CB Primer GS

Analysts

Peter [email protected](London) 774 5035

Scott [email protected](New York) 212-357-7922

Goldman Sachs Convertible Research

The Global Convertible Handbook


Goldman Sachs Global Convertible Securities Research Group

LondonPeter [email protected](London) 774 5035

Arup [email protected](London) 774 5130

New YorkScott [email protected](New York) 8902 8535

BloombergType GSCB on Bloomberg


ForewordThe Emergence of Convertibles as a Global Asset ClassThe last two years have been marked by the emergence of convertibles as a trulyglobal asset class. Market capitalization of the universe now exceeds US$400billion with issuance levels having risen steadily through the 1990s. However,convertibles remain something of a ‘hidden’ asset class (Figure 1) with limitedinterest from both institutional and retail investors. This Handbook represents ageneral introduction to one of the fastest growing and most attractive securityclasses in the financial markets.

Figure 1: Securities Market Capitalization Comparisons (US$)

Convertible Bond Market 400bn

Swiss Equity Market* 382bn

Australian GDP 350bn

Canadian Equity Market* 316bn

Brady Bond Market 150bn

* Source: FT/S&P Actuaries World IndicesTM and Goldman Sachs

Convertibles are hybrid securities with features of both debt and equity. As suchthey may appeal to both equity and fixed income investors and can be useful infulfilling a broad array of corporate financing requirements. The last few yearshave been marked by a blurring of the lines between debt, convertible securitiesand equity with an accelerating trend to the creation of custom-made financinginstruments to fill the needs of a variety of issuer types. Figure 2 highlights just afew of the most familiar structures now used.

Figure 2: The Equity-linked Financing Spectrum

Source: Goldman Sachs convertible research

In this Handbook we first examine the basic characteristics of traditional (orvanilla) convertible securities before broadening our analysis to include a widevariety of convertible structures and methods of analysis.

TM ‘Financial Times / Standard & Poor’s Actuaries World Index’ is a trademark of The Financial Times Limited andStandard & Poor’s, and used under license by Goldman, Sachs & Co.


Why Focus on Convertibles?Convertibles deserve the interest of financial market professionals for several keyreasons:

1. Investment Opportunities. Attractive investment opportunities havepersistently arisen over the last decade in the convertible markets.

2. Issuance Opportunities. Convertibles are a uniquely flexible financing toolfor issuers and are increasingly present in the portfolio of company (andgovernment) financing alternatives.

3. Hedging and Valuation Driven Opportunities. The convertible marketoffers profitable opportunities for investors focused on technical valuationwith both hedge funds and asset swappers being active market participants.

4. Product Proliferation. The dramatic growth and diversification of theconvertible market over the last five years has led to the development ofnumerous new convertible structures with a broad array of applications forinvestors and issuers alike.

5. Retail Suitability. The three elements of principal protection, income, andequity participation make convertibles a highly attractive security class forcertain types of retail investors.

Using the Global Convertible HandbookThe Handbook comprises three sections. In the first section (Chapters 1-8), wehave compiled an extensive introduction to the global convertible markets.Among the subjects covered are:

Basic convertible characteristics and behavior;

Special convertible structures;

Investing in convertibles;

Issuing convertibles;

Performance of convertibles as an asset class; and

Theoretical valuation of convertibles.

In the second section (Chapter 9), we have prepared market overviews of themajor global convertible markets along with a directory of the largest convertiblescurrently outstanding.

In the third section (Chapters 10-13), we include a glossary of terms and abibliography.


In compiling the Global Convertible Handbook, we have drawn on the expertiseand work of numerous of our Goldman Sachs colleagues. We highlight, inparticular: Michael Abbott, Anand Aithal, Indrajit Bardhan, Mark Buisseret,Gavin Brake, Matthieu Duncan, Jiro Masuda, Michael Price, and John Rustum.

Peter Warren

June 1997


Table of Contents

1. Introduction to Convertible Securities 1Description of Convertible Securities 2Quotation and Identification 4Basic Characteristics and Behavior 6Call Protection and Put Options 17

2. Convertible Price Behavior 19How Convertibles Behave When Stock Prices Move 20How Convertibles Behave When Interest Rates Move 26

3. Other Equity-linked Structures 29Automatically Convertible Equity Securities (ACES) 31Convertible Quarterly Income Preferred Shares (Convertible QUIPS) 37Credit Enhanced Debt Indexed To Stock (CrEDITS) 40Exchangeable Structures 42Original Issue Discount (OID) Convertible Securities 45Reset Features 48Yield Enhanced Stock (YES, also known as PERCS) 51

4. Approaches to Convertible Investment 57Investing in Convertibles 58Investment Scenarios 63Convertible Specific Investment Risks 70Stripping Convertible Bonds 72

5. Investing in Convertibles as an Asset Class 77Performance of Convertibles as an Asset Class 78Rationalizing Convertible Outperformance 88

6. Issuing Convertible Securities 91The Issuer’s Perspective 92Fulfilling Financing Objectives - Why Issue a Convertible? 95Deciding on the Appropriate Structure 98


7. Valuing Convertible Securities as Derivatives 103Theoretical Approaches to Convertible Valuation 104Valuing a Hypothetical Convertible 110

8. Convertibles in the Euromarket 115Structure of the Euroconvertible Market 116

9. Convertible Market Profiles 119Introduction to Market Profiles 120Further Information 120France 123Germany 127Hong Kong 131India 135Italy 139Japan 143Korea 155Philippines 159Switzerland 163Taiwan 167Thailand 171UK 175US 179Rest of Asia/Australia 191Rest of Europe 193Other Emerging Markets 197

10. Glossary of Convertible Terms 199

11. Figures in Text 207

12. Select Bibliography 211

13. Appendices 213Appendix 1: US Convertible Bond Total Returns (%) 1957-95 214Appendix 2: Convertible Market Acronyms 215


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1. Introduction to Convertible Securities

Description of Convertible SecuritiesWhat is a Convertible?Convertible BondsConvertible PreferredsHybridsExchangeables

Quotation and IdentificationConvertible BondsConvertible Preferreds

Basic Characteristics and BehaviorDefinition of a ‘Vanilla’ ConvertibleConvertibles Compared to Bonds with WarrantsTwo Views of Convertible SecuritiesThe Convertible GraphIn the Money, Balanced, Out of the MoneyWhy do Investors pay a Premium to Own a Convertible?Simple BreakevenAdvanced Breakeven

Call Protection and Put OptionsThe Call FeatureAbsolute (or Hard) Call ProtectionProvisional (or Soft) Call ProtectionCalling Convertibles to Force ConversionCalling Convertibles for CashThe Put Feature


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Description of Convertible SecuritiesWhat is a Convertible?A convertible is typically a fixed income-type security that is also convertibleinto a predetermined number of shares of the issuer. Hence its volatility andexpected returns at issue are less than those of the issuer’s common stock butgreater than those of its straight (non-convertible) debt. A convertible is not,however, a mere combination of a company’s equity and fixed income securities.

Convertibles are a separate asset class that can uniquely meet a broad arrayof issuer and investor objectives.

Convertibles come in four main forms: convertible bonds, convertible preferredstock, hybrids and exchangeables.

Convertible BondsA convertible bond is a fixed income obligation of a company. Each bond pays afixed cash sum, the coupon, usually either annually or semi-annually. The issueris also obliged to return the principal amount of its borrowings (the face value) tothe bondholder at a specified redemption date or maturity if the holder so desires.Since most coupon-paying convertibles are issued at par, this obligation in effectconstitutes a guarantee that investors will ‘get their money back’ if the company issolvent at the redemption date.

Convertible PreferredsConvertible preferred stock typically pays a fixed dividend on a quarterly basis.The issuer’s obligation to pay this dividend lasts as long as the security remains inexistence. In most cases the convertible preferred stock has no redemption dateand, as with common stock, the issuer has no obligation to ever repay theproceeds from the sale of the preferred.

Convertible preferred stockholders have a lower claim on the assets of the issuerthan convertible debtholders. They do, however, have a claim senior to commonstockholders. In the case of cumulative convertible preferreds, cash dividends canonly be paid to common stockholders if all past and present dividends owed topreferred holders have been paid. In the case of non-cumulative preferreds,dividends may be paid to common stock holders as long as preferred dividendshave been paid for the present period even if past preferred dividends havebeen omitted and remain unpaid.

Convertible bonds have historically been more widely issued than convertiblepreferreds.

HybridsUnder the umbrella of the convertible market, there are a variety of additionalsecurities which combine elements of equity and fixed income instruments in a

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single security. Examples include: Automatically Convertible Equity Securities(ACES), Convertible Quarterly Income Preferred Shares (Convertible QUIPS),Yield Enhanced Stock (YES), and Credit Enhanced Debt Indexed To Stock(CrEDITS).

ExchangeablesInstruments for which the issuer and the underlying shares are differentcompanies are known as exchangeables. Although they share many of theattributes of convertibles, there are also significant differences and we discussthem in detail in Chapter 3.


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Quotation and IdentificationConvertible BondsFor convertible bonds, prices are quoted as a percentage of the face value of thebond, exclusive of accrued interest. Thus, if a price of a convertible with a facevalue of $1,000 is ‘105%’, the investor pays a price of $1,050. In practice, marketpractitioners usually omit the word ‘percent’ when quoting a price, so the pricewould be quoted as simply ‘105’.

The term par is often used to signify 100% of the face value. In the simplest andmost common cases the issue price of a convertible is 100% of its face value.Here the term ‘par value’ becomes interchangeable with the term ‘face value’.Each unit percentage of face value is referred to by market practitioners as a point.Thus, the difference between a price of 105 and a price of par is 5 points.

In addition to the quoted offer price, purchasers of convertible bonds generallyhave to compensate the seller for interest accrued from the time of the last couponpayment up to the sale date. The method of calculation of this accrued interestmay vary between markets. In the Euroconvertible markets it is usually calculatedon a 30/360 day basis.

Convertible bonds are usually identified by their coupon and their maturity date.For example ‘ABC Corp. 5% of 15 March 2007’ refers to a bond issued by ABCCorp. which pays a coupon equal to 5% of the bond’s face value each year andwhere the principal amount of the bond is due for repayment on 15 March 2007.Sometimes the notation is shortened to ‘ABC Corp. 5% 2007’.

Convertible PreferredsConvertible preferreds are typically quoted on the same basis as common stock.Thus, if a convertible preferred is quoted as being offered at $55, then this is theprice actually paid by a purchaser. There is usually no concept of a purchaserpaying an additional sum in respect of preferred dividends accrued since the lastdividend payment date. However, as with common stocks, convertible preferredscan trade on an ex-dividend basis.

Convertible preferreds are usually identified by the fixed dividend they carry.Thus, if ABC Corp. has a convertible preferred which pays a total dividend of $3per year, then it is referred to as the ‘ABC Corp. $3 convertible preferred’. If anissuer has several different issues (or series) of preferreds (either convertible ornon-convertible), then the issue may additionally be referenced by its series as‘ABC Corp. $3 convertible preferred series B’ or, more simply, ‘ABC Corp. $3cvt pfd B’.

Rather confusingly, convertible preferred dividends are sometimes incorrectlyreferred to in percentage terms. Thus, ABC Corp.’s convertible preferred mightbe referred to as ‘ABC Corp. 6% cvt pfd B’, meaning that the fixed $3 dividend


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represents 6% of the preferred’s original issue price of $50. Note that the ‘6%’does not refer to the actual yield on the preferred in the secondary market - if thepreferred’s price is $55 then the current yield (or running yield) will be 5.45%(=$3÷$55).


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Basic Characteristics and BehaviorDefinition of a ‘Vanilla’ ConvertibleConvertibles can appear in a large number of guises, being tailored to the needs ofa specific issuer or an individual market and encompassing the whole array ofcombinations between pure debt and pure equity. Consequently, it is difficult toformulate a precise definition that at the same time encompasses all thosesecurities with convertible-like features. The most common approach is toconsider the traditional, or ‘plain vanilla’, convertible and to evaluate variationswithin this framework.

Whereas the borrowing company has obligations, the convertible holder hascorresponding rights. Specifically, investors have the right (but not theobligation) to exchange their bond and forfeit future interest payments andredemption of principal, usually at any time (ie American-style exercise), in returnfor a predetermined number of shares. The number of shares receivable per bondis known as the conversion ratio.

Although no cash changes hands when a convertible bond is converted, we candetermine the price at which a convertible investor buys shares (the conversionprice) by dividing the par value of the bond by the conversion ratio. Thus, a bondwith a face value of $1,000 which can be exchanged for 100 shares effectivelygives investors the right to buy shares at a conversion price of $10.

Convertibles Compared to Bonds with WarrantsBecause convertibles have both equity and bond characteristics they are oftenlikened to the combination of a straight bond and a warrant. A bond is aredeemable security which pays a fixed rate of interest while a warrant bears nointerest or right to return of principal, but does give investors the right (but not theobligation) to buy a fixed number of shares at a fixed price during a specifiedperiod.

However, the two instruments are not identical. For the bond with warrantcombination (sometimes known as a bond cum warrant), investors subscribe forshares by handing in their warrants and a predetermined cash sum while the bondremains in existence. For a convertible, in contrast, the warrant is embeddedwithin the instrument. That is to say, investors can only subscribe for theembedded warrant by submitting the whole instrument for conversion. This maybe referred to as a useable bond with warrant combination. For a bond cumwarrant, the decision to exercise the warrant depends on the opportunity cost offoregoing cash. For a convertible, the decision as to when to exercise isconditional upon the opportunity cost of foregoing ownership of a corporate bond.

Note also that a bond cum warrants package can be (and usually is) stripped intoits components and traded separately in the secondary market whereasconvertibles can only trade as an unified package.

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Two Views of Convertible SecuritiesA convertible is part debt, part equity. The importance of these two factors indetermining the overall valuation of a convertible varies according to therespective valuations placed on it by equity and fixed income investors.

Equity investors can view a convertible as a combination of the following:

Equity;

A put option to exchange the equity for a straight bond; plus

A swap to the conversion date that gives the investor bond coupons inexchange for dividends.

Figure 3: The Equity Perspective on Convertibles


Fixed income investors, in contrast, can view the same convertible as acombination of the following:

A straight bond; plus

A call option that allows the investor to exchange the bond for equity.

Figure 4: The Fixed Income Perspective on Convertibles


Typically, the price of a convertible will reflect at least the higher of thevaluations ascribed to it by debt and equity investors.

The Convertible Graph Figure 5 shows how the typical convertible reacts to movements in share prices inan environment of unchanging interest rates. The line labeled ‘Fixed IncomeValue’ represents the value of the instrument to bond investors in the absence ofan equity option. This fixed income value (sometimes called its investment

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value or bond value) will be affected by a number of factors discussed below, butin the simple analysis it is not correlated with movements in share prices. Thus,Fixed Income Value is a straight line on Figure 5.

Figure 5: Basic Convertible Price Behavior


By definition, the equity value of a convertible varies with the share pricebecause a convertible bond allows an investor to convert into a predeterminednumber of shares. The number of shares to which an investor is entitled perconvertible is the conversion ratio.

The line labeled ‘Parity’ shows the equity value embedded within the convertible.Parity is simply the share price multiplied by the conversion ratio, so it rises prorata with the share price.

Where the currency denomination of the convertible bond is different from thecurrency of the underlying shares, then parity is calculated by multiplying theshare price expressed in terms of the bond currency by the conversion ratio(cross-currency parity).

As an illustration of parity, consider ABC Corp.’s 5% 2007 convertible bonddescribed in Figure 6. In this example assume that the bond has a face value of$1,000 and the company’s current stock price is $80. Further, assume that eachconvertible entitles the investor to convert into 10 shares of ABC common stock -ie the conversion ratio is 10. If the holder of this convertible were to converttoday, then 10 shares with a current value of $80 each would be delivered. Thus,the total value of the shares received upon conversion of one bond would be $800,


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or 80% of the bond’s face value. Or, using the terminology of convertible marketpractitioners, parity is 80.

