAPX the fixed payment of $1,620,548. It is as though VAAPX sold out of its position in stock, thereby avoiding the loss of about $3.5 million, and moved into a fixed-income position, thereby picking up a gain of about $1.6 million.

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Equity swaps

 Example 2

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Ne Net effect fect: VA VAAP APX X converts erts an eq equity ty positi tion

• n into a

fixed ed income me positi tion

• n.

VAAPX VAAPX MWD

Fixed ed rate of 6.5% Return n on S&P P 500 Total Return n Index ex Dividends dends and capital al gain

US larg rge e cap p stoc

• ck

Equity swaps

 Example 2

 It is important to note that the conversion of

VAAPX’s equity assets into fixed income is not

• perfect. VAAPX does not hold a portfolio precisely

equal to the S&P 500 Total Return Index. As an alternative, VAAPX can request that MWD give it a swap based on the precise portfolio that VAAPX wishes to sell off. In that case, however, MWD would assess a charge by lowering the fixed rate it pays or raising the rate VAAPX pays to it.

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Equity swaps

 Example 2

 Suppose instead that VAAPX does not want to

move the proceeds into a fixed-rate investment. VAAPX could structure a swap to pay it a floating rate or the return on some other equity index.

 For example, an asset allocation from US large-cap

stocks to US small-cap stocks could be accomplished by having MWD pay the return on the S&P 500 Small Cap 600 Index.

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Equity swaps

 Example 2

 Suppose VAAPX wanted to move out of a position

in US stocks and into a position in UK large-cap

• stocks. It could structure the swap to have MWD

pay it the return on the FTSE (Financial Times Stock Exchange) 100 Index.

 Note, however, that this index is based on the prices of

UK stocks as quoted in pounds sterling. If VAAPX wanted the exposure in pounds, the payments from MWD to VAAPX would be made in pounds. VAAPX could, however, ask for the payments in dollars.

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Commodity swaps and others

 Just as currencies, interest rates, and

equities can be used to structure swaps, so too can commodities and just about anything that has a random outcome and to which a corporation, financial institution, or even an individual is exposed.

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Commodity swaps and others

 Commodity swaps

 Example 1: Airlines enter into swaps to hedge

their future purchases of jet fuel. They agree to make fixed payments to a swap dealer on regularly scheduled dates and receive payments determined by the price of jet fuel.

 Example 2: Gold mining companies use swaps to

hedge future deliveries of gold.

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Commodity swaps and others

 Commodity swaps

 Example 3: Other parties dealing in such

commodities as natural gas and precious metals

• ften use swaps to lock in prices for future

purchases and sales.

 Example 4: Swaps can be based on non-storable

commodities, like electricity and the weather. In the case of weather, payments are made based

• n a measure of a particular weather factor, such

as amounts of rain, snowfall, or whether-related damage.

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Variations of swaps

 Basis swaps

 A typical basis swap involves one party paying

Libor and the other paying the T-bill rate.

 The term “basis” refers to the spread between two

prices, usually the spot and future prices. Here it is simply the spread between two rates, Libor and the T-bill rate.

 Because Libor is always more than the T-bill rate,

the two parties negotiate a fixed spread such that the party paying Libor actually pays Libor minus the spread (or the T-bill rate plus the spread).

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Variations of swaps

 Basis swaps

 Libor is the borrowing rate of high-quality London

banks, and the T-bill rate is the default-free borrowing rate of the US government. The difference between Libor and the T-bill rate is thus a reflection of investors’ perception of the general level of credit risk in the market.

 Basis swaps are usually employed for speculative

purposes by end users who believe the spread between Libor and the T-bill rate will change.

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Variations of swaps

 Constant maturity swaps

 In a constant maturity swap, one party pays a

fixed rate, or a short-term floating rate such as Libor, and the other party pays a floating rate that is the rate on a security known as a “constant maturity treasury (CMT)” security.

 CMT security, which is the underlying instrument

to this CMT swap, is a hypothetical US Treasury note, meaning that its maturity is in the 2- to 10- year range, with a constant maturity.

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Variations of swaps

 Constant maturity swaps

 The reference to a particular CMT cannot be

referring to a single note, because the maturity of any security decreases continuously. For example, for a two-year CMT security, when there is an actual two-year note, that note is the CMT

• security. Otherwise, the yield on a CMT security is

interpolated from the yields of securities with surrounding maturities.

