lecture note 05_bonds with other features (1)

8/17/2019 Lecture Note 05_Bonds With Other Features (1)

1/66

Lecture Note Five:

Bonds with Other Features

FINA0804/3323 Fixed Income Securities

Faculty of Business and Economics University of Hong Kong

Dr. Huiyan Qiu

5-1


2/66

Outline

Callable bond

What is a callable bond? Why callable bond?

Pros and cons of calling a bond

Valuing a callable bond

Convertible bond: Basics

Floaters and inverse floaters

Repurchase agreement

Reference: Fabozzi’s chapter 17, 19

5-2


3/66


4/66

What is a Callable Bond?

Acallable bondallows the issuer to buy back

the whole issue at a pre-specified price at some

point in the future.

Some terms• Thestrike price (or exercise price or call price):the price at which the issuer can buy back thebonds (typically par value plus one year’s

interest).• Call protection period:the period during whichthe issuer cannot call the bonds.

5-4


5/66

Why Callable Bond?

Callable bonds give borrowers the option to

refinance when interest rates are low. In other

words, it is one way companies hedge against

possible decreases in future interest rates.• Before 1970 almost all corporate bonds wereissued with call features.

• Between 1970 and 1990, about 80% of fixed rate

corporate bonds were callable.• Now, less than 30% of corporate bonds are callabledue to the development of the interest ratederivatives markets.

5-5


6/66

Why Callable Bond? (cont’d)

Some firms may still find callable bonds

desirable because by issuing callable bonds they

can send a strong positive signal to the markets

about the quality of their business.• If a firm is confident about their business andbelieves that their credit quality will improve inthe future (which will lower their borrowing costs),

it makes sense for them to issue a callable bond.• As soon as the market realizes their better values,they can simply call the old expensive bond andreplace it with a bond which pays lower coupons.

5-6


7/66

Callable Bondholders

The presence of a call option results in two

disadvantages to the bondholder.

Disadvantage 1:Callable bonds expose

bondholders toreinvestment risk:• Investors are exposed to additional reinvestmentrisk due to the call option.

• Issuers will call the bonds when the price of the

bond is higher than the strike price, whichhappens when the interest rate is low enough.

• Bondholders are forced to reinvest the proceedsreceived in redemption at a lower interest rate.

5-7


8/66

Callable Bondholders (cont’d)

Disadvantage 2:The price appreciation

potential for a callable bond in a declining

interest-rate environment is limited:

•

As interest rate drops, the price of a straight debtwill increase (in theory, no limit). However, in thecase of callable bonds, bonds are expected to beredeemed when interest rate drops, therefore wehave a limit on the price appreciation. This iscalled “price compression”.

Investors are willing to accept the call risk if

higher yield is offered.

5-8


9/66

Issuers: Reasons for Calling a Bond

There can be different reasons for a bond issuer

to call a bond.

1.To remove an undesirable protectivecovenant in the bond indenture

2. An improved credit rating

3.Drop in the market-wide interest rate

5-9


10/66

To Remove an Undesirable Covenant

An old debt indenture requires the firm to have

an interest coverage ratio of at least 2

• Interest coverage ratio= Earnings before

interest and taxes divided by Interest expenseThe firm wants to lower this requirement to 1.5

but has failed to negotiate with old bond holders

The firm can “call” the old bond (if the old bond is

callable) and issue new ones where the newrequired interest coverage ratio is 1.5

5-10


11/66

An Improved Credit Rating

If the rating of a firm has improved, for example,

from junk (below BBB) to investment grade

(BBB and above), the firm may consider “calling”

the old bond• The firm can now issue debt at a more favorablerate

• Investors are willing to accept a lower yield to

maturity or lower coupon rate because the firmhas become less risky

5-11


12/66

Drop in the Interest Rate

If the market-wide interest rates drop, the firm

may want to “call” the old bond (with a higher

coupon rate) and replace it by a lower-coupon

bond• The firm gains the present value of the couponssaved

• The new bond may or may not have a longer

maturity than the old bond

5-12


13/66

Pros and Cons of Calling a Bond

By calling a bond and refunding by issuing a new

bond, the firm usually benefits from a lower

coupon rate – the firm gains the present value of

the coupons saved.This saving has to be balanced against the costs

of calling a bond, which include:

• Paying the call premium.

