CFA 2018 level 3 schweser practice exam CFA 2018 level 3 question bank CFA 2018 CFA 2018 r30 risk management applications of swap strategies IFT notes

Risk Management Applications of Swap Strategies

IFT Notes

Risk Management Applications of Swap Strategies
1. Introduction .............................................................................................................................................. 3
2. Strategies and Applications for Managing Interest Rate Risk ................................................................... 3
2.1. Using Interest Rate Swaps to Convert a Floating-Rate Loan to a Fixed-Rate Loan (and Vice Versa) 3
2.2. Using Swaps to Adjust the Duration of a Fixed-Income Portfolio ..................................................... 5
2.3. Using Swaps to Create and Manage the Risk of Structured Notes .................................................... 6
3. Strategies and Applications for Managing Exchange Rate Risk ................................................................ 6
3.1. Converting a Loan in One Currency into a Loan in another Currency ............................................... 6
3.2. Converting Foreign Cash Receipts into Domestic Currency............................................................... 9
3.3. Using Currency Swaps to Create and Manage the Risk of a Dual-Currency Bond ........................... 10
4. Strategies and Applications for Managing Equity Market Risk ............................................................... 10
4.1. Diversifying a Concentrated Portfolio .............................................................................................. 10
4.2. Achieving International Diversification ............................................................................................ 11
4.3. Changing an Asset Allocation between Stocks and Bonds .............................................................. 12
4.4. Reducing Insider Exposure ............................................................................................................... 14
5. Strategies and Applications Using Swaptions ......................................................................................... 14
5.1. Using an Interest Rate Swaption in Anticipation of a Future Borrowing ......................................... 14
5.2. Using an Interest Rate Swaption to Terminate a Swap ................................................................... 15
5.3. Synthetically Removing (Adding) a Call Feature in Callable (Noncallable) Debt ............................. 17
5.4. A Note on Forward Swaps................................................................................................................ 17
6. Conclusions ............................................................................................................................................. 17
Summary ..................................................................................................................................................... 18
Examples from the Curriculum ................................................................................................................... 20
Example 1 ................................................................................................................................................ 20
Example 2 ................................................................................................................................................ 21
Example 3 ................................................................................................................................................ 22
Example 4 ................................................................................................................................................ 22

Example 5 ................................................................................................................................................ 23
Example 6 ................................................................................................................................................ 24
Example 7 ................................................................................................................................................ 25
Example 8 ................................................................................................................................................ 25
Example 9 ................................................................................................................................................ 26

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Example 10 .............................................................................................................................................. 26
Example 11 .............................................................................................................................................. 27
Example12............................................................................................................................................... 27
Example 13 .............................................................................................................................................. 28
Example 14 .............................................................................................................................................. 29
This document should be read in conjunction with the corresponding reading in the 2018 Level III CFA®
Program curriculum. Some of the graphs, charts, tables, examples, and figures are copyright
2017, CFA Institute. Reproduced and republished with permission from CFA Institute. All rights reserved.
Required disclaimer: CFA Institute does not endorse, promote, or warrant the accuracy or quality of the
products or services offered by IFT. CFA Institute, CFA®, and Chartered Financial Analyst® are
trademarks owned by CFA Institute.

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1. Introduction
A swap is a transaction in which two parties agree to exchange a series of cash flows over a specific
period of time. At least one set of cash flows must be variable (not known at the beginning of the
transaction). The other set of cash flows can be either fixed or variable.
The main types of swaps that we will cover in this reading are:
 Interest rate swaps
 Currency swaps
 Equity swaps

2. Strategies and Applications for Managing Interest Rate Risk
2.1. Using Interest Rate Swaps to Convert a Floating-Rate Loan to a Fixed-Rate Loan (and Vice
Versa)
LO.a: Demonstrate how an interest rate swap can be used to convert a floating-rate (fixed-rate)
loan to a fixed-rate (floating-rate) loan
Most banks prefer to make floating rate loans, because they want to pass on interest rate risk to the
borrowers. Typically a borrower agrees to borrow at a floating rate, though the borrower prefers a fixed
rate. The borrower will then use a swap to convert its floating rate loan to a fixed rate loan.
Exhibit 1 demonstrates this scenario.

IBP borrows $25 million from a bank PLB at a floating rate of LIBOR + 3%.

To convert this loan to a fixed rate loan it enters into a swap with a dealer SPI. It will pay fixed rate of
6.27% to the dealer and in exchange will receive LIBOR from the dealer. The net effect is that IBP will
pay a fixed rate of 6.27% plus 3% i.e. 9.27%.

