Thus, duration of a swap is: Duration of receive-fixed and pay-floating swap = duration of a long position in a fixed rate bond – duration of a short position in a floating rate bond >
Trang 1Reading 30 Risk Management Applications of Swap Strategies
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Swaps are contractual agreements that are used to
exchange or swap a series of cash flows over a specific
period of time e.g interest payments in floating-rate
loans
Characteristics:
flows must be variable; the other set of cash flows
can be fixed or variable
•Swap is similar to a series of forward contracts
•It has zero market value at initiation
exchange of money at the start
Types of swaps:
party pays fixed interest rate payments and other
party pays floating interest rate payments in
exchange or when both parties pay floating-rate
payments When both parties pay floating rates then
floating rates are different
•Interest rate swaps have less credit risk relative to
ordinary loans because interest payments are
netted and there is no exchange of notional
principal
reduces the credit risk but it does not prevent the
LIBOR component of the net swap payment from
offsetting the floating loan interest payment
debt service obligation i.e one party make payments
in one currency and the other party makes payments
in another currency
payments is based on the return of a stock price or
stock index
least one set of payments is based on the course of a
commodity price i.e price of oil or gold
Uses of swaps:
an asset or liability i.e by converting a fixed-rate
loan into a floating-rate loan or vice versa
i.e investors can enter into a swap instead of investing in a security
interest rate risk
Limitation: Swaps involve credit risk i.e risk that counterparty may default on the exchange of the
interest payments
Comparison: Financial Futures, FRAs, and Basic Swaps
Position Objective Financial Futures FRAs& Basic Swaps Profit if Rates
Rise
Receive Floating Profit If Rates
Fall
Received Fixed Example:
Company A has a commitment to borrow at a fixed rate
of 5.2% and company B has a commitment to borrow at
a floating rate of LIBOR + 0.8% Both companies enter into a swap contract i.e
rate of 5% per annum on a notional principal of
$100 million
6-month LIBOR rate on $100 million notional principal
liability to a floating rate liability for A and vice-versa for B
Generally, swaps are not used to manage the risk
associated with anticipated debt payments; rather, they
are used to manage the risk on a series of debt
obligations that either already exists or is in the process
of being taken out
2.1
Using Interest Rate Swaps to Convert a Floating-Rate Loan to a Fixed-Floating-Rate Loan (and Vice
Versa) Borrowers prefer to use swaps to manage their interest rate exposure However, swaps involve taking a speculative position i.e when floating rate loan is
Trang 2converted to a fixed rate loan and if rates fall, borrower
will not be able to take advantage of falling interest
rates as he/she is locked in to a synthetic fixed-rate loan
Structure of Swaps:
A fixed rate on a swap is determined such that the PV of
the two payment streams (fixed & floating)are equal
The floating rates on the swap are set corresponding to
the dates on which the loan interest rate is reset
The notional principal on the swap is set equal to the
face value of the loan
NOTE:
Payment at a rate of LIBOR is determined by using a rate
that was established at the previous settlement date or
the beginning of the swap if this is the first settlement
period
Duration of Swap:
Floating rate bond’s duration ≈ Amount of time
remaining until the next coupon payment E.g
For a bond with quarterly payments:
Duration of fixed-rate bonds is between 0.6 and 1.0 and
is assumed to equal 75% of its maturity for the purposes
of this reading
Example:
One year (receive floating, pay fixed) swap with
semi-annual payments will have duration =
- (0.75 × maturity of swap contract)
=
× - (0.75 × 1) = 0.25 – 0.75 = -0.50
One year (receive floating, pay fixed) swap with
× - (0.75 × 1)
= 0.125 – 0.75 = –0.625
Two year swap (receive floating, pay fixed) with
× - (0.75 × 2) = 0.25 – 1.50 = -1.25
Two year swap (receive floating, pay fixed) with
×–(0.75 × 2)
= 0.125 – 1.50 = –1.375
NOTE:
Issuer has negative duration and lender/investor has
positive duration
similar to issuing a fixed-rate bond and using the proceeds to buy a floating rate bond Thus, duration of a swap is:
Duration of receive-floating and pay-fixed swap = duration of a long position in a floating rate bond – duration of a short position in a fixed rate bond < 0