Figure 6: Calculating Parity

Convertible Terms Issuer ABC Corp.

Coupon 5% semi-annual

Maturity 15 March 2007

Face Value $1,000

Conversion Ratio 10

Current Stock Price $80

Calculation Parity = Stock Price * Conversion Ratio

= $80*10

= $800 or 80 Points


In the Money, Balanced, Out of the Money In discussing convertible bonds, it is market convention that they are referred towith one of three designations: in the money, balanced (or at the money), and outof the money. These are drawn from the terminology of the option market andrefer to the equity option embedded in the convertible. Figure 7 applies theseterms to our basic convertible chart. We discuss these terms in much more detail(and introduce junk convertibles) in Chapter 2.


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Figure 7: Market Terminology


Why do Investors pay a Premium to Own a Convertible? In principle, an equity-oriented investor ought to be willing to pay at least parityfor a convertible. If a convertible trades significantly below parity then (allowingfor transaction costs and foregone accrued interest) arbitrageurs would buy theconvertible and convert it into shares, thereby creating a riskless profit. Parityrepresents the intrinsic value of a convertible to an equity investor.

Likewise, a fixed income investor ought to be willing to pay at least a price wherethe yield to maturity on the convertible is equivalent to the yield investors woulddemand for a non-convertible bond which is identical in all other respects.

As discussed above, a convertible consists of more than just equity and more thanjust a straight bond. Consequently, some investors may be willing to pay apremium over parity (the conversion premium or, simply, premium) to own aconvertible while others may be willing to pay a premium (known as the riskpremium) over the intrinsic investment value.

Figure 8 illustrates the concept of premium. In the regions labeled ‘In theMoney’, ‘Balanced’ and ‘Out of the Money’, the Parity and Fixed Income Valuelines determine the lower bounds of the convertible’s price. The convertible’svalue will at least lie on this boundary and in most cases the actual convertibleprice will be at a premium to these values. The conversion premium (or equity

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premium) is the area between the convertible price and the parity line. The riskpremium is the area between the convertible price and the fixed income value line.

Figure 8: Introducing Premium


Returning to the example of ABC Corp., consider the hypothetical situation wherethe convertible is issued on 15 March 1997 and all the other terms of theconvertible are as illustrated in Figure 9. If the convertible is issued at a price of$1,000 while the underlying shares are worth $800, then investors would pay apremium of $200 to own the convertible rather than the underlying stock. Putanother way, investors pay par for something where parity is 80. This is apremium of 20 points (= 100 - 80) or, in percentage terms, a premium of 25% overparity.


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Figure 9: Calculating Premium over Parity




Parity 80

Convertible Price 100

Calculation Points Premium = Convertible Price - Parity

= 100 - 80

= 20 Points

Percent Premium = Points Premium ÷ Parity

= 20 ÷ 80

= 25%


A similar calculation can be made for a convertible’s premium over fixed incomevalue. The issuer must pay interest on the debt portion but not the warrantportion. Although ABC Corp. may raise $1,000 from the sale of each convertible,its interest cost is less than that from the sale of $1,000 of straight debt alone.

Assume that when the convertible is issued, the yield to maturity on 10 year USTreasuries is 6.81%. Further assume that in order to hold ABC Corp.’s straightdebt for 10 years, which carries some risk of default, rather than ‘riskless’ USTreasuries the market requires an additional 2% (or 200 basis points) in yield. Inother words, were the company to raise straight debt the interest cost would be8.81% rather than the 5% interest cost of the convertible. Conversely, we canview the fixed income floor of the convertible as being at 75, because at that pricethe yield to maturity on the convertible is 8.81%. For a convertible priced at par,the premium over fixed income value is 25 points, or 33% (Figure 10).


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Figure 10: Calculating Risk Premium

Calculations Issuer ABC Corp.



Investment Value 75


Convertible Terms Points Risk Premium = Convertible Price - Investment Value

= 100 - 75

= 20 Points

Percent Risk Premium = Points Risk Premium ÷ Investment Floor

= 25 ÷ 75

= 33%


Simple Breakeven Historically, equity investors determined how much premium to pay by implicitlyassuming that the convertible would eventually be converted into equity. Usingthis approach, a ‘fair’ premium is simply the cumulative incremental income fromnow until conversion that an investor would get from owning a convertible ratherthan an equivalent amount of equity. At issue, most plain vanilla convertiblesyield more than their underlying shares. This reflects the fact that in most marketsbond yields are greater than equity yields.

The key valuation measure for this approach is called breakeven. This is ameasure of the amount of time necessary to recover the conversion premiumthrough the convertible’s income advantage. Although there are various measuresof breakeven, the correct approach is to compare the cash premium which aninvestor must pay to own stock via a convertible with the additional annualincome which the convertible gives compared with an investment of an equivalentamount in the underlying equity.

Once calculated, investors can compare breakeven with the number of years thatthe convertible is guaranteed to remain in existence. Most convertibles can beredeemed by the issuer before they mature (ie the convertible is at some pointcallable), so investors look at breakeven relative to the time from now to the dateon which the convertible first becomes callable (the first call date).

From an investor’s perspective, the shorter the breakeven the better. If breakevenis within the non-call period then investors should recover the conversion

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premium through income advantage alone. Once investors have recovered thepremium, any further income advantage is effectively ‘free’.

Note that when calculating breakeven, convertible investors do not typicallyfactor in any growth or reduction in dividends (bond coupons are guaranteed,common stock dividends are not) and do not account for the time value of moneyin calculating cash flow advantage.

In terms of our earlier example, assume that ABC Corp.’s stock has a dividendyield of 2%. Investors have a choice: either they spend $1,000 buying theconvertible bond or they spend the same amount buying shares directly. Each$1,000 bond gives an annual income of $50, whereas investing this amount inABC Corp.’s stock gives an annual income of $20. As calculated above, parity is80, or $800 per bond. Since the investor has to pay $1,000 to own the convertible,this represents a $200 cash premium. Figure 11 demonstrates the breakevencalculation for this convertible.


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Figure 11: Calculating Breakeven




Parity 80


Stock Dividend Yield 2%

Premium = 20 Points or $200 per $1,000 bond

Calculations Annual Income Advantage = Annual income from convertible -

Annual income from an investment ofthe same amount in stock

= Convertible income per bond - (Cashpaid for convertible * stock dividendyield)

= $50 - ($1,000*2%)

= $50 - $20

= $30

Breakeven = Number of years needed to recoverconvertible’s premium through itsincome advantage over the commonstock

= Cash Premium ÷ Annual IncomeAdvantage

= $200 ÷ $30

= 6.66 years


Advanced Breakeven The simple breakeven approach suffers from three main defects:

1. It does not typically factor in any change in stock dividend over the life of the instrument.

2. It is of limited use to investors who are looking at convertibles as analternative to investing in fixed income instruments.


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3. It does not take into account the different risk profile of convertibles relative toequities - a convertible security is more than just a yield-augmented stocksubstitute.

A more advanced approach is therefore to use a mathematical model which aimsto value explicitly the convertible’s embedded option, taking into account bothincome and capital flows relative to those on the stock and relative to those on afixed income security of equivalent credit quality. This contrasts with thebreakeven approach which ignores risk and capital flows and only considersincome flows relative to the underlying equity.

A mathematical model allows the investor to see how a convertible is valued withrespect to past and present parameters (eg current interest rates, share prices, andhistorical volatility). However, the model is in no sense predictive. Investors whoare unable to hedge those variables which affect theoretical valuations (eg shareprices or interest rates) cannot substitute theoretical valuations for fundamentalanalysis of the underlying equities and the interest rate environment.

We review in Chapter 7 the methodology for building a simple convertible model.


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Call Protection and Put Options The Call Feature A call feature gives the issuer the right to redeem a convertible before maturity ata predetermined price. This call price is usually at par or at a small premium topar. In addition to the call price, the company must generally pay investors theamount of interest that has accrued between the previous coupon payment dateand the call date.

Absolute (or Hard) Call Protection The right to redeem a convertible can be valuable for an issuer and consequentlyit detracts from the value of the bond to an investor. Thus, to protect the investorwhen a convertible is first issued there is usually a period of time during whichthe issuer may not call the bond. This is known as absolute (or hard) callprotection.

Provisional (or Soft) Call Protection From the end of hard call protection until maturity, the bond is generally callablewithout precondition. In some cases, the bond may be callable only if the issuer’sshare price trades above a certain level for a predetermined number of days suchas 30 (or 20) out of 30 days. This is known as provisional (or soft) callprotection. Usually the share price trigger is set between 130% and 150% of theconversion price. A bond with such a feature would be referred to as having130% provisional call protection or 150% provisional call protection.

Calling Convertibles to Force Conversion When a bond is called, investors have the right to choose whether to accept thecall price or to convert into shares. In making this decision, investors willcompare the call price (plus accrued interest) with parity (note that investorsusually forfeit any accrued interest if they convert).

Thus, if parity is above the call price, a decision to call a bond will force investorsto convert into equity. This is the intention behind most call decisions - ultimateequity conversion is, after all, what most companies have in mind when theydecide to issue a convertible.

In practice, issuers usually try to force conversion through a call only when parityis well above the call price. This is because most convertible indentures requirethe issuer to give between 30 and 90 days notice of call. Investors will only makeup their minds whether to convert or redeem the bonds at the last moment. Thus,during the notice period the issuer runs the risk that a share price decline mightbring parity below the call price and suddenly the issuer will have to find cashinstead of shares to pay off convertible bondholders. The more volatile a shareprice, the greater the margin of error that issuers should allow. As a rough rule ofthumb, issuers usually wait until parity is 10%-15% above the call price plus


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accrued interest before calling a bond. Securities houses may facilitate thisprocess of calling a convertible by underwriting the call for the issuer.

A company’s decision to force conversion may also be affected by other factors.Some managers may be concerned about the potential earnings dilution, althoughmost analysts focus on fully diluted rather than primary figures. Moresignificantly, companies with high yielding stocks may find that the after-tax costof interest payments on the convertible is less than the (non tax-deductible) cost ofpaying dividends on the underlying shares and so may decide against a call.Conversely, managements that are more sensitive to balance sheet considerationsmay be more likely to force conversion into equity.

Calling Convertibles for Cash 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 fall or if thecompany’s credit improves in the years following a convertible issue.

At issue, the coupons paid on convertible debt are less than those paid oncomparable straight debt (the issuer is selling more than just a future incomestream, so investors do not require equivalently high yields). However, if interestrates subsequently decline (or issuer credit quality improves) the issuer may findit profitable to redeem the convertible for cash and refinance with cheaper straightdebt. This also removes a potential source of dilution. Alternatively, thecompany could issue a new convertible.

Calls for cash redemption are much rarer than calls for conversion. This isbecause interest rates tend to be less volatile than stock prices and becausemanagements tend to have a bias in favor of conversion.

The Put Feature Almost all convertibles have call features, whereas put features are less common.A put feature gives investors the option to force the issuer to redeem a convertibleon a predetermined date or dates prior to maturity at a predetermined price. Theissuer is usually required to redeem the convertible for cash (hard put). However,some convertibles give the issuer the option of redeeming the issue with shares(soft put), as long as the market value of the shares issued is at least equivalent toa predetermined value. For a convertible which is issued at its face value, the putprice will either be par (par put) or, more commonly, above par (premium put).

The effect of having a put option is to increase the investment value of aconvertible in that it allows holders the option to shorten maturity on theinstrument. In assessing yields and fixed income value investors will typicallylook at the yield to put rather than the yield to maturity. The decision as towhether to exercise the put will depend on the put price relative to the value of theconvertible at the put date in the absence of the put feature.


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2. Convertible Price Behavior

How Convertibles Behave when Stock Prices MoveBalanced ConvertiblesIn the Money ConvertiblesOut of the Money ConvertiblesJunk Convertibles

How Convertibles Behave when Interest Rates MoveImpact of Interest Rates on Convertible PricesInterest Rates on ‘Risk-Free’ SecuritiesCreditworthinessCallabilityWhen do Investors Convert?


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How Convertibles Behave when Stock Prices Move Balanced Convertibles A balanced (or at the money) convertible is generally thought of as one whoseprice is influenced by movements in both share prices and interest rates. As avery rough rule of thumb, a noncallable bond which has three years to maturitymight be considered balanced if the premium over parity was between 15% and40% while the premium over fixed income value was between 15% and 25%.

Figure 12 is the price and parity chart for the Cookson 7% 2004 convertible bond.Through the period shown, the convertible participated in much, but not all, of theappreciation of the underlying shares (AB) and then participated in some, but notall, of the subsequent share price weakness (CD).

Figure 12: Cookson 7% 2004 - Anatomy of a Balanced Convertible

In the Money Convertibles In the money convertibles are those where the actual share price is above theconversion price.

As share prices rise, a convertible becomes more sensitive to equity influencesand less sensitive to interest rates because rising share prices increase theconvertible’s parity value without increasing its fixed income value. Thus, fromthe perspective of an investor looking at convertibles as an alternative to a straightbond, in the money convertibles carry greater risk than out of the money issues.


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An important consideration for investors who use convertibles as an alternative toequities is how much of the share price's upside potential the convertible willcapture. This will depend on the convertible’s call protection. If an in the moneybond is callable and it would be rational for an issuer to exercise that call, theninvestors will not be willing to pay a premium to own the convertible.

Consequently, as the share price rises the premium will contract towards zero,implying underperformance (in terms of capital appreciation) relative to the stock.Indeed, it is possible for callable convertibles to trade at a discount to parity sinceany accrued interest will be lost if conversion is forced. Once the premium hasfallen to this level, the convertible should move one-for-one with the shares on theupside. (If the discount were to get any wider there would be an arbitrageopportunity.)

Figure 13 profiles the price and parity of a callable convertible bond (Michelin2.5% 2001) through a prolonged period of share price appreciation. As theconvertible approached its call price (A), premium contracted rapidly withconvertible investors unwilling to pay a premium for an instrument liable to becalled away from them.

Figure 13: Michelin 2.5% 2001 - Anatomy of an In the Money CallableConvertible

In contrast, issues with call protection will experience less premium contraction,so the convertible produces a similar capital return plus a higher income return,thereby producing a superior total return. If a bond has hard call protection, thecontraction that does take place usually reflects one of two things. It reflectseither: (1) the fact that as the bond price rises with the share price the value of theembedded put option falls; or (2) a rapidly growing dividend (and hence rapidlyfalling income advantage).


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Figure 14 profiles price and parity for a convertible with hard call protection until5 July 2000 (Daimler Benz 4.125% 2003). In this example, premium fell far moreslowly (than in Figure 13) although eventually it did tend toward zero as thevalue of both the embedded put option and the incremental yield advantagediminished.

Figure 14: Daimler 4.125% 2003 - Anatomy of an In the Money NonCallable Convertible

Issues with provisional call protection will experience premium contraction, butonly as the share price approaches the call trigger rather than the conversion price.The practical implications of provisional call protection are therefore:

Investors are guaranteed a certain amount of capital appreciation (30%-50%)before the call becomes effective;

Calls only take place to force conversion; and

Issuers do not need to have a margin of error when dealing with provisionalcall protection since parity is already at a 30%-50% premium to the call price.

Out of the Money Convertibles As parity declines, the convertible’s price becomes less sensitive to the shareprice and more sensitive to changes in interest rates; ie the convertible’s delta(rate of change) with respect to underlying share price movements falls. This isbecause a decline in the convertible’s price increases the yield on the security andthis in turn attracts buying support from fixed income funds (who will look ateither the convertible bond’s yield to maturity or yield to call) and equity incomefunds (who will be interested in the running yield on a convertible bond).


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Figure 15 profiles price and parity for Korea Electric Power Company (KEPCO)5% 2001. In this example, the convertible price has not fallen below 96 (AB)despite periods of stock price weakness (CD EF). At point B the convertible istrading out of the money with low sensitivity to stock price movements.

