Convertible Bonds

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R E S E A R C H :

I N T E R N A T I O N A L

Convertibles

February 2002

For enquiries pleasecontact:

Christopher Davenport(44-20) [email protected]

Luke Fletcher(44-20) [email protected]

Convertible BondsA Comprehensive Beginner�s Guide

Convertible Bonds – February 2002

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Executive Summary ............................................................................................................................... 3Summary ................................................................................................................................................ 4The Basics .............................................................................................................................................. 5Convertible Bonds, an Investor�s Perspective ........................................................................................ 23Convertible Bonds, an Issuer�s Perspective ........................................................................................... 30Convertible Structures............................................................................................................................ 34Pitfalls and Protection ............................................................................................................................ 44Convertible Pricing Models.................................................................................................................... 47Appendix ................................................................................................................................................ 50Glossary.................................................................................................................................................. 57

Table of Contents


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This report1 is primarily intended as an aid to investors who wishto explore opportunities in convertibles and other equity-linkedstructures and would appreciate more background on the natureof the product. We outline practical and theoretical aspects of themarket in six sections. There is also a glossary of terms.

The basicsA convertible is a hybrid security, offering aspects of both equity and straightbond investment. Using a hypothetical example, the key features of a typicalissue are introduced, defined and their importance illustrated. The interpretationof a convertible as a derivative instrument is also explained, together withdefinitions of such terms as delta and gamma.

Convertibles from an investor�s perspectiveFrom an equity investor�s point of view, a convertible bond resembles thepurchase of a certain number of shares, the purchase of downside protectionand possible purchase of additional yield. From a fixed-income investor�sperspective, a convertible bond looks like the purchase of a straight bond and thepurchase a right to participate in an element of the appreciation of the underlyingequity. The purchase of a convertible is often perceived as a compromise inan uncertain world, as it will typically underperform the underlying share ina rising share price environment and underperform bonds in a falling equityprice environment.

Convertibles from an issuer�s perspectiveThe same principal of uncertainty applies to issuers of convertibles: withno presumption concerning the direction of share prices, the issuance ofa convertible can look an attractive option relative to the issuance of pureequity or pure straight debt.

Convertible structuresConvertibles can be structured across the pure-bond to pure-equity spectrumto appeal to distinct investor groups. We introduce non-vanilla convertiblestructures such as mandatory �DECs� in this section.

Pitfalls and protectionsAppreciating the importance of prospectus detail is crucial in convertibleanalysis; we identify some protection issues.

Pricing modelsWe present a brief intuitive description of the nature of the theoretical modelsmost frequently employed to value convertible bonds.

1 We would like to thank Laura Bordigato for her extensive contribution to this publication.


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A convertible bond is a debt security that can be converted into a fixednumber of shares per bond. If a bondholder decides not to exercisethe option to exchange bonds for shares, the bond will fall due forrepayment of principal at maturity.

Summary


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➤ Convertible bonds as hybrid securities

➤ The ‘vanilla’ structure

➤ Terminology

➤ Convertibles as derivatives

➤ Convertible price sensitivities — the ‘Greeks’

Convertible bonds as hybrid securitiesConvertible bonds are hybrid securities, part debt and part equity. They arecorporate bonds that may be exchanged at the option of the holder for a fixednumber of ordinary shares. Convertibles are usually redeemable in cash atmaturity and typically pay a fixed coupon over their life.

From an investor�s point of view, convertibles are attractive relative to straightcorporate debt as they offer the holder the potential to participate in the appreciationof the underlying equity. Convertibles offer some of the defensive characteristicsusually associated with fixed income paper. They pay regular coupons and are seniorto ordinary share capital, providing an element of downside protection. It is thisdefensive quality combined with the prospect of participation in the event of shareprice strength that is fundamental to the product�s appeal.

Investors should not conclude that convertibles simply provide investors with thebest of both worlds, however. Equities will typically outperform convertibles in arising share price environment, while a company�s straight debt is likely to outperformits convertible debt in a falling share price environment. An investor would benefitmore from investing directly in the underlying shares of a company (in a risingprice environment), and in its straight debt (if the share price is falling). However,investment returns are not predictable. The uncertain nature of investment returnsincreases the attraction of convertible securities, in our opinion. Convertiblesecurities offer a hybrid mix of equity exposure and fixed income defensiveness.

At maturity, a convertible is worth whichever is the greater of its cash redemptionvalue and the market value of the shares into which it converts.

To recap, convertible bonds offer the following:

➤ Upside participation in a rising equity market (thus outperforming straight debt);

➤ Downside protection in a declining equity market (thus outperforming straightequity); and

➤ Possible income advantage to the underlying shares.

In analysing the performance of convertibles as a separate asset class, one canobserve that they characteristically display levels of volatility and return greaterthan straight debt, but lower than straight equity.

The Basics


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The �vanilla� structureA convertible in its simplest �plain vanilla� form is essentially a corporate bond withan embedded equity option.

At issue, the investor pays an up-front amount (the �issue price�) to receive annualor semi-annual coupon payments and a cash redemption value at maturity (as withstraight corporate debt). A convertible differs from straight debt in that the holderhas the right to exchange the bond, usually at any time, for a predetermined numberof the company�s ordinary shares (the �conversion ratio�), without any extra payment.

In the event of conversion, the investor will renounce title to the corporate bond andany future income streams from it (including the final redemption payment), in favourof ownership of the predetermined number of shares underlying the bond. The valueof these shares will naturally be determined by their prevailing market price.

Plain vanilla structures are rare, however, as most convertible bonds include callfeatures. Below is an example of a simple callable convertible. The example is usedto provide a glossary of terms useful in explaining and valuing convertibles bonds ingeneral. We use a hypothetical convertible bond, the John Smith Corp. ConvertibleEUR 4% 2007. Below are the terms of the bond at issue:

Figure 1. John Smith Corp 4% 2007 — Convertible Data at Issue

Coupon 4%Coupon Frequency 2 (semi-annual)Issue Date 1 January 2002First Coupon Date 1 July 2002Maturity 1 January 2007Nominal Value �1000Issue Price 100Redemption Value 100Conversion Ratio 10 shares per bondConversion Price �100Call Protection Hard Call 3 years

Soft Call 2 years; Trigger @ 130%Call Price 100Put Feature -Issue Size �300m

Source: Schroder Salomon Smith Barney Convertibles.

As the convertible contains an option on the shares of the company, the investorwill want to remain aware of the price and other details of the underlying.

Figure 2. John Smith Corp — Ordinary Share Data

Stock Price �80Stock Volatility 25%Dividend per Share �2Dividend Yield 2.5%


During the life of the convertible, an investor will wish to monitor the followingcharacteristics of the convertible: convertible price, parity and premium. An investorwill also monitor the yield of the bond compared to yields on fixed income paperwith similar characteristics (maturity, coupon, issue size).


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John Smith Corp Convertible EUR 4% 2007 has the following characteristics:

Figure 3. John Smith Corp 4% 2007 — Convertible Data at Issue

Convertible Price 100Parity 80Premium 25%Current/Running Yield 4%Yield To Maturity 4%


TerminologyConvertible bonds are usually identified by issuer name (John Smith Corp), currency(EUR), coupon (4%) and maturity date 2007, though this may be abbreviated to issuername, coupon and maturity.

Coupons are the interest payments made on a bond by the issuer. The couponpayments are typically fixed at issue and are a percentage of the bond�s nominalvalue. For the John Smith Corp Convertible EUR 4% 2007, the coupon paymentsare calculated as follows:

40000,1*%4

min*

�entPerYearCouponPaym�entPerYearCouponPaym

alValueNoCouponentPerYearCouponPaym

===

As the John Smith Corp Convertible EUR 4% 2007 pays coupons semi-annually,half of this �40 amount will be paid to investors in the bond on each coupon date(1 July and 1 January each year).

Interest accrues between coupon payment dates. Purchasers of convertible bondsgenerally have to compensate the seller for the interest accrued from the time ofthe last coupon payment date, to the date they purchase the bond.

An investor buying the John Smith Corp Convertible EUR 4% 2007 for settlement4 June 2003, will pay the �clean price2� of the bond, plus the interest accrued on thebond since the last coupon payment date (1 January 2003).

The interest accrued on the John Smith Corp Convertible EUR 4% 2007 for theabove purchase would be calculated as follows:

( )

( )

88.16

000,1*%4*365154

**365

�erestAccruedInt

�erestAccruedInt

NomValueCouponDays

erofDaysActualNumberestAccruedInt

=

��

��

�=

��

��

�=

2 The clean price is the one conventionally used for quoting the price of both straight-bonds and the convertibles. It is expressed

as a percentage of nominal value and exclusive of accrued interest.

Quotation

Coupon

Accrued interest


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If we assume that the convertible�s �clean price� on 4 June 2003 is 102, an investorpurchasing the bond would pay:

( )( )

88.036,1Pr88.16000,1*%102Pr

min*PrPr

�icePurchase��icePurchase

erestAccruedIntalValueNoiceCleanicePurchase

=+=

+=

The convertible price inclusive of accrued interest is also referred to as theconvertible�s �dirty price�.

It is worth noting the following points:

➤ According to the prevailing market convention, the ratio that expresses the timeover which interest accrues is given by the actual number of days between thelast coupon and the settlement date, divided by 365 days (in the year). Some olderbonds specify calculation of accrued interest with respect to a 30-day month and360-day year, however.

➤ By historical convention, French convertible bond prices are quoted in �dirtyprice� format (inclusive of accrued interest) and in nominal terms, not as apercentage of the nominal value.

The maturity date is the date on which the issuer must redeem unconverted bondsat the redemption price.

The John Smith Corp Convertible EUR 4% 2007 would mature on 1 January 2006 at100% of its nominal value or �1,000 per bond. However, it would be rational forholders of the bonds to convert them prior to the final maturity date if the market valueof the shares into which they convert exceeds the cash redemption value of the bond.

A convertible�s nominal value may also be referred to as its face value. Each JohnSmith Corp Convertible EUR 4% 2007 convertible has a nominal value of �1,000.

A nominal value of 1,000 (in the relevant bond currency) is often the marketstandard in the Euroconvertible markets, though it is typically ¥1,000,000 in theJapanese domestic and Euroyen markets. As described above, the convertible�sprice, issue price and redemption value are all expressed as a percentage of thebond�s nominal value; French convertibles are an exception to this rule, however,being quoted in unit form.

The convertible price is the price at which it trades in the market. It is generallyquoted as a percentage of its par amount.

The major influences on the convertible price are as follows:

➤ Movements in the underlying stock price;

➤ Underlying stock volatility perceptions;

➤ Changes in the credit perception of the issuer;

➤ Movements in interest rates on risk-free securities;

➤ Prospective dividends; and

➤ The passage of time.

Maturity

Nominal value

Convertible price


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When the issue price of the convertible is equal to the bond�s nominal value, we saythat the convertible has been issued at �par�. The term �par� is often used to represent100% of the face value of a bond. The John Smith Corp Convertible EUR 4% 2007was issued at par, as its issue price (�1,000) was equal to 100% of the convertible�snominal value.

If a bond is issued at a price below its nominal value, it is referred to as an �originalissue discount� (OID) bond.

The influence of market forces will cause the price of a convertible bond to deviatefrom its nominal or face value over its life.

At maturity, a convertible�s redemption price is often equal to its issue price,implying redemption at the bond�s nominal value.

Where the redemption value of a bond is above its nominal value, it is said toredeem at a premium to par and is a �premium redemption� structure. In this case,the redemption price of the convertible is normally expressed as a percentageof its original issue price (and nominal value).

The John Smith Corp Convertible EUR 4% 2007 was issued at 100% of facevalue and will redeem at 100% of face value.

The number of shares a convertible can be exchanged for is represented by its�conversion ratio�. Though this ratio is determined initially at issue, it will usuallybe adjusted to account for stock splits, special dividends and other dilutive events.

The John Smith Corp Convertible EUR 4% 2007 has a conversion ratio of 10.This means that each John Smith Corp bond of �1,000 nominal can be convertedfor 10 John Smith Corp ordinary shares.

The conversion ratio is calculated by dividing a convertible�s nominal value by itsconversion price.

iceConversionalValueNoRatioConversion

Prmin=

The price at which underlying shares are indirectly purchased, assuming conversiontakes place and the convertible has been purchased at par, is shown by the �conversionprice�. Although no cash changes hands upon conversion, we can determine the priceat which a convertible investor initially buys shares by dividing the face value of thebond by its conversion ratio.