similar to issuing a floating-rate bond and using the proceeds to buy a fixed rate bond Thus, duration
of a swap is:
Duration of receive-fixed and pay-floating swap = duration of a long position in a fixed rate bond – duration of a short position in a floating rate bond
> 0
Thus, Receive fixed rate swaps increases the duration of an existing position
Pay fixed swaps decreases the duration of an existing position
When floating rate loan is converted to fixed rate loan:
with variable interest rate in case of floating payments decreases
• Market risk rises*
When fixed rate loan is converted to floating rate loan:
associated with variable interest rate in case of floating payments rises
positive duration position
*Market value risk refers to uncertainty associated with the market value of an asset or liability, due to change in interest rates i.e when interest rates rise (fall), value of assets or liability decreases (increases)
floating rate assets and fixed-rate liabilities are preferred because when interest rate ↑, CFs on floating-rate assets ↑ whereas payments on fixed-rate liabilities do not change
fixed rate assets and floating-rate liabilities are preferred
Cash flow risk refers to the uncertainty associated with the size of the cash flows
For example, floating-rate instruments have cash flow risk because their cash flows are adjusted according to changes in interest rates These securities are not subject
to market value risk
Trang 32.2 Using Swaps to adjust the Duration of a Fixed-Income Portfolio
Duration is affected by the maturity and payment
frequency of the swap When a swap maturity is
different from the maturity of a bond e.g swap expires
before the maturity of a bond, investor needs to initiate
another swap Therefore, the most preferred approach is
to use the swap with a maturity at least equal to the
period during which the duration adjustment is applied
The following formula is used to estimate the notional
principal of a swap that is used to manage the duration
(interest risk) of a portfolio:
where,
NP= notional principal
MD target = target or desired market duration
MD B = current market duration of portfolio
MD swap = market duration of a swap
NOTE:
Different durations affect the notional principal required
2.3 Using Swaps to Create and Manage the Risk of Structured Notes
Structured notes are short-term or intermediate-term
floating rate securities financial instruments that qualify
as fixed income instruments, but they contain features
similar to options, swaps, and margin transactions
Uses of Structured notes:
Structured notes are used by investors (e.g insurance
companies and pension funds) to add exposure in their
portfolios to those asset classes or markets in which they
are prohibited to invest directly due to investment
mandates and regulatory constraints
2.3.1) Using Swaps to create and manage the risk of
Leveraged Floating-Rate Notes
A leveraged floating rate note or leveraged floater is a
type of leveraged structured note In a leveraged
floater, the coupon is a multiple of a specific market rate
of interest (i.e LIBOR) e.g
Coupon rate = 1.5 × LIBOR
Example:
A firm XYZ issues a leveraged floating rate note or leveraged floater with following features to company ABC:
• Principal = FP
Firm XYZ used those proceeds to buy a fixed-rate bond issued by Company A This bond will have:
Firm XYZ enters into a swap contract as a fixed rate payer and floating rate receiver
• Fixed rate = FS
• Floating-rate = LIBOR Thus, net cash flows are as follows:
Firm XYZ will pay on the leveraged floater = –1.5 (LIBOR)
(FP)
Firm XYZ will receive from the bond = + ci (1.5) (FP) Firm XYZ will receive from the swap as Floating rate
receiver = + 1.5 (LIBOR) (FP)
Firm XYZ will pay as a Fixed rate payer in a swap =
–1.5 (FS) (FP)
Net effect: XYZ earns = 1.5 (ci – FS) (FP) fixed if the interest rate received on the fixed rate exceeds the swap rate
Advantage: No capital is needed to engage in this sort
of transaction because cost of buying a fixed rate bond will be financed by the proceeds from issuing the structured note
Risks involve:
Firm XYZ has to assume some credit risk i.e risk of default
by Company A as well as the risk of default by the swap counterparty
2.3.2) Using Swaps to Create and Manage the risk of
Inverse Floaters Inverse Floater is another type of structured note In inverse floater,
Coupon rate = b – LIBOR
Practice: Example 3, Volume 5, Reading 30
Practice: Example 2,
Volume 5, Reading 30
Practice: Example 1,
Volume 5, Reading 30
Trang 4Example:
Company A issues an inverse floater that pays rate = b –
LIBOR and has a notional principal = FP