Figure 15: KEPCO 5% 2001 - Anatomy of an Out of the MoneyConvertible

Note that the precise identity of the ‘buyer of last resort’ (ie the investor whoprovides the floor for the convertible price) will depend on the credit quality ofthe issuer and the shape of the yield curve. Fixed income investors who look atcapital flows as well as income flows in their yield calculations are more (less)likely to buy issues trading well below (above) their redemption price. Also,fixed income funds may restrict their investment to issuers who meet certaincredit quality thresholds whereas equity income funds are unlikely to face similarrestrictions.

As the share price falls, the value of the convertible’s embedded option falls.Ultimately, this equity call option can be worth so little that the convertible willtrade purely as a straight bond. At this point, the convertible's valuation will begoverned by the same factors as those which would influence a similar corporatestraight bond.

Junk Convertibles The assumption that a convertible price has a ‘floor’ depends on the market’scontinuing faith in an issuer’s ability to meet its interest and principal repaymentobligations. If the market’s faith is shaken, then investors will demand a higheryield (and hence lower price) to induce them to hold the bond.

Figure 16 redraws the earlier Figure 5 to account for junk convertibles.


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Figure 16: Junk Convertibles – The Investment Floor ‘Disappears’


Thus, fixed income value can become a moving target which varies with investorsentiment. This is particularly true for companies perceived to be in financialdistress. The same investor sentiment should lead simultaneously to a fall in theissuer’s share price since in any liquidation of the company shareholders will havea lesser claim on any remaining assets. Thus, although there is no causal linkbetween the two, in practice bondholders can use low and rapidly declining shareprices as an indicator of falling credit quality. In the event of a default orliquidation of the issuer, the ultimate floor for the bond price will depend on theamount of funds available to meet the claims of convertible holders.


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Figure 17 profiles price and parity for a junk convertible bond (NTS Steel 4.0%2008). In this example, the convertible price continued to fall with the shareprice, reflecting a strong correlation between NTS Steel credit quality and thecompany’s share price.

Figure 17: Anatomy of a Junk Convertible - NTS Steel 4.0% 2008


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How Convertibles Behave when Interest Rates MoveImpact of Interest Rates on Convertible Prices The level of interest rates (in the convertible bond currency) can affect aconvertible price for two reasons:

It may have an effect on the valuation of the underlying equity (if the sharesare denominated in the same currency as the bond); and

It will affect the valuation of the convertible’s fixed income ‘floor’, and henceits valuation, particularly in the out of the money and junk regions.

Interest Rates on ‘Risk-Free’ Securities The key determinant of a convertible’s fixed income floor will be the interest rateat which a sovereign borrower can borrow money in its own currency for anygiven period of time. This represents the risk-free interest rate - investors canalways lend to sovereign issuers (in their own currency) with certainty of return ofprincipal since the sovereign entity has the ability to tax or issue new currency. Ifthe rate at which a sovereign entity can borrow changes, then other things beingequal, we would expect to see an equivalent change in the interest rates the marketdemands from non-sovereign issuers.

Creditworthiness The yield which the market demands from a corporate borrower will be greaterthan that demanded from a sovereign borrower, because of the risk that thecompany will default on its payment obligations. The difference between theactual yield on a (nonconvertible and non-callable) corporate bond and that on arisk-free sovereign bond is known as the credit spread.

The size of this credit spread can vary according to the market’s perception of therisk of default and on the general availability of investors willing to assume agiven level of risk. If an issuer has straight debt outstanding, it is relativelystraightforward to determine the appropriate credit spread to use in determining aconvertible’s bond value. In the absence of such an issue, credit analysts will usea variety of techniques to evaluate the appropriate spread, including detailedanalysis of the individual company and credit spreads on issuers from comparableindustries or countries.

Callability Normally, investors compare the yield on a convertible with the yield on a risk-free security of equal duration plus a credit spread. However, most convertiblesmay be called before maturity. In these circumstances, the true bond value for aconvertible will be the bond value for a non-callable, nonconvertible bond ofidentical maturity minus the value of the interest rate call option which theinvestor has ceded to the issuer. This is normally calculated using an option-


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adjusted spread (OAS) model and is of particular use in situations where interestrates have declined significantly since a convertible was issued.

When do Investors Convert? Generally investors do not convert unless the decision is forced upon them by acall notice or impending maturity. As long as the convertible remainsoutstanding, the investor can hold both a put (albeit one that may be far out of themoney) and usually some form of income advantage. The circumstances where aninvestor might convert are:

Arbitrage. If a convertible is trading at a discount to parity, there may be anarbitrage opportunity.

Income advantage. If a convertible is deep in the money and the dividendincome available on conversion exceeds the bond coupon, then investors mayconvert. Raising the dividend may be the only way for issuers to ‘force’conversion of a non-callable bond.


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3. Other Equity-linked Structures

Automatically Convertible Equity Securities (ACES)Introduction to ACESACES StructureWhat Does the Investor Receive at Maturity?CallabilityBreaking Down ACESExchangeable ACES

Convertible Quarterly Income Preferred Shares (Convertible QUIPS)Introduction to Convertible QUIPSConvertible QUIPS StructureThe Issuer’s PerspectiveValuation and PerformanceConvertible MIPS

Credit Enhanced Debt Indexed To Stock (CrEDITS)Introduction to CrEDITSCrEDITS Structure

Exchangeable StructuresIntroducing ExchangeablesStructure of an ExchangeableMandatory ExchangeablesNotationPrivatization Exchange Notes (PENs)

Original Issue Discount (OID) Convertible SecuritiesIntroduction to OID SecuritiesDescriptionValuationConsiderations for Issuers and Investors


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Reset FeaturesIntroduction to Reset FeaturesDownward ResetsUpward ResetsNegative GammaCredit Correlations

Yield Enhanced Stock (also known as PERCS)Introduction to Yield Enhanced Stock (YES)Description of the StructureWhat Does the Investor Receive at Maturity?Breaking Down YESCallability


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Automatically Convertible Equity Securities (ACES)Introduction to ACES Automatically Convertible Equity SecuritiesSM (ACES) are a mandatoryconvertible security also known by the acronyms DECSSM, PRIDESSM andSAILSSM. ACES are mandatorily convertible into common stock at maturity andoffer investors high current income in the form of a dividend or coupon. In returnfor this yield enhancement, ACES investors give up part of the potential stockprice appreciation in the form of a conversion premium.

ACES are the most equity-like convertible security currently in the market-place.Quite simply, ACES can be thought of as stock where proportionately more of thetotal return comes through income and less of the total return comes throughcapital gains or losses. In the event of share price weakness, ACES shouldsomewhat outperform common stock due to their enhanced yield. In the event ofshare price strength, ACES should slightly underperform the underlying commonstock since they are convertible into it at a premium.

ACES Structure ACES are high income convertible securities that mandatorily convert intocommon stock at maturity. As with other convertibles, ACES pay income,typically trade at a premium to conversion value and carry call protection. Unlikevanilla convertibles, they typically have shorter maturities and they mandatorilyconvert into stock at maturity.

Typical ACES are:

Structured as preferred stock;Usually issued at the same price as the underlying common stock;Convertible at a premium;Paying a fixed quarterly dividend (or coupon, if issued as a bond) whichprovides a significantly higher yield (typically, 500 to 600 basis points atissuance) than the common stock;Usually non-callable for either three years or the life of the security;Often listed on the NYSE or AMEX (helping liquidity); andAutomatically converted into common stock at the end of their life (usuallythree to four years).

The number of shares received upon conversion will depend on the common stockprice at maturity relative to the common stock price when the ACES was issued.

SM ACES is a servicemark of Goldman Sachs & Co.SM DECS is a servicemark of Salomon Brothers Inc.SM PRIDES is a servicemark of Merrill Lynch & Co.SM SAILS is a servicemark of CS First Boston.


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As an example of the ACES structure at issue, consider the Dole Food $2.75ACES issued in August 1996 (Figure 18).

Figure 18: ACES Terms at Issuance

Dole Food Co. $2.75 ACESPrice/Par Value $39.25

Stock Price at Issue $39.25

Dividend on ACES $2.75

Dividend on Common Stock $0.40

Conversion Premium 20.1%

Conversion Price $47.125

Minimum Conversion Ratio 0.8329

Maximum Conversion Ratio 1.0000

Mandatory Conversion Date 15 August 1999

Call Protection 15 August 1999

Note. This particular issue has a small twist - the issuer is not the company, but rather atrust with the trust holding the Dole shares which are issuable on conversion. Despite thisfeature, these ACES are structured and trade much like any other ACES.Source: Goldman Sachs convertible research

What Does the Investor Receive at Maturity?Assuming the ACES is held to maturity, three pay-off scenarios are possible atmandatory conversion:

1. The stock price exceeds the conversion price. The investor receives 0.8329shares of Dole Foods, the minimum conversion ratio. The value of the sharesreceived is calculated by multiplying the conversion ratio by the current stockprice.

For example, if the stock price is $60 at maturity, the investor receives aneconomic value of $49.97 ($60 * 0.8329).

2. The stock price is between the issue price ($39.25) and the conversionprice ($47.125). The investor receives the number of shares of the commonstock equal in value to the issue price, calculated as:

# Shares Received = Stock Price at Issuance ÷ Stock Price at Maturity

For example, if the stock price is $45 at maturity, the investor receives 0.8722shares with a value of $39.25, or the issue price of the ACES.


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3. The stock price is below the issue price. The investor receives one share ofcommon stock.

Figure 19: Dole Food ACES Payoff Profile at Maturity


Determining the value of the shares received at maturity is only part of theequation. The investor’s total return must also take into account the incrementaldividends received throughout the life of the security. The total return for theDole Food ACES if held to maturity is shown in Figure 20.

This analysis underlines the fact that on a total return basis, ACES are quitesimilar to common stock. While the Dole ACES can outperform the commonstock when the stock price declines, they should participate in a significant part ofthe upside (96% for Dole ACES) when the common stock appreciates.


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Figure 20: Total Return Analysis for Dole Food ACES if Held toMaturity

AnnualTotalStockReturn

Stock Price atMandatoryConversionDate

Value ofSharesReceivedatMaturity

AnnualACESDividend

ACESAnnualTotalReturn

ACESParticipationin StockPriceMovement

-35% $ 9.58 $ 9.58 $ 2.75 -30.5% 87.1%

-30 12.26 12.26 2.75 -25.1 83.8

-25 15.36 15.36 2.75 -19.9 79.4

-20 18.90 18.90 2.75 -14.6 73.1

-15 22.90 22.90 2.75 -9.4 62.9

-10 27.41 27.41 2.75 -4.3 42.7

-5 32.45 32.45 2.75 0.9 N/M

0 38.05 38.05 2.75 6.0 N/M

5 44.24 39.25 2.75 7.0 140.1

10 51.04 42.51 2.75 9.7 97.0

15 58.49 48.72 2.75 14.5 96.5

20 66.62 55.49 2.75 19.2 96.2

25 75.46 62.85 2.75 24.0 96.0

30 85.03 70.82 2.75 28.7 95.8

35 95.37 79.43 2.75 33.5 95.7

Note. Analysis assumes ACES are purchased on issue date and held to maturity. Analysisassumes ACES dividend of $2.75 and common dividend of $0.40 per annum for the life ofthe security.Source: Goldman Sachs convertible research

CallabilityOne additional consideration is the possibility of the security being called by theissuer prior to maturity. Although most ACES are not callable for the life of thesecurity, some of these structures are callable in the year prior to mandatoryconversion. As with a plain vanilla convertible, the issuer will typically call theconvertible only when the common stock price exceeds the conversion price.

If the stock price has declined during the first three years, the company will havevery little incentive to redeem the ACES prior to maturity. Alternatively, if thecommon stock has performed strongly, the probability of the issuer calling theACES is high. If it is clear that the minimum conversion ratio will be in effect,the company has strong incentive to call the ACES. If the conversion ratio is stillbetween the maximum and minimum, the issuer must weigh the saving in


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incremental dividends (ie the dividend on shares is typically lower than on theACES) versus the possibility that the stock will go higher and the company willbe required to issue fewer shares.

Breaking Down ACESA useful approach to valuation involves breaking the ACES structure into itsparts. This allows the investor to view the ACES as a combination of foursecurities:

1. Long one share of common stock;

2. Short one at the money call option struck at the ACES issue price ($39.25 inthe Dole Food example);

3. Long a fraction (0.8329 in the Dole Food example) of an out of the money callstruck at the conversion price ($47.125); and

4. Long the present value of the ACES’ incremental income above the dividendpaid on the stock.

The combination of short one at the money call and long a fraction of one out ofthe money call leaves the investor with a net loss relative to simply owning thecommon stock. To compensate for this loss, the investor receives a greaterdividend than is paid on the common stock. Thus, in our Dole Food example, theACES will be fairly valued if the price is equivalent to the package in Figure 21.

Figure 21: Valuing ACES

Dole Foods ACES Price =Dole stock price

+ 0.8329 call struck at $47.125

- one call struck at $39.25

+ Present Value of remaining dividend on ACES

- Present Value of dividends on common stock


The above equation invites further analysis. For an investor to be indifferentbetween the common stock and the ACES, the present value of the yieldadvantage must equal the cost of buying an at the money call and selling part ofan out of the money call option:


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PV(Yield Advantage) = At the money call

– 0.8329 out of the money call

If the present value of the yield advantage is higher, the ACES is more attractive.If the value of the call spread is greater, then the common stock is more attractiveto an investor, despite the higher yield on the ACES.

Exchangeable ACESExchangeable ACES are convertible into a stock other than that of the issuingcompany. The ACES structure can be very useful in helping a company tomonetize its stake in another company with possible advantages including:

1. Guaranteed Sale. ACES guarantee the issuer that it will sell the stock, unlikean exchangeable bond which has the possibility of becoming ‘busted’ andremaining on the company’s balance sheet until maturity.

2. Possibility of Premium Pricing. In comparison with selling stock outright,ACES allow the issuer the possibility of retaining some of any stock priceappreciation.

3. Tax Advantages. ACES allow the issuer to defer capital gain recognitionuntil the ACES are exchanged while receiving the proceeds at the time ofissue.


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Convertible Quarterly Income Preferred Shares (Convertible QUIPS)Introduction to Convertible QUIPS Convertible Quarterly Income Preferred SharesSM (convertible QUIPS) are aconvertible security also known by the acronyms Convertible TOPrSSM andTECONSSM .

From the investor’s viewpoint, convertible QUIPS are essentially convertiblepreferred securities, ie they are structured as preferred stock convertible intocommon shares at a premium and they pay quarterly dividends to the investor.

A typical convertible QUIPS appears to an investor with the followingcharacteristics:

Structured as preferred stock with a $50 par value;

Structured to have a maturity of 15-30 years with non-callability for three tofive years;

Convertible at a premium; and

Expected to pay a fixed quarterly dividend which is not eligible for DividendReceived Deduction.

The actual structure of a convertible QUIPS is rather more complicated than thatof a traditional convertible preferred security although most investors will beindifferent between the two structures, allowing comparable pricing levels toexist.

Convertible QUIPS Structure The issuing company establishes a wholly owned special purpose vehicle (SPV)whose sole purpose is to issue preferred stock. The SPV, which is essentially apass-through entity, sells the convertible QUIPS to investors. The SPV then lendsthe proceeds of the convertible offering to the parent in return for a convertiblesubordinated debenture with identical terms to the convertible QUIPS.

SM QUIPS is a servicemark of Goldman Sachs & Co.SM Convertible TOPrS is a servicemark of Merrill Lynch & Co., Inc.SM TECONS is a servicemark of JP Morgan & Co.


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Figure 22: Breaking Down a Convertible Quips


As an example of the convertible QUIPS structure at issue, consider Host Marriott$3.375 convertible QUIPS issued in November 1996 (Figure 23).

Figure 23: Convertible QUIPS Terms at Issuance

Host Marriott $3.375 Convertible QUIPS Issue Price/Par Value $50


Dividend on QUIPS $3.375

Dividend on Common Stock 0.0%

Conversion Premium 23%

Conversion Ratio 2.6876

Call Protection Hard Call Protection to 2 December 1999

Maturity 2 December 2026


The Issuer’s Perspective By issuing a convertible QUIPS rather than a traditional convertible preferred, theissuer achieves significant benefits, including:

Increased equity credit from rating agencies. The issuer can receive partialequity credit because the bonds do not appear on the issuer’s balance sheet asdebt, but as a ‘minority interest’ in the SPV.