RatioConversionalValueNoiceConversion minPr =

The conversion ratio on the John Smith Corp Convertible EUR 4% 2007 iscalculated as follows:

Issue price

Redemption value

Conversion ratio

Conversion price


10

100Pr10000,1Pr

minPr

�iceConversion

�iceConversion

RatioConversionalValueNoiceConversion

=

=

=

The �100 conversion price can be thought of in option terminology as theconvertible�s �strike price�. An investor may convert the bond into the underlyingshares at any time. The investor will receive 10 shares having theoreticallypaid �100 for each of them, regardless of the prevailing stock price at the timeof conversion.

An investor in a convertible bond estimates the likelihood of (eventual) conversionby monitoring the course of the stock price.

If the share price > conversion price, the convertible is said to bein-the-money

If the share price < conversion price, the convertible is said to beout-of-the-money

If the share price is reasonably close the conversion price, theconvertible is said to be at-the-money

The share price of John Smith Corp at the time of the convertible issue is�80 (see Figure 3 above). As the conversion price on the John Smith Corp ConvertibleEUR 4% 2007 (�100) is above the share price of the stock, the convertible is said tobe out-of-the-money. If the stock price were to approach and rise above �100, the JohnSmith Corp Convertible EUR 4% 2007 would gradually become classified as moreat-the-money and then in-the-money.

Parity is the market value of the shares into which a convertible bond may beconverted. Parity is expressed in terms of the bond currency and is normally quotedas a percentage of par, except in the case of French bonds where it is quoted relativeto a bond�s nominal value.

( )alValueNo

icereCurrentShaRatioConversionParitymin

Pr*=

For the John Smith Corp Convertible EUR 4% 2007, parity is calculated as follows:

( )

( )

%80000,1

80*10min

Pr*

=

=

=

Parity�

�Parity

alValueNoicereCurrentShaRatioConversionParity

Parity


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Parity on the convertible will move in line with changes in the underlying shareprice. Additionally, movements in the exchange rate between the stock and bondwill influence parity on a cross-currency bond (where the bond currency differsto that of the underlying equity).

Premium on a convertible is the difference between the bond�s price and its equityvalue or parity. Premium is expressed as a percentage of parity.

( )Parity

ParityiceeConvertiblemium −= PrPr

The premium on the John Smith Corp Convertible EUR 4% 2007 is:

( )

( )

%25Pr80

80100Pr

PrPr

=

−=

−=

emium

emium

ParityParityiceeConvertiblemium

A convertible�s premium will change with movements in convertible price andparity. It is the difference between the two and represents how much more theinvestor is paying to control a given number of shares via the convertible.

One justification for the payment of a premium is the downside protection offeredby a convertible, over the life of the bond. A convertible investor retains the optionto receive the redemption value of the bond at maturity instead of converting intothe underlying shares (which may fall in price).

Yield advantage is another justification for paying a premium (in cases where thecurrent yield on the convertible is greater than the dividend yield of the commonstock). In many cases, while waiting for the optimal moment to convert, an investorreceives extra income from investment in the convertible. In our example, the JohnSmith Corp Convertible EUR 4% 2007 will pay �40 in income per annum.From Figure 3, we can see that the underlying stock has a dividend of �2 per share.The shares underlying the convertible would return only �20 a year. Convertibleinvestors will receive �20 more in income than investors who bought the equivalentnumber of John Smith Corp shares will.

dendYieldEquityDivieldeRunningYiConvertiblntageeYieldAdvaConvertibl −=

�Breakeven� on a convertible may be thought of as the length of time (in years)that it takes for a convertible�s premium to be made up by the yield advantage of theconvertible. �Breakeven� is a crude measure that makes no adjustment for the presentvalue of future monetary cash flows.

3 For a definition of Convertible Running Yield and Equity Dividend Yield, see Current or running yield below.

Premium

Yield advantage3

Breakeven


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( )[ ]RatioConversionrShareDividendPeCouponemiumAbsoluteBreakeven

*Pr

−=

For the John Smith Corp. Convertible EUR 4% 2007:

( )[ ]

( )[ ]

yearsBreakeven

Breakeven

��Breakeven

RatioConversionrShareDividendPeCouponemiumAbsoluteBreakeven

1020

20010*240

200*

Pr

=

=

−=

−=

We argue above that the yield advantage of a convertible relative to its underlyingshare is a justification for a convertible�s premium. However yield advantage isseldom the only justification. In this case it would take 10 years for the extra incomeon the bond to offset the premium on the convertible. The John Smith CorpConvertible EUR 4% 2007 only has a five-year maturity.

The current yield on a convertible is similar to the dividend yield on a stock;both are defined below.

icevertibleCurrentConCouponldRunningYie

icereCurrentSharShareDividendPeeldDividendYi

Pr

Pr

=

=

At issue, the running yield on the John Smith Corp Convertible EUR 4% 2007 was:

%4000,140

Pr

=

=

=

ldRunningYie�

�ldRunningYie

iceversionCurrentConCouponldRunningYie

A convertible�s current or running yield will change over the life of a bond as theconvertible price varies. For convertibles that are by convention quoted with accruedinterest included in the price, it is common to see the current yield expressed as thecoupon divided by the quoted price, adjusted for the unit size. As this is inconsistentwith the use of the term in relation to the majority of convertibles that are quoted inclean price form, in some cases analysts will use a notional clean price.

Current or running yield


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A bond�s yield to maturity (YTM) is the rate of return that an investor will receiveif the bond is held to maturity4. A convertible�s YTM is inversely correlated tomovements in its price: the higher the convertible price, the lower its YTM andvice-versa, other things being equal.

A convertible�s bond floor, or investment value, is calculated by consideringthe fixed income attributes of a convertible security alone. The investment valueof a convertible is found by discounting to present value the cash flows of theconvertible, (its coupons and redemption value). This is the same calculation thatwould be applied to a normal fixed income security to determine its value.

The discount rate generally applied to a bond�s cash flows is the risk-free raterelevant for the maturity of the bond, plus a credit spread, which measures the creditquality of the issuer5. Without its embedded conversion option, a convertible wouldbe worth no more than its fixed income value (its bond floor, or investment value).

Using the risk-free rate plus credit spread method described above, the investmentvalue on the John Smith Corp Convertible EUR 4% 2007 bond at issue was89.91% of its par value. Please refer to the Appendix for a more detailed breakdownof this calculation.

The Libor, or swap curve (for the relevant underlying currency) is conventionallyused in the Euroconvertible market as a proxy for the risk-free rate6. When choosinga credit spread, one is forced to make an assumption on the credit quality of the issuer,by inspecting the credit spread on corporate bonds for similarly rated issuers, forexample. The credit spread assumption is fundamental to the valuation of a convertibleas it can significantly affect the measures used to judge the merits of a bond.

The bond floor should provide the convertible price with a minimum price floor,subject to prevailing interest rates and the credit of the issuer. In theory, independentof the performance of the underlying share price, the convertible should be worth atleast its bond floor. However an investor should be aware that a dramatic fall in theshare price of a company can affect the perception of the correct credit level for thatissuer, which will tend to lower the perceived level of the bond floor.

A convertible�s risk premium is calculated as the difference between its price andbond floor, expressed as a percentage of the bond floor.

( )BondFloor

BondFlooriceeConvertiblemiumRisk −= PrPr

4 This is a somewhat simplistic definition as it ignores the reinvestment of coupon interest. For a more complete definition of YTM,

please see the Appendix.

5 An alternative method for calculating the bond floor considers the spot yield curve and discounts each future payment using the

appropriate spot rate plus credit spread.

6 Ideally sovereign debt of the nation associated with the currency in question should be used. For example the Treasury yield curve

should be used for US dollar bonds. Though swap rates are higher than Treasury rates, there is a compensatory effect in that the

spread over swaps for a given corporate bond will be tighter than the spread over Treasuries.

Yield to maturity (YTM)

Bond floor, orinvestment value

Risk Premium


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The risk premium on the John Smith Corp. Convertible EUR 4% 2007 at issue was:

( )

( )

%22.11Pr91.89

91.89100Pr

PrPr

=

−=

−=

emiumRisk

emiumRisk

BondFloorBondFlooriceeConvertiblemiumRisk

The difference between a convertible�s price and its bond floor can be seen as thevalue that the market places on the option to convert. The risk premium measureshow much of a �premium� to the bond floor a fixed-income investor is required topay for an option on the underlying shares.

Many convertibles have call features. A call feature gives the issuer the right toredeem a convertible before maturity (from the call date) at a predetermined price(the call price). The call price of a bond is typically at par, or at the accreted valueof the bond, in the case of an OID or premium redemption security.

The John Smith Corp Convertible EUR 4% 2007 can be called at par, or 100% ofits nominal value. However, it cannot be called for at least three-years (the bondhas three-years of �hard non-call� (HNC) protection), as shown in Figure 2. HNCprotection has value to a convertible investor. It guarantees the holder of the bondexposure to the underlying share and to any yield advantage that this may implyfor an identifiable period of time.

The John Smith Corp Convertible EUR 4% 2007 cannot be called unconditionallyuntil after this initial three-year, HNC period has expired, however. The conditionsof the bond�s �soft call� (sometimes referred to as its provisional call), must also besatisfied. A �soft call� usually requires the price of the shares underlying a convertibleto trade above a predetermined percentage of the initial conversion price, for aspecified period of time (often 20 of 30 consecutive business days). Our notionalbond has two years of �soft call� protection following its three years of HNCprotection. The issuer can only call the bond if the stock trades at 130% of theinitial conversion price, or �130, for at least 20 days.

In addition to the call price, the company issuing a call notice will generally haveto pay investors the amount of interest that has accrued on the security betweenthe previous coupon payment date and the call date.

Call protection


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When a bond is called, investors have the right to choose whetherto accept the call price plus accrued interest7, or to convert into theunderlying shares. In making this investment decision, an investorshould compare the value of the call price plus accrued interest withthe current market value of the shares they would receive on conversion,parity; (note that on conversion, investors normally forfeit anyaccrued interest).

If parity is greater than the call price plus accrued interest, the issuer’sdecision to call the bond back will, in effect, force investors to convertinto shares.

The intention behind most call decisions is to force conversion. If forcing equityconversion is the company�s ultimate goal, the issuer may delay calling the bonduntil parity is well above the call plus accrued interest price. This is to ensure thatmovements of the share price during the required notice period of the call (typicallybetween 30 and 90 days), will not affect the result of the call (investors will maketheir decision to convert or redeem their bonds during the notice period).

Sometimes it may be rational for an issuer to call a bond even if parity is wellbelow the call price. This may be the case either if interest rates have fallen orif the company�s credit has improved and so that it may be able to refinance onmore attractive terms. Calls for cash redemption are much rarer than callsforcing conversion.

While many convertibles have call features, investor put options are less common.A put feature gives the holder of the convertible the right to require the issuer toredeem a convertible on a predetermined date or dates prior to maturity at a fixedprice. The issuer is usually required to redeem the convertible for cash. However,some convertibles give the issuer the option of delivering shares, or a mix of cashand shares, as long as the market value of the shares issued or mix paid is at leastequivalent to the predetermined cash value of the put.

The issue size is the nominal amount of convertible bonds sold by the issuing firm.

Convertibles as derivativesA convertible is a hybrid instrument. We can think of parity as the equity componentof a convertible and the bond floor as its fixed-income component. This being thecase, the premium to parity of a convertible represents the cost to an equity investorof owning the bond. Similarly, a fixed income investor will consider the riskpremium on a convertible as the cost of owning it.

7 Assuming the call notice specifies payment of accrued interest. In instances where the call date falls on a coupon payment date,

this issue does not arise.

Put features

Issue size


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The different views taken by fixed income and equity investors on the make upof a convertible is consistent with the very different views each have on the valueunderlying a convertible.

Equity investors tend to view a convertible as a combination of:

➤ Equity � a convertible holder has control over a fixed number of shares.In terms of value, an investor �owns� parity.

➤ A put option � a convertible holder has control over the underlying shares, but ifthe stock price falls, the investor can choose not to convert and instead to receivea cash redemption amount at maturity. It is sometimes easier to think of the rightnot to convert as a put option, if one imagines the investor automatically beingdelivered the fixed number of shares at maturity and then having the (notional)right to sell the package of shares back again at the cash redemption amount.The rational investor will exercise this right if the redemption value is greaterthan parity; the investor pays a premium to own this embedded put option.