• When LIBOR > b, rate = -ve
Company A uses proceeds from issuing an inverse
floater to buy a fixed-rate note with a notional principal
of FP and coupon rate of ci × (FP)
Company A then enters into a swap contract as
receive-fixed, pay-floating to match the structured note
i.e
• It receives fixed rate = + FS × (FP)
• It pays floating rate = - LIBOR × (FP)
Thus, net cash flows are as follows:
Company A pays on the inverse floater = –(b – LIBOR)×
(FP)
Company A receives from the fixed-rate bond =
+ ci × (FP)
Company A receives fixed rate = + FS (FP)
Company A pays floating rate = - LIBOR × (FP)
Overall cash flow to Company A will be positive when b
< (FS + ci) i.e
larger its cash flows from the overall transactions
note will be for potential investors
inverse floater, company A should set value of “b”
at a reasonably high level but below FS + ci
to set “b” It cannot set FS and ci because ci is based on both the level of market interest rates and the credit risk of the issuer of the fixed-rate bond
Negative cash flow risk faced by Lenders: To manage negative interest payment risk i.e when LIBOR > b, inverse floater investor should buy an interest rate cap with the following features:
• An exercise rate of b
of the swap/loan
Whenever L>b, Caplet pay-off = (L – exercise rate) × NP
Limitation: To avoid negative interest rate problem, the
lender would have to accept a lower rate i.e “b” would
be set a little lower by the borrower/issuer of the inverse floater
RATE RISK
Currency swaps can be used by investors to manage
exchange rate risk They are also useful to manage
interest rate risk but only in situations when exchange
rate risk exists
3.1 Converting a Loan in One Currency Into a Loan in another Currency
Currency Swaps can be used to transform a loan
denominated in one currency into a loan denominated
in another currency
in each currency and the principal amounts are
exchanged at the beginning and end of the life of
the swap
their comparative advantages regarding
borrowing in different countries i.e each firm
borrows in the market in which it has a
comparative advantage in terms of lower
borrowing rate
Example:
Company B is a U.S based firm and it borrows yen and engages in a swap with the company A that borrows dollars with parallel interest and principal repayment schedules:
When a firm needs to borrow in foreign currency it can use currency swap to do so instead of directly borrowing foreign currency from the foreign market due to the following advantages:
Practice: Example 4, Volume 5, Reading 30
Trang 5Advantages:
lower rate (because there it may be better known
as creditor) and then swap domestic currency for
foreign currency that it needs for foreign
expansion
assuming some credit risk i.e by entering into a
swap contract, credit risk faced by a firm is that
swap counterparty will default on its swap
payments Note that when a firm issues debt
directly in foreign currency where the lender is of
high credit quality, it faces no credit risk; only
lenders will face credit risk in this case
Example:
A firm ABC needs ₤30 million expand into Europe To
implement this expansion plan, a firm needs to borrow
Euros Suppose current exchange rate is €1.62/₤ Thus, a
firm needs to borrow €48.60 million Instead of directly
borrowing Euros, a firm can use currency swap e.g if a
firm issues fixed rate pound denominated bond for 30
million pounds with interest rate of 5% (annual interest
payments)
A firm enters into a currency swap contract in which it
will pay 30 million pounds to dealer and receives 48.60
Euros The terms of a swap are i.e
• Firm will pay 3.25% in Euros to a dealer
Exchange of principals at contract initiation:
swap dealer
Firm ABC
Cash flows at each settlement:
₤30,000,000 × 0.05 = ₤1,500,000
dealer = ₤30,000,000 × 0.045 = ₤1,350,000
= €48,600,000 × 0.0325 = €1,579,500
It should be considered that the interest received from
the dealer does not completely offset the interest that a
firm owes on its bond
Reason:
A firm ABC cannot borrow in pounds at the swap market
fixed rate because its credit rating is not as good as the
rating that is implied in the LIBOR market term structure
Therefore, a firm will need to pay an additional interest
of (0.05 – 0.045) × ₤30,000,000 = ₤150,000
represents a credit risk premium which a firm is required to pay it regardless of whether it borrowed directly in the foreign market or indirectly through a swap
At swap and bond maturity:
swap dealer and uses that amount to discharge its liabilities
dealer
NOTE:
If a firm wants to issue debt in foreign currency at a floating rate:
currency and