Deduction of payments for tax purposes. It is currently the case that, giventhat the issuer has essentially ‘sold’ convertible subordinated debentures to theSPV, it is entitled to deduct the coupon payments for tax purposes.


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Valuation and Performance A convertible QUIPS can generally be valued as traditional convertible preferredstock although the structural differences outlined above may affect the valuationtechniques for certain types of investor. Specifically, from the viewpoint of someUS taxable corporate investors, the loss of the Dividend Received Deduction willmake the convertible QUIPS less attractive than a similarly priced traditionalconvertible preferred. These investors should compare convertible QUIPS totraditional convertible debt for valuation purposes.

In the secondary market, convertible QUIPS perform similarly to traditionalconvertible preferred securities. They somewhat outperform common stock onthe downside given their enhanced yield and implied investment value; equally,they slightly underperform the common stock on the upside given theirconvertibility into the underlying common stock at a premium.

Convertible MIPS Originally, convertible QUIPS were called convertible Monthly Income PreferredSharesSM (convertible MIPS). Given that these securities were issued out ofLimited Partnerships and Limited Liability Companies, they were required to payincome on a monthly basis (for US tax reasons). More recently, the structure hasevolved into issuance from a Delaware Business Trust allowing for quarterlypayments.

SM MIPS is a servicemark of Goldman Sachs & Co.


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Credit Enhanced Debt Indexed To Stock (CrEDITS)Introduction to CrEDITSCredit Enhanced Debt Indexed To Stock (CrEDITS) is a recent market innovationwhich allows companies to enhance the credit quality of new convertiblesecurities. CrEDITS are identical in all respects to other convertibles except thatthe principal and coupon payments are guaranteed by an irrevocable Letter ofCredit from a highly rated financial institution.

Since the instrument is guaranteed it receives the higher credit rating of thefinancial institution. Effectively, that institution charges a fee to guarantee theinstrument and there is a corresponding reduction in yield to maturity to theinvestor. This is particularly effective if the financial institution attributes asubstantially better credit quality to the issuing company than do investors in theconvertible market (ie the guarantee will cost less than the yield foregone byconvertible investors). While the issuer must pay a Letter of Credit fee for theguarantee it is able to take advantage of the market’s favorable view towardsstrong investment grade credits.

CrEDITS StructureTaking a hypothetical example, if BB-rated Company X wishes to issue a fiveyear (non-call three years) convertible security with a 15% initial conversionpremium, investors are willing to buy it with a 6% coupon (and therefore yield tomaturity) at issue (Figure 24).

Figure 24: Simplified Annual Cost to Issuer of Normal Convertible

Annual coupon cost = 6% per annumSource: Goldman Sachs convertible research

The same investors are willing to buy a similar structure but with principal andincome guaranteed by AA-rated Financial Institution Y and with just a 4%coupon. If Financial Institution Y is willing to lend its credit to guaranteeing thesecurity for less than the 2% annual yield differential implied by the two pricingsthen it will make economic sense for the issuer to incorporate the guarantee in thestructure.

Beyond this hypothetical situation, the CrEDITS structure can allow an issuer toconsider a far broader variety of possible structures (eg 0% coupon, higherpremium, and aggressive call provisions) which may not have been salablewithout the credit-enhancement feature. Figure 25 is a much simplified depictionof the mechanics underlying CrEDITS.


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Figure 25: Simplified Annual Cost to Issuer of CrEDITS

Annual coupon cost plus cost of guarantee = 5.25% per annumSource: Goldman Sachs convertible research

Attraction to Investors The use of the CrEDITS structure greatly increases the number of potentialinvestors in a convertible offering given the broader investor base for investmentgrade instruments. Recent successful CrEDITS transactions have come fromIPCL (Indian Petrochemicals Corporation) in India and GVC in Taiwan. At anintuitive level, it is very attractive for a convertible investor to be able to combinein one security: (1) the upside potential of an emerging market or growth stock;(2) a name with high stock volatility; and (3) high quality downside protectionuncorrelated to the shares.


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Exchangeable StructuresIntroducing ExchangeablesExchangeable structures are similar to convertibles in that they are typicallycharacterized by the attachment of an equity option to a fixed income instrument.The difference is that whereas the guarantor of a convertible is the same companyas that of the shares to be issued, the guarantor of an exchangeable is a differentcompany to that of the underlying shares (although typically the guarantor holdsthose underlying shares). This type of structure is often used by a companydivesting a holding in another company.

Structure of an ExchangeableTaking an actual example, in December 1996 the German bank BankgesellschaftBerlin issued a bond guaranteed by its own credit but exchangeable into shares ofthe German retailer Metro. The security was similarly structured at issue to aconventional convertible although there were certain key differences. As Figure26 illustrates, the security combines elements of the issuer’s credit with certainproperties of the underlying shares.

Figure 26: (Bankgesellschaft Berlin) Metro Exchangeable Terms andValuation at Issue

(Bankgesellschaft Berlin) Metro Exchangeable SecurityIssuer Bankgesellschaft Berlin

Coupon 3.25%

Maturity 3 December 2001

Exchange Property Metro Shares

Metro Share Price Volatility 24%

Dividend on Metro (E) 1%

Bankgesellschaft Berlin Credit Aa1

Call Protection Hard Call Protection to December 1999.140% Provisional thereafter


From an investor perspective, there are three important valuation factors whenconsidering exchangeables:

1. Stock price volatility. In valuing an exchangeable security, an investorshould consider the volatility of the underlying shares, not that of the issuershares.

2. Credit Correlation. When valuing a convertible, investors should factor inthe probability of a significant correlation between the share price and the


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credit of the issuer (especially for weaker credits). In the case of anexchangeable, this correlation is typically far less marked (or non-existent)with a positive implication for valuation.

3. Efficient Callability. Given that many European exchangeables have beenissued by large financial institutions we would expect an unusually highdegree of efficiency in calling them.

Mandatory ExchangeablesThe inherent problem for an issuer in the sale of equity through an exchangeablearises in the event that the stock price has traded down at maturity and it has notactually sold the underlying shares. Instead it faces a substantial cash call of theredemption value. Clearly a mandatory security eliminates this risk given thatconversion will be compulsory at some point in its life. As a result,exchangeables modeled on the ACES structure have been widely issued in the US.

NotationExchangeable securities are generally listed with the issuer first in brackets andthen the company of the underlying shares second. For example (Deutsche)Allianz 1% 2001 was issued by Deutsche Bank exchangeable into the shares ofAllianz.

Privatization Exchange Notes (PENs)Exchangeable securities are an increasingly important financing tool for use ingovernment privatization programs. Essentially, Privatization Exchange Notes(PENs) are similar to the instruments profiled above except that the issuing entityis a sovereign government and the exchange property are the government heldshares in a partly privatized corporation. Both the Italian and Pakistanigovernments have issued such structures and we profile below the issue terms ofthe (Italian Government) INA PENs.


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Figure 27: Summary Issue Terms for the (Italian Government) INAPENs

Lira Tranche US$ Tranche Issuer Italian Government Italian Government

Underlying Shares INA INA

Issue Size LIT 1,610bn US$ 1.06bn

Coupon 6.5% 5%

Maturity 28 June 2001 28 June 2001

Hard Call Protection Hard to 1 July 2000 Hard to 1 July 2000

Rating (Moody’s) Aa3 Aa3



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Original Issue Discount (OID) Convertible SecuritiesIntroduction to OID SecuritiesThe section below reviews original issue discount (OID) convertible securities.Within this description are included both zero coupon and deep discount (low)coupon convertibles. The zero coupon convertible structure was developed inearly 1985 in the US, and often goes by the acronym LYONs, or Liquid YieldOption Notes®. Discount coupon convertibles are similar to zero coupon ones but(as the name suggests) pay a small coupon.

DescriptionOriginal issue discount convertible bonds are distinguished from vanillaconvertible bonds in several ways. We have reviewed the structure (below) usingthe Marriott International, Inc. zero coupon convertible bond issued in October1996 as an example (Figure 28).

Figure 28: Issue Terms for Marriott International, Inc. 0% 2011

Coupon 0.00%

Yield to Maturity at Issue 4.25%

Issue Price Per Bond $532.15

Par Value $1,000

Initial Premium 20.0%

Initial Conversion Price $60.75

Conversion Ratio 8.760

Call Protection Expires 25 March 1999

Initial Call Price $603.71

Issue Size (face amount in millions) $540.3

Issue Date 25 March 1996

Maturity Date 25 March 2011

First Put Date 25 March 1999

First Put Price $603.71

Second Put Date 25 March 2006

Second Put Price $810.36


No or low coupon paid on the convertible. In the case of a zero, theconvertible pays no coupon, but instead the ‘interest payments’ are effectively

® LYONs is a registered servicemark of Merrill Lynch & Co.


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deferred until final redemption. The bonds are issued at a deep discount to parvalue (typically issue price is between 20% and 40% of par) and have a yieldto maturity reflecting the accretion from the issue price to par. For a discountconvertible, the security pays a low coupon and again the remaining value ofthe ‘interest payments’ is deferred, giving the bonds a higher yield to maturitythan current yield.

The Marriott International convertible bond pays no coupon, but had a yield tomaturity at issue of 4.75%. The initial issue price was $532.15 per bond (witha par value of $1,000). The difference between the par value and the initialissue price ($467.85) can be viewed as the value of the deferred interestpayments over the life of the bond.

Put options. Almost all OID convertibles carry the option for the investor toput them after the first three to five years and then every five years thereafter.On these dates, the investor has the option to sell the convertible back to theissuer at a pre-determined price. This price is usually equal to the initial priceof the bond plus an amount equal to accretion at the yield to maturity whichapplied at issue.

In the case of the Marriott International convertible, the investor has two putoptions. On 25 March 1999 (three years after issuance), the bonds can be putback to the company at $603.71, and on 25 March 2006 the bonds can be putback to the issuer at a price of $810.36.

Call protection. OID structures typically carry three to five years of callprotection. As with other convertibles, the issuer will generally give 15 to 30days of call notice before they can redeem the securities.

The Marriott convertible bonds carry call protection until 25 March 1999. Atthat time, the bonds may be called by the company at their accreted value. Forexample, on 25 March 1999 the call price is $603.71, representing the issueprice of $532.15 plus the accreted value of $71.56 (equivalent to 4.25%accrued over three years on the initial price of $532.15).

Conversion premium. OID convertibles are typically issued with a relativelylow conversion premium of approximately 10%-20%. However, given thatthese securities are convertible into a fixed number of shares, the ‘impliedpremium’ actually increases as the value of the convertible accretes to par.

For example, the initial conversion premium on the Marriott convertible bondswas 20%, with a fixed conversion ratio of 8.76. This represented an initialconversion price of $60.75 (issue price divided by conversion ratio). Theconversion price adjusts upward over the life of the convertible as the impliedcall/put/redemption prices accrete upwards. The conversion price at maturitywill be $114.15 (calculated as the final value of $1000 divided by the fixedconversion ratio of 8.76).


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ValuationIn the wide spectrum of convertible structures, OID convertible bonds are theclosest to a fixed income security. Although most OID convertibles are issuedwith a maturity of 15 to 25 years, investors typically view the bonds as a shortmaturity instrument due to the put options. At the put dates the investor has theoption to receive the initial price plus the accrued value of the unpaid couponfrom the issuer regardless of how the common stock has performed over that timeperiod.

In simple terms, an OID convertible can be valued as a 3- to 5-year straight bond(depending on when the first put occurs) plus a 3- to 5-year call option. In thecase of Marriott International, the bonds could be valued at the issue date as acombination of a three year zero coupon bond plus a 3 year call option onMarriott stock.

Considerations for Issuers and InvestorsOne motivation for companies to issue zero coupon convertible bonds is the taxtreatment. Although no cash interest is actually paid by the issuer, it can deductthe accrued interest on the convertible. This makes a zero coupon convertibleadvantageous from a tax and cash flow perspective. Proposed legislation in theUS may eliminate this tax advantage, making the zero coupon structure lessattractive for potential issuers given that they will no longer be allowed to deductthe accrued interest.

On the other hand, investors must pay taxes on the convertible’s accrued interesteven though they have not received an actual cash coupon. This ‘phantom’interest is taxed as ordinary income. This makes the zero-coupon unattractive toseveral different types of investor groups. In addition, the investor must foregothe accreted value of the convertible if the security is converted.


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Reset FeaturesIntroduction to Reset FeaturesReset features allow for an alteration to the conversion ratio of a convertiblesecurity under certain circumstances. Typically the reset will offer somecompensation in the event of share price depreciation over the life of the security(or a part thereof). Reset features are becoming an increasingly popular feature inthe convertible market.

Downward ResetsDownward reset clauses allow for an increase in the number of shares investorsreceive on conversion in the event that the share price is below the conversionprice on a certain pre-specified date (or dates). Typically, this will result in areset of the conversion price to the level of the share price but only up to a point.The downward reset floor sets a limit to the amount by which the exchange pricemay be altered and is typically expressed as a percentage of the conversion price.

Figure 29: Pay Off Profile at Maturity for a Mandatory Convertiblewith Reset Feature


Figure 29 profiles the expected pay-off of a mandatory resettable convertible atmaturity. The unbroken line (ABCE) corresponds to parity and the horizontalkink in the line (BC) reflects the alteration of the conversion ratio by reset.Depending on the share price at the reset date, the conversion ratio may be reset toany point along the line BC; parity following reset can therefore be on any of thepossible lines between the angles of lines ABD and ACE.

Upward ResetsUpward reset clauses allow for a decrease in the number of shares investorsreceive on conversion in the event that the share price is above the conversionprice on a certain pre-specified day or days. Typically, this will result in a reset ofthe exchange price to the level of the share price. Upward resets typically do not


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exceed the initial conversion price ie holders of the convertible do no worse thanunder the original circumstances of issue.

Negative GammaThe inclusion of reset features in convertibles can lead to unusual price action atcertain share price levels. For example the first month of 1997 was characterizedby widespread discussion of negative gamma in Japanese bank convertibles. Thephrase negative gamma refers to the situation where a convertible’s sensitivity tothe price of the underlying shares is rising at the same time as the actual value ofthe underlying shares is falling.

Figure 30: Negative Gamma Illustrated


Referring to Figure 30 (above), the key point to note is what is happening aroundpoint B as the share price falls. As the reset floor is approached, the rate of fallof the convertible price (delta) increases for a given share price fall. Thischaracteristic can create increasing pressure on the share price as arbitrageurs sellmore stock to cover their increasing exposure to share price downside -accelerating the share price decline in the process.

This creates a situation which is the reverse of conventional convertible deltahedging techniques where arbitrageurs are long volatility (and expect to sell stockas the stock price rises and buy stock as the stock price falls). Instead arbitrageurswill be short volatility and will buy stock as the stock price rises and sell stock asthe stock price falls.

Note: there are clearly limitations to the usefulness of the charts in understandingthe trading patterns of these instruments given that they only represent pay-off atmaturity versus the dynamic trading patterns of instruments over time.


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Credit CorrelationsThe concept of negative gamma is not unknown to the convertible market giventhat there will often be a strong correlation between share price and credit inweaker credit quality convertibles. A good example are the US airline industryconvertibles in 1994-95 where premiums for several instruments tended tocontract on share price weakness and to expand on share price strength. What isless familiar is the development of negative gamma in high quality instruments iethe disappearance of downside protection on stock price weakness is implicit inthe structure rather than being conditional on perceptions of weakening credit.


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Yield Enhanced Stock (YES also known as PERCS)Introduction to Yield Enhanced Stock (YES)Yield Enhanced StockSM (YES) is a convertible security also known by theacronyms PERCSSM and CHIPSSM. YES mandatorily converts into common stockat maturity and offers investors a higher current dividend than the underlyingcommon stock. Investors’ participation in stock price appreciation is capped.