• Flotation costs for the replacement bond issue• The loss of the opportunity to call the bond in thefuture if interest rates were to drop even further.The timing of calling is very crucial.

5-13


14/66

Refunding Benefit: Example 1

Suppose there is a $100-par perpetual callable

bond with the following characteristics:

• Coupon rate = 10%

•

Strike price = $100• No call protection

Suppose all interest rates drop to 7%. Then

• Calling the old debt

• Issuing new debt at 7%

If the costs of refinancing are 1.25% of par, what

is the refunding benefit?

5-14


15/66


Refunding benefit

= ($3/0.07) – ($100 × 1.25%)

= $42.86 – $1.25 = $41.61

5-15


16/66


Suppose a firm issued a semi-annual par coupon

bond with the following characteristics:

• Maturity = 30 years

•

Par = $100• Coupon rate = 12%

• Strike price = $105

• Call protection for the first 5 years

At the end of the 5th year, rates are 9%.

5-16


17/66


There are 25 years remaining. The present value

of the firm’s liabilityif the debt is not calledis

$129.64.

•

N = 50, PMT = 6, Rate = 4.5%, FV = $100.Ifthe bond is called at the strike price and a

new bond is issued with a 9% coupon rate.

• The coupon rate is reduced by 3% for 25 years.

Present value of coupon saving is $29.64. (N = 50,PMT = 1.5, Rate = 4.5%, FV = $0).

• The call premium is $105 – $100 = $5.

5-17


18/66


Suppose the flotation costs are 2% of par. The

overall refinancing costs is

• Refinancing costs = Flotation costs + Call

premium = (2% × $100) + ($105 – $100) = $7

Refinancing benefit= PV of savings –

Refinancing costs = $29.64 – $7.00 = $22.64

5-18


19/66

Valuing a Callable Bond

Callable bond can be considered as having two

components:a non-callable bondanda call

option.

A valuation model must produce arbitrage-free

values; that is, a valuation model must produce avalue for each on-the-run issue that is equal toits observed market price. To price the bond wewill use abinomial interest rate tree model.

5-19


20/66

Valuing a Callable Bond (cont’d)

The construction of binomial interest rate tree will becovered in later lecture. We take the following tree as

given.

5-20


21/66

Valuing a Callable Bond: Example

Consider a three-year bond with 5.25% annual

coupon payment. We employ thebackward

induction methodology to compute the price of

bond (non-callable or callable at par in one year.)

Following figure shows the calculation of theprice of the bond that iscallable at parin one

year. The slides followed provide the detail of thecalculation.

5-21


22/66

Valuing a Callable Bond

5-22


23/66

Calculation

If the bond is not called in year 2, the price of the

bond then is

• At nodeNHH, $105.25/1.067573 = $98.5881

• At nodeNHL, $105.25/1.055324 = $99.7324• At nodeNLL, $105.25/1.045296 = $100.6892

At nodeNLL, the bond will be called since the

bond price is higher than the strike price $100.There are $5.25 coupon payment at the end of

year 2.

5-23


24/66

Calculation (cont’d)

If the bond is not called in year 1, the price of the

bond then is

• At nodeNH,

• At nodeNL,

At nodeNL, the bond will be called since the bond

price is higher than the strike price $100.

There are $5.25 coupon payment at the end ofyear 1.

5-24


25/66


At node N, now, the bond price is

The price of the callable bond is$101.4307.

For thenon-callable bond, the price of the

bond at nodeNL is

5-25


26/66


The price of the non-callable bond at node N,now, is

Therefore, the value of the option embedded inthe callable bond is

5-26


27/66

Option-Adjusted Spread

Option-adjusted spread (OAS)

• OAS is the spread such that the market price of asecurity equals its model price when discountedvalues are computed at risk-neutral rates plusthat spread.