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Thus using a swap IBP was able to remove its interest rate exposure. It is important to note that by
doing this IBP is speculating on rising interest rates. If rates do go up, IBP will benefit from the swap.
However, if interest rates fall, IBP will not be able to take advantage of the falling rates.
Swaps can also be used to convert fixed rate loans to floating rate loans. This is illustrated in Example 1.
Refer to Example 1 from the curriculum.
Some important points to note are:
 A bank has issued a fixed rate loan and but wants to convert this to a floating rate loan.
 It can do so by entering a pay-fixed, receive-floating swap.
 If market rates go up that hurts the fixed rate lender as it will continues to receive the fixed rate
agreed at initiation of the loan.
 If the credit risk of the borrow goes up that will also hurt the fixed rate lender.
LO.b: Calculate and interpret the duration of an interest rate swap.
A pay-fixed, receive-floating swap is equivalent to issuing (going short) a fixed rate bond and using the
proceeds to buy (going long) a floating rate bond. Hence, the duration of a pay-fixed, receive-floating
swap is equal to the duration of a short position in a fixed-rate bond the duration of a long position in a

floating-rate bond and.
Consider a one-year pay-fixed, receive-floating swap with quarterly settlements. This swap can be
thought of as the combination of:
1. A long position in a one-year floating rate bond with quarterly payments AND
2. A short position in a one-year fixed rate bond with quarterly payments
If we can determine the duration of these two instruments the swap duration can easily be calculated.
Duration of a floating rate bond: The price of a floating rate bond (floater) typically does not drift much
from par value. On reset dates the price of a floater reverts to par value assuming there is no change in
credit risk. For this reason the interest risk or duration of a floater is low. Specifically it can be shown
that the duration of a floater is equal to half the time between reset dates. If a floater has reset dates
every quarter (i.e. every 0.25 years), the duration is approximately 0.25/2 = 0.125 years.
Duration of a fixed rate bond: The duration of a one-year zero coupon bond is 1 year. Now consider a 1year bond which makes a fixed coupon payment every quarter. Intuitively the duration of this bond will
be less than 1 but more than 0.5 because a large percentage of payments are being made at the end of
the year. It can be shown that the duration of such as bond is approximately 0.75 years. From the
perspective of an issuer (short position) the duration will be -0.75.
Given the above discussion, the duration of a one-year pay-fixed, receive-floating swap with quarterly
settlements = 0.125 – 0.75 = - 0.625.
Note that in general pay-fixed, receive-floating swaps will have a negative duration and pay-floating,
receive-fixed swaps will have a positive duration.

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2.2. Using Swaps to Adjust the Duration of a Fixed-Income Portfolio
Consider a scenario where a company controls a $500 million fixed-income portfolio that has a duration
of 6.75. It wants to reduce the portfolio duration to 3.5 by using swaps. The main questions that it faces
are:
1. Should the company use pay-fixed, receive floating swaps or pay-floating, receive fixed swaps?
2. What should be the terms of the swap?
3. What should be the notional principal?
Should the company use pay-fixed, receive floating swaps or pay-floating, receive fixed swaps?
To reduce the duration, we must add a negative-duration position. Hence, the swap should be pay-fixed
swap, receive-floating.
What should be the terms of the swap (maturity, payment frequency)?
The swap should have a maturity at least as long as the period during which the duration adjustment
applies. Otherwise the company would have to initiate another swap after the expiry of the first swap.
We know that the duration of a fixed rate bond is approximately 75% of its maturity. Hence:
 A one-year swap with semi-annual payments would have a duration of 0.25 – 0.75 = –0.50.
 A one-year swap with quarterly payments would have a duration of 0.125 – 0.75 = –0.625.
 A two-year swap with semiannual payments would have a duration of 0.25 – 1.50 = –1.25.
 A two-year swap with quarterly payments would have a duration of 0.125 – 1.50 = –1.375.
The different durations affects the notional principal required. Hence an appropriate payment frequency
can be chosen after the third question is answered.
LO.d: Determine the notional principal value needed on an interest rate swap to achieve a desired level
of duration in a fixed-income portfolio.
What should be the notional principal?
Suppose the company adds a position in a swap with a notional principal of NP and a modified duration
of MDURS. The NP can be calculated as:
3.50 − 6.75
𝑁𝑃 = $500,000,000(
)
𝑀𝐷𝑈𝑅𝑆

If the company uses a one-year swap with semiannual payments, then as calculated above its duration
would be -0.50. The required notional principal will be:
3.50 − 6.75
𝑁𝑃 = $500,000,000(
) = $3,250,000,000
−0.50
A notional principal of more than $3 billion would be a very large swap and probably too large to
execute.
If the company enters a five-year swap with semi-annual payments. Its duration would be 0.25 – 3.75 =
–3.50. Then the notional principal would be:

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3.50 − 6.75
𝑁𝑃 = $500,000,000(
) = $464,290,000
−3.50
Hence using a longer duration, gives us a much reasonable amount of notional principal.
In general, the notional principal of a swap necessary to change the duration of a bond portfolio worth B
from MDURB to a target duration, MDURT, is:
𝑀𝐷𝑈𝑅𝑇 − 𝑀𝐷𝑈𝑅𝐵

𝑁𝑃 = 𝐵(
)
𝑀𝐷𝑈𝑅𝑆
Refer to Example 2 from the curriculum.
LO.c: Explain the effect of an interest rate swap on an entity’s cash flow risk
By using swaps, cash flow risk is reduced because the uncertain future floating rate payments on loans
are essentially converted into fixed rate payments. These fixed payments can be more easily planned
for, resulting in the reduction of cash flow risk.