YES offers a significantly different return profile from that of a vanillaconvertible security. In the event of share price weakness, YES should slightlyoutperform the common stock given its enhanced yield. In the event of shareprice strength, YES should underperform the common stock given that upsideparticipation is capped at a pre-specified level.

Description of the StructureThe typical YES is:

Structured as preferred stock;

Usually issued at the same price as the underlying common stock;

Capped at a premium of 30%-45% above the stock price at issue;

Paying a fixed quarterly dividend which provides a significantly higher yieldthan the common stock at issuance;

Often listed on the NYSE or AMEX (improving liquidity);

Usually callable at any time prior to the mandatory conversion date; and

Automatically convertible into common stock at the end of its life (usuallythree to four years).

The number of shares received upon conversion will depend on the common stockprice at maturity relative to the common stock price when the YES was issued.

As an example of the YES structure at issue, consider the SunAmerica $3.188PERCS issued in October 1996 (Figure 31).

SM YES is a servicemark of Goldman Sachs & Co.SM PERCS is a servicemark of Morgan Stanley & Co.SM CHIPS is a servicemark of The Bear Stearns Companies Inc.


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Figure 31: YES Terms at Issuance

SunAmerica $3.188 PERCSIssue Price/Par Value $37.50


Dividend on PERCS $3.188

Dividend on Common Stock $0.300

Cap Premium 35.0%

Cap Price $50.625

Mandatory Conversion Date 31 October 1999

Call Protection 6 November 1996


What Does the Investor Receive at Maturity?It is quite simple to calculate what the investor receives if the YES is held tomaturity. At the time of mandatory conversion, only two scenarios are possible:

1. The stock price exceeds the cap price. The investor receives the number ofshares of common stock equal in value to the cap price, calculated as:

# Shares Received = Cap Price ÷ Stock Price at Maturity

In the case of the SunAmerica PERCS, if the stock price is $60 at maturity, theinvestor receives 0.8438 shares with a value of $50.625 or the cap price of theYES.

2. The stock price is below the cap price. The investor receives one share ofcommon stock.

It should also be noted that a reduced conversion ratio (versus 1) is only activatedif the issuer formally calls the security before maturity. Typically a call period of30-60 days will be specified and the call price will be calculated on a ‘look-back’basis ie the price is calculated as the average of the share price between six andtwo days prior to the announcement of the call.


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Figure 32: SunAmerica PERCS Payoff Profile at Maturity


Determining the value of the shares received at maturity is only part of theequation. The investor’s total return must take into account the incrementaldividends received throughout the life of the security. Assuming it is held tomaturity, the total return for the SunAmerica PERCS is shown in Figure 34.

This analysis shows how the high dividend and the conversion cap impact theYES’ total return. While the SunAmerica PERCS modestly outperforms thecommon stock when the stock price declines, it participates in more than 100% ofthe upside for modest stock price appreciation. In the case of a significant stockprice movement on the upside, the PERCS should underperform the commonstock due to the cap.

Breaking Down YESA useful approach to valuation is to break the YES structure into its parts. Usingthis approach, the YES is essentially identical to a buy-write options strategy andcan be viewed as a combination of three securities:

1. Long one share common stock;

2. Short one out of the money call option struck at the YES cap price ($50.625 inthe SunAmerica example);

3. Long the present value of the YES’ incremental income above the dividendpaid on the stock.

The higher yield on the YES relative to the common stock is essentially themoney gained by selling the out of the money call option. However, unlike atraditional buy-write strategy, the premium is not received in an initial lump sum


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but is instead paid out in quarterly dividends. Thus, in our SunAmerica example,the YES will be fairly valued if the price is equivalent to the package in Figure33.

Figure 33: Valuing YES

SunAmerica PERCS Price= SunAmerica stock price

- one call struck at $50.625

+ Present Value of remaining dividends on PERCS

- Present Value of remaining dividends on common stock


The above equation invites further analysis. For an investor to be indifferentbetween the common stock and the YES, the present value of the yield advantagemust equal the value of the call:

PV(Yield Advantage) = One call struck at $50.625

If the present value of the yield advantage is higher, the YES is more attractive. Ifthe call value is greater, then the common stock is more attractive to an investor,despite the higher yield on the YES.


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Figure 34: Total Return Analysis for SunAmerica PERCS if Held toMaturity

AnnualTotalReturnon stock

Stock Price atMandatoryConversionDate

Value ofSharesReceivedatMaturity

AnnualYESDividend

YESAnnualTotalReturn

YESParticipationin StockPriceMovement

-35% $ 9.40 $ 9.40 $ 3.188 -27.9% 79.8%

-30 11.96 11.96 3.188 -22.6 75.4

-25 14.92 14.92 3.188 -17.4 69.4

-20 18.30 18.30 3.188 -12.1 60.6

-15 22.13 22.13 3.188 -6.9 46.3

-10 26.44 26.44 3.188 -1.8 17.7

-5 31.25 31.25 3.188 3.4 N/M

0 36.60 36.60 3.188 8.5 N/M

5 42.51 42.51 3.188 13.6 272.4

10 49.01 49.01 3.188 18.7 187.3

15 56.13 50.63 3.188 19.9 132.8

20 63.90 50.63 3.188 19.9 99.6

25 72.34 50.63 3.188 19.9 79.7

30 81.49 50.63 3.188 19.9 66.4

35 91.36 50.63 3.188 19.9 56.9

Note. Analysis assumes PERCS are purchased on issue date and held to maturity.Analysis assumes PERCS dividend of $3.188 and common dividend of $0.30 per annumfor the life of the security.Source: Goldman Sachs convertible research

CallabilityThe issuer can typically call YES at any time prior to the mandatory conversiondate at a pre-specified call price. Despite this call feature, the holder of a YESsecurity is ‘protected’ from losing future dividends. Specifically, the callschedule will ensure that the YES holder is paid for the dividend advantage of theYES over the common stock between the call date and maturity. The YES callprice declines daily at a fixed rate until a few months before the mandatoryconversion date. The call schedule assumes a flat stock dividend and is notadjusted if the stock’s dividend decreases or increases.

As a result of these unique call features, the issuer has little motivation to call theYES early. Only under a scenario where the stock price increases significantly


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above the cap and the company anticipates a decline in its stock price in the futurewould it make sense for a company to call the security.


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4. Approaches to Convertible Investment

Investing in ConvertiblesSummary Valuation InfluencesThe Rationale for Investing in ConvertiblesConvertible Strategies for Equity-Oriented InvestorsConvertible Strategies for Fixed Income and Risk-Averse InvestorsConvertible FundsHedge Funds

Investment ScenariosMarket TimingMarket RetrenchmentsTrading Range StrategiesSectoral ConsiderationsHigh Risk SituationsEmerging MarketsMisvaluationEquity ‘Kickers’Improving Credit QualityEconomic Recovery

Convertible Specific Investment RisksBuyer BewareAnti-Dilution ProvisionsTakeover ProvisionsScrew Clauses

Stripping Convertible BondsOrigins of Convertible StrippingStripping a ConvertibleSecondary Market Implication


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Investing in ConvertiblesSummary Valuation InfluencesSummarizing our previous discussions, we can conclude that a convertible’s valuewill be positively correlated with:

Stock prices. The higher the stock price, the greater is parity and the intrinsicvalue of the convertible to an equity investor.

Volatility. The greater the volatility of the underlying stock, the greater thevalue of the convertible’s embedded warrant.

Credit quality. The greater the credit quality of the issuer, the lower therequired credit spread on its straight debt and the higher the fixed incomevalue of the convertible.

Call protection. In issues without call protection investors are effectivelyshort a call to the issuer. The longer the call protection, therefore, the lesserthe value of the option that investors are short.

Conversely, a convertible’s value will be negatively correlated with:

Interest rates. Higher interest rates on risk-free securities reduce the fixedincome value of the convertible and hence negatively impact valuation. Notethat even though higher interest rates are typically a positive for warrantvaluations, the negative impact on fixed income valuations usually dominates.This is because for most newly issued convertibles the fixed income value is atleast 70%-80% of the issue price, while the warrant component is only 20%-30%.

Stock yield. Higher (and/or rising) stock yields are a negative factor forwarrant valuation and also in terms of the intrinsic yield-enhancementrationale for holding a convertible.


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Figure 35: Convertible Valuation Influences

Valuation InfluenceRises/Increases

Convertible Price

Call Protection ↑↑

Credit Quality ↑↑

Interest Rates* ↓↓

Stock Yield ↓↓

Stock Prices ↑↑

Stock Price Volatility ↑↑

* Assumes that the value of a convertible’s fixed income component outweighs its equityoption component.


The Rationale for Investing in Convertibles As we review below, there are a number of compelling reasons for incorporatingconvertibles into investment strategies. It is a commonly expressed fallacy,however, that convertibles are a good investment vehicle because they giveinvestors the best of both worlds, outperforming bonds when share prices rise andoutperforming stock when share prices fall. The investor would have done betterstill investing directly in shares when share prices rise (since there can beassumed to be some contraction of the convertible’s premium) and would havebeen better off owning straight debt when share prices fall (since the convertiblewill still fall to some degree whereas the value of straight debt will be relativelyuncorrelated to the stock price).

The trouble with the methodology used in the previous paragraph is that it relieson the benefit of hindsight. Rather than use ex-post analysis it is better to use ex-ante analysis which explicitly recognizes that investment decisions carry risks - atthe time of the investment the investor could not know whether share priceswould subsequently rise or fall. Thus, a better way to express the possibleadvantages of convertibles is to say that:

Unlike bonds, they offer a degree of upside participation when share pricesrise;

Unlike stock, they offer a degree of downside protection when share pricesfall; and

They typically provide some degree of yield advantage over common stock.

Thus, we can conclude that a convertible will have a volatility and expected returnless than those of the issuer’s common stock but greater than those of its straightdebt.


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Over shorter periods of time the relationship between the various asset classesbreaks down, with different assets outperforming at different times. Indeed, overthe 1973-95 period convertibles as an asset class actually came close toreplicating the performance of the S&P 500. This subject is discussed in moredetail when we examine the historic performance of convertibles in Chapter 5.

Convertible Strategies for Equity-Oriented Investors Equity investors use convertibles either to enhance the income component of theirtotal returns or to better manage risk in their equity portfolios. They tend to bemost sensitive to the levels of premium over parity, the length of call protectionand the yield advantage over the common stock. They tend to favor balanced andin the money convertibles.

An attractive convertible is usually one that offers a favorable asymmetry in itsreturns. For example, a convertible that gives a 70% participation in any upwardmove in the stock, but only gives a 40% participation in any downside mightnormally be considered attractive. The lower the premium and the longer the callprotection, the greater the upside participation, while the higher the yield relativeto an issuer’s straight debt, the greater the degree of downside protection.

One of the key insights of convertible analysis is that the more volatile astock, the greater the asymmetry between upside participation and downsideprotection. Figure 36 shows a simplified example of a noncallable convertiblewith one year to maturity (at a price of par) that is trading at 110, a 10% premiumto parity. In Case A the stock can either rise or fall 20% over the year, whereas inCase B it can move 40% in either direction. At maturity, the convertible will beworth the higher of parity or its par redemption value. If the share price rises, thepremium shrinks to zero - the convertible holder will participate in more of theshare upside if this 10% premium can be amortized over a 40% stock rise ratherthan a 20% stock rise. On the downside, the redemption floor is the sameirrespective of how much the stock falls. Case B, which gives investors 75% ofthe stock upside but only 25% of the downside, is more attractive than Case A,which only gives 50% both ways.


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Figure 36: Illustration of Convertible Asymmetry

Case A Case B Time to Maturity 1 year 1 year

Convertible Price 110 110

Parity 100 100

Expected 1 Year Stock Movement ±20% ±40%

Convertible Price at Maturity if StockRises by Maximum Expected

120

140

Convertible Price at Maturity if StockFalls by Maximum Expected

100

100

Upside Participation 10 points or 50%of move in parity

30 points or 75%of move in parity

Downside Participation 10 points or 50%of move in parity

30 points or 25%of move in parity


Occasionally, fund managers shy away from convertibles saying that ‘if I like acompany I’ll buy its stock and if I think that the shares are going down I won’tbuy them’. The fallacy of this argument is that the investor fails to recognizethat any investment decision is subject to uncertainty and the investor isclaiming a (sometimes unwarranted) degree of infallibility. After all, ifinvestors really are convinced that a stock is going up, then they should not buystock either, but should rather buy more leveraged instruments such as warrants orcall options.

Convertible Strategies for Fixed income and Risk-Averse Investors Fixed income investors and other risk averse investors use convertibles as a meansof enhancing overall portfolio returns without excessively increasing their risk.Typically, they use out of the money and balanced convertibles (which tend to beless sensitive to premiums over parity).

There are two related investment strategies that may be pursued by fixed incomeinvestors in the convertible market: (1) buying misvalued out of the moneyconvertibles as a direct alternative to debt; and (2) buying balanced convertibleswith the objective of introducing some conservative equity exposure to aportfolio.

1. Convertibles as an alternative to debt. Out of the money convertiblesperiodically become mispriced relative to the straight corporate bond marketand offer valuation driven opportunities to fund managers.


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2. Using convertibles to introduce equity exposure to portfolios. Fixedincome investors will periodically use convertibles as a means to achievelimited levels of equity exposure within essentially fixed income portfolios.

Convertible Funds Dedicated convertible funds are a growing investor group which tend to look at allof the factors which affect convertible valuation.

Hedge Funds Hedge funds seek to exploit the asymmetry between returns on stocks and otherassets in order to create a riskless return. The most common form of hedge wouldinvolve a long position in a convertible and a short position in the underlyingstock.


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Investment Scenarios The following cases illustrate scenarios where investors may wish to considerinvesting in convertibles.

Market Timing Very often, investors will want to gain exposure to a stock but find it difficult tobuy ‘at the bottom’. Buying a balanced or in the money convertible as analternative gives investors immediate exposure to the stock. If it subsequentlyturns out that the stock has indeed bottomed out, then investors can switch out ofthe convertible into the stock, having already participated in some of the upsidefrom the trough. Conversely, if the share price falls further, then the convertibleoffers the investor some downside protection.

Figure 37 profiles the Nedlloyd Group 4.5% 2001 convertible. Investors whobought this instrument at issue were protected from some of the share pricedepreciation (A) and eventually participated in some of the renewed share pricestrength (B). Clearly, the eventual convertible price appreciation (C) wasreflective not only of share price appreciation but also of: (1) more generallyimproved market sentiment on the stock (ie Nedlloyd credit had some leverage tothe share price) and (2) a generally positive credit spread and bond marketenvironment.

Figure 37: Nedlloyd Group 4.5% 2001

Market Retrenchments Although equities tend to outperform bonds over long periods, equity growth isnot smooth over time. Investors who want long run exposure to a company, butwho think that in the short term either the stock or the market is due for a


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retrenchment, can switch into a convertible. If the shares subsequently go down,the conversion premium should expand, implying relative outperformance. Oncethe investor believes the correction is over he can switch back into the stock.

Figure 38 shows the premium on the Quintiles Transnational 4.25% 2000convertible bond over the time since its issue. Significantly, convertible bondholders have moved within a narrower band of upside/downside moves than hasthe value of parity since January 1997. That is to say, the premium has expandedon share price weakness (AB) to give relative outperformance versus theunderlying shares.

Figure 38: Quintiles Transnational 4.25% 2000 Premium (%)


Trading Range Strategies If an investor is bullish on a stock in the long term but believes that in the shortterm it will trade within a narrow range, they can swap into a higher yieldingbalanced or in the money convertible and enhance their total return whilemaintaining exposure to any upward movement in the stock. In effect, investorsare being ‘paid to wait’ for an eventual upturn. The Royal Sun Alliance 7.25%2008 convertible (Figure 39) is an example where investors achieved yield-enhanced exposure to a range-bound stock (AB) before participating in theeventual stock price break out (CD).