➤ A dividend swap � a convertible holder indirectly owns a certain numberof shares but receives coupons instead of dividends until the earlier of maturityor conversion. This is equivalent to owning a dividend swap that gives theequity investor coupons in exchange for dividends. Assuming there is an incomeadvantage for the convertible holder, the investor will pay a premium to ownthis embedded dividend swap.

Fixed income investors tend to view convertibles as a combination of:

➤ A straight bond � a convertible holder owns a straight corporate bond that payscoupons and has a cash redemption value at maturity. A convertible�s bond floorrepresents this straight bond value.

➤ A call option � a convertible holder has the right to exchange his corporatebond for a predetermined number of the company�s ordinary shares, usuallyat any time. This is equivalent to owning a call option that gives the fixed-incomeinvestor the right to buy shares by giving up the convertible. At maturity thisis equivalent to a call with a strike price approximately equal to the conversionprice (for a single currency bond). Unlike a conventional option, there is no cashpayment on exercise. The converting bondholder �gives up� the straight bondhe controlled until the moment of conversion though has paid a premium toown the embedded call option (the risk premium).

We can show graphically how the value of a convertible and its debt and equity varywith the share price:

Equity investorviewpoint

Fixed incomeinvestor viewpoint


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Figure 4. Convertible Price, Parity and Bond Floor against Share Price

Share Price

Bond Floor Parity Convertible

Premium


Figure 5. Risk Premium against Share Price

Bond Floor Convertible

Risk premium


We note that:

➤ The bond floor of a convertible tends not to be correlated with movements in theshare price, unless a fall in the stock price is perceived to affect the credit qualityof the issuer (shown in the extreme left of Figures 4 and 5 above).


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➤ Parity varies proportionally with the share price (in non-cross currency bonds),as it is equal to the share price (expressed in the bond currency) multiplied by theconversion ratio. In single currency bonds the slope of the parity line representsthe conversion ratio.

➤ Figure 4 shows how investors purchasing shares via a convertible forfeita degree of equity appreciation, as the convertible price is less sensitiveto share price variations than pure equity.

➤ The difference between the convertible price and the bond floor (the riskpremium) represents the value of the embedded call option to a fixedincome investor.

➤ The difference between the convertible price and parity (premium) representsthe value of the embedded put option (downside protection) and the dividendswap (yield advantage) to an equity investor.

➤ Figure 4 illustrates how, as the equity price rises, the premium narrows toa point where the convertible derives its value from the equity component only.When the share price rises, both the value of the put option and the value of thedividend swap decrease. The put value decreases as it becomes less likely thatinvestors will exercise the option to �sell� shares for cash redemption at maturity.Simultaneously the dividend swap value may decrease in a callable bond,as it becomes more likely that the issuer will call the bond back and investorsexpect the period of yield advantage to shorten.

➤ When the equity price declines, the premium expands. The more the share pricefalls, the more the convertible price is supported by and trades increasingly inline with its bond floor.

Convertible price sensitivities � the GreeksA convertible�s price is positively correlated with:

➤ The underlying stock price � the higher the underlying stock price, the greaterthe value of parity (the equity component of a convertible), so the greater thevalue of the convertible.

➤ Volatility of the underlying stock � the higher the volatility of the underlyingshare, the greater the value of the convertible�s embedded option (put or call,according to the equity or the fixed-income investor�s perspective), so thegreater the value of the convertible.

➤ Issuer credit quality �the better the credit quality of the issuer, the lower thecredit spread over Libor or the benchmark government yield curve requiredto discount a bond�s coupon payments and redemption value. The lower thediscount factor applied to a bond�s cash flows, the higher its bond floor andthe greater its value.

➤ Call protection � the longer the call protection on a bond, the longerthe guaranteed period of yield advantage and the greater the value of theconvertible�s embedded dividend swap, so the greater the value of theconvertible. Longer options also tend to be more valuable than shorter ones.


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A convertible�s price is negatively correlated with:

➤ Stock dividends � the higher the dividend, the lower the yield advantage ofthe convertible over the share.

➤ Interest rates � the higher the prevailing interest rate, the higher the discountrate for coupon payments and redemption value, the lower the bond floor andconvertible�s value. It is also true that the higher the interest rate, the greaterthe value of the convertible�s embedded call and so the greater the convertible�svalue. Thus a convertible�s price is less sensitive to interest rates movementsthan an otherwise identical straight-bond.

We can describe the impact of various factors on the price of a convertible usingthe following concepts, which are more commonly referred to as the �Greeks�;the �Greeks� are outputs of convertible pricing models.

➤ Delta — measures the sensitivity of the convertible price to changesin parity

➤ Gamma — measures the sensitivity of delta to changes in parity

➤ Vega — measures the sensitivity of the convertible price to changesin underlying stock volatility

➤ Rho — measures the sensitivity of the convertible price to changesin interest rates

➤ Theta — measures the sensitivity of the convertible price to thepassage of time

DeltaDelta measures the sensitivity of a convertible�s price to changes in parity.It is the equity sensitivity of the convertible, in absolute terms. Conventionally,delta is expressed as the change in convertible price for a one-point change inparity. Thus, a 40% delta means that if parity rises by 1 point, the convertibleprice will rise by 0.4 points (40% of the one-point change in parity).

Delta changes along the convertible price curve. The higher the value of parity, thehigher the convertible�s delta. The range of delta along the convertible curve variesbetween 0% and 100%. As the convertible�s price moves from out-of-the-moneyto in-the-money (due to a rise in the underlying share price and therefore parity),its delta will increase as the convertible�s equity component becomes more significant.Further comments on delta from a theoretical perspective are available in the Appendix.

GammaGamma is the rate of change in delta for movements in the underlying share price.Conventionally, it is expressed as the change in delta for a one-point change in parity.

For material share price moves, delta can be a poor guide to the sensitivity of theconvertible to a move in parity. In general the convertible is more equity sensitivein rising markets and less sensitive in falling markets than the delta would suggest.Gamma is the measure of the intensity of this effect.


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This topic will be covered later when discussing �gamma trading�. A theoreticaltreatment of gamma and a chart of its sensitivity to the share price level areavailable in the Appendix.

VegaVega is the sensitivity of the convertible price to changes in the volatility of theunderlying stock. Conventionally, vega is expressed as the change in the fair valueof the convertible for a one percentage point increase in the assumption forstock volatility.

In order to find a theoretical value for a convertible (its theoretical �fair value�),it is necessary to input assumptions to a convertible pricing model:

➤ A credit spread (or spread over Libor), used to establish the rate for discountingthe bond�s coupon payments and its redemption value;

➤ Dividends on the underlying share, to maturity; and

➤ A volatility assumption for the underlying stock.

Vega measures the sensitivity of fair value to changes in the assumed level ofstock volatility. There are no short names in common use for the dividend andspread sensitivity.

The convertible price curve is set for an assumed level of stock volatility:it shows how the convertible price changes when parity changes, given theassumed volatility.

In approximate terms the closer the convertible is to being at-the-money, the moresensitive the convertible price is to changes in assumed volatility. A chart of vegaagainst parity is available in the Appendix.

RhoRho measures the sensitivity of a convertible price to movements in interest rates.Conventionally, it is expressed as the change in convertible price for a given onebasis point move in interest rates (a parallel shift in the whole yield curve).

Rho is the fixed income sensitivity of the convertible just as delta was defined asthe equity sensitivity.

Delta increases as parity (the equity component of the convertible) increases.Conversely, rho increases when parity decreases, or as the convertible starts tradingmore on its fixed interest characteristics.

A more thorough treatment of Rho is to be found in the Appendix.

ThetaTheta is the change in convertible price with the passage of time. Conventionally,it is expressed as the percentage change in convertible price for the passage of oneday, all other things being equal. For a near-the-money convertible, the passage oftime is normally negative for the value of a convertible, the time decay of the optionelement outweighing any upward drift in the bond floor (see Figure 23 in the Appendix).


21

Convertible bonds, a simple classificationFigure 6 reproduces the chart showing convertible behaviour for different shareprice levels. It is used here to generate a simple classification system for convertiblesin different share price zones.

Figure 6. Behaviour of Convertible in Different Share Price Zones

Share Price

Parity Bond Floor Convertible

Busted OTM ATM ITM Discount


The classification refers to the relationship of the stock price to the conversion price.To reiterate our earlier comment;

If the share price > conversion price, the convertible is said to bein-the-money

If the share price < conversion price, the convertible is said to beout-of-the-money

If the share price is reasonably close the conversion price, theconvertible is said to be at-the-money

We add here two other, more extreme classifications:

If the share price falls dramatically, leaving the convertible trading ata price so deeply out-of-the-money that its equity component becomesimmaterial, it is sometimes referred to as busted debt8, or a highyield convertible

If the share price rises dramatically and parity is greater than theconvertible price (ie a negative premium), the convertible is said totrade at a discount9 to parity

8 The phrase �busted debt� or �busted convertible� has no precise definition. Many will not apply the description

unless there has been a deterioration of the credit as well as a fall in parity.

9 A discount convertible trades at a negative premium to parity. Arbitrage opportunities from exploiting any anomaly

are frequently hindered by market inefficiencies.


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At issue a convertible is, generally speaking, priced slightly out-of-the-money.However, convertibles in each category outlined above will tend to have certainpremium, delta, gamma and rho characteristics. Figure 7 gives a description of eachcategory in terms of the typical value of the parameters for a basic convertible:

Figure 7. Typical Characteristics of Convertible Bonds Categories

Busted OTM ATM ITM Discount

Premium >100% 100-40 40-10 <10% <0%

Delta 0-10% 10-40% 40-80% >80% 100%

Gamma None Varied High Low None

Rho High High Low None None


It is possible to draw conclusions about an investor�s priorities from the nature of theconvertibles owned:

➤ A high premium over parity may indicate that the investor attaches particularimportance to downside protection and yield advantage.

➤ Delta represents the equity sensitivity of a convertible. It indicates the level ofexposure an investor wishes to have to the equity market.

➤ Since gamma is a measure of how responsive the equity sensitivity of aconvertible is to share price movements, high gamma bonds are natural holdingsfor those anticipating dramatic share price movements (in either direction).

➤ Rho represents the interest rate sensitivity of a convertible. A high level ofrho indicates that the convertible is trading predominantly as a debt instrument.Holders of such bonds are likely to be mainly interested in theirstraight-bond component.

Thus it is possible to draw conclusions about a bondholder�s investment objectivefrom the characteristics of the securities owned. We identify the objectives andstrategies of different investor types and analyse their preference for different typesof convertible below.


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➤ Convertibles for equity investors

➤ Convertibles for fixed income investors

➤ Convertibles for hedge funds

➤ Change in the investor base over the life of the convertible

Convertibles for equity investorsWe stated above that equity investors perceive the purchase of a convertible asequivalent to the purchase of a certain number of shares, the purchase of downsideprotection and the purchase of possible yield advantage.

tageYieldAdvanotectionDownsideEquityeConvertibl ++= Pr

The downside protection over the life of the convertible can be seen as an embeddedEuropean put option to sell shares at the redemption price at maturity. This right willbe exercised if parity on the bond is less than the cash redemption value (the strikeprice of the notional put) at maturity.

The yield advantage can be characterised as an embedded dividend swap, whichgives the investor coupons in exchange for dividends until the convertible bond isconverted or redeemed.

Whatever other attributes an equity investor looks for in a convertible, it is likelythat they will maintain a preference for bonds whose risk and return characteristicsdo not deviate radically from equities themselves. Convertibles that trade onvery low premiums are obvious candidates for equity investors, for example.Such convertibles typically have high deltas and a relatively distant investmentvalue (ie a high-risk premium).

Some equity investors are attracted by the income characteristics of certainconvertibles. This is particularly so if the premium paid is quickly made up for byan income advantage over the underlying shares. Instances in which the premiumis amortised before the first call date of the convertible will have obvious appeal(see the definition of �breakeven� on page 13 for more details).

The cash for cash switching strategyAn investor selling shares to buy a bond convertible into the same underlying shareson a cash for cash basis is reducing the number of shares he controls, assuming theconvertible stands on a premium.

From our notional example earlier, if John Smith Corp shares are trading at �125,an equity investor with 40,000 shares has a cash investment of �5 million.

Convertible Bonds, an Investor�sPerspective


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If the John Smith Corp Convertible EUR 4% 2007 is trading at 129% (clean) ona premium of 3.2%, the equity investor�s �5 million potential sale proceeds wouldpurchase �3,876,000 nominal of the convertible bond, ignoring accrued interesteffects; (the �5 million proceeds divided by the clean price of the bond (129%)).As each bond converts into 10 shares (the conversion ratio of the bond), the investorin reality �buys� control of only 38,760 shares (from 40,000 above).

