Choudhry. Fixed Income Securities Derivatives Handbook

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232 Selected Cash and Derivative Instruments

investment vehicles—funds, such as wholly owned Citigroup subsidiaries

Centauri and Dorada Corp, that are set up to invest in particular areas or

sectors.

FIGURE 13.1 illustrates the coupon calculation on a typical inverse

ﬂ oater and how changes in the LIBOR rate affect the payment.

FIGURE 13.1

Terms of a Hypothetical Inverse Floater

Nominal value $100,000,000

Issue date 5-Jan-2000

Maturity date 5-Jan-2003

Note coupon 15.75% – (2 x LIBOR)

Day-count basis actual/365

Index 6-month LIBOR

Current LIBOR rate 5.15%

Rate ﬁ xing Semiannual

Initial coupon 5.45%

Minimum coupon 0%

USD LIBOR COUPON PAYABLE

1.00% 13.75%

1.50% 12.75%

2.00% 11.75%

2.50% 10.75%

3.00% 9.75%

3.50% 8.75%

4.00% 7.75%

4.50% 6.75%

5.00% 5.75%

5.50% 4.75%

6.00% 3.75%

6.50% 2.75%

7.00% 1.75%

Hybrid Securities 233

The inverse ﬂ oater in ﬁ gure 13.1 pays a slightly above-market initial

coupon given a positive yield curve. Investors beneﬁ t because they get a

coupon whose sensitivity is equal to two times the changes in LIBOR.

FRNs in general are highly interest rate sensitive. This is because the

leverage involved in the coupon calculation endows them with the high-

est duration of any instrument traded in the ﬁ xed-income market. The

note in ﬁ gure 13.1, for example, has a calendar maturity of three years. As

shown in

FIGURE 13.2, however, its modiﬁ ed duration is much higher.

Inverse ﬂ oaters are very ﬂ exible instruments. They can, for instance, be

linked to any reference index and thus serve as vehicles for different views

concerning various short- or long-term interest rates, such as the central

bank repo rate, 10-year swap rates, or a government benchmark. The

notes’ leverage can also be altered according to investors’ risk preferences.

The ﬁ xed element can be chosen for the same reason. Equally, the ﬁ xed

element can be set to move upward or downward as required at next term.

Inverse ﬂ oaters can also give investors exposure to markets they wouldn’t

otherwise have access to. Someone who has a particular view on a speciﬁ c

foreign interest rate, for example, but who can’t invest in that market’s

securities for some reason can buy an inverse FRN that is linked to the

foreign index but pays coupon in the domestic currency.

Hedging Inverse Floaters

Borrowers often issue inverse ﬂ oating notes in one currency and swap

the proceeds into another that ﬁ ts their funding needs better using a cur-

rency swap. They may then hedge their interest rate exposure on the note

through an interest rate swap. The counterparty swap bank, in turn, will

hedge its own exposure. The interest rate swap structure used to hedge the

note in ﬁ gure 13.1 is shown in

FIGURE 13.3.

In ﬁ gure 13.3, the note issuer enters into a swap in which it

❑ pays 6-month LIBOR

❑ receives the note coupon rate

FIGURE 13.2

Duration of a Year Inverse Floater

Duration of 3-year note with 5.30% coupon 2.218 years

Duration of 3-year inverse ﬂ oater (x 3) 6.654 years

234 Selected Cash and Derivative Instruments

The swap bank, which takes the other side of the transaction, receiving

LIBOR and paying the coupon rate, must now hedge its own exposure

with another swap. To understand the structure of this second swap, it

helps to consider the note coupon of 15.75 percent minus two times

LIBOR as composed of the following two transactions:

❑ the note holder receives 15.75 percent

❑ the note holder pays two times LIBOR

In its arrangement with the note issuer, the bank is thus receiving three

times LIBOR and paying 15.75 percent. The hedging swap it enters into

consists of a payment of three times LIBOR in return for three times the ﬁ xed

swap rate of 5.30, or 15.90 percent. This total is higher than the ﬁ xed compo-

nent of the coupon by 15 basis points. This difference is the cost of ﬁ xing

a cap, to hedge against the exposure presented by the ﬂ oor on the note.