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Figure 39: Royal Sun Alliance 7.25% 2008

Sectoral Considerations Sometimes investors may feel that fundamental considerations should lead themto alter the balance of their portfolio. In cases where these shifts in fundamentalsare difficult to assess, it may make more sense to own a risk-adjusted instrumentsuch as a convertible rather than stock. For example, if there are tentative signs ofeconomic recovery, then investors should consider investing in convertibles oncyclical stocks.

Likewise, convertibles may allow investors to achieve exposure to the commoditysector while managing their risk exposure. In the gold sector, for example,Ashanti 5.5% 2003 (Figure 40) vastly outperformed its underlying ADRs as theirprice fell.


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Figure 40: Ashanti 5.5% 2003

High Risk Situations In cases where there is explicitly a high degree of risk in the businesses of theunderlying issuer (for example, a recovery situation or a company developing anuntried technology) the attractions of a more defensively-oriented instrument areclear. Figure 41 profiles the price and parity of the VLSI 8.25% 2005 convertiblebond from issue in September 1995. The premium expansion on stock priceweakness (AB) highlights the usefulness of the convertible in managing portfoliorisk.

Figure 41: VLSI 8.25% 2005



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Emerging Markets Given the implicitly high levels of risk and prospective returns in the emergingmarkets, convertibles offer an attractive route to manage market exposure. Forexample, the price of the Bangkok Bank 1.5% 2006 convertible bond hardly fell(AB) during the period of stock price weakness (CD) following issue (Figure 42).

Figure 42: Bangkok Bank 1.5% 2006

Misvaluation Sometimes a convertible may simply be mispriced relative to the equity (forexample, if breakeven is inside call protection) and thereby provide an obviousbuying opportunity. Additionally, conversion difficulty or lack of stock borrowcan leave convertibles trading at a discount to parity, creating opportunities forlong term investors to convert into the underlying shares at a profit.

Equity ‘Kickers’ For more risk averse investors, the most common investment approach is to buyconvertibles where the fixed income value represents 85%-95% of the value of theinstrument, so the degree of downside protection is high but there is some upsideexposure if the stock rallies. Since equities have historically outperformed bondsover the long run, this strategy tends to increase overall returns. It may also, ofcourse, introduce a higher degree of systemic risk to portfolios.

At issue (A), the A1/AA- (Moody’s/S&P) rated Aegon 4.75% 2004 convertiblebond (Figure 43) fitted the profile of a relatively low risk premium instrument yetwithin two years was trading at 250% of its issue price (B) - high return for lowinitial risk. As the value of the convertible rose, the equity exposure (and thusrisk) of the instrument had, of course, risen correspondingly.


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Figure 43: Aegon 4.75% 2004

Improving Credit Quality During the early phases of an economic recovery, the credit quality of manyissuers, particularly the weaker credits often found in the convertible market, isperceived to improve and convertibles can offer exposure to these tighteningspreads. Likewise in the emerging markets, out of the money convertibles mayallow exposure to credit improvement situations. Banamex 7% 1999 (Figure 44)appreciated 76% from March (A) to September (B) 1995 despite having minimalequity sensitivity.


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Figure 44: Banamex 7% 1999

Economic Recovery Interest rates typically reach their lows early in an economic recovery andthereafter, as interest rates rise to counter rising inflationary pressures, bonds tendto underperform equities. In theory, fixed income funds can increase their returnsduring the latter part of an economic cycle by increasing their weightings inconvertibles.


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Convertible Specific Investment RisksBuyer Beware Any investor in doubt over the exact structure of a convertible should review indetail the prospectus (or ultimately the trust deed) for that instrument.

We briefly highlight below three issues which have historically been a problemfor convertible investors.

Anti-Dilution Provisions Most convertibles protect investors in the event that actions are taken which mightdilute the convertible holders’ equity interest in the company. In Asia (ex-Japan),there have, however, been a number of instances in which convertible holdershave been disadvantaged. In particular, convertible holders have provedvulnerable to the issuance of company-issued warrants on the shares into whichtheir investments convert. In such situations, the new option will often be struckat (or close to) the money thus avoiding the need for a conversion ratio adjustment(ie many prospectuses fail to take account of the time value of money in suchsituations).

Takeover Provisions Convertible investors should also be sensitized to the provisions of individualprospectuses in the event that the issuing company is taken over. At least threedifferent possible scenarios exist on takeover:

1. Conversion to underlying shares. The security may become convertible intoits underlying shares on completion of the takeover. While the acquisition willtypically imply a ‘takeover premium’ in the share price (and hence parity), theinvestor is clearly losing the long-term value of the put option and theincremental yield advantage. In the time between announcement of thetakeover and completion, the level of the premium should reflect theprobability the market assigns to successful completion of the takeover.

2. Redemption at a specified price. The convertible may become redeemable ata specified price on completion of the takeover. This price will typically bepar, a slight premium to par or an accreted value to reflect the age of a discountsecurity.

3. New guarantor and conversion property. The convertible may remainoutstanding with the newly merged company as guarantor and convertible intothe shares of the new company. In the event that the offer was partly in cash,the security may be convertible into a combination of cash and shares.Valuation of the convertible will partly be driven by an assessment of thecredit of the newly merged company.


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Often convertible holders will be offered a choice between more than one of thescenarios listed above. Additionally, some convertible prospectuses now carrytakeover protection specifying an increase in the conversion ratio in the event oftakeover. The extent of the change is typically correlated to the length of theremaining call protection.

Screw Clauses Although not the most tasteful term in the financial markets, the expression‘screw clause’ accurately describes the provision common to most prospectuseswhich specifies that, upon conversion, no adjustment will be made for interest ordividends. In simple terms, this means that upon conversion investors often donot receive any income accrued since the previous coupon payment.


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Stripping Convertible Bonds Origins of Convertible Stripping Straight fixed income investors have always been active participants in theconvertible market at times when convertibles are trading close to their fixedincome floor and with the equity component virtually worthless. More recently(1995-96), however, another type of market participant has grown in importance,focusing on the ‘stripping’ of the fixed income component from convertibles toleave a residual equity option.

There were three catalysts for this development:

1. The increasing sophistication of the broader investor base;

2. The dramatic growth in the size of the convertible market during the early1990s; and

3. The dramatic sell-off in a number of the Asian credit markets in 1994.

The Asian convertible market was even more acutely impacted by this latterdevelopment than were the (small) corporate bond markets in the region. Thiswas largely a result of the relatively unsophisticated nature of many convertiblemarket participants. They typically originated from outside Asia and had alimited knowledge of the credits underlying the bonds they owned, plus a lowtolerance for serious risk-of-loss. A dislocation between the convertible marketand the local credit market thus developed creating opportunities for credit-oriented investors who understood the underlying credits and were willing to buyin a volatile market.

These investors initially focused on the limited number of securities trading attheir fixed income floor but focus eventually shifted to encompass those issued bya favored credit but trading above their fixed income floor and with some equityvalue. This raised the question of how to ‘strip’ the bond from the equity portion,leaving an option which could subsequently be hedged. Ideally, were theconvertible bond to be more valuable in the future than the ‘stripped’ elements, itwould be possible to re-combine the two and create the regular convertible bondonce more.

Stripping a Convertible We review below a very simplified version of the methodology which has evolvedfor stripping convertible bonds. For the purpose of simplicity we have discussedthe subject in the context of three hypothetical counterparties.

Having identified interest in a strip transaction Counterparty 1 first buys aconvertible from the market. The convertible is then sold by Counterparty 1 toCounterparty 2 with Counterparty 1 retaining an option on that convertible bond.


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The option allows Counterparty 1 to participate in the equity exposure andCounterparty 2 to hold the fixed income component (Figure 45).

Figure 45: Anatomy of a Convertible Strip (Part 1)


Typically, Counterparty 2 will then enter into a swap exchanging the fixed ratecoupon payments on the convertible for a floating rate at their cost of funding(Figure 46).

Figure 46: Anatomy of a Convertible Strip (Part 2)


Counterparty 2 now effectively holds floating rate payments backed by the creditof the convertible issuer. A spread versus Libor can be backed out of thesetransactions so that Counterparty 2 can compare the implied credit of the originalissuing company to other floating rate positions in that company’s credit. Figure47 summarizes the transactions undertaken.


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Figure 47: Anatomy of a Convertible Strip (Summary)


In practice, Counterparty 1 and Counterparty 3 are typically combined into oneentity selling a package known as a Callable Asset Swap. The process works asfollows:

Counterparty 2 buys the convertible from Counterparty 1 at the fixed incomevalue of the convertible.

Counterparty 2 swaps the fixed rate income stream on the convertible for afloating rate income stream with Counterparty 1 and embeds within theagreement an option to terminate the agreement and call the bonds back.

Counterparty 1 retains the option to end the transaction at any time enablingthem to extract any appreciation in the value of the equity option.

From the perspective of Counterparty 2, it will typically view the purchase assimply that of a callable Floating Rate Note guaranteed by the company thatissued the original convertible. This process is summarized in Figure 48.


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Figure 48: Convertible Stripping in the ‘Real World’


Secondary Market Implication Convertibles may be stripped by market participants who do not incorporate a calloption in the transaction (and therefore lose the ability to repackage them). Thiscan result in liquidity becoming seriously impaired. This has been particularlynotable in Asia where several issues have been 50% (or more) stripped, andsecondary market liquidity has correspondingly diminished.


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5. Investing in Convertibles as an Asset Class

Performance of Convertibles as an Asset ClassPersistent Long-run Outperformance of Convertible BondsBackgroundAnalysis RevisitedReturn, Risk and Correlation - Outstanding Long-term Convertible PerformanceCorrelation Analysis

Rationalizing OutperformanceExplanations for OutperformanceCaveats


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Performance of Convertibles as an Asset Class Persistent Long-run Outperformance of Convertible BondsThe analysis of the performance of convertible securities as an asset class isintrinsically complicated given the hybrid nature of the instruments involved. Wesummarize below some of our findings based on extensive research conducted byIbbotson Associates in association with Goldman Sachs over the past few years.

Over the period for which reliable long-run data are available (ie since theearly 1970s), the total return performance of US convertibles has virtuallyreplicated that of the S&P 500 with significantly lower risk.

The total returns for convertible bonds have demonstrated a much highercorrelation with the S&P 500 than with the corporate bond universe.

Convertibles are useful in optimizing performance in both fixed income andequity portfolios.

We highlight three possible reasons for this apparent long-run outperformanceof convertible instruments: (1) exposure to a universe of significantly higherbeta underlying stocks (than the S&P 500) through a period of long-run excessreturns from equities, (2) ostensibly inefficient company timing in callingconvertible instruments, and (3) attractive convertible pricing at issue.

Background In 1992, Goldman Sachs sponsored a study of long-term convertible bondperformance. The study was intended to be an objective examination of therationale for investing in convertible bonds and aimed to compare the intuitivelogic for convertible investment with the empirical evidence.

The resulting article, written by Scott L. Lummer and Mark W. Riepe ofIbbotson Associates is now acknowledged as one of the seminal works on theconvertible market (Convertible Bonds as an Asset Class; 1957-1992 The Journalof Fixed Income Vol. 3 No. 2, September 1993). We believe it has been acontributing factor in the growth in size and sophistication of the US convertiblemarket over the last few years.

Analysis Revisited Three years after the original study, we encountered a strong demand from ourclient base for a revision of the article’s data to include the market movements ofthe three years to year-end 1995, particularly given the bond market volatility andthe equity market strength through that period. For that reason, we invitedIbbotson Associates to revisit the analysis and to update it to include the periodfrom 1992 to year-end 1995.


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We include below summary data and conclusions in a format which mirrors thatof the original report. In particular, we focus on the key return, risk andcorrelation data which comprised the second section of the report.

Return, Risk and Correlation - Outstanding Long-term ConvertiblePerformanceThe core of the data in the original analysis (Convertible Bonds as an Asset Class)compared the total return of $1 invested in a variety of asset classes betweenDecember 1956 and December 1992. Predictably, convertibles gave a total returnbetween that of the equity market (S&P 500) and the corporate bond market forthe entire period of the study. Less predictably, during the period from 1973 to1992 (for which the most complete data on convertible market performance wereavailable) convertibles gave a total return which actually exceeded that of theequity market with a significantly lower standard deviation.

Figure 49: Growth of $1 Invested at Year-End 1956 in Convertibles

Source: Ibbotson Associates, Goldman Sachs


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Figure 50: Growth of $1 Invested at Year-End 1973


The updated analysis (Figure 49 and Figure 50) underlines the exceptionalongoing performance of the convertible asset class. There have been almostidentical compound annual returns for convertible bonds (11.70%) and theS&P 500 (11.84%) from January 1973 to December 1995, with a much lowerstandard deviation of 12.4% for convertible bonds versus 17.3% for the S&P500 (Figure 51 and Figure 52).

Figure 51: Summary Statistics Since 1956

1957 - 1995

Asset Class

CompoundAnnualReturn

Wealth Index

(Dec. 1956 = $1)

StandardDeviation

S&P 500 10.89% $56.32 16.37%

Convertible Bonds 8.53% $24.33 13.84%

Long-term Corporates 7.12% $14.62 10.84%

Intermediate-term Corporates 7.36% $16.05 8.15%



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Figure 52: Summary Statistics Since 1972

1973 - 1995

Asset Class

CompoundAnnualReturn

Wealth Index

(Dec. 1972 = $1)

StandardDeviation

S&P 500 11.84% $13.11 17.27%

Convertible Bonds 11.07% $12.73 12.47%

Long-term Corporates 9.66% $8.34 12.44%

Intermediate-term Corporates 9.91% $8.79 8.93%


In order to allow a more comprehensive examination of these numbers, Figure 53and Figure 54 break them out into shorter time periods. We highlight inparticular: (1) the large deviations away from expected returns within thesesmaller time periods, and (2) the fact that the total return performance ofconvertible bonds within the most recent period (1993-95) is consistent with long-run expectations, falling between that of the S&P 500 (15.26%) and that ofintermediate-term corporate bonds (8.79%) at 11.35%.

Figure 53: Risk and Return - 5 Year Increments 1957-1995

ConvertibleBonds

S&P 500

Intermediate -term Bonds

Long-termCorporates

Period

Comp.Ann

Return

Stand.Dev.

Comp.Ann

Return

Stand.Dev.

Comp.Ann

Return

Stand.Dev.

Comp.Ann

Return

Stand.Dev.

1957-1962 3.19% 16.08% 8.88% 21.33% 4.26% 2.99% 4.46% 5.01%

1963-1967 9.36 12.67 12.39 13.79 0.76 2.75 0.30 3.60

1968-1972 0.23 17.65 7.53 10.70 6.48 7.59 5.85 9.87

1973-1977 6.79 10.79 -0.21 17.62 7.81 6.09 6.29 8.72

1978-1982 16.48 13.86 14.05 18.44 7.15 9.81 5.57 5.99

1983-1987 11.45 14.18 16.49 21.08 14.3 6.45 14.06 1.36

1988-1992 12.49 8.86 15.89 15.48 11.2 3.89 12.50 7.01

1993-1995 11.35 7.14 15.26 9.54 8.79 4.78 10.47 7.64



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Figure 54: Risk and Return - 5 Year Increments 1957-1995


In order to place convertibles on an equal footing with respect to risk, alphas werecomputed over the 1973-95 period for convertibles and long- and intermediate-term corporate bonds. The results (Figure 55) indicate that both asset classeshave had returns above expectations given their level of risk.

Figure 55: Convertible, Long-term and Intermediate-term Bonds:Calculation of Jensen’s Alpha and Beta 1973-1995

Asset

Alpha

Alpha t-statistic

Beta

Beta t-statistic

Convertibles 0.12% 1.42 0.60 32.82

Long-term Corporates 0.11% 0.70 0.26 7.24

Intermediate-termCorporates

0.14% 1.47 0.18 8.46



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Note. Alpha is reported in percent excess return per month. The regression isrun using monthly total returns over the period 1973 - 1995. The regression is ofthe form:

ri - rT-Bill = ai + ßi (rS&P) - rT-Bill) + E

where:

ri = monthly total return on asset i

rT-Bill = monthly total return on T-Bills

rS&P = monthly total return on the S&P 500

Figure 56 shows annual returns for the S&P 500 and convertibles over the period1973 to 1995. In simple terms, it demonstrates that convertibles and commonstocks typically move together, but with yearly fluctuations tending to belower for convertibles. The correlation between convertible and S&P 500monthly returns over the January 1973 to December 1995 period is 0.89.