From an equity investor�s perspective, when the share price underlying a convertiblerises, the convertible price will tend to rise, but by less than parity. Thus convertibleswill typically underperform the underlying share because the premium contracts.Intuitively, the value of the downside protection will decrease and the risk of losingthe yield advantage will increase due to increased call risk. The premium is actuallythe amount that an equity investor stands to lose when switching into a convertibleif the share price rises.

When the underlying share price falls, the convertible price will tend to fall,but by less than parity because the premium expands on the downward move.Thus convertibles will tend to outperform the underlying shares because of premiumexpansion. The premium expansion is actually the amount that equity investorsstand to gain from switching into a convertible if the share price falls.

Equity investors switching into convertibles at very low premium levels(and consequently, high delta levels) often get a highly asymmetric risk/return profile:

➤ If the underlying shares keep rallying the convertible price will rise on almosta 1:1 basis, because the premium is so low (its delta will be tending towards100%). Though the convertible may underperform the underlying shares,this underperformance should be slight.

➤ If the underlying shares fall, the convertible will fall but the decline will besoftened by expansion of the bond�s premium. In such a scenario, a convertiblewill tend to outperform the underlying shares.

Thus the cash-for-cash switching strategy suggests:

➤ Equity investors should consider selling shares and switchinginto convertibles when the premium is very low because of theasymmetrical nature of prospective returns

➤ If the share falls and the premium widens, investors should considerswitching back into shares to crystallise a profit, bearing in mind thata rally in the share price could wipe out his gain

➤ This strategy may outperform simple ‘buy and hold’ strategies foreither shares or convertibles in a range-bound but volatile market;investors following this strategy will tend to buy in-the-moneyconvertibles (high delta, low premium)

Impact of ashare price rise

Impact of ashare price fall


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Convertibles for fixed income investorsFor a fixed income investor, the purchase of a convertible is equivalent to thepurchase of a straight bond plus the purchase of upside participation in any underlyingshare price appreciation. The straight-bond component is the bond floor and upsideparticipation comes from the embedded call option to purchase the underlying shares.The risk premium is the premium to the bond floor a fixed-income investor paysin order to gain access to participation in upward moves in the underlying shares.

When the underlying share price (and consequentially, the convertible price)rises, the risk premium on the convertible will expand, as the call becomes morein-the-money.

When the underlying share price (and convertible price) falls, the risk premiumcontracts, as the call becomes more out-of-the-money. The convertible price willfall, but as long as the fall in the underlying share price does not affect the creditquality of the issuer, the convertible�s bond floor (its fixed interest value) shouldsupport its price.

Risk premium expansion is the potential advantage that a fixed income investorstands to gain by switching from a straight bond into a convertible, if the underlyingshare price rises. Conversely, the risk premium can be seen as the amount that a fixedincome investor stands to lose from switching by a straight bond into a convertible,if the underlying share price falls.

The position of convertibles as a �halfway house� between fixed income and straightequity is especially relevant for the many institutional investors who are bound bya requirement to invest only in bonds, or to keep a large proportion of their portfolioin fixed-income securities. As convertibles are often classified as bonds, fixed-incomeinvestors may use them to inject equity elements into their portfolios without losingthe support offered by the bond floor.

Out-of-the-money convertiblesTraditionally, fixed-income investors with a low risk profile have preferred to buyout-of-the-money convertibles since they trade close to their bond floor and can offerinexpensive call options on the price performance of the underlying shares. Despiteoffering only a small element of equity sensitivity, an out-of-the-money call stillgives an investor the chance to participate in any appreciation of the underlying stock(even if only moderately, on account of the low delta that typifies an out-of-the-moneyconvertible security). On the other hand, they will have paid almost nothing for thisoption, so they will lose little if the underlying share price falls. Since rho is high onan out-of-the-money convertible, it will respond to movements in interest rates andcredit spreads in a similar fashion to a straight bond. As the underlying share pricerises, moving the convertible more into the money, fixed income investors may betempted to lock in their profit and sell the convertible, due to the expansion of therisk premium.

Implications of shareprice moves


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In some cases, fixed income investors may not be motivated at all by upsideparticipation in underlying share appreciation and may only be interested in thebond component of the convertible. In this case they will buy deep out-of-the-moneyconvertibles, as they will be reluctant to pay any premium to the perceived bond floor.This type of investor may find a yield advantage in convertibles compared to theirrelated straight-bonds due to anomalies in the secondary market in which convertiblesare traded. Moreover the relative coupon structure and sometimes the subordinationof the convertible can differentiate it from other debt of the issuer. Often theconvertible will present a higher risk/higher reward profile than other corporate debt,making it attractive to certain investors, under certain circumstances.

Callable asset swapsA callable asset swap is a contract between two counterparties, which seeks torepackage the convertible so that one counterparty owns only the fixed incomecomponent of the convertible and the other owns just the call option on the underlyingshares. We explain below why a fixed income investor should enter into an assetswap agreement instead of just buying a straight bond. Predictably, yield advantageplays a key role.

In reality a �callable asset swap� is not an asset swap at all, but a contract in whichthe option investor physically sells the convertible to the bond investor who becomesthe beneficial owner of the security and receives the coupon payments and theredemption value on maturity. The option investor, by retaining an option to buy backthe convertible in future, has attempted to isolate and dispose of the straight bond partof the convertible, while retaining the right to repurchase the convertible should theywant to convert, for example.

The terms of the contract specify the cash amount due for selling the convertibleand the formula for calculating the price at which the convertible may be bought back.The cash amount corresponds to the value of the convertible�s bond floor. This flooris calculated at a given credit spread over Libor. The price at which the convertiblemay be repurchased is worked out as another bond floor, calculated using a lowercredit spread. This lower spread, termed the �recall spread�, is also specified inthe contract.

The credit spread at which a fixed income investor can buy the bond element ofa convertible in a callable asset swap, may be higher than the credit spread impliedin the price of a straight-bond with the same profile. Thus, a fixed-income investormay have the chance to buy a straight bond proxy with the same apparent level of risk,but at an advantageous yield. We say apparently because in reality the bond investoris short a credit option to the option investor. The value of this option is reflectedin the higher credit spread (and therefore, higher yield).

Convertibles for hedge investorsIt is possible to construct a portfolio that is theoretically insulated from share pricemovements. This portfolio is based on a long convertible position and a short positionin the underlying share. In order to hedge the long convertible position against changesin the underlying share price, the number of shares that must be sold is indicated bythe convertible�s delta or �hedge ratio�. The number of underlying shares per bondnecessary to hedge a convertible position is given by the bond�s delta multiplied byits conversion ratio.


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Delta hedging and gamma tradingIf the delta � the change in the convertible price for a one-point change in parity �of a convertible was 40%, it would be necessary to sell a number of shares equal to40% of the number into which the bond may be converted, to hedge it successfully.

Delta hedging insulates convertibles against small movements in the underlyingstock price. Providing the correct hedge ratio is employed, it is possible tocompensate for small share price moves on the long position in the convertible.

When the move in the underlying shares is not small, the effect of convexity(gamma) on the convertible price cannot be ignored. For significant movementsin the underlying share, the hedged portfolio will return a positive amount regardlessof the direction of the underlying price move, all other things (including the effectsof time decay) being equal.

As the share price underlying a convertible rises, the convertible�s delta willalso rise. This causes the hedge ratio to increase meaning that more shares need tobe sold to keep the portfolio delta neutral. As the underlying share price falls, theconvertible�s delta falls and some shares must be bought back in order to re-hedgethe portfolio. The positive gamma effect ensures that hedged investors are alwaysbuying shares after a price fall and selling after a price rise: this is one mechanismthrough which hedge investors generate profits from their portfolios.

Figure 8 below uses the details of the notional John Smith Corp. Convertible EUR4% 2007 issue, used above:

Figure 8. John Smith Corp. Convertible EUR 4% 2007 Long Convertible Position

Convertible Price �1000

Conversion Ratio 10

Underlying Share Price �80

Delta 40%

Gamma 0.5%


In order to hedge the long position of one bond against changes in the underlyingshare price, we need to take a short position in four shares:

sharesSaleShareDeltaShortShareSaleDeltaShort

DeltaRatioConversionShareSaleDeltaShort

4%40*10

*

===

When the underlying share price rises, the convertible�s delta also rises. This meansthat the convertible should participate in a greater proportion of any future shareprice appreciation, on an upward move in the underlying stock price, (the effect ofgamma). However, the short position in the underlying share has not been altered,despite the convertible�s higher delta.

As a result of this, the profit on the long convertible position should be greater thanthe loss suffered on the short position in the underlying stock, as the shares rise.The net position from the trade will be a profit.


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Conversely, as the underlying share price falls (causing the delta of the convertibleto fall), the bond will participate in a diminishing proportion of the decline, due tothe effect of gamma. The short position in the underlying share remains based onthe original, higher delta (40%). The loss on the convertible long position shouldbe smaller than the profit on the short sale of the underlying stock. Again, the netposition from the trade will be a profit.

The size of any profit on this type of trade is dependent on both the move in theunderlying stock and on the bond’s gamma profile. It is also worth consideringthe following:

➤ The greater the move in the underlying share price, the greater the chance ofsignificant gamma trading profits.

➤ Stock volatility is a measure of the propensity of the underlying share to movesharply. The higher the underlying stock volatility, the greater the potentialprofits from the hedged convertible position.

➤ The gamma trading strategy works by adjusting the stock short necessary(by buying back or selling shares) for changes in the share price (and thereforedelta) level. Hedged investors will be natural buyers and sellers of shares asthey maintain the portfolio hedge, according to a bond�s theoretical delta.

➤ Delta hedging is most effective when a convertible is theoretically cheap � an investor will expect to capture more volatility than he has �paid for�.Theoretical fair value depends on several variables including the assumedvolatility of the underlying shares. An investor will estimate the level ofunderlying stock volatility and input this in to a convertible pricing model.Convertibles trade at prices that can be higher or lower than theoretical fairvalue, due to supply and demand. �Implied volatility� is the stock volatilitythat is theoretically implied in the convertible price. A convertible is definedas �theoretically cheap�, if it trades below theoretical fair value and�theoretically rich�, if it trades above fair value.

➤ To conclude, hedge investors using this strategy to trade their convertibleportfolios, are employing a technique known as �gamma trading�. Gammatrading is not infallible, however. Shares do not always exhibit sufficientvolatility for the strategy to make money. The loss of value as a result oftime decay (theta) can prove the more important factor.

Hedge funds are often highly leveraged and can produce a substantial profit for alow initial investment. The leverage comes from their ability to create the necessarystock short by borrowing the underlying shares at a reasonable fee. Naturally, hedgefunds will prefer convertibles with underlying shares that are both highly volatileand easily borrowable.


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Changes in the investor base over the life of the convertibleAt issue, a convertible can normally be classified as one of the following:

➤ An equity alternative � a low premium and a relatively low bond floor;

➤ A yield alternative � a high premium and a relatively high bond floor; or

➤ A total return alternative � incorporating a medium premium to parity andinvestment value (risk premium).

The majority of new issues will naturally fall into the third �balanced� or �total return�category. Such bonds typically attract a wide range of investors including mixed fundsand hedge funds. The investor base will change as the underlying share price movesup or down, moving the convertible more in or out-of-the-money, however.

An out-of-the-money convertible is more likely to be purchased by a fixed-incomeinvestor, who will consider selling his position to lock in a profit as the convertiblebecomes more in the money. An in-the-money convertible is likely to be purchasedby an equity investor who will consider selling the bond as it begins to moveout-of-the-money and its delta starts to fall.

This chapter has explained how a convertible may be viewed fromseveral different angles and may fulfil differing investment objectives fordifferent investor bases. We have identified key valuation elements andtrading strategies including:

➤ Buying high delta convertibles as a substitute for equity;

➤ Buying high yielding convertibles as a substitute for corporatebonds; and

➤ Buying convertibles perceived as ‘theoretically cheap’ forhedge funds


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➤ Convertible financing

➤ Financing objectives and prospective issuers

➤ To call or not to call?