its domestic currency at a fixed rate and it pays the dealer foreign currency at a floating rate
Or
domestic currency
its domestic currency at a floating rate and firm pays foreign currency at a floating rate
The choice to pay a fixed or floating rate in a swap contract depends on expectations regarding the direction of interest rate movements i.e if a firm believes that interest rates will fall (rise) in the future, it will prefer
to be a floating (fixed) rate payer in a swap contract
Difference between currency swaps and interest rate swaps:
principal However, it is important to note that not all currency swaps involve the payment of notional principal
currency swaps are not netted as they are in different currencies
3.2 Converting Foreign Cash Receipts into Domestic Currency
A currency swap can be used to convert the foreign currency cash flows to domestic cash flows when an investor has investment in foreign currency e.g for a Practice: Example 5,
Volume 5, Reading 30
Trang 6foreign currency bond, foreign subsidiaries generate
cash in foreign currency
Example:
A U.S firm receives quarterly cash flows of €10 million
The exchange rate is €0.90/$ The swap fixed rates are
8% in U.S and 7.5% in Europe
Step 1: To determine the implied notional principal in
FC i.e Euros, Foreign cash flows are divided by
foreign interest rate
NP × (0.075 / 4) = €10,000,000
NP = 10,000,000 / (0.075/4) = €533,333,333
Step 2: To Calculate the corresponding principal in
Dollars, foreign NP is converted into
corresponding domestic NP (i.e $) using the
current exchange rate:
€5,333,333,333 / €0.90/$ = $592,592,593
NOTE:
A swap is entered with the above calculated NP
Step 3: To Calculate the $ interest payment, the
domestic NP is multiplied by the domestic
interest rate
$592,592,593 ×(0.08/4) = $11,851,852
conversion of quarterly cash flows in Euros for one
year
NOTE:
In this case, the swap parties are not required to
exchange notional principals (neither initially nor at
maturity)
Risks inherent in such transactions:
Credit Risk: A firm faces credit risk that the swap
counterparty may default on its obligations
Risk associated with uncertainty of cash flows generated
by foreign subsidiary i.e
flows will not be converted at locked-in rate
• When a firm generates < €10m, a firm is still
obligated to pay €10m to the swap counterparty
3.3 Using Currency Swaps to Create and Manage the Risk of a Dual-Currency Bond Dual currency bond is a bond in which the interest is paid in one currency and the principal is paid in another It can be used by a multinational company that generates cash in foreign currency which is sufficient to pay interest only and principal is paid in domestic currency
Synthetic Dual-currency Bond = Ordinary bond issued in
one currency (domestic currency)+ Currency swap (with no principal payments)
To offset dual-currency bond, investor can synthetically short the dual-currency bond by taking opposite position i.e
Synthetic dual-currency bond = buy domestic bond +
currency swap
When synthetic dual-currency bond is cheaper than the actual dual-currency bond → profit can be earned by:
Taking long position in the synthetic bond + short position
in the actual dual-currency bond Example:
Synthetic dual currency bond
• A firm issues a bond in $ that will make interest payments in $
payments) to pay interest in Foreign Currency and receive interest in $ This will offset the interest payments made in dollar-denominated bond Thus, effectively a firm will make interest payments
in foreign currency
• At maturity date of bond & swap: The firm will pay
off the $-denominated bond and there will be no payments on the swap
In an equity swap:
on the total return of some equity index e.g S&P
500 or an individual stock
• The other party pays a fixed rate, a floating rate, or
Practice: Example 7, Volume 5, Reading 30
Practice: Example 6, Volume 5, Reading 30
Trang 7the return on another index
Strategies:
market and interest rates are falling → Swap equity
return for fixed rate
market and interest rates are increasing→ Swap
equity return for floating rate
Uses of Equity swaps:
necessary adjustments to portfolios by synthetically
buying and selling stock without actually trading
the stock
•It can be used to exploit restrictions of short selling
stocks or other legal limits i.e margins, capital
controls etc
•It involves lower transaction costs relative to cash
transactions
shares (to retain voting rights) without bearing
equity risk
concentrated portfolio
diversification without actually investing in foreign
securities
•It can be used to alter the asset allocation of the
portfolio
Limitation: Equity swaps have a pre-defined expiration