Figure 13.1 speciﬁ es that the inverse ﬂ oater has a minimum coupon

on 0 percent. The ﬂ oor is passed on from the note issuer to the swap bank

via the swap. This, in effect, caps the note holders’ LIBOR exposure at

7.875 percent (15.75 divided by two). The bank’s swap leaves it exposed

to a rise in LIBOR above this level. To be fully hedged, the bank must buy

an interest rate cap on LIBOR with a strike rate of 7.875 percent. The cap

costs 15 basis points, which explains the spread over the coupon rate in

the swap structure.

Indexed Amortizing Notes

Another type of hybrid security is the indexed amortizing note, or IAN.

IANs were introduced in the U.S. market in the early 1990s in response to

demand by investors in asset-backed notes known as collateralized mort-

FIGURE 13.3

Structure of Swaps Hedging an Inverse Floater

15.75%

– (2 x LIBOR)

LIBOR 3 x LIBOR

3 x 5.30%

(inc cap cost)

15.75%

– (2 x LIBOR)

Note

Issuer

Note

Holder

Swap

Bank

The

Market

Hybrid Securities 235

gage obligations, or CMOs. IANs have been issued by banks, corpora-

tions, and, in large volumes, by U.S. government agencies.

IANs are short- to medium-term unsecured notes, most commonly

with ﬁ ve-year maturities. They have ﬁ xed-coupons and variable nomi-

nal values—that is, after a “lock-out period,” during which it remains

stable, their principal is paid down according to a schedule determined

by the level of a reference index, such as 6-month LIBOR, relative to a

speciﬁ ed base rate. In this respect, IANs are similar to mortgage-backed

notes, which also amortize. Mortgage-backed notes’ amortization,

however, is determined by the principal payments and prepayments

of their underlying pools of mortgages. Because mortgage payments

follow less clearly deﬁ ned patterns than the reference indexes, IANs are

considered to have an advantage over mortgage-backed securities. They

also typically pay yields that are higher than those of conventional debt

securities of similar credit quality.

FIGURE 13.4 shows the terms of a

hypothetical IAN.

FIGURE 13.4

Terms of a Hypothetical IAN

Issuer Mortgage agency

Nominal value $250,000,000

Legal maturity Six years

Coupon 2-year Treasury plus 100 bps

Interest basis Monthly

“Lock-out period” Three years

Reference index 6-month LIBOR

6m LIBOR ﬁ xing on issue 5.15%

Minimum level of note 20%

AVERAGE LIFE SENSITIVITY

LIBOR RATE AMORTIZATION RATE AVERAGE LIFE (YEARS)

5.15% 100% 3

6.00% 100% 3

7.00% 21% 4.1

8.00% 7% 5.6

9.00% 0.00% 6

236 Selected Cash and Derivative Instruments

The note in ﬁ gure 13.3 pays a coupon equal to the current 2-year

government benchmark plus a ﬁ xed spread of 1 percent. It has a legal

maturity of six years, but it will mature in three years if, two years from

the issue date, 6-month LIBOR stands at 6 percent or below. Amortiza-

tion takes place on subsequent rate-ﬁ xing dates according to the speciﬁ ed

schedule. If at any time less than 20 percent of the nominal value remains,

the note is canceled.

IAN issuers typically hedge their exposure through swap arrange-

ments that mirror the notes’ structure. A simple hedge is shown in

FIGURE 13.5

. It is more common, however, for the arrangement to involve

a series of options on swaps, or swaptions. When volatility in the ﬁ xed-

income market is high and the yield curve steeply positive, swaptions

tend to have greater value, so the IAN coupon in those circumstances

might be especially attractive.

Advantages for Investors

It has already been noted that IANs offer relatively high yields for rela-

tively short maturities and that their amortization structures are easier

to understand than those of mortgage-backed securities. In addition to

these advantages, the notes, like the other instruments described here,

can be tailored to meet individual investor requirements. The features

most frequently subjected to this tailoring are the legal maturity and

the lockout period, with the yield premium decreasing as the latter

approaches the former. Although the most common reference index is

LIBOR, it can also be a government benchmark or an interbank rate

such as the swap rate.