2.3. Using Swaps to Create and Manage the Risk of Structured Notes
(Note: This section is not explicitly mentioned in the learning objectives.)
Structured notes are short- or intermediate-term floating-rate securities that have some type of unusual
feature that distinguishes them from ordinary floating-rate notes. The unusual feature can be:
 Leverage, which results in the interest rate on the note moving at a multiple of market rates.
 Inverse floater, which means that the interest rate on the note moves opposite to the market
rates.
Important points to note are:
From the perspective of a party which issues the structured note:
 An interest rate swap can be used to manage the risk related to a structured note with a coupon
at a multiple of a floating rate by adjusting the notional principal on the swap to reflect the
coupon multiple for the structured note. The swap should be receive-floating, pay fixed swap.
 An interest rate can be used to manage the risk of the issuance of an inverse floating-rate note
by paying the floating rate to the swap dealer. When interest rates rise (fall), the inverse floater
payment decrease (increase) and this effect is passed on to the dealer, which in turn pays a fixed
rate.
Refer to Example 3 from the curriculum.
Refer to Example 4 from the curriculum.

3. Strategies and Applications for Managing Exchange Rate Risk
3.1. Converting a Loan in One Currency into a Loan in another Currency

LO.e: Explain how a company can generate savings by issuing a loan or bond in its own currency and
using a currency swap to convert the obligation into another currency

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Consider the following example from the curriculum. ROTEC is a British company which plans to expand
in Europe and needs euros. The options available to ROTEC are:



It could issue a euro-denominated bond, but it is not as well known in the euro market, hence its
cost of borrowing will be higher.
It could issue a pound-denominated bond and convert it to a euro-denominated bond using a
currency swap. This will lower its cost of borrowing.

Exhibit 4 illustrates this scenario:

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Panel A shows the flow of funds at the start of the transaction.
Panel B shows the interest payments and swap payments made each year.
Panel C shows the flow of funds at the end of the life of the swap and the maturity date of the bond.
A currency swap can be of the following types:
 Fixed-Fixed.
 Fixed-Floating.
 Floating-Fixed.

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

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Floating-Floating.

The example discussed above was a fixed-fixed swap. ROTECH could enter into a different swap to pay

fixed and receive floating or pay floating and receive fixed depending on its view of interest rates. If it
believes that interest rates are likely to fall it will choose floating rates. If it believes that interest rates
are likely to rise it will choose fixed rates.
Consider the swap discussed in Exhibit 4. Suppose that mid-way through the life of the swap, ROTECH
has a view that euro interest rates are going down. To act on this view, it could enter into a plain vanilla
interest rate swap in euros with SB or some other dealer. It would promise to pay the counterparty
interest in euros at a floating rate and receive interest in euros at a fixed rate. This transaction would
shift the euro interest obligation to floating. Exhibit 5 illustrates this scenario.

Refer to Example 5 from the curriculum.

3.2. Converting Foreign Cash Receipts into Domestic Currency
LO.f: Demonstrate how a firm can use a currency swap to convert a series of foreign cash receipts
into domestic cash receipts
If a company has foreign subsidiaries then it will regularly generate cash in foreign currencies. This cash
will be repatriated back in domestic currency on a regular basis. If these cash flows are predictable in
quantity, then by using a currency swap we can lock the rate at which they are converted.
Consider the example from the curriculum where a US based company COLS has a foreign subsidiary in
Japan. It converts income generated in Japan into US dollars four times a year. To lock in its conversion
rate for the entire year, it enters into a currency swap with a dealer USMULT. Through this swap COLS
will make fixed payments in Japanese yen and receive fixed payments in US dollars at a fixed exchange
rate. Exhibit 6 illustrates this scenario.

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Risks faced by COLS in the above swap are:
 Credit risk of the counterparty defaulting.
 Risk that its operations will not generate ¥300 million.
Refer to Example 6 from the curriculum.

3.3. Using Currency Swaps to Create and Manage the Risk of a Dual-Currency Bond
(Note: This section is not explicitly mentioned in the learning objectives.)
In a dual currency bond, the interest is paid in one currency and the principal is paid in another. Dual
currency bonds are equivalent to issuing an ordinary bond in one currency and combining it with a
currency swap with no principal payments.
Refer to Example 7 from the curriculum.

4. Strategies and Applications for Managing Equity Market Risk
LO.g: Explain how equity swaps can be used to diversify a concentrated equity portfolio, provide
international diversification to a domestic portfolio, and alter portfolio allocations to stocks and
bonds
This LO is covered in sections 4.1, 4.2 and 4.3

4.1. Diversifying a Concentrated Portfolio
Consider a scenario where a charitable organisation receives a large donation of a single stock. This
donation can result in a high degree of concentration. However, the charitable organization may be
constrained from selling the stock or may not wish to sell the stock. In such cases, to achieve

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diversification without selling the stock, equity swaps can be used.
Exhibit 8 illustrates this scenario.