date; thus, in order to manage equity risk continuously, a
manager needs to periodically renew equity swaps with
terms determined by the new market conditions on the
renewal date
Example:
On April 1, Hedge Fund A enters into a 3-year equity
swap Hedge Fund A pays the average S&P 500 return in
exchange of 90-day LIBOR (count 30/360) on a quarterly
basis
4.1,
4.2 &
4.3
Diversifying a Concentrated Portfolio,
Achieving International Diversification and
Changing an Asset Allocation between
Stocks and Bonds
A.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
B 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 Risks:
Tracking error: It refers to the difference in return generated by Domestic stock holdings and return on the Index which is used as a proxy It poses a cash flow problem for an investor when domestic stock generates negative return whereas index (used as a proxy) generates positive return
Higher cost: In addition, due to currency risk and market risk faced by counterparty, a firm needs to compensate counterparty (swap dealer)by paying higher costs in the form of a spread
C.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 Example:
The following table shows the current allocation and new allocation for both equity and bonds
Stock
Current ($150 million, 75%)
New ($180 million, 90%)
Required Transaction
Large cap
$90 million (60%)
$117 million (65%)
Buy $27 million
(30%)
$45 million
Small cap
$15 million (10%)
$18 million
Bonds
Current ($50 million, 25%)
New ($20million, 10%)
Required Transaction
Government
$40 million (80%)
$15 million (75%)
Sell $25 million
Corporate
$10 million (20%)
$5 million (25%)
Sell $5 million
Source: Volume 5, Reading 30, Section 4.3
Strategy: The swaps can be initially structured as follows:
Trang 8Consider the following:
SP500 represents the large-cap equity sector
SPSC represents the small-cap equity sector
LLTB represents the government bond sector
MLCB represents the corporate bond sector
oPay LIBOR on $27 million
oPay LIBOR on $3 million
oPay return on LLTB on $25 million
Alternative ways:
• Pay return on LLTB on $25 million
Fixed income swaps v/s Equity Swaps:
the total return on a
bond or bond index
against some other
index i.e LIBOR
fixed payment of interest represents a major portion of total return; whereas in equities, dividends represent a small amount of capital gains
• The total return is not
known until the end of
the settlement period
negative, it is possible
for the overall payment to be negative
Risks inherent in Equity and Fixed income swaps:
between the performance of the various sectors of equity and fixed-income portfolios and the
performance of the indices which are used as proxy and on which swap payments are based
return, if fixed-income payments > equity receipts, the investor faces cash flow problem to meet his swap obligations Investor can generate cash from his actual stock and bond portfolios in the form of dividends and interest payments In order to receive capital gains on stock or bond portfolio, investor needs to liquidate a portion of his portfolio However,
it is not reasonable to do so because the basic reason behind using swaps was to offset negative
performance of portfolio without actually liquidating
it
flow problem could also arise when the stocks outperform index and consequently a firm is required
to make net outflow Or when a stock generates positive return whereas index generates negative return, then the firm owes payments on both legs of the swap
NOTE:
Equity swaps are used by executives, to offset negative return associated with stock options Such actions can result in significant agency cost problems for the company
A SWAPTION is an option to enter into a swap Swaptions
can be used to enter into interest rate, equity, currency,
and commodity swaps Interest rate swaptions represent
the largest swaptions market and are highly liquid
be exercised only at expiration or American style
i.e can be exercised at any time prior to
expiration
has a specific set of terms i.e
oNotional principal
oUnderlying interest rate
oTime to expiration
oExercise rate i.e a fixed rate at which the swaption holder can enter into the swap as either a fixed-rate payer or fixed-rate receiver It
is always specified at the initiation of the swaption
Practice: Example 8, 9, 10 & 11, Volume 5, Reading 30
Trang 9seller which represents cost of the option
expensive the receiver (payer) swaption
Ways to exercise Swaption:
actually entering into the swap or
receiving an equivalent amount of cash from the
seller
NOTE:
The method used to exercise a swaption is