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Variations of swaps

 Constant maturity swaps

 The distinguishing characteristic of a CMT swap is

that the maturity of the underlying security exceeds the length of the settlement period. For example, a CMT swap might call for payments every six months, with the rate based on the one- year CMT security. In contrast, a standard swap setting every six months would nearly always be based on a six-month security.

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Variations of swaps

 Overnight index swaps (OISs)

 An OIS commits one party to paying a fixed rate

as usual. The floating rate, however, is the cumulative value of a single unit of currency invested at an overnight rate during the settlement

• period. The overnight rate changes daily.

 Example

 Imagine Institution #1 has a $10 million loan that it is

paying interest on, and the interest is calculated based

• n the overnight rate.

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Variations of swaps

 Overnight index swaps (OISs)

 Example

 Institution #2, on the other hand, has a $10 million loan

that it is paying interest on, but the interest on this loan is based on a fixed, short-term rate of 2 percent.

 As it turns out, Institution #1 would much rather be

paying a fixed interest rate on its loan, and Institution #2 would much rather be paying a variable interest rate – based on the overnight rate – on its loan, but neither institution wants to go out and get a new loan and they can’t renegotiate the terms of their current loans. In this case, these two institutions could create an overnight index swap (OIS) with each other.

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Variations of swaps

 Amortizing and accreting swaps

 In these swaps, the notional principal changes

according to a formula related to the underlying.

 The more common of the two is the amortizing

swaps, sometimes called an “index amortizing swap”, in which the notional principal is indexed to the level of interest rates. The notional principal declines with the level of interest rates according to a predefined schedule.

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Variations of swaps

 Amortizing and accreting swaps

 This feature makes the amortizing swap similar to

certain asset-backed securities, such as mortgage-backed securities, which prepay some

• f their principal as rates fall. An index amortizing

swap is often used to hedge this type of security.

 An accreting swap, is an interest rate or currency

swap where the notional principal grows as it reaches maturity.

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Variations of swaps

 Amortizing and accreting swaps

 Also called accreting principal swap, accumulation

swap, construction loan, drawdown swap, and step-up swap.

 This swap may be used where the borrower

anticipates the need to draw down funds over a certain period of time but wants to fix the cost of the funds in advance. An example of a situation where an accreting swap might be sought, is to fix the costs in response to a project's funding requirements.

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Variations of swaps

 Diff swaps

 These swaps combine elements of interest rate,

currency, and equity swaps. In a typical diff swap,

• ne party pays the floating interest rate of one

country and the other pays the floating interest rate of another country. Both sets of payments, however, are made in a single currency.

 One set of payments is based on the interest rate

• f one currency, but the payment is made in the

currency of another country.

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Variations of swaps

 Diff swaps

 This swap is a pure play on the interest rate

differential between two countries and is basically a currency swap with the currency risk hedged. Alternatively, in equity diff swaps, the return on a foreign stock index is paid in the domestic currency.

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Variations of swaps

 Arrears swaps

 An arrears swap is a special type of interest rate

swap in which the floating payment is set at the end of the period and the interest is paid at that same time. This procedure stands in contrast to the typical interest rate swap, in which the payment is set on one settlement date and the interest is paid on the next settlement date.

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Variations of swaps

 Capped swaps

 In a capped swap, the floating payments have a

limit as to how high they can be.

 Floored swaps

 In a floored swap, the floating payments have a

limit on how low they can be.

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Swaptions

 A swaption

 An option to enter into a swap.

 A payer swaption

 A payer swaption allows the holder to enter into a

swap as the fixed-rate payer and floating-rate receiver.

 A receiver swaption

 A receiver swaption allows the holder to enter into

a swap as the fixed-rate receiver and floating-rate payer.

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Swaptions

 Other characteristics of swaptions

 Swaptions have specific expiration dates.  Swaptions can be European style (exercisable

• nly at expiration) or American style (exercisable

at any time prior to expiration).

 A swaption is based on a specific underlying

swap.

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Swaptions

 Example

 Consider a 2×5 European payer swaption that

expires in two years and allows the holder to enter into a three-year swap with semiannual payments every 15 January and 15 July.