Convertible financingWe have looked at the idea of investing in a convertible as an alternative to investingin either equity or straight debt. We said that in general, investors would do betterinvesting directly in shares, when the underlying share price rises and would dobetter owning straight debt, when the underlying share price falls than they wouldowing a convertible. We also pointed out the limitation of this argument: at the timeof the investment, an investor cannot know whether the share price will rise or fall.We concluded that much of the appeal of convertible securities (from an investor�sviewpoint) is their ability to achieve high expected returns with low volatility.

In the same way, one can consider an issuer�s choice of financing using aconvertible rather than equity or straight debt.

If the underlying share price of a convertible were to rise above the conversionprice, investors would (eventually) convert into equity. In theory, the issuer mayhave been better off economically issuing straight debt since, on conversion, thecompany will in effect sell its stock at a discount to the prevailing market price.However, one could also argue that the convertible will have proved a better formof financing than straight equity. Assuming eventual conversion the issuer has, ineffect, made a (deferred) sale of equity at issue date. The issue price of this equitywill be at a premium to the stock price on the date of issue.

If the underlying share price were to fall and conversion fails to take place, thecompany would theoretically have done better selling straight equity. However,as with the investor at the time of purchase, the issuer cannot know in advancewhether the share price will rise or fall. In the weak share price scenario, a convertiblewill have been a better form of financing than straight debt � if the bond is notconverted, it is equivalent to a debt issue at a lower coupon.

Convertible Bonds, an Issuer�sPerspective

On a share price rise

On a share price fall


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Financing objectives and prospective issuersIssuing a convertible may fulfil different financing objectives:

Potential deferred sale of equity forward at a premiumThe issuer of a convertible typically locks in a conditional sale price for theunderlying shares that is higher than the market price of those shares in the market,at the time of the issue. The premium to the current share price also means that theissuer receives greater proceeds than would be received in the case of an equity issue(of the same number of shares), even if the equity placing were not issued at adiscount to the prevailing market price. A company that believes the market isundervaluing its shares and expects the share price to rise, will prefer to sell equityforward at a fairer price via a convertible than to sell shares immediately at thecurrent undervalued price. If the company is sure that the share price will rise, itshould issue debt to raise money, but some companies may have difficulty doingthat, such as a start-up company or a company that is already highly geared. Theissue of a convertible avoids the stigma sometimes associated with a rights issue orother pure equity issuance. It sends a relatively positive signal to the market aboutthe company�s view of its own share price prospects.

Monetising equity investments�Exchangeable10� structures can permit issuers to monetise stakes they hold in othercompanies at attractive funding rates.

Securing low-cost fundingAny company that cannot or does not want to pay high coupons will find convertiblesa cheaper source of debt financing. Additionally, in the case of exchangeable bonds,the issuer will retain dividend distributions on the underlying shares until conversion.Thus the issuer will be able to fund the coupon/yield obligations partly through thecontinued receipt of dividends on the underlying shares.

Tax/cash-flow advantagesUnder most tax jurisdictions, only interest payments on debt are tax-deductible;dividends are paid out of after-tax income. Thus convertible debt financingis generally more tax efficient than equity issuance. In the case of zero couponconvertibles, no cash interest is actually paid, but in most tax regimes the companycan deduct the interest implied by the accretion rate of the convertible, creating acash-flow advantage. In the case of exchangeable bonds, issuers are allowed to deferthe crystallisation of tax liabilities on the sale of shares under many tax regimes,as the full beneficial ownership of the underlying shares transfers to the investorsonly on conversion.

10 For more information on �exchangeables�, see page 41. They are convertible bonds issued by one company that can be converted

into the shares of a different company.


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Delaying dilutionCompared with the immediate issuance of equity, the issuance of a convertiblemay be beneficial for earnings per share. This is particularly true in cases wherethe probability of conversion is low, as analysts will typically employ undiluted EPScalculations. Moreover convertible investors do not have voting rights, so the issuanceof a convertible defers the dilution of voting rights in the company. Closely heldcompanies, for whom the issuance of voting shares may compromise control, mayhave a particular interest in raising equity capital via convertibles.

Exploiting market conditionsOne advantage of issuing a convertible is that it can be completed as an �overnight�transaction, whereas an equity issue typically takes several weeks. Speed ofexecution is a key advantage of convertible bond issuance.

Targeting a diverse and distinct investor baseThe diversification of the convertible investor base enables issuers to access awider investment audience than they might via solely the equity market or fixedinterest market alone.

For example a company that has recently completed an equity issue may find iteasier to raise further capital via a convertible rather than returning to the equitymarket. Some companies issue convertibles to widen their shareholder base andincrease visibility. A company that wishes to raise finance via a straight debt issue,but which has a weak credit rating, might find it easier to target the convertibleinvestor. The convertible investor base may be more inclined to accept a greaterrange of credits since much of an issue�s appeal derives from its option component.Due to the speed with which large convertible issues are allocated and priced, anddue to the wide investor base, the size of a convertible issue can sometimes evenexceed that of equity or straight debt issue, allowing a company to maximiseissue proceeds.

The suitability of a convertible to meet to an issuer�s objectives will depend tosome extent on how it is structured. For example:

➤ A low coupon corresponds to the objective of lowering the cost of financing;

➤ A high probability of conversion corresponds to the objective of deferring thesale of the stock at a premium; and

➤ A company wishing to keep the debt/equity ratio low will be more inclinedto issue a convertible preferred share, while those wishing to increase gearingwill be more likely to issue a convertible bond.

To call or not to call?Often the ultimate goal of a convertible issuer is for their convertible bond to beconverted into shares. Call features allow the issuer to precipitate conversion bysending out a call notice. The company has a dilemma when deciding whether or notto issue a call notice, however. If parity falls under the redemption value between thedate investors are notified of the call and the call date itself, conversion is unlikelyto be forced and the company would end up redeeming the security for cash.


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Companies rarely call their convertibles at the optimum moment (which willdepend on complex income and options considerations).

The decision not to call a convertible may be the result of:

➤ The uncertain course of the share price during the call period;

➤ The desire to avoid dilution; or

➤ Other balance sheet and profit and loss account considerations.


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➤ Equity-linked financing

➤ Zero coupon and Original Issue Discount (OID) convertibles

➤ A plain vanilla convertible compared with a bond + warrant

➤ Convertible preferreds

➤ Mandatory convertibles

➤ DECs

➤ PERCs

➤ Exchangeables

➤ Default swaps

➤ Reset features

Equity-linked financingConvertibles are hybrid securities with both fixed income and equity characteristics.

We have shown how convertibles can present investment opportunities for both equityand fixed-income investors and how convertible securities can present attractivefinancing opportunities for issuers. We will show here that it is possible to structureconvertible securities such that they bear a greater resemblance to an equity-alternativeinstrument, or to a straight debt-alternative instrument, satisfying the demand ofinvestors and issuers alike.

Figure 9. The Convertible Structure Range – From Debt to Equity

Straight

Debt

Zero CouponConvertible

Original IssueDiscount

Convertible

Plain VanillaConvertible

ConvertiblePreferred

MandatoryConvertible

StraightEquity


Zero coupon and Original Issue Discount (OID)convertiblesIn the wide range of convertible structures, Original Issue Discount (OID)convertibles (including most 0% coupon bonds) are the closest to the straightdebt end of the spectrum.

Convertible Structures


35

Deferred interest paymentsZero coupon convertibles are typically issued at a deep discount to par value and areredeemable at par. The difference between the par value and the initial issue price canbe viewed as the value of notional interest payments over the life of the convertible,which are deferred until final redemption. The yield to maturity reflects the accretionof the convertible price from the issue price to par.

Some OID convertibles pay a low coupon. Like zero-coupon OID�s, the remainingvalue of the interest payments is reflected in the difference between the initial issueprice and the redemption price at maturity. The yield to maturity reflects the accretionfrom the discount issue price to par, taking into account the value of the couponpayments received.

A similar structure is obtained when a convertible is issued at par and redeems at apremium. The performance of a �premium redemption� structure and an OID structurewill be similar. Generally the bond floor will accrue to the redemption value. Even ifthe share price is weak, the convertible price will also tend to accrete towards itsredemption value.

Figure 10. Accretion of Bond Floor and Convertible Price to Redemption Value — Zero Coupon, OID andPremium Redemption Structures

Time

Price

Maturity

RedemptionValue

CB Price

CB BondFloor

Note: The course of the convertible price is affected by many factors. The graph above shows a regular rate of price accretion over time.


Put featuresZero coupon and OID convertibles often carry put options allowing the investor tosell the convertible back to the issuer at a pre-determined price, on specified dates.This price will typically be equal to the accreted price of the security. The accretedprice can be thought of as the issue price plus the value of unpaid notional couponsfrom issue. It is normally calculated as the price at a given date, such as to givea certain rate of return (usually the yield to maturity at issue) if held to maturityand redeemed.


36

Call protectionZero coupon and OID convertibles frequently offer investors periods of both hardand soft call protection.

MaturityRecent US zero coupon convertibles have had final maturities of 20-years or more.European zero-coupon and OID issues have typically had maturities of betweenfive and 10-years. However, in both cases, it can be that the important date from aninvestor�s perspective is the first put date. This point is illustrated most clearly whenone considers a convertible that has a put and a call at the same price and on the samedate. This date can be thought of as the effective maturity date of the bond. If it isnot in the investor�s interest to exercise the put option forcing early redemption of theconvertible, it will probably be in the issuer�s interest to force the investor to choosebetween redeeming the bonds or converting them. Even if the bond does survive thedate without being put or called, it is unlikely to attract a significant premium.

Contingent featuresContingent features typically relate to restrictions on either conversion or oninterest payments: contingent conversion features and contingent interest paymentfeatures. A contingent conversion feature limits the investor�s ability to convert.The incorporation of such a clause in the terms of an issue is generally against theinvestor�s interest. Contingent interest payment features allow the payment of a smallamount of interest to the convertible bondholder and is dependent on the averagemarket price of the convertible reaching a specified level.

From the investor�s perspectiveZero coupon and OID bonds are frequently more defensive instruments than couponconvertibles because of the deep discount or premium redemption feature that theygenerally possess. Figures 11 and 12 compare a notional zero coupon, premiumredemption convertible and a notional conventional convertible with the same yieldto maturity (YTM).

Figure 11. Zero Coupon Bond with Premium Redemption Structure

Issue Price 100

Coupon 0%

Redemption Value 117

Maturity 4 yearsYTM 4%

Conversion Ratio 14 shares per bond


Figure 12. Plain Vanilla Convertible Structure

Issue Price 100

Coupon 4%

Redemption Value 100

Maturity 4 yearsYTM 4%

Conversion Ratio 14 shares per bond



37

Given the same YTM, the coupon-bond has a higher probability of being convertedat maturity. If at maturity parity is 106, the coupon-bond will be converted into theunderlying shares as the redemption price of 100 is below parity. The zero couponbond, on the other hand, will be redeemed at 117 in this instance. In other words,the �effective conversion price�, the price at which the investor is indifferent betweenredemption and conversion, is much higher on the zero coupon, premiumredemption convertible than on the coupon-convertible.

Figure 13 shows the payoff of the two structures:

Figure 13. Coupon Convertible and Zero Coupon, Premium Redemption Convertible — Rate of ReturnAssuming Held to Maturity

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

1 10 19 28 37 46 55 64 73 82 91 100

109

118

127

136

145

154

163

172

181

190

parity

rate

of r

etur

n

zero conventional


The pay-off analysis demonstrates that given the same YTM, the zero coupon,premium redemption issue offers inferior upside participation to appreciationin the underlying share price; the zero coupon, premium redemption structurehas a lower delta.

In practice, put features in a zero coupon bond tend to increase the value of thebond floor, further enhancing the attraction of the structure to fixed interest investorsand reducing its equity sensitivity.

From the issuer�s perspectiveMajor motives for issuing zero coupon and OID bonds lie in the tax and cash-flowadvantages of the structure. Although no cash interest is actually paid, the issuer cannormally deduct the notional accretion on the convertible from taxable profits for taxpurposes. However, investors must pay taxes on the accretion. Even in circumstancesin which the tax is recoverable, the cash flow implications of this can constitutea negative feature of zeros for certain investors.


38

A plain vanilla convertible compared with a bond + warrantWe have described how a convertible can be considered a combination of a straightbond and a call option, both with the same maturity. There is however a differencebetween buying a convertible and buying a �bond cum warrant� issue (a bond issuedwith a long maturity call option attached):

➤ A bond cum warrant package can be usually stripped into its components andtraded separately in the secondary market. A convertible is a �package� and thecall is embedded in the instrument so that investors can only own the embeddedoption by buying the whole instrument.