• Assume the 5.25% callable three-year coupon bondin our example is currently selling for $100.7874(versus $101.4307 previously calculated). The OAS

of the callable bond is then 45 basis points.• Note:the computation can be done using trial anderror method or solver in excel.

5-27


28/66

What is a Convertible Bond?

Aconvertible bondis a bond with a call option

to buy the common stock of the issuer.

• At the discretion of the bondholder, the convertible

bond can be converted into a predeterminedamount of the company’s equity at certain timesduring its life.

Exchangeable bondsgrant the bondholder the

right to exchange the bonds for the common stockof a firm other than the issuer of the bond.

5-28


29/66

Convertible Bond: Basics

The number of shares of common stock that the

bondholder will receive from exercising the call

option of a convertible bond or an exchangeable

bond is called theconversion ratio.• Upon conversion, the bondholder typically receivesfrom the issuer the underlying shares. This isreferred to as aphysical settle.

•

There are issues where the issuer may have thechoice of paying the bondholder the cash value ofthe underlying shares. This is referred to as acash settle.

5-29


30/66

Conversion Value and Minimum Value

Theconversion valueof a convertible bond is

the value of the bond if it is converted

immediately

Theminimum valueof a convertible bond is the

greater of

• its conversion value, and• its straight value (the value without theconversion option)

5-30


31/66

Market Conversion Price

Themarket conversion priceis the price thatan investor effectively pays for the common stockif the convertible bond is purchased and thenconverted into the common stock

5-31


32/66

Why Pay a Premium?

An investor who purchases a convertible bond

rather than the underlying stock typically pays a

premium over the current market price of the

stock.• As the stock price declines, the price of theconvertible bond will not fall below its straightvalue. The straight value acts as a floor for theconvertible bond price.

• The investor realizes higher current income fromthe coupon interest paid on the convertible bondthan would be received as dividends paid on thenumber of shares equal to the conversion ratio.

5-32


33/66

Investment Characteristics

The investment characteristics of a convertible

bond depend on the stock price

• If the stock price is low the straight value isconsiderably higher than the conversion value no conversion

• Bond equivalent or busted convertible

• If the stock price is high

•

Equity equivalent• Between the two cases

• Hybrid security

5-33


34/66

Convertible Bond: Example

XYZ convertible bond:

• Maturity = 10 years

• Coupon rate = 10%

•

Conversion ratio = 50• Par value = $1,000

• Current market price of the bond = $950

• Straight value (the value of the non-convertible

bond) = $788Current market price of XYZ common stock =

$17; Dividends per share = $1 per year

5-34


35/66

Convertible Bond: Example (cont’d)

Conversion value = $17 × 50 = $850

Market conversion price = $950 / 50 = $19

Market conversion premium per share

= $19 – $17 = $2Market conversion premium ratio = 2/17 ≈ 11.8%

The bondholder receives $100 annual coupon

payment versus $50 dividend if the bond isconverted into 50 shares. ($2 per share versus $1

per share.)

5-35


36/66

Downside Risk with a Convertible Bond

The downside risk of convertible bond is often

estimated by comparing the market price of the

bond with the straight value since the price of

the bond cannot fall below its straight valueThe downside risk is measured as a percentageof the straight value

The higher the premium over straight value, allother factors constant, the less attractive theconvertible bond.

5-36


37/66

Downside Risk with a Convertible Bond

Despite its use in practice, the measure of

downside risk is flawed because the straight

value (floor) changes as interest rates change.

Anadvantage of buying the convertible ratherthan the common stock is the reduction in

downside risk.

Thedisadvantageof a convertible relative to

the straight purchase of the common stock is theupside potential give-up because a premium pershare must be paid.

5-37


38/66

Pros and Cons of Investing in a Convertible Bond

Suppose that an investor is considering purchase

of the XYZ stock or the XYZ convertible bond.

• The stock can be purchased in the market for $17

•

By buying the convertible bond, the investor iseffectively purchasing the stock for $19

One month later, XYZ stock rises to $34, with

everything else remaining the same

• The stock investor would realize a gain of $17 anda return of 100%.