pre-determined by the parties when the contract is created
Types of swaptions:
1 Payer swaption: It is an option that allows the holder
to enter into a swap as a fixed-rate payer,
floating-rate receiver It is similar to a put option on a bond
2 Receiver swaption: It is an option that allows the
holder to enter into a swap as fixed-rate receiver,
floating-rate payer It is similar to a call option on a
bond
A swaption is similar to an option on a Coupon Bond
of a Future Borrowing
A swaption can be used:
Using swaption to create a swap:
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
expiration > exercise rate of swaption, a firm can exercise the payer swaption
expiration < exercise rate of swaption, a firm will not exercise the payer swaption; rather, it can enter into a swap at the market rate
Swap There are two ways to terminate an existing swap:
i By entering into an offsetting swap:
into an offsetting swap with a different counterparty:
• Both of the swaps (new & original) would remain in place
equivalent and would offset each other
payments at one rate and receive a stream of fixed payments at another rate
into an offsetting swap with original counterparty:
swaps
net cash outflow to other party would pay a lump sum of the PV of the difference between the two streams of fixed payments
ii By buying a swaption
should use receiver swaption to convert its pay-fixed position to a pay-floating position
Practice: Example 12, Volume 5, Reading 30
Trang 10b)When interest rates are expected to rise, a borrower
should use payer swaption to convert its pay-floating
position to a pay-fixed position
in callable (Noncallable) Debt
In a callable bond, the issuer has a right to retire the
bond early This right is referred to as the call option and
the issuer receives this right by paying a higher coupon
rate on the bond
For Issuers:
5.3.1) Strategy used by an Issuer to synthetically remove
call feature from a Callable bond by using a
swaption
We know that receiver swaption is similar to a call option
on a bond
Therefore, a call option can be synthetically removed
from a callable bond by Selling a Receiver Swaption
valuable and becomes more likely to be
exercised
becomes valuable
cancel the bond’s call feature Both options will
remain in place; however, both options should
behave in a similar manner
interest on a callable bond as bond is called back
However, it starts paying interest on a receiver
swaption which he sold for a premium
swaption effectively leads to decrease in issuer’s
cost i.e it reduces the coupon rate on a callable
bond
party and thus, the seller (i.e issuer in this case) has
no guarantee that exercise will occur at the
optimal time
Synthetically removing a call feature from a Callable
bond is also known as “monetizing a call”
NOTE:
Exercise rate of swaption does not include credit spread because the swaption can be used to manage the risk associated with changes in interest rates only
5.3.2) Strategy used by an Issuer to synthetically add call feature in a non-Callable bond by using a
swaption
We know that receiver swaption is similar to a call option
on a bond
Therefore, a call option can be synthetically added to a
non-callable bond by Buying a Receiver Swaption
becomes valuable
• Thus, when rates decline, issuer starts receiving interest on receiver swaption and effectively cancels out its current fixed rate obligation on a
non-callable bond
buys receiver swaption which effectively leads to increase in issuer’s cost i.e increases coupon rate
on a bond
For Investors:
Strategy used by an Investor to synthetically add call feature in a non-Callable bond by using a
swaption:→Selling a receiver swaption i.e by selling a receiver swaption, an investor effectively sells a call option on a bond similar to a callable bond
effectively increase the coupon rate on the bond
Strategy used by an Investor to synthetically remove call feature in a Callable bond by using a swaption:→Buying
a receiver swaption i.e by buying a receiver swaption,
an investor effectively receives the right to receive fixed rate when interest rates fall and thus cancels out the call feature of a callable bond
To synthetically add or remove put options, payer swaptions can be used
For Issuers:
Strategy used by an Issuer to synthetically add a put option in a non-Putable bond by using a swaption: We know that payer swaption is similar to a put option on a bond
add a put to an otherwise non-putable bond by
selling a payer swaption The premium received by
the issuer will effectively reduce the coupon rate
Practice: Example 14, Volume 5, Reading 30
Practice: Example 13,
Volume 5, Reading 30