 The payments will be made at the rate of 6.25%

and will be computed using the 30/360

• adjustment. The underlying swap is based on

Libor, and the notional principal is $10 million.

 A swaption has a price or premium, which is an

amount paid by the buyer to the seller up front.

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Swaptions

 Uses of swaptions

 Swaptions are used by parties who anticipate the

need for a swap at a later date, but would like to establish the fixed rate today, while providing the flexibility to not engage in the swap later or engage in the swap at a more favorable rate in the market.

 Swaptions are used by parties to speculate on

interest rates. Their prices move with interest rates, and like all options, they contain significant leverage.

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Swaptions

 Uses of swaptions

 Swaptions are used by parties entering into a

swap to give them the flexibility to terminate the swap.

 Example: Suppose a party in a swap is paying

fixed and receiving floating. If it owned a receiver swaption, it could exercise the swaption, thereby entering into a swap to receive a fixed rate and pay a floating rate. It would then have offset the floating parts

• f the swap, effectively removing any randomness from

the position. But the only way the party could do so would require having previously purchased a swaption.

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Swaptions

 Swaption payoffs

 Consider a European payer swaption that expires

in two years and is exercisable into a one-year swap with quarterly payments, using 90/360 as the day-count adjustment. The exercise rate is 3.60%. The notional principal is $20 million. Now suppose we are at the swaption expiration and the information on the term structure is as follows:

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Swaptions

 Swaption payoffs

 Under these conditions, the swap fixed payment is

0.0092, equating to an annual fixed rate of 3.68%.

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Maturity urity (day ays) Rate e (%) %) Disc scou

• unt

nt factor tor 90 3.45 0.9914 180 3.58 0.9824 270 3.70 0.9730 360 3.75 0.9639

Swaptions

 Swaption payoffs

 The holder of the swaption has the right to enter

into a swap to pay 3.60%, whereas in the market such a swap would require payment at a rate of 3.68%. Therefore, here at expiration, this swaption does appear to offer an advantage over the market rate.

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Swaptions

 Swaption payoffs

 Possible ways to exercise this swaption

 The holder can exercise the swaption, thereby entering

into a swap to pay 3.60%. The quarterly payment at the rate of 3.60% would be $20,000,000(0.0360)(90/360) = $180,000. The swaption holder would then be engaged in a swap to pay $180,000 quarterly and receive Libor. The first floating payment would be at 3.45% and would be $20,000,000(0.0345)(90/360) = $172,500. The remaining floating payments would, of course, be determined later. In particular, the second floating payment on day 180 would be determined on day 90.

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Swaptions

 Swaption payoffs

 Possible ways to exercise this swaption

 Alternatively, the holder can exercise the swaption,

thereby entering into a swap to pay 3.60%, and then enter into a swap in the market to receive fixed and pay

• floating. The fixed rate the holder would receive is

3.68%, the market-determined fixed rate at the time the swaption expires. The quarterly fixed payment at 3.68% would be $200,000,000(0.0368)(90/360) = $184,000. Technically, the Libor payments are still made, but the same amount is paid and received. Hence they are effectively offset.

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Swaptions

 Swaption payoffs

 Possible ways to exercise this swaption

 The holder can arrange to receive a net payment stream

• f $184,000 - $180,000 = $4,000. In this case, the

counterparty to the second swap is probably the same as the counterparty to the swap created by exercising the swaption, who would be the counterparty to the

• swaption. Because the floating payments are eliminated,

the amount of cash passing between the parties is reduced, which mitigates the credit risk.

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Swaptions

 Swaption payoffs

 Possible ways to exercise this swaption

 The holder can receive an up-front cash payment. We

can easily determined the amount. It is simply the present value of four payments ($4,000 each), which we can obtain using the discount factor shown in the previous table.

 4,000(0.9914 + 0.9824 + 0.9730 + 0.9639) = $15,643

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Swaptions

 Swaption payoffs

 Other than transaction costs and the credit risk

associated with the newly created swaps, each of these means of exercising a swaption has the same value. Of course, the two parties would have to agree up front which of these means to use at expiration. Cash settlement is the most common.

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Forward swaps

 Forward swaps are forward contracts to enter

into swaps. They are not as widely used as swaptions but do offer the advantage, as is always the case with forwards, that one does not have to pay any cash up front as with an

• ption premium.

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