• The bond holder would realize a gain of $1,700 –$950 = $750 and a return of 79%.

5-38


39/66


One month later, XYZ stock falls to $7, with

everything else remaining the same.

• The stock investor buying the stock would realizea loss of $10 and a return of – 59%.

• The bond holder would realize a loss of $950 –$788 = $162 and a return of – 17%.

Downside riskis reduced as the bondholder

has the opportunity to recoup the premium pershare through the higher current income from

owning the convertible bond.

5-39


40/66


Call risk: convertible issues are callable by the

issuer.

• Most convertible bonds are callable (for the issuer)and some are puttable (for the bondholder).

Takeover Risk

• Corporate takeovers represent another risk toinvesting in convertible bonds.

•

As the stock of the acquired company may nolonger trade after a takeover, the investor can beleft with a bond that pays a lower coupon ratethan comparable-risk corporate bonds.

5-40


41/66

Options Approach to Valuation

An investor who purchases a non-callable /non-

puttable convertible bond would be entering into

two separate transactions:

•

buying a non-callable/non-puttable straight bond• buying a call option on the stock, where thenumber of shares that can be purchased with thecall option is equal to the conversion ratio

5-41


42/66


Consider a common feature of a convertible bond:

the issuer’s right to call the bond.

• If called, the investor can lose any premium overthe conversion value that is reflected in themarket price.

• Therefore, the analysis of convertible bonds musttake into account the value of the issuer’s right tocall the bond.

• This depends, in turn, future interest ratevolatility, and economic factors that determinewhether it is optimal for the issuer to call the bond

5-42


43/66


The Black-Scholes option pricing model cannot

handle this situation.

• Instead, the binomial option pricing model can beused simultaneously to value the bondholder’s calloption on the stock and the issuer’s right to callthe bonds.

• The bondholder’s put option can also beaccommodated.

• To link interest rates and stock prices together,statistical analysis of historical movements ofthese two variables must be estimated andincorporated into the model.

5-43


44/66

Floating Rate Note: Introduction

A floating rate note (FRN) is a bond with coupon

rate reset periodically accordingly to a

benchmark interest rate, or indexed to this rate.

Possible benchmark rates:• US Treasury rates, LIBOR, prime rate, ....

The coupon rate on a floating rate note is often

equal to the benchmark interest rate plus apremium (called spread).

5-44


45/66

Floating Rate Jargon

Other terms commonly used for floating-rate

notes are

• FRNs

•

Floaters and Inverse Floaters• Variable-rate notes (VRNs)

• Adjustable-rate notes

FRN usually refers to an instrument whose

coupon is based on a short term rate (3-month T-bill, 6-month LIBOR), while VRNs are based on

longer-term rates (1-year T-bill, 2-year LIBOR)

5-45


46/66

Cash Flow Rule for Floater

Consider a semi-annual coupon floating rate

note, with the coupon indexed to the 6-month

interest rate.

•

On each coupon date, the coupon paid is based onthe previous 6-month rate.

• The note pays par value at maturity.

•Only the next coupon is known at the currentdate. The later ones are random.

5-46


47/66

Example: Two-Year Floater

Consider a two-year floater with coupon rate set

to equal the six-month T-bill rate. The current

six-month T-bill rate is 5.54%. Suppose the

future six-month T-bill rates turn out as follows.

Find the cash flows from $100 par of the note.

5.54% 6.00% 5.44% 6.18%

Floater Cash Flows:

2.77 3.00 2.72 103.09

0 0.5 1 1.5 2

5-47


48/66

Valuation of Floater

Consider a $100 par of a floater with coupon rate

set to equal the six-month rate and maturing at

timeT. What is the price of the floater on the

coupon date before the maturity date, that is,

timeT – 0.5?

where is the annualized six-month rate fromt–0.5 tot.

5-48


49/66

Valuation of Floater (cont’d)

What is the price of the floater two coupon dates

before the maturity date, that is, timeT – 1?