FIGURE 13.5

IAN Hedge Arrangement

Fixed

coupon

LIBOR + spread

(funding cost)

Fixed

coupon

Note

Holder

Issuer

Swap

Bank

Hybrid Securities 237

Synthetic Convertible Notes

Synthetic convertible notes are securities with ﬁ xed coupons, typically set

at a relatively low level, whose total return is linked to an external source,

such as the level of an equity index or the price of a speciﬁ c security. In one

common structure, the note is redeemable above par if the reference index

or security value exceeds a stated minimum. The notes thus give investors

the opportunity to proﬁ t from the benchmark’s performance while provid-

ing the safety net of redemption at par should this performance fall short.

Another typical synthetic convertible structure is the zero-coupon note.

These notes are issued at par and redeemable at par, or higher, if a speciﬁ ed

equity index performs better than a stated level.

FIGURE 13.6 shows the terms of a hypothetical sterling synthetic con-

vertible note linked to the FTSE 100 equity index. This note will pay

par on maturity unless the FTSE 100 has risen by more than 10 percent

from its level on the issue date. In that case, the redemption value will be

par plus the amount of the index rise. The note also pays a coupon of 0.5

FIGURE 13.6

Terms of a Hypothetical Synthetic Convertible Note

Nominal value $50,000,000

Term to maturity Two years

Issue date 17-Jun-99

Maturity date 17-Jun-01

Issue price $100

Coupon 0.50%

Interest basis Semiannual

Redemption proceeds Min [100, Formula level]

Formula level 100 + [100 x (R(I) – (1.1 x R(II)) / R(II)]

Index FTSE-100

R(I) Index level on maturity

R(II) Index level on issue

Hedge terms

Issuer pays LIBOR

Swap bank pays Redemption proceeds in accordance with

formula

238 Selected Cash and Derivative Instruments

percent, which is roughly ﬁ ve percentage points less than the 2-year sterling

yield at the time. The synthetic convertible described is thus suitable only

for investors who are very bullish on the prospects of the FTSE 100.

Investor Benefits

Like convertible bonds, synthetic convertible notes provide investors with

ﬁ xed coupons plus the possibility of proﬁ ting from the performance of the

reference index. Unlike the ordinary convertible, however, the synthetic

pays in cash rather than in shares of the associated equity.

The reference for a synthetic convertible can be virtually any publicly

quoted ﬁ nancial instrument or relationship. Payouts have been linked, for

instance, to the exchange rate of two currencies, the days on which LIBOR

falls within a speciﬁ ed range, and the performance of a selected basket of

stocks, such as technology shares.

Interest Differential Notes

Interest differential notes, or IDNs, are hybrid securities that enable inves-

tors to take a position based on their views about interest rates in two

different currencies. Notes in the U.S. market are usually denominated in

U.S. dollars; Euromarket notes have been issued in a wide range of cur-

rencies.

IDNs have a number of variations. Some pay a variable coupon and

a ﬁ xed redemption amount; others pay a ﬁ xed coupon and a redemption

amount that is determined by the level or performance of a reference in-

dex. Still other IDNs have payoff proﬁ les linked to the difference between

interest rates in two speciﬁ ed currencies or between rates for two different

maturities in one currency.

FIGURE 13.7 shows the terms and potential returns of a 5-year IDN.

The terms specify that the note’s coupon will increase as the difference be-

tween U.S. dollar LIBOR and euro LIBOR widens, and vice versa. Below

the list of terms are various returns that are possible in different interest

rate scenarios. These are stated as spreads over the 5-year government

benchmark yield. For instance, at the initial LIBOR differential of 2.65,

it is stated that the IDN will return 95 basis points over the benchmark.

The returns given are not guaranteed, of course, since they are based on

the unrealistic assumption the interest differential will remain at the level

indicated through to the ﬁ nal coupon-setting date. The listed returns do,

however, demonstrate that the note’s spread over the benchmark widens as

the difference between the two rates increases. And the note will continue

to offer a premium over the government yield even if the rate difference

declines, as long as this decline doesn’t exceed 100 basis points each year.