Figure 56: Convertible Bonds and S&P 500 Yearly Total Returns 1973-1995


Figure 57 provides summary statistics for convertible bonds and stocks in monthswhen the S&P 500 rose and fell. Convertibles tend to be up (down) when stocks


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are up (down), but the magnitude of the monthly total return is smaller forconvertibles.

Figure 57: Analysis of Monthly Total Returns in Up and Down Markets1973-1995

In Months when the S&P 500: Increases Decreases

S&P 500 Convertibles S&P 500 Convertibles

Arithmetic Mean Rtn. 3.70% 2.57% -2.99% -1.44%

Standard Deviation 2.99% 2.17% 3.08% 2.35%

Number of Months 166 166 110 110


Correlation Analysis One of the key insights of mean-variance optimization is that the addition of arisky asset to a portfolio can reduce portfolio risk if the asset has low correlationswith the other portfolio assets. Figure 58 presents the correlations of monthlytotal returns for convertibles with the major US asset classes.

The results indicate that convertibles have been highly correlated with both largeand small cap stocks, but much less correlated with the various fixed income assetclasses. This implies convertibles will provide effective diversification in fixedincome-oriented portfolios.


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Figure 58: Correlation of Convertible Bonds with Other Major USAsset Classes

Correlation with ConvertibleBonds

Large-Capitalization Stocks 0.89

Small-Capitalization Stocks 0.85

Long-term Treasury Bonds 0.44

Intermediate-term Treasury Bonds 0.37

Treasury Bills -0.06

Long-term Corporate Bonds 0.47

Intermediate-term Corporate Bonds 0.53

Mortgage-backed Securities 0.40

Real Estate -0.08

Note. Correlations are generally calculated using monthly total returns over the period1973 to 1995. The exceptions are mortgage-backed securities, which use the period 1976to 1995, and real estate which uses quarterly returns for the period March 1978 toSeptember 1995.Source: Ibbotson Associates, Goldman Sachs

Mean-variance optimization derives the security or asset class weight for aportfolio that provides the maximum expected return for a given level of risk, or,conversely, the minimum risk for a given expected return. Mean-varianceoptimization requires estimates of expected return, standard deviation and cross-security correlation. Estimates of these factors are given in Figure 59 and Figure60.

To estimate the long-run expected return on convertible bonds we use the model:

E[rconv] = Rf + DP + OP

where:

E[rconv] = Expected Return on the Convertible Rf = Risk-free Rate DP = Default Premium OP = Option Premium

1. Risk-free Rate. The yield on the non-callable US Treasury 20-year bond as ofDecember 1995 (6.03%) was used as the risk-free rate. A long rather than a


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short maturity bond was used because the requirement was for a risklesssecurity with a relatively long-term and stable yield.

2. Default Premium. Clearly there is a default risk attached to convertibleinstruments and their yields must be high enough to provide additionalcompensation to cover expected losses from default. In order to estimate thisrisk (or the default premium) the study takes the difference between thearithmetic means of annual total returns for long-term corporate and long-termTreasury bonds over the longest period for which reliable data are available.Using the years 1926 to 1991, the estimated default premium is 5.7% - 5.1% =0.6%. This approach is based on the premise that convertibles are a class ofcorporate bonds, although clearly the average credit quality of the convertibleuniverse may differ to some extent from that of the straight corporate universe.

3. Option Premium. The option premium represents the difference betweenwhat investors are willing to pay for a convertible instrument and a non-convertible one with identical characteristics. The option premium isestimated by assuming that investors adjust their long-run expectations to whatis realizable. The observed difference in the arithmetic means of annual totalreturns on straight and convertible bonds since 1973 has therefore been used asour estimate of option premium for the purposes of analysis.

Figure 59: Estimates of the Long-Run Expected Return and StandardDeviation for Convertible Bonds and Major US AssetClasses

Asset Class

ExpectedReturn

StandardDeviation

Convertibles 8.95% 12.47%

Large-Capitalization Stocks 13.39 20.42

Small-Capitalization Stocks 16.86 34.37

Long-term Treasury Bonds 6.03 12.22

Intermediate-term Treasury Bonds 5.76 7.01

Treasury Bills 4.15 2.75

Long-term Corporate Bonds 6.88 11.80

Intermediate-term Corporate Bonds 6.12 8.43

Mortgage-backed Securities 6.98 10.52

Real Estate 6.71 15.15


Given the above data it is clearly possible to determine the percentage of aportfolio which should be allocated to convertible bonds and indeed, in theoriginal report (Convertible Bonds as an Asset Class), the allocation to


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convertibles in a minimum variance portfolio was calculated as a provocative 5%(the updated underlying numbers are largely in line with the previously calculatedseries and it seems reasonable therefore to infer a similarly high convertibleallocation).

Figure 60: Correlation Matrix for Convertible Bonds and Major AssetClasses

Conv.

Large-Cap.Stocks

Small-Cap.Stocks

Long-termTreas.Bonds

Inter.-termTreas.Bonds

Treas.Bills

Long-termCorp.Bonds

Inter.-termCorp.Bonds

Mort-backSecurities

RealEst.

Convertibles 1

Large-Cap. Stocks 0.89 1

Small-Cap. Stocks 0.84 0.81 1

Long-term Treas. Bonds 0.62 0.49 0.21 1

Inter.-term Treas. Bonds 0.60 0.41 0.14 0.92 1

Treas. Bills 0.02 -0.03 0.01 -0.04 0.21 1

Long-term Corp. Bonds 0.70 0.61 0.35 0.94 0.91 -0.07 1

Inter.-term Corp. Bonds 0.73 0.61 0.39 0.91 0.95 0.13 0.97 1

Mort.-backed Securities 0.60 0.48 0.11 0.89 0.92 0.08 0.96 0.93 1

Real Est. 0.27 -0.03 0.48 -0.07 0.02 0.24 0.04 0.12 -0.13 1



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Rationalizing OutperformanceExplanations for Outperformance There are a number of possible explanations for the long-run outperformance ofconvertibles as an asset class:

1. Pricing at Issue. Using conventional bond plus warrant valuation models,convertibles typically appear underpriced at issue and the unwinding of thisundervaluation may be a driver of strong long-term performance. Thisundervaluation should probably be expected given that: (i) convertibleissuance will often cause a short-term dip in the share price and (ii) secondaryshare offerings are typically priced at a discount anyway.

It may also be the case that ‘underpricing’ is a cost of entry to the market giventhe size of many convertible offerings. It is certainly the case that instrumentswhich appear undervalued from the investor perspective may likewise beattractive from the issuer perspective given the tax treatment of the couponpayments on a convertible bond. That is to say, an issuing company confidentof the long-run strength of its share price (ie of conversion) may prefer to issuea convertible bond in order to secure tax-deductibility on their couponpayments. This differential between investor valuation and issuer valuation isone of the reasons we are confident about strong future performance of theconvertible market.

2. Callability. Companies rarely call their convertibles at the precisely‘optimum’ moment as assessed by investor theoretical models. This apparentinefficiency typically allows some additional performance versus theoreticalexpectation. Again, however, this windfall for the convertible holder does notnecessarily reflect issuer inefficiency given their different considerations.Specifically, the decision not to call a callable instrument may be the result of:(1) a desire to avoid dilution; (2) an unwillingness to allow convertible holdersa free put on their stock in the period between the call announcement and thecall date; or (3) rating agency and/or balance sheet considerations.

3. Higher Betas. The high total returns of US convertibles over the last 20 yearsmay in part reflect exposure to a universe of significantly higher betaunderlying stocks (than the S&P 500) in a period of long-run excess returnsfrom equities.


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Caveats Analysis of a relatively small and under-researched asset class gives rise todifficulties in the generation and assimilation of data. Among the notes of cautionwe would highlight:

1. A Dynamic Market. The profile of the convertible market will change overtime as the market moves in and out of the money. There is a danger that asingle index for convertible performance will shift in profile (eg averagepremium) over time. The one point we would make in response to that is thatgiven the long-run nature of the data, the long-term market profile may berelatively consistent.

2. Data Reliability. Extending our analysis back 40 years involves using acollection of data series, the reliability of which is subject to question. Wewould caution that the data from before 1973 in particular is the best availablerather than necessarily being of high quality in its own right.


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6. Issuing Convertible Securities

The Issuer’s PerspectiveThe Attraction of Convertible FinancingThe Theoretical Rationale for Convertible IssuanceCost of Capital

Fulfilling Financing Objectives - Why Issue a Convertible?Lower Cash CostPotential Deferred Sale of Equity in the Future at a PremiumTax-Deductible InterestRating Agency ConsiderationsReduction of DilutionMonetization of an Equity InvestmentEase of IssuancePrivatizationAbility to Finance in SizeIncremental Investor DemandManaging the Issuer Equity AccountSignaling

Deciding on the Appropriate StructureThe Decision ProcessACESYESConvertible PreferredsVanilla Convertible DebtDiscount Convertible DebtZero Coupon Convertible DebtNew Issue OptionsIdentifying the Prospective Issuer


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The Issuer’s Perspective The Attraction of Convertible Financing Convertible securities are the most flexible financing instruments in the securitiesmarket and there are numerous factors driving the increasing popularity ofconvertible issuance around the world. We highlight some of the most importantbelow. Convertibles can offer the opportunity to:

Issue subordinated debt capital in large size;

Minimize EPS dilution versus debt or equity;

Access an alternative (and fast-growing) investor base;

Minimize balance sheet impact through the issuance of preferreds;

Achieve the most tax-efficient combination of low balance sheet impact andtax-deductibility on coupon payments; and

Finance quickly with low requirements on management time.

The Theoretical Rationale for Convertible Issuance It is sometimes erroneously stated that vanilla convertible debt financing givesissuers the best of both worlds because:

The conversion price is usually set at a premium to the current stock price, sothat if conversion takes place the issuer will get a better price for its stock thanif it simply sold shares now.

The coupon cost of a convertible is less than that of straight debt, so that ifconversion does not take place the company has issued cheap debt by issuing aconvertible.

The problem with this line of reasoning is that it is highly selective. If the issuer’sshare price does rise so much that conversion takes place in the future, then aconvertible will indeed have been a better form of financing than a sale of stocktoday at current prices, but better still in terms of maximizing shareholder valuewould have been a sale of straight debt. Conversely, if conversion fails to takeplace, then issuing a convertible would prove to have been better than raisingstraight debt, but better still would have been a pure sale of equity.

Rather than considering the issuer’s investment rationale on an ex-post basis, abetter approach is to consider the issuer’s decision on an ex-ante basis, when theissuer cannot be certain of the outcome.


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Cost of Capital Figure 61 illustrates the relative future cost of capital to an issuer of a vanillaconvertible security under different assumptions of share price growth. In thisfigure, the cost of straight debt capital is defined as the yield (interest) cost offinancing. Typically, this yield cost is higher than either the yield cost ofconvertible debt or the dividend cost of equity financing. However, from theperspective of existing shareholders, a sale of further stock has an additional costif the share price subsequently grows, since it implies that equity has been soldtoo cheaply.

Figure 61: Relative Cost of Capital of Differing Financing Alternatives

Note. The ‘equity’ line crosses above 0% annual stock price growth to reflect a notionalstock dividend yieldSource: Goldman Sachs convertible research

Looking at the relative outcomes in Figure 61, it can be seen that if thecompany’s share price grows by between x% and y% during the period underconsideration then convertible financing will be the cheapest alternative. Thus,any company that believes that its share price growth will be in this range shouldconsider convertible financing. More plausibly, any issuer that is uncertain aboutthe future of its stock price should certainly consider using convertibles as part ofa portfolio of financing alternatives.


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This is just the beginning of the cost of capital analysis, however, and Figure 62extends it to incorporate a far broader array of equity-linked securities.

Figure 62: A Broader Cost of Capital Comparison


Most importantly, in addition to the purely quantitative reasons there arecompelling qualitative reasons for a company to issue convertibles. Indeed, itwould be fallacious to state that companies select financing alternatives based oncost of capital analysis alone. The reductio ad absurdum of this perspectivewould be that companies issue equity solely because they have a negative view ontheir own business prospects. We review some of the reasons companies areincreasingly using convertible financings in the following section.


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Fulfilling Financing Objectives - Why Issue a Convertible? Lower Cash Cost At the simplest level, companies can reduce their straight borrowing rate byissuing convertible securities. For example, a company able to issue 10 year debtin the straight market at 150 bps over government rates might be able to finance at50 bps less than government rates if it issued a convertible. There would, ofcourse, be an opportunity cost attached to such a strategy, ie if the share price hasappreciated above the conversion price at maturity, it would probably have beencheaper for the company to have issued straight debt rather than a convertible.

Potential Deferred Sale of Equity in the Future at a Premium A company needing to raise money in the short term but believing its share pricewill move higher in the longer term may use the issuance of a convertiblestructure to get a potentially higher price for its stock at issue than it wouldotherwise receive through a secondary stock offering.

Tax-Deductible Interest Under most tax jurisdictions, dividends are paid out of after-tax income, makingcommon stock and preferred dividends expensive; in contrast, interest expense ondebt is tax-deductible.

One advantage to the issuer of convertible debt in relation to common stock is thatuntil debt is converted, its expense is deductible. This can make the after-tax cashexpense of a convertible compare favorably to the dividend expense of the sharesinto which it may be converted. This characteristic also helps to account for somecompanies apparent inefficiency (from an investor perspective) in callingconvertibles.

For any debt issued at a discount to its maturity value, the yield to maturity isgreater than the current yield. In many countries, the yield to maturity rate is therate at which the corporation can claim and deduct interest expense.

Rating Agency Considerations The issuance of convertible debt allows a company to issue subordinated debtcapital. Given that debt interest expense is generally tax deductible, the cash flowto an issuer is always better with convertible debt than with convertible preferred.A company might issue preferred, however, in order to improve its balance sheetratios and, at the margin, to enhance its ratings. Because preferreds often have nomaturity (and thus no fixed obligation to return the principal to the investor) andno binding requirement to make fixed payments at fixed intervals, rating agenciesconsider convertible preferreds to be a less onerous balance sheet burden thandebt obligations.


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Reduction of Dilution Because convertibles allow companies to potentially issue equity at a premium,the dilution to existing shareholders is significantly less than if the company hadissued straight equity. In addition, the management of a closely held companymay use the issuance of a convertible to defer the dilution of voting rights in theircompany.

In general, the primary earnings per share of a company will not take into accountany additional shares that are potentially created by conversion of an outstandingconvertible, as long as the convertible was originally issued with a significantconversion premium. However, a company will also report fully diluted earningsper share using the number of shares outstanding assuming all convertibles areconverted.

Monetization of an Equity Investment Companies with substantial cross-holdings in other companies will often seek theopportunity to monetize these investments. Monetization by outright sale may notbe attractive either because the share price is too low, or the company wishes toavoid immediate realization of a capital gain. The issuance of an exchangeablemay help an issuer resolve both of these issues.

Ease of IssuanceUnder certain scenarios convertible issues can even be completed within a fewhours of launch. This type of transaction is often known as an ‘overnight’convertible given the ability for issuers to announce the deal after the market closeand then to price and allocate before the market opening the next morning.

Privatization Exchangeables can also be a useful tool for governments in their privatizationprograms. Two recent transactions have seen issues from the Italian governmentand the Pakistani government with the respective governments as guarantor andthe privatized company as exchange property. We review Privatization ExchangeNotes (PENs) in more detail when discussing exchangeables in Chapter 3.