A charitable organization CWF has received a large donation of ZYKT stock. To achieve diversification,
without selling the stock, it enters into an equity swap with a dealer CAPS. It would pay the returns on
the stock to the dealer and in return receive returns on the S&P index from the dealer.
A risk faced by CWF is that if ZYKT performs very well and S&P has negative returns, then it will incur a
huge cash outflow.
Refer to Example 8 from the curriculum.

4.2. Achieving International Diversification
Consider the example from the curriculum, where an organization USRM has $500 million invested in US
stocks. The appropriate benchmark for this portfolio is the Russell 3000 index. The organization wants to
invest 10% of its portfolio internationally. It can achieve this objective in the following ways:



Option 1: Sell $50 million and invest internationally. But transaction costs will be high.
Option 2: Enter into an equity swap. Transaction costs will be lower.

Exhibit 9 illustrates the second option.

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USRM enters into a swap with dealer AGB. It will pay the returns on Russell 3000 to the dealer and in
exchange receive returns on equity markets in Europe, Australia and the Far East (EAFE).
By using this swap risks faced by USRM are:
 If Russell 3000 outperforms EAFE then it will result in a negative cash flow.
 Tracking error: USRM’s domestic stock holding generates a return that will not match perfectly
the return on the Russell 3000.
Refer to Example 9 from the curriculum.

4.3. Changing an Asset Allocation between Stocks and Bonds
A combination of equity swaps and fixed income swaps can be used to change asset allocation.
Consider the example from the curriculum, where an investment management firm TMM wants to
change its asset allocation. The table below shows the current position and the desired position and the
transactions required to go from current position to the desired position.

Stock

Current
($150 Million, 75%)

New
($180 Million, 90%)

Transaction

Large cap

$90 million (60%)

$117 million (65%)

Buy $27 million

Mid cap

$45 million (30%)

$45 million (25%)

None

Small cap

$15 million (10%)

$18 million (10%)

Buy $3 million

Bonds

Current
($50 Million, 25%)

New
($20 Million, 10%)

Transaction

Government

$40 million (80%)

$15 million (75%)

Sell $25 million

Corporate

$10 million (20%)

$5 million (25%)

Sell $5 million

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To avoid transaction costs, instead of executing these transactions, TMM can execute a series of swaps
that would provide the same results.
The swaps required are:
Equity swaps
Receive return on S&P500 on $27 million
Pay Libor on $27 million
Receive return on SPSC on $3 million
Pay Libor on $3 million
Fixed-income swaps
Receive Libor on $25 million
Pay return on LLTB on $25 million
Receive Libor on $5 million
Pay return on MLCB on $5 million
By eliminating LIBOR and by combining the equity and fixed income swaps, we get a single swap with
the following payments.
Receive return on SP500 on $27 million
Receive return on SPSC on $3 million
Pay return on LLTB on $25 million
Pay return on MLCB on $5 million
Exhibit 10 illustrates this swap.

As discussed in earlier sections, by using this swap, risks faced by TMM are:
 Negative cash flow risk.

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

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Tracking error risk

Refer to Example 10 from the curriculum.

4.4. Reducing Insider Exposure
(Note: This section is not explicitly covered in the learning objectives.)
The founders of a company usually have a highly concentrated position in the stock of the company. To
achieve diversification without selling the company stock they can use equity swaps.
Refer to Example 11 from the curriculum.

5. Strategies and Applications Using Swaptions
LO.g: Explain how equity swaps can be used to diversify a concentrated equity portfolio, provide
international diversification to a domestic portfolio, and alter portfolio allocations to stocks and
bonds
This LO is covered in sections 5.1 and 5.2.
A swaption is an option to enter into a swap. It is like an interest rate option because it has an exercise
rate. For example: You have an option to enter into a three-year swap with semi-annual payments with
an exercise rate of 7%.

There are two types of swaptions:
1. A payer swaption allows the holder to enter a swap as a fixed rate payer.
2. A receiver swaption allows the holder to enter a swap as a fixed rate receiver.

5.1. Using an Interest Rate Swaption in Anticipation of a Future Borrowing
Consider a scenario where a company anticipates that it will take out a loan at a future date. The
company expects that the bank will require it to be a floating rate loan. To eliminate interest rate risk it
will use a swap to convert this loan into a fixed rate loan. If the company wants to enter into the swap at
an attractive rate, it can use a swaption.
Exhibit 12 illustrates this scenario. Company BCHEM wants to borrow in the future at a floating rate
from bank ANB. It wants to enter into a swap to pay fixed rate if the rates are attractive. To do so it buys
a swaption from dealer DTD.
In Panel A the company pays the dealer, the swaption premium. In Panel B, we examine what happens
starting when the swaption expires one year later. In part (i) of Panel B we assume that at expiration of
the swaption, the rate in the market on the underlying swap, is greater than the swaption exercise rate.
The swaption will therefore be exercised. The company will make fixed payments to the dealer and in
return will receive floating payments form the dealer. These floating payments will be used to offset its
floating payment to the bank.
In Part (ii) of Panel B, at expiration of the swaption, the rate in the market on the underlying swap is less
than or equal to the swaption exercise rate. The swaption will therefore not be exercised. The company
will still enter into a swap with the dealer, but it will do so at the lower market rate.