Hybrid Securities 239

For purposes of analysis, this IDN can be regarded as a ﬁ xed-coupon

bond plus the double indexation of an interest rate differential. Indexation

here refers to a reference rate based on an index. The double indexation

creates two long positions in a 5-year dollar-denominated ﬁ xed-rate note

and two short positions in a euro-denominated ﬁ xed-rate note. The short

positions remove the euro exchange-rate risk, so investors are exposed only

to the euro interest rate risk, which is the desired exposure.

As with other hybrid securities, issuers of IDNs hedge their exposure

with swaps. For the note in ﬁ gure 13.7, the hedge would involve both dol-

lar and euro interest rate swaps.

FIGURE 13.7

Terms of a Hypothetical Interest Differential Note

Term to maturity Five years

Coupon [(2 x USD LIBOR) – (2 x EUR LIBOR)

– 0.50%]

Current USD LIBOR 6.15%

Current EUR LIBOR 3.05%

Rate differential 3.10%

First coupon ﬁ x 5.70%

Current 5-year

benchmark rate 4.75%

Yield spread over

benchmark 0.95%

CHANGE IN LIBOR LIBOR SPREAD SPREAD OVER

SPREAD (BPS P.A.) AT RATE RESET BENCHMARK

75 4.78% 2.34%

50 3.90% 1.88%

25 3.15% 1.21%

0 2.65% 0.95%

–25 1.97% 0.56%

–50 1.32% 0.34%

–75 0.89% 0.12%

–100 0.32% –0.28%

240 Selected Cash and Derivative Instruments

Benefits for Investors

IDNs and similar instruments enable investors to put on positions that

reﬂ ect their views on the direction or level of foreign interest rates without

taking on currency, or exchange-rate, risk. The IDN in ﬁ gure 13.7, for

example, would appeal to investors with a particular view on the U.S.-

dollar and euro yield curves. Say the dollar curve is inverted, and the euro

curve positively sloping. Investors buying this IDN would be earning a

high yield while expressing a view—for example, is the market going up

or down—that is different from the market consensus.

IDNs can be structured to enable investors to take positions on the

yields in different currencies at the same maturity. A note’s coupon, for

example, could be determined by the difference between the 10-year

government benchmark yields in two speciﬁ ed countries. The notes can

also be linked to spreads between yields at different maturities in the same

currency. This would be a straight yield-curve, or relative-value, trade in a

domestic or foreign currency.

IDNs do expose investors to interest rate risk. If the rate differential

moves in the opposite direction from the one desired, the coupon is

reduced and the yield may fall below that available on the benchmark

bond.

241

Securitization and

Mortgage-Backed Securities

CHAPTER 14

erhaps the best illustration of the ﬂ exibility, innovation, and user-

friendliness of the debt capital markets is the rise in use and impor-

tance of securitization. As deﬁ ned in Sundaresan (1997, page 359),

securitization is “a framework in which some illiquid assets of a corpora-

tion or a ﬁ nancial institution are transformed into a package of securities

backed by these assets, through careful packaging, credit enhancements,

liquidity enhancements and structuring.”

The ﬂ exibility of securitization is a key advantage for both issuers and

investors. Financial-engineering techniques employed by investment banks

today enable bonds to be created from any type of cash ﬂ ow. The most typical

such ﬂ ows are those generated by high-volume loans such as residential mort-

gages and car and credit card loans, which are recorded as assets on bank or

ﬁ nancial-house balance sheets. In a securitization, the loan assets are packaged

together, and their interest payments are used to service the new bond issue.

In addition to the more traditional cash ﬂ ows from mortgages and loan

assets, investment banks underwrite bonds secured with ﬂ ows received by

leisure and recreational facilities, such as health clubs, and other entities,

such as nursing homes. Bonds securitizing mortgages are usually treated as

a separate class, termed mortgage-backed securities, or MBSs. Those with

other underlying assets are known as asset-backed securities, or ABSs. The

type of asset class backing a securitized bond issue determines the method

used to analyze and value it.

The asset-backed market represents a large and diverse group of securi-

ties suited to a varied group of investors. Often these instruments are the