➤ Investors in a bond cum warrant can typically exercise their option bysubscribing cash instead of bonds leaving the bond portion in existence.For a convertible, this is not the case.

Convertible preferredsConvertible preferreds are a common structure in the US convertible market.The instrument is a preferred stock that pays a fixed dividend (usually quarterly)and carries rights of conversion into the issuer�s ordinary shares.

In many cases, convertible preferreds are not redeemable. The issuer is not obligedto return any principal value back to the holder, but will have the obligation to paythe dividend indefinitely. Owners of convertible preferreds have a lower claim onthe assets of the issuer than convertible holders, but a senior claim to ordinary shareholders.

Mandatory preferred stocksDECsDECs stands for �Dividend Enhanced Common Stock� (or sometimes �DebtExchangeable for Common Stock�). A DECs is typically structured as a convertiblepreferred share that pays a fixed quarterly dividend. The yield at issue is invariablyhigher than the current yield of the underlying common stock. A DECs willautomatically convert into the underlying ordinary shares of the issuer at maturity;in some cases a DECs can also be converted prior to maturity.

As with a traditional convertible security, the coupon and premium are set at issue.The term �conversion premium� has a different meaning for a DECs, however.The conversion terms (ie conversion ratio) of a DECs vary according to the level ofthe underlying share price at the date of conversion. The �true� premium is a movingtarget. By convention, the premium quoted is that based on the lowest conversionratio (or highest conversion price) that could apply. DECs typically have a maturityof three to four years.

The number of shares received upon conversion depends on the price of theunderlying shares at maturity or in cases where early conversion is possible,at the time of conversion. The minimum conversion price is normally the shareprice at issue and the maximum conversion price is typically some 25% higher.

The issue price of a DECs is sometimes the price of the share at issue thoughmany now have an issue price of US$50, however. For simplicity, the examplebelow assumes the issue price is the share price at issue.

Adjusted conversionratio


39

The conversion price will be set according to the following rule:

➤ When the underlying share price is at or below the share price at issue,the conversion ratio is 1:1; one preferred share is convertible into oneordinary share.

➤ As the share price moves between the price at issue and the maximum conversionprice, the conversion ratio is adjusted downwards and a preferred share becomesconvertible into less than one ordinary share. The ratio is set such that the valueof the shares delivered on conversion equals the share price at issue.

➤ Above the maximum conversion price, the conversion ratio no longer falls andis fixed at the minimum level set at issuance. The figure quoted for premiumat issue is based on this conversion ratio.

This rule is summarised in Figure 14.

Figure 14. Conversion Ratio and Value of Share Received on a DECs Issued at Share Price at Issue

Stock Price Number of Shares Received Value of the Shares Received

Stock Price < Issue Price 1 Stock Price at conversion

Issue Price < Stock Price < Conversion Price Issue Price/ Current Stock Price Issue Price

Stock Price > Conversion Price Minimum Conversion Ratio (issue price/maximum conversion price)

Conversion Ratio * Stock Priceat conversion


Where the issue price of the DECs is US$50 rather than the share price at issue,the conversion ratio calculated needs to be multiplied by a factor given by the ratioof 50 to the share price at issue. For example if the share price at issue is US$25,the applicable conversion ratio will be twice that in the table above.

Figure 15. Total Return Analysis on a DECs

Total Return

Common Share Price

Equity

Straight-Debt

DECs

Issue Price

Dividend Advantage

Cap

Max Conversion Price


The post facto performance characteristics of a DECs are as follows:

Total return analysis


40

Below the issue price:

➤ Conversion ratio = 1:1;

➤ Equity participation = 100%;

➤ The DECs outperforms the underlying share due to its yield advantage.

Between the issue price and the maximum conversion price:

➤ The conversion ratio decreases towards the minimum;

➤ No equity participation;

➤ The total return of the DECs can still exceed that of the share due to thedividend advantage

Above the maximum conversion price:

➤ Conversion ratio set to minimum;

➤ The DECs underperforms the underlying common stock;

➤ There is positive upside participation.

Many investors perceive a DECs as a form of ordinary share where an element ofequity participation is sacrificed in exchange for a higher yield. A DECs is usuallynon-callable for life.

PERCsPERCs (Preferred Equity Redemption Cumulative Stock) are typically structuredas mandatory preferred convertibles with a maturity of three to four years.

The number of shares received upon conversion depends on the underlying shareprice at conversion relative to the �cap level� set at issue. A PERCs structure offsetsa higher yield against lower upside participation. As the underlying share pricerises above a pre-set cap level, a PERCs becomes convertible into fewer and fewerunderlying shares, keeping the total return payoff constant. The conversion ratiois calculated as:

Figure 16. Conversion Ratio on a PERCs

Stock Price Shares of Common Stock Received

Stock price > Cap Price Cap Price / Stock Price at Conversion

Stock Price < Cap Price 1


➤ Under the cap level, one preferred share is convertible into one underlying shareso that the equity participation is 100%.

➤ Above the cap level, the conversion ratio is below 1:1. One preferred shareis convertible into less than one share of the underlying, so that the equityparticipation is limited.

Adjusted conversionratio


41

Figure 17. Payoff Analysis for a PERCs

Total Return

Common Share Price

Equity

Straight-Debt

PERCs

Cap Level

Dividend AdvantageCap

Source: please add source.

Under the cap level:

PERCs outperform the underlying common stocks due to the dividend advantage.

Above the cap level:

The total return of the PERCs is kept constant. The PERCs no longer has sensitivityto the rising share price, so above a certain level the share will deliver a superiorreturn, in spite of the PERCs� dividend advantage.

ExchangeablesExchangeables are bonds issued by one company that exchange into the shares of adifferent company. They can be issued in both mandatory and non-mandatory form.

From the issuer�s perspectiveExchangeable bonds can permit a company to dispose of or monetise a shareholdingin another company, regarded as a non-core asset. Not surprisingly, the justificationfor issuance bears a strong resemblance to that for any convertible. If the issueremains unconverted, the issuer will have secured low cost funding. If it ends upbeing converted, the issuer will have succeeded in disposing of the non-core stakeat a premium to the price that ruled at the time of issue. In many tax jurisdictionsthe disposal of a stake by means of an exchangeable bond enables the issuer to deferthe crystallisation of tax liabilities on the sale.

Governments have also considered exchangeables as an effective way of monetisingshareholdings as part of privatisation programmes. The appeal is not only the abilityto manage privatisations when equity markets are unreceptive, but also to lock inlow cost efficient funding.

Payoff analysis


42

From an investor�s perspectiveExchangeable bonds have potential credit advantages and disadvantages for theinvestor. The dislocation of credit risk and underlying share price performance risk canbe a potential benefit for the holder of the exchangeable, though could also potentiallylead to a doubling of credit and performance risk, given the dual exposures.

Default swapsAs with any other bond, the investor has exposure to the default risk of the issuer.To gain protection, a convertible investor may enter into a default swap.

In a default swap, the credit seller pays a premium quoted as a fixed interest rate(in basis points), usually every three months, on the principal amount of the swap(the total nominal being hedged). The counterparty to the transaction assumes therisk of default. They will make a single contingent payment to the investor if theissuer of the security defaults.

A default swap contract usually specifies what constitutes a default event. These willnormally include events such as:

➤ Bankruptcy;

➤ Failure to pay;

➤ Obligation acceleration/default;

➤ Repudiation/moratorium; and

➤ Restructuring of the debt.

Increasingly in modern default swap contracts, the single contingent payment inthe event of default is replaced by the payment of the principal amount against thedelivery of the bond itself.

Reset featuresA convertible in which the terms of conversion are subject to adjustment basedon the behaviour of the price of the underlying share is termed a reset convertible,though reset clauses can be included in the terms and conditions of many convertiblestructures. Reset features allow for a change to the conversion price of a convertiblein the event of share price depreciation (downward reset) or appreciation (upwardreset) on a certain pre-specified date or dates.

Downward reset clauses allow for an increase of the conversion ratio in the event thatthe underlying share price is below the initial conversion price on (or shortly before)the specified reset dates: the investor will be given more shares on conversion as theirvalue has declined. The new conversion price is typically based on the average shareprice level over a specified period shortly before the reset date. In most cases theaverage is adopted as the new conversion price. Disregarding movements in the shareprice between the averaging period and the reset date, and assuming the average is notbelow the minimum conversion price discussed below, parity is set at 100%.


43

A reset clause specifies a reset floor, which is the minimum level to which theconversion price may be reset: even if the average share price goes below this level,the adjustment of the conversion price will be limited by this floor.

Sometimes there is also the possibility of an upward reset of the conversion pricein the event that the underlying share price is above the ruling conversion price on(or shortly before) specified reset dates: an investor will be given fewer shares onconversion as they have appreciated in value. Such structures are unusual, however.Generally, even for bonds where the conversion price can be reset up or down, thelevel of the conversion price set at issue will be the cap for an upward reset.

These features are interesting for their implications on delta and gamma. In theproximity of the reset floor, the expected number of shares that will be deliveredon mandatory conversion rises; (mandatory reset convertibles were popular inJapan during the 1990s particularly). Share price falls increase the theoretical hedgenecessary to remain delta neutral; (the number of shares a resettable convertiblesecurity can be exchanged for increases as the share price falls).

In effect, delta on a resettable convertible security rises as the underlying shareprice falls below the minimum reset level and therefore gamma will be negative.This feature can create substantial pressure on the share price as arbitrageurs continueto sell shares to cover their increasing exposure (increasing delta) to the underlyingshare price, accelerating the share price decline in the process. Arbitrageurs capturevolatility by selling shares as the share price rises and buying shares as the share pricefalls: they are �long� volatility. When the share price is close to the reset floor, the resetfeature mechanism will make them do the opposite, selling stocks as the share pricefalls: so they will be �short� volatility.

The DECs structure mentioned above falls under the general heading of a resetconvertible. It is a mandatory reset convertible with one reset at maturity.


44

➤ The prospectus

➤ Convertible pitfalls and protection

The prospectusAs convertible investors do not physically own the shares into which they haverights of conversion, they rely on the terms and conditions outlined in the bond�sProspectus and Trust Deed (or Indenture) for protection. These include manycovenants regarded as standard in the terms and conditions of straight bonds,which prevent the issuers undertaking certain courses of action which are detrimentalto the interests of bondholders. Convertibles are vulnerable to certain actionsover and above those of straight bonds, however. These fall into two general categories:

1 Events that would tend to lower the fair premium of the convertible. One exampleof this would be a takeover for cash that leaves the bondholder with rights ofconversion into cash, or near cash.

2 Events, such as rights issues, that tend to have a dilutive effect on the underlyingshare price.

These matters are dealt with in more detail below.

The prospectus will also provide information on the dividend and couponentitlements of a convertible bond.

Convertible pitfalls and protectionSpecial distributions to shareholdersDistributions that cause the underlying share price to fall (on announcementor ex-date) reduce the value of the convertible, unless there is some form ofcompensation to convertible holders. The convertible price reduction will beapproximately equal to the amount of the distribution expressed in parity termsmultiplied by the delta of the convertible. The sensitivity of the value of theconvertible to common dividends is well known, and convertible models willgive a lower fair value for the convertible, the higher the dividend assumptions.Unanticipated capital distributions such as special dividends however, will putconvertible bondholders that are not protected by anti-dilution provisions,in a situation that is unfavourable and unexpected. In some cases, convertiblebondholders may be forced into early conversion in order to participate inthe distribution.

Most modern convertible prospectuses contain language designed to protect holdersagainst capital distributions. However, the definition of a capital distribution canvary in its generosity. Some prospectuses define a capital distribution as one thatpushes the annual yield on the underlying shares above a specified level. Whetherthis yield is set in relation to the previous year�s dividend or some absolute level,investors generally regard these clauses as acceptable.

Pitfalls and Protection


45

In some prospectuses, only distributions that exceed net earnings since the issueof the convertible count as a special distribution. In these cases, there is generallymore scope for disadvantgeous treatment of the convertible bondholder.

Anti-dilution provisionsAnti-dilution provisions cover a range of situations that can result in dilutionof the underlying share price (and therefore the number of shares underlying theconvertible). The provisions will stipulate the situations in which convertible holdersare compensated for a dilutive event by receiving an improvement in the conversionterms, and the formula for any such adjustment. The intention is generally to increasethe conversion ratio such that parity (that is the equity value of the convertible)is left unchanged, after accounting for the fall in the share price resulting fromthe dilutive event.