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Exhibit 12

Thus by using a swaption the company has obtained the right to pay a fixed rate of 7% or less. However,
this comes at a cost in the form of the premium. Whether it was worth paying this premium will depend
on how far the market ended above 7% at the time the loan was taken out.
Refer to Example 12 from the curriculum.

5.2. Using an Interest Rate Swaption to Terminate a Swap
Two possible strategies for early termination of a swap: enter an offsetting swap and buy a swaption.
Consider this example. Internet Marketing Solutions (IMS) takes out a $20 million one-year loan with

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quarterly floating payments at Libor from a lender called Financial Solutions (FINSOLS). Fearing an
increase in interest rates, IMS engages in a pay-fixed, receive-floating swap that converts the loan into a
fixed-rate loan at 8 percent. IMS believes, however, that the interest rate outlook could change, and it
would like the flexibility to terminate the swap, thereby returning to the status of a floating-rate payer.
To give it this flexibility, IMS purchases an American-style receiver swaption for $515,000. The swaption

allows it to enter into a receive-fixed, pay-floating swap at a fixed rate of 8 percent at the swaption
expiration. The swap and swaption counterparty is Wheatstone Dealer (WHD). Exhibit 13 illustrates this
scenario.

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In Panel A, IMS takes out the loan from FINSOLS. It engages in the swap with WHD, thereby committing
to pay fixed and receive Libor. IMS pays WHD $515,000 for the swaption.
In Panel B(i), at the expiration of the swaption, the market swap rate is greater than or equal to 8
percent. This panel shows the cash flows if the loan plus swap (note that the loan is floating rate) is
converted to a fixed rate using the market fixed rate because the swaption is out-of-the-money.
In Panel B(ii), the market swap rate is less than 8 percent and the loan is converted back to a floatingrate loan by exercising the swaption.
From the above example we can see that the swaption offers the holder the opportunity to terminate
the swap at the exercise rate or better.
Refer to Example 13 from the curriculum.

5.3. Synthetically Removing (Adding) a Call Feature in Callable (Noncallable) Debt
(Note: This section is not explicitly mentioned in the learning objectives.)
The core points are:
 We can sell a receiver swaption to offset the call feature on a bond.
 We can buy a receiver swaption to add a call feature to a bond.

Refer to Example 14 from the curriculum.

5.4. A Note on Forward Swaps
(Note: This section is not explicitly mentioned in the learning objectives.)
The core point is: Forward contracts on swaps do exist. These are called forward swaps.

6. Conclusions
We can use interest rate swaps to:
 Covert floating rate loan to fixed rate loan.
 Adjust duration on a fixed income portfolio.
We can use currency swaps to:
 Convert loan from one currency to another.
 Convert foreign currency receipts to domestic currency.
We can use equity swaps to:
 Diversify concentrated portfolio.
 Achieve international diversification.
 Change an asset allocation between stocks and bonds.
We can use swaptions to:
 Change payment pattern of anticipated future loan.
 Terminate a swap.

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Summary
a. demonstrate how an interest rate swap can be used to convert a floating-rate (fixed-rate) loan to a
fixed-rate (floating-rate) loan;
Swaps can also be used to convert fixed rate loans to floating rate loans. For example,

b. calculate and interpret the duration of an interest rate swap;




Duration of a floater is equal to half the time between reset dates. If a floater has reset dates every
quarter (i.e. every 0.25 years), the duration is approximately 0.25/2 = 0.125 years.
Duration of a 1-year bond which makes a fixed coupon payment every quarter is approximately 0.75
years.
The duration of a one-year pay-fixed, receive-floating swap with quarterly settlements = 0.125 –
0.75 = - 0.625.
 Pay-fixed, receive-floating swaps will have a negative duration.
 Pay-floating, receive-fixed swaps will have a positive duration.

c. explain the effect of an interest rate swap on an entity’s cash flow risk;
By using swaps, cash flow risk is reduced because the uncertain future floating rate payments on loans
are essentially converted into fixed rate payments. These fixed payments can be more easily planned
for, resulting in the reduction of cash flow risk.
d. determine the notional principal value needed on an interest rate swap to achieve a desired level of
duration in a fixed-income portfolio;
Notional principal of swap = Portfolio value * (Target duration – Original duration) / Swap duration
Consider a scenario where a company controls a $500 million fixed-income portfolio that has a duration
of 6.75. We want to reduce the duration to 3.50 using a five-year swap with semiannual payments. Since

we want to reduce the duration we should use a pay fixed receive floating swap.
For a five-year pay fixed receive floating swap the duration is -5*0.75 + 0.25 = -3.50
Notional principal of swap = 500 million * (3.50 – 6.75) / (3.50) = 464,290,000
e. explain how a company can generate savings by issuing a loan or bond in its own currency and using a
currency swap to convert the obligation into another currency;