5-49


50/66

Valuation of Floater (cont’d)

Working backwards to the present, repeatedly

using this valuation method, proves that the

price of a floater is always equal to par on a

coupon date.

• The coupon (the numerator) and interest rate (thedenominator) move together over time to make theprice (the ratio) stay constant.

A floater can be replicated by a dynamic strategyof rolling six-month par bonds until floatermaturity, collecting the coupons along the way.

5-50


51/66

Valuation of Floater: Complications

The valuation of floater is more complicated than

presented.

• If the spread is not equal to zero, the coupon rateand the discount rate are different.

• There might be restrictions imposed on theresetting of the coupon rate.

• For example, a floater may have a maximum couponrate called a cap or a minimum coupon rate called a

floor.

5-51


52/66

Inverse Floating Rate Notes

Unlike a floating rate note, aninverse floater is

a bond with a coupon that variesinverselywith a

benchmark interest rate.

Inverse floaters come about through theseparation of fixed-rate bonds into two classes:

• a floater, which moves directly with some interestrate index, and

•

an inverse floater, which represents the residualinterest of the fixed-rate bond, net of the floating-rate.

5-52


53/66

Fixed/Floater/Inverse Floaters

5-53


54/66


FIXED RATE BOND

The fixed rate bond can be split into a floater and an inversefloater unevenly.50/50 is the most popular split.

5-54


55/66


The sum of the face value of the floater and

inverse floater must equal the face value of the

fixed-rate bond.

The sum of the interest paid on the floater and

inverse floater must always equal the interestpaid on the fixed-rate bond.

• Therefor a maximum/minimum interest rate(cap/floor) is implicitly imposed on floater/inversefloater.

5-55


56/66

Floater and Inverse Floater: Example

An investment banking firm purchases $100million of a two-year 5.5% coupon bond in the

secondary market. Coupon is paid semi-annually.

The firm issues $50 million of floaters and $50million of inverse floaters. The coupon rate on

the floater is set to equal the six-month T-bill

rate. Suppose the future six-month T-bill rates

turn out as follows.

5.54% 6.00% 5.44% 6.18%

5-56


57/66


What is the cash flows to the floater and theinverse floater?

What is the coupon rate for the inverse floater?

Answer:for the first period, the coupon rate onthe floater is 5.54%. The coupon payment is

The coupon payment from the fixed rate bond is

Therefore, the coupon payment on the inverse

floater is .

5-57


58/66


(cont’d) The coupon rate on the inverse floater isthus

5-58


59/66

Repurchase Agreement (Repo)

An agreement between two parties whereby oneparty sells securities to another party in return

for cash and agrees to repurchase equivalent

securities at an agreed price and on an agreed

future date.

• Repos may be seen as being akin tocollateralizedborrowing and lending.

•

Legally, however, the transaction under a repoinvolves an outright sale of the securities thatpasses full ownership of the securities to thepurchaser.

5-59


60/66


61/66

Use of Repo: An Example

On August 31, 2007, the 30-year T-bond with acoupon of 5.00% and maturing on May 15, 2037,

was quoted at a clean price of 102.50. The

general collateral repo rate for a term of one

month was 4.775%.

A bond dealer receives an order from a client to

buy this bond forward in one month’s time. What

is the forward price that dealer should quote?Why? How should the dealer hedge the exposure,

assuming that the deal is done on August 31,

2007?5-61


62/66


The dealer will first compute the forward price asfollows:

• Borrow cash in the repo markets for a one-monthterm on August 31, 2007. (Cash borrowed is usedto buy the bond used in repo as collateral.)

• Figure out how much has to be paid in the repomarkets on September 30, 2007, to retrieve thecollateral.

• This is the forward price at which the dealers willbreak even. Any additional profit margin woulddepend on the extent of competition.

5-62


63/66


August 31, 2007:Using repo to finance thepurchase of the bond.

5-63


64/66


September 30, 2007:close the repo position.Buy back the bond and deliver to the client.

5-64


65/66


Calculation:

Break-even forward price =

5-65


66/66

End of the Notes!

lecture note 05_bonds with other features (1)

Documents