Stock-splitConversion ratios are almost always adjusted in case of the most straightforwardof dilutive events, the stock-split. If the stock-split were on a one-for-one basisfor example, the conversion ratio would be doubled.

Merger or takeoverIn the case of a merger or takeover of the issuing company by another company,the treatment of the convertible bondholder will depend on the conditions of theprospectus or trust deed. In some cases there is no protection.

In general, where there are provisions for a merger or takeover event, there is adistinction in treatment of a bid (mainly) for cash and one that is (mainly) for shares.In an all-share bid by a quoted company, it is generally considered reasonable forthe rights of conversion to be transferred into the shares of the new entity on a basisequivalent to the terms of the deal (the �see through� basis). The bidder would alsoassume responsibility for the coupons and repayment of the convertible, if necessary.There is no presumption as to whether such a turn of events will be advantageousfor convertible holders. It will depend, inter alia, on the volatility of the new companyrelative to that of the old, the dividend policies of the new company and itscredit status.

The danger in the event of a cash bid is that the exchange property of the convertiblebecomes cash. In this situation, the lack of potential movement in the exchangeproperty would extinguish the premium. A number of devices can be applied toaddress this situation. In some convertibles there is a �ratchet� mechanism in whichthe conversion ratio is adjusted by a specified amount if the takeover takes placewithin a given time frame. In others there is an adjustment to the conversion ratio,which is based on the average premium of the convertible over a specified timeperiod. Sometimes the takeover language also includes an investors put at par,accreted price, or some other value.

Income entitlementIn the European convertible market, a measure of standardisation now exists on thequestion of dividend entitlement. The general rule is that accrued interest is not paidon a convertible on conversion and the shares delivered on conversion will rank paripassu with existing shares. There are, however, a number of exceptions to this rule.


46

In particular, if holders are �forced� to convert by the sending out of a call notice,there is often language giving protection against the �unfair� scenario in whicha long period has passed since a convertible coupon has been paid yet convertingbondholders have just missed a dividend payment. Some transactions specifydividend entitlement that amount to delivery of ordinary shares that are ineligiblefor one or more dividends. For example, the entitlement to dividends may bebased on the financial year in which conversion takes place.

Clean-up callsIf a certain percentage of the bond has already been converted into shares, the issuermay be entitled to call any remaining bonds thus forcing conversion. The percentagewill be often set at around 90% of the convertible issue size.


47

➤ Recursive techniques

➤ Approximations using European options

Recursive techniquesMost convertible pricing models are based on the binomial tree approach.This employs a recursive procedure in a manner similar to that employed in valuingAmerican options. This approach can deal with most of the common features foundin convertibles � it can capture not only the value of the early conversion right,but also calls, puts and other characteristics. The major limitation of the binomial treeapproach is that it allows the share price to follow a stochastic path, but treats all otherinputs, such as bond yields, dividends and FX rates as being either predetermined ordependant on the share price. Of these, the lack of a random element in the interestrate assumption is particularly significant limitation. Additionally, if bonds andequities are positively correlated, the technique will tend to overstate the value ofthe convertible.

Models have been developed to allow more variables to be modelled incorporatingstochastic bond yields and bond yields that are correlated to equity prices.Generally they employ recursive procedures similar to those of simple binomialtrees. The number of factors in a model refers to how many variables are modelled.A one-factor model varies just underlying stock prices, whereas a two-factor modeltakes account of movements in interest rates as well.

The major disadvantage of a two-factor model is its complicated nature and lackof transparency. In a one-factor model, it is necessary to input the following:

➤ An assumption of the Libor spread (or spread to Treasuries; the creditspread assumption);

➤ Dividends on the underlying share until maturity; and

➤ A volatility assumption for the underlying stock.

With a two-factor model the number of assumptions increases. An investor mayhave a feel for the volatility assumptions they wish to employ for a share, but wouldhave no intuition as to the appropriate bond volatility and correlation.

Building a binomial treeAs with other options models, binomial trees deal with probabilities. It is easyto misunderstand the nature of these probabilities, however. They do not relateto the chance of certain events occurring in the real world, but are set such that theexpected price of the share at any given date is constrained to equal the theoreticalforward price at that date. These �shadow� probabilities are referred to as �riskneutral probabilities�. The forward price is based on arbitrage considerations anddriven by interest rates and dividend assumptions, rather than expectations.

Convertible Pricing Models


48

The tree works by dividing the life of the bond into specific moments in time, witha range of convertible prices considered for each. Apart form the final (maturity date)range each price is calculated from two prices from the chronologically succeedingrange. The relationship between the price and the two prices from which it iscomposed being given by the volatility of the share and a drift factor.

One starts by associating a value for the convertible with each share price level atthe maturity date of the bond. In general, for share price levels above the conversionprice the value is parity and for share price levels below the conversion price it is100%. One now simply works backward through the tree. The next stage will be oneperiod nearer the present day, with the period length being determined by the termof the convertible and the number of steps chosen. A new distribution for this stageis established and a value is assigned to a range of outcomes. In some cases the valuefor the convertible associated with each node calculated in this manner will need tobe replaced if some feature of the bond makes this appropriate. For example if thebond is puttable at 100 on a certain date, then all observations under 100 at thisdate will simply be replaced with 100.

This process continues until one arrives at the present day with a fair value forthe bond.

Formulae for the share price outcomes at maturity, the probability of an up, theprobability of a down and the drift rate per period are based on simple algebraand can be found in options text books.

Approximations using European optionsWe have established that the value of a convertible to an equity investor can besummarised as:

geomeAdvantaValueofIncaluePutOptionVParityiceeConvertibl ++=Pr

In simple, non-callable convertibles we can thus calculate the theoretical valueby establishing valuations for the components:

➤ Parity is simply the conversion ratio multiplied by the current stock priceexpressed in the bond currency.

➤ The put option value can be calculated using the Black Scholes model(the derivative pricing model based on the binomial tree approach). The put isinterpreted as the right to sell a parity number of shares at the redemption price.Thus the model is set for a plain vanilla European put exercisable only at maturity.If the adopted horizon is some other date, crude adjustments to estimate thevalue of the put will be necessary.

➤ The income advantage value is calculated as the present value of theincome advantage.

From an equityinvestor’s perspective


49

By adopting this approach, an equity investor can obtain a very clear impressionof what they are paying for when they buy a convertible at a premium. However,the approach fails when there is a good chance of voluntary early conversion orwhen there is a period in which the bond is callable. When the call is provisional,even approximations in which the first call date is treated as the effective horizonare unreliable.

We showed that the value of a convertible to a fixed income investor can besummarised as:

ValueCallOptionBondFlooriceeConvertibl +=Pr

We can find the theoretical value of a non-callable convertible by calculating thevalues of its components:

➤ The bond floor value is calculated as the present value of the future couponpayments and the cash redemption value, discounted at the relevant Libor spreadplus a credit spread.

➤ The call option value can be calculated using the Black Scholes model set fora vanilla European call, exercisable at maturity.

Again the major advantage of this approach is its transparency for investors.The problem is that the approach is only theoretically correct if the bond happens tobe non-convertible and non-callable for life. The extent of the potential error dependson how different the terms of the convertible in question are to this basic description.If the bond is convertible at any time, the approach is deficient in that it ascribeszero value to the early exercise option. However where there is a significant incomeadvantage in the convertible, the early exercise right is of little or no value anyway.In the case of callable bonds, an adjustment is necessary to approximate for the impactof this feature. If the bond is callable, an adjustment to the effective strike price,based on the forward bond floor, is available. Where there is a provisional call period,however, the application of the European option methodology breaks down.

From a fixed incomeinvestor’s perspective


50

IntroductionThis appendix contains additional information on the following subjects referredto previously: yield to maturity (YTM), bond floor, delta, gamma, vega, rho, theta,and fugit.

Yield to maturity (YTM)YTM can only be calculated through a process of iteration. The formula belowshows the relationship between the bond price, the (annual) YTM, the coupon andthe redemption amount in a simplified case where there is an exact number of yearsuntil maturity and the bond and coupons are paid annually.

( ) ( )�= +

++

=m

imi YTM

RYTMCiceeConvertibl

1 11Pr

Where:

m = years to maturity;

C = coupon; and

R = redemption value.

In the case of the John Smith Corp Convertible EUR 4% 2007, the YTM of the issueis that which solves the equation:

( ) ( )%4

1000,1

140000,1

5

15 =

++

+= �

=ii YTM

�YTM��

Bond floorOne formula that can be used to calculate a convertible�s bond floor bears a strongresemblance to the YTM formula above.

( ) ( )�= +

++

=m

imi d

Rd

CeBondFloorConvertibl1 11

Where:

m = years to maturity;

C = coupon;

R = redemption value

d = discount rate (the risk free rate (m) + a credit spread)

The formula applies where there is a whole number of years to maturity. A somewhatmore complex formulation is required when there are fractional periods, though theprincipal of finding the discounted present value of the fixed payments is the same.When there are fractional periods, the value is �dirty�. In order to quote it, we needto deduct the accrued interest and to express the result as a percentage of par.

Appendix


51

The discount rate is calculated using the risk-free rate for the maturity of the bond,plus a credit spread that reflects the credit quality of the issuer. In Europe, it iscommon to adopt the swap rate (Libor) in the currency in which the convertibleis denominated as the risk-free rate. It is necessary to make an assumption onthe credit quality of the issuer.

If the euro-Libor rate (the risk-free rate) for the five-year, euro-denominated JohnSmith Corp convertible is 5.423% and appropriate credit spread for John Smith Corpis 100bp, the appropriate discount rate for the John Smith Corp Convertible EUR 4%2007 is 6.423%.

Solving for the bond floor on the John Smith Corp Convertible EUR 4% 2007 atissue gives:

( ) ( )�=

=+

++

=5

15 098.899

06423.01000,1

6423.0140

ii ��eBondFloorConvertibl

Expressed as a percentage of par, this is 89.91% (�899.1/�1,000).

Another method calculates the spot yield curve and discounts each future paymentusing the appropriate spot rate plus the credit spread.

DeltaFigure 18 displays the sensitivity of the price of the convertible to changes in parity.It shows that in geometric terms, delta is the slope of the tangent drawn on theconvertible price curve at the level of the current share price (parity).

Figure 18. Convertible Price against Parity

Parity

Conv

ertib

le

P0 P1

CB1

CB0

Source: Schroder Salomon Smith Barney.


52

Figure 18 shows how the tangent can be an accurate representation of convertibleprice movements only for small share price movements.

If parity moves from P0 to P1, then

( ) 01*01 CBCBDeltaPP −≈−

If we consider infinitesimal changes, d, then

)()Pr(

)Pr(*)(

ParitydiceeConvertibldDelta

iceeConvertibldDeltaParityd

=

=

Figure 19. Delta against Parity

Delta

0

10

20

30

40

50

60

70

80

90

100

Parity


GammaGamma is the rate of change of delta for movements in the underlying share price:

)()(

ParitydDeltadGamma =

Conventionally, gamma is expressed as the change in delta for a one-unit increasein parity.

We can interpret:

➤ Delta as the first partial derivative of the convertible price curve with respect toparity; it measures the slope of the tangent drawn on the convertible price curveat the current level of parity.

➤ Gamma as the second partial derivative of the convertible price curve withrespect to parity; it measures the degree of convexity of the convertible pricecurve at the current level of parity.


53

)()Pr(

)()(

2

2

ParitydiceeConvertibldGamma

ParitydDeltadGamma

=

=

We can isolate an approximate formula to estimate the change in the price of aconvertible for a given absolute change in parity:

2*21*Pr ParityMoveGammaParityMoveDeltaiceMoveeConvertibl +=

This is a simple approximation by linear interpolation; if the initial delta is D1, thefinal delta is approximately D2:

( )ParityMoveGammaDD *12 +=

So the average delta over the whole move is:

( )

ParityMoveGammaDD

ParityMoveGammaDDD

DDD

A

A

A

*2

2*

2

1

11

21

+=

++=

+=

The formula above shows the convertible price move is the average delta multipliedby the parity move:

21 *2

1**2

* ParityMoveGammaParityMoveDeltaParityMoveGammaDParityMove +=��

��

� +

It can also be derived from a simple Taylor series expansion.

For small stock price fluctuations, delta multiplied by the parity move can be agood approximation for changes in the convertible price. Adjusting for the effectof gamma is particularly important for larger share price movements, as the effectof convexity on the convertible price can be significant.