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Currency Swaps
If a company needs to borrow a foreign currency, it can generate savings by issuing a loan or bond in its
own currency and using a currency swap to convert the obligation into another currency.
Example: ROTEC is a British company which plans to expand in Europe and needs euros. The options
available to ROTEC are:
 It could issue a euro-denominated bond, but it is not as well known in the euro market, hence its
cost of borrowing will be higher.
 It could issue a pound-denominated bond and convert it to a euro-denominated bond using a
currency swap. This will lower its cost of borrowing.
f. demonstrate how a firm can use a currency swap to convert a series of foreign cash receipts into
domestic cash receipts;






If a company has foreign subsidiaries then it will regularly generate cash in foreign currencies. This
cash will be repatriated back in domestic currency on a regular basis. If these cash flows are
predictable in quantity, then by using a currency swap we can lock the rate at which they are
converted
Example: A US-based company, COLS, has a foreign subsidiary in Japan. It converts income
generated in Japan into US dollars four times a year. To lock in its conversion rate for the entire
year, it enters into a currency swap with a dealer USMULT. Through this swap COLS will make fixed
payments in Japanese yen and receive fixed payments in US dollars at a fixed exchange rate.
Risks faced by COLS:
 Credit risk of the counterparty defaulting.
 Risk that its operations will not generate ¥300 million.

g. explain how equity swaps can be used to diversify a concentrated equity portfolio, provide
international diversification to a domestic portfolio, and alter portfolio allocations to stocks and bonds;






Equity swaps can be used to diversify a concentrated equity portfolio, provide international
diversification to a domestic portfolio, and alter portfolio allocations to stocks and bonds.
Strategy for diversifying a concentrated Portfolio: By using an equity swap, the concentrated
portfolio return can be swapped for diversified portfolio return e.g. swapping return on 30 stocks for
return on index i.e. S&P 500.
Strategy for achieving international Diversification: By using an equity swap, domestic return can

be swapped for international portfolio return e.g. swapping return on S&P for return on EAFE index.
Strategy for changing asset allocation: By using an equity swap, small-cap equity can be swapped
for large-cap equity or equity can be swapped for debt.

h. demonstrate the use of an interest rate swaption 1) to change the payment pattern of an anticipated
future loan and 2) to terminate a swap.



A swaption is an option to enter into a swap. It is like an interest rate option because it has an
exercise rate.
There are two types of swaptions:

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1. A payer swaption allows the holder to enter a swap as a fixed rate payer.
2. A receiver swaption allows the holder to enter a swap as a fixed rate receiver.




Using interest rate swaption to change the payment pattern of an anticipated future loan: A
swaption gives the flexibility to the buyer of the swaption to enter into the swap at an attractive
rate. For example, if a firm plans to borrow in the future at floating rate, it can offset its risk of rising
interest rates by buying a payer swaption i.e.
 When fixed rate in the market at swaption expiration > exercise rate of swaption, a firm can
exercise the payer swaption.
 When fixed rate in the market at swaption expiration < exercise rate of swaption, a firm does
not exercise the payer swaption; rather, it can enter into a swap at a market rate.
Using interest rate swaption to terminate a swap: There are two ways to terminate an existing
swap:
i.
By entering an offsetting swap:
ii.
By buying a swaption.
a) When interest rates are expected to fall, a borrower should use receiver swaption to
convert its pay-fixed position to a pay-floating position.
b) When interest rates are expected to rise, a borrower should use payer swaption to convert
its pay-floating position to a pay-fixed position.

Examples from the Curriculum
Example 1
Consider a bank that holds a $5 million loan at a fixed rate of 6 percent for three years, with quarterly
payments. The bank had originally funded this loan at a fixed rate, but because of changing interest rate
expectations, it has now decided to fund it at a floating rate. Although it cannot change the terms of the
loan to the borrower, it can effectively convert the loan to a floating-rate loan by using a swap. The fixed
rate on three-year swaps with quarterly payments at Libor is 7 percent. We assume the number of days
in each quarter to be 90 and the number of days in a year to be 360.
A. Explain how the bank could convert the fixed-rate loan to a floating-rate loan using a swap.
B. Explain why the effective floating rate on the loan will be less than Libor.
Solution to A:

The interest payments it will receive on the loan are $5,000,000(0.06)(90/360) = $75,000. The bank
could do a swap to pay a fixed rate of 7 percent and receive a floating rate of Libor. Its fixed payment
would be $5,000,000(0.07)(90/360) = $87,500. The floating payment it would receive is
$5,000,000L(90/360), where L is Libor established at the previous reset date. The overall cash flow is
thus $5,000,000(L – 0.01)(90/360), Libor minus 100 basis points.
Solution to B:
The bank will effectively receive less than Libor because when the loan was initiated, the rate was 6
percent. Then when the swap was executed, the rate was 7 percent. This increase in interest rates hurts

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the fixed-rate lender. The bank cannot implicitly change the loan from fixed rate to floating rate without
paying the price of this increase in interest rates. It pays this price by accepting a lower rate than Libor
when the loan is effectively converted to floating. Another factor that could contribute to this rate being
lower than Libor is that the borrower’s credit risk at the time the loan was established is different from
the bank’s credit risk as reflected in the swap fixed rate, established in the Libor market when the swap
is initiated.
Back to Notes.