54

Figure 20. Gamma against Parity

Gamma

0

0.2

0.4

0.6

0.8

1

1.2

Parity


Gamma changes along the convertible price curve. Gamma is always positive inconventional convertibles (as delta increases for increases in parity), and it is ata maximum when the convertible is close to, or at-the-money.

VegaVega is the sensitivity of the convertible price to changes in the volatility of theunderlying stock. It can be expressed as follows:

)()Pr(

ilityStockVolatdiceeConvertibldVega =

Figure 21. Vega against Parity

Vega

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Parity



55

As can be seen from Figure 21, vega is always positive on a standard convertible andis greatest when the convertible is close to, or at-the-money. A change in the stockvolatility assumption may not have a material impact on fair value if the convertibleis out-of-the-money or deep in-the-money.

RhoRho measures the sensitivity of the convertible price to movements in interest rates.Rho can be expressed as follows:

)()Pr(

teInterestRadiceeConvertibldRho =

Figure 22. Rho against Parity

Rho

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Parity


Rho is always a negative number in conventional convertibles, as an increase ininterest rates has a greater negative impact on the value of the bond floor, than itdoes a positive impact on the value of the embedded call option. As the bond floorbecomes the most important component of a convertible�s valuation (the convertibleis out-of-the-money), the sensitivity of the convertible price to changes in interestrates increases.

ThetaTheta is the change in convertible price with the passage of time. Conventionally,it is expressed as the percentage change in the convertible price for the passageof one day, all other things being equal.

)()Pr(

TimediceeConvertibldTheta =


56

As a convertible approaches final maturity, we see two opposite effects on theconvertible price:

➤ The value of the embedded call option decreases and so the convertible pricedecreases; and

➤ The bond floor trends towards the redemption value over time. Convertiblestrading below redemption value will rise towards this value over time.

At-the-money convertibles will usually suffer from the first of these effects, with thetabeing a negative number. Out-of-the-money convertibles (including original issuediscount bonds, for which the effective strike price is considerably in excess of theshare price), the drag to redemption of the bond element can be the more potent force.Figure 23 shows the effect of the passage of time on a notional four-year convertible.For the line marked ATM, parity is 100 throughout, and the line marked OOM parityis 80 throughout. The notional bonds both have 1% coupons in a 5% interest rateenvironment, so there is a natural upward drift in the bond floor in both cases.

Figure 23. Time Decay for At-The-Money and Out-Of-The-Money Convertibles

90

92

94

96

98

100

102

104

106

108

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4

time

valu

e

ATM OOM



57

The accreted value is the price at which an OID or premium redemption bond yieldsthe same as it did when it was issued. If, for example, a 10-year zero-coupon bondwere issued at a price of 50 to yield 7.2%, after five years the accreted value wouldbe 70.7. At that price the bond would yield 7.2% to maturity at 100 after a furtherfive years.

This is the value of the accrued portion of the coupon on a convertible bond.Generally, it is the coupon amount divided by the number of days in a year,multiplied by the number of days since the last coupon was paid. To calculateaccrued interest accurately, the bond�s method of accrual needs to be known.Different methods predominate in different markets.

This type of option allows the holder to exercise into the underlying asset at anytime during the life of the option.

These provide for an adjustment in the conversion terms in the event of specialstock dividends, stock splits or other corporate events that can result in the dilutionof the underlying share price.

A convertible is said to be at-the-money if the current share price is close to theconversion price.

A balanced convertible is a convertible that trades at a price where it is neither apure equity substitute nor trading on its bond floor, but is balanced between the two.

A binomial tree option-pricing model estimates the theoretical value for an option.Adaptations of the approach are commonly applied to convertible bonds. They takeaccount of events such as puts and calls that take place during the life of the instrument.

The option-pricing model derived by Fischer Black and Myron Scholes is usedto estimate the theoretical fair value of option contracts based on a range of inputsand assumptions.

The bond floor is the value of the straight fixed income element of the convertibleif rights of conversion are ignored. The bond floor should support the price of aconvertible if the underlying equity falls, thereby allowing holders of the bondto outperform holders of the equity.

This is a straight bond issued with a long maturity call option attached. The bondcum warrant can be stripped and traded separately in the secondary market.

The breakeven calculation for a convertible measures the time taken for the bond�sincome or yield advantage to offset the cost to the investor of a bond�s conversionpremium. It is a simple measure that takes no account of dividend growthprojections or discounting for present value.

A call feature gives a convertible issuer the right to redeem a convertible bond priorto maturity at a price determined at issue. Holders of convertibles who receive a callnotice will generally have time to exercise their rights of conversion before repaymenttakes place; thus a call option can frequently be interpreted as required early conversion.

Glossary

Accreted value

Accrued interest

American-style option

Anti-dilution provisions

At-the-money

Balanced convertible

Binomial tree

Black-Scholes option-pricing model

Bond floor (orinvestment value)

Bond with/cum warrant

Breakeven

Call feature(or call option)


58

The clean price is the price of a convertible bond quoted without accrued interestincluded. Most convertibles are quoted this way.

When an issuer is entitled to call any remaining bonds if a certain percentage ofthe bond issue has already been converted into shares, it is termed a �clean-up call�.The percentage is often set at around 90% of the convertible issue size.

A contingent conversion feature makes a convertible investor�s ability to convertcontingent upon some factor such as the share price attaining a specified level.

Contingent interest payment features allow the payment of a small amount ofinterest to the convertible bondholder if the average market price of the convertiblefalls to a specified level.

See premium.

At issue, the conversion price is the price at which shares are effectively �bought�upon conversion, if the convertible is purchased at the issue price. It is calculatedby dividing the issue price of the bond by the conversion ratio.

The conversion ratio is the number of shares into which each bond can be converted.

These are preferred shares issued by a company that are convertible at the option ofthe investor into the common shares of that company. They pay a fixed dividend andare often issued in perpetual form so therefore may not be redeemable.

This is the price at which the convertible is traded in the market. It is generallyquoted as a percentage of par (the face value of the bond).

The coupon is the interest payment per bond. It is normally quoted as a percentageof the face value.

The credit spread is the spread over the swaps curve (or sometimes Governmentbond curve) at which the issuer is assumed able to issue a straight bond that isotherwise identical to the convertible.

A convertible that is denominated in a different currency to that of theunderlying shares.

Current yield is the income per unit of currency invested. It is calculated by dividingthe coupon by the current convertible price.

DECS stands for Dividend Enhanced Convertible Securities or Debt Exchangeablefor Common Stock. DECs are mandatory convertibles, typically issued as preferredstock paying quarterly fixed dividends.

Delta is a measure of the sensitivity of the convertible bond price to share pricemovements. It is defined as the expected change in the convertible price for a smallabsolute change in parity.

This is the minimum size in which the bond can be traded.

The dirty price is the clean price of a convertible bond plus its accrued interest.It is the actual price an investor will pay for a bond.

Clean price

Clean-up call

Contingent conversion

Contingent interestpayment

Conversion premium

Conversion price

Conversion ratio

Convertible preferreds

Convertible price

Coupon

Credit spread

Cross currencyconvertible

Current (or running)yield

DECs

Delta

Denomination

Dirty price


59

The dividend yield is an indication of the income generated by each share.It is calculated by dividing the annual dividend per share by the share price.

This type of option gives the holder the right to exercise an option only on thematurity date.

This is a convertible bond issued by one company that can be converted intothe shares of a different company.

Gamma measures the sensitivity of the convertible bond�s delta to share pricemovements. It is the change in delta for a one-point change in parity.

The Greenshoe is an over-allotment option that allows an underwriter to increasethe number of bonds issued, typically by 10%-15%, when there is strong demandfor an initial offering.

A period of time specified in the indenture of a bond during which the issueris not allowed to call the bond from the investor under any circumstances.

A convertible bond�s hedge ratio is also referred to as �delta�. The hedge ratioshows the equity sensitivity of a convertible bond and enables an investor tocalculate how many shares they would need to sell to hedge their equity exposure.

If the share price falls dramatically, leaving the convertible so deeply out-of-the-money that its equity component becomes immaterial, it is sometimes referredto as a high-yield convertible. Issues for sub-investment grade companies arealso referred to as high-yield convertibles.

Implied volatility is the convertible pricing model volatility input used that bringsthe fair value of a convertible into line with its market price.

A convertible is said to be in-the-money if the current share price is greater thanthe conversion price.

The issue price is the price at which convertible bonds are sold to investors at issue.

This is a convertible in which the bondholder is obliged to convert into theunderlying equity at maturity.

The maturity date is the final redemption date of the bond.

This is the face value of the bond. It is often 1,000 of the relevant currency inthe Euroconvertible market and ¥1,000,000 in the Japanese and Euroyen markets.The current price, issue price and redemption price of most convertibles are expressedas a percentage of the nominal value.

A convertible issued at a discount to par is termed an original issue discount convertible.

A convertible is said to be out-of-the-money if the current share price is below theconversion price.

Par is the face value of a bond.

A convertible in which the investor has a put option prior to final maturity at par.

Dividend yield

European option

Exchangeable bond

Gamma

Greenshoe

Hard call protection

Hedge ratio

High-yield convertible

Implied volatility

In-the-money

Issue price

Mandatory convertible

Maturity

Nominal value

Original issuediscount (OID)

Out-of-the-money

Par

Par put convertible


60

Parity is the market value of the shares into which the bond may be converted.It is calculated by multiplying the conversion ratio by the current share price expressedin bond currency terms. It is normally expressed as a percentage of a bond�snominal value.

PERCs stands for Preferred Equity Redemption Cumulative Stock. PERCs area mandatory convertible bond structure that caps upside participation in astock�s performance.

A convertible�s premium is the percentage by which the market price of theconvertible bond exceeds parity. It represents the extra cost an investor must pay tobuy the shares a bond converts into via a convertible. It is calculated by subtractingparity from the convertible price and is expressed as a percentage of parity.

A convertible in which the investor has a put option prior to final maturity with a putprice above par.

This describes a convertible bond that is issued at par but redeems at a premiumto par.

A put gives investors the option to sell back the convertible bond to the issuer ata fixed price on a given date or dates.

In some convertibles there is a ratchet mechanism in which the conversion ratio isadjusted by a specified amount if a takeover takes place within a given time frame.

The redemption price is the price at which the issuer must redeem bonds at maturity.

The date on which a change of conversion terms takes place on a reset convertible istermed the reset date.

Reset features allow for a change in the conversion price of a convertible in theevent of share price depreciation (downward reset) or appreciation (upward reset)on certain specified dates.

The limit below which the conversion price on a reset convertible cannot fall.

In most reset convertibles, the share price upon which the new conversion price isbased is calculated by reference to the average share price observed in a specifiedreset period.

Rho measures the sensitivity of the convertible price to movements in interest rates.It is expressed as the change in the convertible price for a one basis point move ininterest rates (a parallel shift in the yield curve).

The risk premium is the difference between the convertible price and the bond floorexpressed as a percentage of the bond floor.

This is a period of time during which the issuer may only call the bond if the shareprice has traded above a predetermined premium to the conversion price for a setperiod of time. This predetermined premium is known as the call trigger. The calltrigger is often stated as a percentage of the conversion price; thus �subject toa 140% trigger� means that the call trigger is 140% of the conversion price.

Parity

PERCs

Premium

Premium put convertible

Premium redemptionstructure

Put feature

Ratchet

Redemption price

Reset date

Reset features

Reset floor

Reset period

Rho

Risk premium

Soft call(or provisional call)


61

This is where the coupon level increases at a future date. This can be a contingentevent on for instance, a credit rating downgrade.

Theta is the change in the convertible price with the passage of time. It is expressedas the change in the convertible price for the passing of one day, other thingsbeing equal.

Vega is the sensitivity of the convertible price to changes in the volatility of theunderlying stock. Vega is the change in the fair value of the convertible for a onepercentage point change in the assumption for stock volatility.

Share price volatility is a measure of the dispersion of share price returns. It is definedas the annualised standard deviation of returns. The extent to which the underlyingshare price has fluctuated over a certain period determines the historical or observedvolatility. The assumption for future share price volatility is an input forconvertible valuation.

The yield advantage is the difference between the current yield on the convertiblebond and the stock dividend yield.

Yield to maturity (YTM) is the discount rate that equates the current market priceof a straight bond to the present value of its future cash flows.

Step-up coupon

Theta

Vega

Volatility

Yield advantage

Yield to maturity


62

Notes


63

Notes

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Convertible Bonds