Example 2
A $250 million bond portfolio has a duration of 5.50. The portfolio manager wants to reduce the

duration to 4.50 by using a swap. Consider the possibility of using a one-year swap with monthly
payments or a two-year swap with semiannual payments.
A. Determine the durations of the two swaps under the assumption of paying fixed and receiving
floating. Assume that the duration of a fixed-rate bond is 75 percent of its maturity.
B. Choose the swap with the longer absolute duration and determine the notional principal of the
swap necessary to change the duration as desired. Explain your results.
Solution to A:
The duration of a one-year pay-fixed, receive-floating swap with monthly payments is the duration of a
one-year floating-rate bond with monthly payments minus the duration of a one-year fixed-rate bond
with monthly payments. The duration of the former is about one-half of the length of the payment
interval. That is 1/24 of a year, or 0.042. Because the duration of the one-year fixed-rate bond is 0.75
(75 percent of one year), the duration of the swap is 0.042 – 0.75 = –0.708.
The duration of a two-year swap with semiannual payments is the duration of a two-year floating-rate
bond with semiannual payments minus the duration of a two-year fixed-rate bond. The duration of the
former is about one-quarter of a year, or 0.25. The duration of the latter is 1.50 (75 percent of two
years). The duration of the swap is thus 0.25 – 1.50 = –1.25.
Solution to B:
The longer (more negative) duration swap is the two-year swap with semiannual payments. The current
duration of the $250 million portfolio is 5.50 and the target duration is 4.50. Thus, the required notional
principal is
𝑀𝐷𝑈𝑅𝑇 − 𝑀𝐷𝑈𝑅𝐵
𝑁𝑃 = 𝐵 (
)
𝑀𝐷𝑈𝑅𝑆
4.50 − 5.50
= $250,000,000(
) = $200,000,000
−1.25
So, to lower the duration requires the addition of an instrument with a duration lower than that of the
portfolio. The duration of a receive-floating, pay-fixed swap is negative and, therefore, lower than that

of the existing portfolio.

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Back to Notes.

Example 3
A company issues a floating-rate note that pays a rate of twice Libor on notional principal FP. It uses the
proceeds to buy a bond paying a rate of ci. It also enters into a swap with a fixed rate of FS to manage
the risk of the Libor payment on the leveraged floater.
A. Demonstrate how the company can engage in these transactions, leaving it with a net cash flow
of 2(FP)(ci – FS).
B. Explain under what condition the amount (ci – FS) is positive.
Solution to A:
The company has issued a leveraged floater at a rate of 2L on notional principal FP. Then it should
purchase a bond with face value of 2(FP) and coupon ci. It enters into a swap to pay a fixed rate of FS
and receive a floating rate of L on notional principal 2(FP). The net cash flows are as follows:
From leveraged floater

–2L(FP)

From bond

+(ci)2(FP)

Floating side of swap

+(L)2(FP)

Fixed side of swap

–(FS)2(FP)

Total

2FP(ci – FS)

Solution to B:
The difference between the bond coupon rate, ci, and the swap fixed rate, FS, will be positive if the
bond has greater credit risk than is implied by the fixed rate in the swap, which is based on the Libor
term structure and reflects the borrowing rate of London banks. Thus, the gain of 2(ci – FS)(FP) is likely
to reflect a credit risk premium.
Back to Notes.

Example 4
A company issues an inverse floating-rate note with a face value of $30 million and a coupon rate of 14
percent minus Libor. It uses the proceeds to buy a bond with a coupon rate of 8 percent.
A. Explain how the company would manage the risk of this position using a swap with a fixed rate
of 7 percent, and calculate the overall cash flow given that Libor is less than 14 percent.
B. Explain what would happen if Libor exceeds 14 percent. What could the company do to offset
this problem?

Solution to A:
The company would enter into a swap in which it pays Libor and receives a fixed rate of 7 percent on
notional principal of $30 million. The overall cash flows are as follows:

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From the inverse floater

– (0.14 – L)$30,000,000

From the bond it buys

+ (0.08)$30,000,000

IFT Notes

From the swap
Fixed payment

+ (0.07)$30,000,000

Floating payment

– (L)$30,000,000

Overall total

+ (0.01)$30,000,000

Solution to B:
If Libor is more than 14 percent, then the inverse floater payment of (0.14 – L) would be negative. The
lender would then have to pay interest to the borrower. For this reason, in most cases, an inverse
floater has a floor at zero. In such a case, the total cash flow to this company would be (0 + 0.08 + 0.07 –
L)$30,000,000. There would be zero total cash flow at L = 15 percent. But at an L higher than 15 percent,
the otherwise positive cash flow to the lender becomes negative.
To offset this effect, the lender would typically buy an interest rate cap with an exercise rate of 14
percent. The cap would have caplets that expire on the interest rate reset dates of the swap/loan and
have a notional principal of $30 million. Then when L > 0.14, the caplet would pay off L – 0.14 times the
$30 million. This payoff would make up the difference. The price paid for the cap would be an additional
cost.
Back to Notes.

Example 5
A Japanese company issues a bond with face value of ¥1.2 billion and a coupon rate of 5.25 percent. It
decides to use a swap to convert this bond into a euro-denominated bond. The current exchange rate is
¥120/€. The fixed rate on euro-denominated swaps is 6 percent, and the fixed rate on yen-denominated
swaps is 5 percent. All payments will be made annually, so there is no adjustment such as Days/360.
A. Describe the terms of the swap and identify the cash flows at the start.
B. Identify all interest cash flows at each interest payment date.
C. Identify all principal cash flows at the maturity of the bond.
Solution to A:
The company will enter into a swap with notional principal of ¥1,200,000,000/(¥120/€1) = €10,000,000.
The swap will involve an exchange of notional principals at the beginning and end. The annual cash flows

will involve paying euros and receiving yen. The following cash flows occur at the start:
From issuance of yen bond

+ ¥1,200,000,000

From swap

– ¥1,200,000,000
+ €10,000,000

Net

+ €10,000,000

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Solution to B:
The following cash flows occur at the annual interest payment dates:
Interest payments on bond

(¥1,200,000,000)(0.0525) = – ¥63,000,000

Swap payments
Yen
Euro
Net

+ (¥1,200,000,000)(0.05) = + ¥60,000,000
– (€10,000,000)(0.06) = – €600,000
– ¥3,000,000 – €600,000

Solution to C:
The following cash flows occur at the end of the life of the swap:
Principal repayment on bond

– ¥1,200,000,000

Swap principal payments
Yen

+ ¥1,200,000,000

Euro

– €10,000,000

Net

– €10,000,000

Back to Notes.

Example 6
A Canadian corporation with a French subsidiary generates cash flows of €10 million a year. It wants to
use a currency swap to lock in the rate at which it converts to Canadian dollars. The current exchange
rate is C$0.825/€. The fixed rate on a currency swap in euros is 4 percent, and the fixed rate on a
currency swap in Canadian dollars is 5 percent.
A. Determine the notional principals in euros and Canadian dollars for a swap with annual
payments that will achieve the corporation’s objective.
B. Determine the overall periodic cash flow from the subsidiary operations and the swap.
Solution to A:
With the euro fixed rate at 4 percent, the euro notional principal should be
€10,000,000/0.04=€250,000,000
The equivalent Canadian dollar notional principal would be €250,000,000 × C$0.825 = C$206,250,000.
Solution to B:
The cash flows will be as follows:
From subsidiary operations

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Swap euro payment

–0.04(€250,000,000) = –€10,000,000

Swap Canadian dollar payment

0.05(C$206,250,000) = C$10,312,500

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The net effect is that the €10 million converts to C$10,312,500.
Back to Notes.

Example 7
From the perspective of the issuer, construct a synthetic dual-currency bond in which the principal is
paid in US dollars and the interest is paid in Swiss francs. The face value will be $20 million, and the
interest rate will be 5 percent in Swiss francs. The exchange rate is $0.80/SF. Assume that the
appropriate interest rate for a $20 million bond in dollars is 5.5 percent. The appropriate fixed rates on a
currency swap are 5.5 percent in dollars and 5.0 percent in Swiss francs.
Solution:
Issue a $20 million bond in dollars, paying interest at 5.5 percent. Enter into a currency swap on $20
million, equivalent to SF25 million. The currency swap will involve the receipt of dollar interest at 5.5
percent and payment of Swiss franc interest at 5.0 percent. You will receive $20 million at the start and
pay back $20 million at maturity. The annual cash flows will be as follows:
On dollar bond issued:

– 0.055($20,000,000) =

– $1,100,000

Dollars

+ 0.055($20,000,000) =

+ $1,100,000

Swiss francs

– 0.05(SF25,000,000) =

– SF1,250,000

On swap:

Net

– SF1,250,000

Back to Notes.

Example 8
The manager of a charitable foundation’s $50 million stock portfolio is concerned about the portfolio’s
heavy concentration in one stock, Noble Petroleum (NBP). Specifically, the fund has $20 million of this
stock as a result of a recent donation to the fund. She is considering using an equity swap to reduce the
exposure to NBP and allow the fund to invest indirectly in the Wilshire 5000 Index. The stock is currently
selling for $20 a share, and the fund owns 1 million shares. The manager is not quite ready to reduce all
of the fund’s exposure to NBP, so she decides to synthetically sell off one-quarter of the position.
Explain how she would do this and identify some problems she might encounter.
Solution:
To reduce her exposure on one quarter of her NBP holdings, the manager would have the fund enter
into a swap to sell the total return on $5 million of NBP stock, which is 250,000 shares. The fund will
receive from the swap dealer the return on $5 million invested in the Wilshire 5000.

The swap may result in cash flow problems, however, because the fund must pay out the return on
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