Ability to Finance in Size The size and growing sophistication of the market allows the quick sale of verylarge convertible issues. In particular, the unique structure of convertiblesecurities allows them to appeal to investors from multiple investor basesallowing potentially larger deals than from the straight debt or straight equitymarkets (especially for weaker credits).


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Incremental Investor Demand Convertible issuance allows the issuer to reach a wider investment audience sincethe issuance of a security with a higher income and different capital risk-rewardprofile may appeal to investors who would not (or could not) otherwise invest inthe issuer’s common stock. Some of the most important convertible marketinvestors are drawn from an essentially fixed income background and the issuanceof a convertible may allow them to introduce equity exposure to portfolioswithout dramatically increasing overall portfolio risk.

Issuers who have recently raised equity capital in either a primary or secondaryoffering may find it easier to raise further capital by widening their investor basethrough a convertible offering rather than by returning to the equity market.

Conversely, many issuers who would like to raise straight debt may find thatmarket closed to them because their credit rating is too low. The convertiblemarket, which by its very nature is more accustomed to dealing with a greaterrange of credits, may be more accommodating.

Managing the Issuer Equity Account Issuers view convertibles as one layer of a desired overall capital structure.Convertibles can be an attractive component of this structure offering thecombination of a lower yield versus debt with a potential future issue of commonstock at a premium.

Signaling Convertible issuance sends a positive signal to equity markets. An issuertypically hopes that a convertible will convert and with a vanilla convertible thiswill only occur if the share price rises above the conversion price.


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Deciding on the Appropriate StructureThe Decision ProcessThere are clearly multiple factors at work in making any hybrid equity financingdecision. For six of the most familiar securities, we review below the key factorsto be considered.

ACESThe key advantages of an ACES structure from the issuer perspective include thesubstantial equity credit achieved and the retained upside in the stock resultingfrom the conversion premium. Less attractive is the overall cost of the instrumentversus straight convertible preferred in the event of substantial stock priceappreciation.

Figure 63: Issuer Checklist for ACES*

Security Type Preferred stock

Conversion Feature Mandatory conversion into common stock

Accounting Treatment Preferred stock on balance sheet. Same dilution as common.

Tax Treatment No deductibility

Equity Credit Mandatory conversion means high degree of rating agencyequity credit

* ACES may also be issued as debt with a tax-deductible coupon payment.Source: Goldman Sachs convertible research

YESSimilarly YES achieves substantial equity credit and retains all of the stock upsidein the event of stock price appreciation beyond the cap level. It is however, lessattractive than straight preferred if the stock price appreciates only up to a certainlevel.

Figure 64: Issuer Checklist for YES

Security Type Preferred stock

Conversion Feature Mandatory conversion into common stock

Accounting Treatment Preferred stock on balance sheet. Same dilution as common.

Tax Treatment No deductibility

Equity Credit Mandatory conversion means high degree of rating agencyequity credit



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Convertible PreferredsWe identify three key advantages to issuers of convertible preferreds:1. A broad based market with a high level of investor familiarity;2. Lowest cash cost of any security receiving equity credit; and3. Retained upside in the stock due to the conversion premium.Less attractive are the cost versus straight preferred in the event of stock priceappreciation and the risk of a hung (ie non-converted) convertible in the event ofstock price weakness.

Figure 65: Issuer Checklist for Convertible Preferreds

Security Type Preferred stock Conversion Feature Investor option to convert into common stock Accounting Treatment Preferred security on balance sheet. Typically, less initial

dilution than common stock due to conversion premium. Tax Treatment No tax-deductibility Equity Credit Redemption feature can be structured to enhance equity

credit from rating agencies (stock settlement)


Vanilla Convertible DebtWe identify four key advantages to issuers of vanilla convertible debt:1. Reduced cash cost of financing arising from the sale of the embedded equity

option;2. Established market with very broad investor demand;3. Attractive route for sub-investment grade credits to raise long-term fixed rate

debt; and4. Tax-deductibility of coupons.On the negative side, vanilla convertible debt is less attractive than straight debt ifthe stock price rises substantially. It also receives no equity credit from the ratingagencies.

Figure 66: Issuer Checklist for Vanilla Convertible Debt

Security Type Debt Conversion Feature Investor option to convert into common stock Accounting Treatment Debt on balance sheet. Less dilution than common. Tax Treatment Full tax-deductibility Equity Credit None



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Discount Convertible DebtThe three key advantages of discount convertible debt are:1. Accretion of the instrument’s effective conversion price over time;2. The OID amortization is generally tax-deductible; and3. Low cash cost.

Less attractive is the fact that it is not equity for rating agency purposes and it willappear expensive versus straight debt if the share price rises substantially.

Figure 67: Issuer Checklist for Discount Convertible Debt

Security Type Debt

Conversion Feature Investor option to convert into common stock

Accounting Treatment Debt on balance sheet. Less dilution than common.

Tax Treatment Full tax-deductibility, generally at yield to maturity

Equity Credit None


Zero Coupon Convertible DebtThe three key attractions of zero coupon convertible debt are:1. Accretion of the instrument’s effective conversion price over time;2. The current tax benefits of the OID amortization; and3. Zero cash cost.

On the negative side, it is not equity for rating agency purposes and the (typical)inclusion of investor put features may shorten effective maturity.

Figure 68: Issuer Checklist for Zero Coupon Convertible Debt

Security Type Debt

Conversion Feature Investor option to convert into common stock

Accounting Treatment Debt on balance sheet. Less dilution than common.

Tax Treatment Current deductibility of accretion, generally at yield tomaturity

Equity Credit None



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New Issue OptionsIn Figure 69, we summarize some key structural guidelines for an issuer of aconvertible security.

Figure 69: New Issue Summary Information

Probability ofConversion

BalanceSheet

TreatmentCashCost

RatingAgencyEquityCredit

Straight Debt Zero Debt Medium Zero

Zero Coupon Convertible Very Low Debt Zero Low

Discount Convertible Low Debt Very Low Low

Convertible Debt Medium Debt Low Low

Convertible Preferred High Capital High High

Mandatory Convertibles Certain Capital Highest High

Straight Equity Certain Equity Low Full


Identifying the Prospective IssuerWe review below in general terms some of the factors which can influence thesuitability of a company to issue a convertible:

1. Dividend Yield. A company with a relatively low dividend payout policy isgenerally better positioned to issue a convertible security given that investorstypically require that coupons (or yield to maturity) exceed the dividend yieldon the common stock, to compensate them for stock purchase at a premium.

2. Stock Volatility. The higher the stock volatility, the greater the value of theoption embedded in a convertible.

3. Credit Rating. Investors clearly focus on the credit quality of a prospectiveissuer and on the implicit downside protection of an instrument.

4. Stock Borrowability. Widely available stock borrow enhances the ability ofthe market to provide a liquid market (by hedging outright holdings whereappropriate).

5. Equity Story. A good long term case for future share price appreciationenhances the salability of a new convertible security.


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7. Valuing Convertible Securities as Derivatives

Theoretical Approaches to Convertible ValuationTheoretical ValuationCreating a Theoretical ModelCreating The Binomial TreeThe Credit-Adjusted Discount RateSummaryFurther Issues

Valuing a Hypothetical ConvertibleApplying the MethodologyUsing The Model To Hedge


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Theoretical Approaches to Convertible Valuation Theoretical Valuation Valuation of convertible securities is increasingly driven by theoretical analysis.Certainly, investors seeking a more sophisticated valuation technique shouldconsider the use of theoretical models. We have adapted to more genericapplication (below) a piece published by the Goldman Sachs QuantitativeStrategies Group in 1994.

Creating a Theoretical Model The owner of a convertible bond has the right to receive future coupon andprincipal payments in exchange for stock, subject to certain call and putprovisions as outlined in Chapters 1-2. Although there are several sources ofuncertainty that affect the value of convertibles, matters are simplified below byassuming that the only source of uncertainty is the future price of the underlyingstock. It is assumed that everything else (interest rates and the volatility of thestock, for example) is known with certainty. Stock price uncertainty is generallythe major source of option value in most convertibles.

More specifically, the following assumptions are made:

1. The distribution of future stock prices is lognormal with known volatility.

2. All future interest rates (the riskless rate, the stock loan rate and the issuer’s credit spread) are known with certainty.

3. All the information required about default risk is contained in the credit spreadfor the issuer’s straight bonds (see below how the credit spread is used incalculating present values of future convertible cash flows).

Using these assumptions, the valuation method developed by Black and Scholesfor ordinary options is applicable to convertible bonds. Specifically:

1. A convertible bond can be hedged by shorting the underlying stock to create aninstantaneously riskless hedge; and

2. A convertible can be valued by calculating its expected value over all futurestock price scenarios, provided they are consistent with the known forwardprices of the stock and its volatility.

Creating the Binomial Tree The Cox-Ross-Rubinstein method of formulating the Black-Scholes equationbegins by building a binomial tree of stock prices in a ‘risk-neutral’ world. In thisrisk-neutral world, any security has an expected total return equal to the risklessrate less any rebates for borrowing securities. Each node in the tree represents apossible stock price at a specific time. Figure 70 shows one period of the stock


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tree extending over one short valuation time step of duration t. The whole tree, ofwhich Figure 70 is merely a part, starts on the valuation date and ends at thematurity of the convertible.

Figure 70: One-period Stock Tree


The stock starts at price S. After time t elapses, the stock can move to either Su orSd with equal probability and the difference between Su and Sd is determined bythe volatility of the stock. The mean of Su and Sd is the forward price of the stockafter time t.

After creating the tree of future stock prices, a corresponding tree of futureconvertible bond prices can be built. The value of the convertible tree node iscalculated by starting at maturity, where its value is known with certainty, andthen moving backwards in time down the tree, period by period, to calculate thevalue at earlier nodes. Figure 71 shows the corresponding one-period convertibletree.

Figure 71: One-period Convertible Tree


Let V be the value of the convertible bond at the start of the period. V is found bycomparing the choices available to the issuer and the investor, assuming that each


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behaves in a rational manner and that the only possible convertible values oneperiod in the future are Vu and Vd.

The holding value H of the convertible at the start of the period in a binomialmodel is the expected present value of Vu and Vd, plus the present value of anyconvertible coupons paid during this period. H is the expected value the investorcan realize by waiting for one further time period without converting, assuming noprovisions are applicable during that time. We review below how to calculate thevalue V of the convertible at the current node for all combinations of provisionsthat may be in effect:

1. No active call or put provisions. The investor can either hold the bond forone more period or convert it to stock. Therefore, he will choose to make Vthe maximum of the holding value H and parity.

2. The convertible can be put at a price P. The investor can hold, convert, orput the bond for cash equal in value to P plus accrued interest. He will chooseto make V the maximum of holding value H, parity, and the put value.

3. The convertible is both callable at price C and putable at price P. Theissuer will call the bond when the call value (defined as C plus the accruedinterest) is less than the holding value H. If the bond is called, the investor canstill choose whether to put the bond for the put value, convert it to stock, oraccept the issuer’s call. V is the minimum of holding value H and call value.

Note that put and call provisions allow the investor to receive accrued interest.An investor who converts will forfeit the accrued interest.

The Credit-Adjusted Discount Rate The holding value H of the convertible at any node in the tree is the sum of thepresent values of the coupons paid over the next period, plus the expected presentvalue of the convertible at the two nodes at the end of the period. The next issueis to establish what discount rate should be used to calculate these present values.We include below one possible methodology for deriving the credit-adjusteddiscount rate.

For an ordinary option that exercises into stock, the appropriate discount rate isthe riskless rate r, because hedging the option with stock results in a risklessinvestment over a short time period. However, the riskless rate is not entirelyappropriate for discounting these payoffs because convertible bonds pay couponsand return principal, which, unlike stock, are both subject to default.

First, consider the two extremes of high and low stock prices. If, at the next node,the stock is far above the conversion price, the conversion option will be deep inthe money and is certain to be exercised. Under this scenario, the appropriatediscount rate is the riskless rate r, because the investor is certain to obtain stockwith no default risk.


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Alternatively, if the stock price at the next node is far below the conversion price,the conversion option will be deep out of the money and will certainly not beexercised. In that case, the investor owns a corporate-grade fixed incomeinstrument that will continue to pay coupons and principal. The appropriatediscount rate, d, is the ‘risky rate’ obtained by adding the issuer’s credit spread tothe riskless rate.

To summarize, at high stock prices, where eventual conversion is virtuallyguaranteed, the appropriate discount rate is r; at low stock prices, where eventualconversion is overwhelmingly unlikely, the appropriate rate is d. At intermediatestock prices, the credit-adjusted discount rate, y, is used.

Let p be the probability at a given node that the convertible will convert into stockin the future. Then (1-p) is the probability that it will remain a fixed-incomebond. The convertible at any node is effectively a weighted mixture of default-free stock and a default-prone corporate bond, with p specifying the weightingfactor. The credit-adjusted discount rate should reflect the proportion of risklessand risky assets contained in the convertible. y is defined as the weighted mixtureof the riskless and risky rates, where the weighting factor is p; that is, y=p*r+(1-p)*d.

The value of p is easy to find on a binomial tree and the methodology is explainedbelow. The credit-adjusted rate y is equal to r when p=1 and conversion iscertain. It is equal to d when p=0 and conversion is impossible. By using y fordiscounting, a credit spread can be assigned to the convertible that movessmoothly between zero and the issuer’s credit spread, depending upon how likelyit is that the convertible ultimately converts.

Summary We list below a short summary of the steps followed to construct our binomialmodel for valuing convertible bonds.

1. Build a Cox-Ross-Rubinstein stock price tree that extends from the valuationdate to the maturity of the convertible. In building the tree, ensure that at eachtime level the stock has the appropriate assumed volatility and that the averagestock price matches the stock’s forward price.

2. At maturity, compute the value of the convertible bond as the greater of itsfixed income redemption value and its conversion value. Define theprobability of conversion to be one at nodes where it pays to convert and zerootherwise.


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3. Move backwards in time down the tree, one level at time. At each node withineach level, define the conversion probability as the average of the probabilitiesat the two connected future nodes. Compute the credit-adjusted discount rateat each node using this conversion probability. Then compute the holdingvalue H at each node as the sum of the cash flows occurring over the nextperiod and the expected bond values of the two nodes one period in the future,discounted at the credit-adjusted discount rate.

Further Issues Convertibles are complex securities. They incorporate within one instrumentmany issues, including the question of how to model credit risk. The modeloutlined above is a simplified attempt to incorporate some of a convertiblesecurity’s most important properties. It disregards several complexities touchedupon below in the interest of having a relatively straightforward methodology thatcan be used with easily available security prices, interest rates and credit ratings.

Issues worth bearing in mind include the following:

A convertible with parity much greater than its face value, and thereforecertain to convert at some time in the future, has a credit-adjusted discount rateequal to the riskless rate. In this case, our model discounts the coupons paiduntil conversion at the riskless rate, as though they have no default risk. It ispossible to develop variants of our model in which these coupons arenevertheless discounted at the ‘risky’ rate.

An at the money convertible from an issuer with a sizable credit spread candecrease in value when volatility increases. In options parlance, it can havenegative vega. This nonintuitive result occurs because an increase in volatilityhas two effects. First, it makes the expected payoff from conversion greater.Second, it increases the probability of default, which lowers the convertible’svalue. Sometimes the latter effect outweighs the former.

A convertible bond is a derivative claim on the company’s stock and the stockitself can be regarded as a derivative claim on a company’s assets. From thisperspective, a convertible is really a compound derivative claim on the assetsof the issuer, and it is natural to assume that the distribution of future assetvalues is lognormal. If this is true, however, distribution of future stock pricescannot be lognormal, contrary to the assumptions of our model.

Corporations may default on the future payments of interest and return ofprincipal of their bonds. The value of a convertible depends, therefore, uponthe current and future credit-worthiness of the issuer. A convertible maytherefore be approached as a credit derivative with the value of the derivativedepending upon the volatility of the changes in the credit spread. In the modeloutlined above, it is assumed the credit spread remains constant throughout theconvertible’s lifetime.


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Valuing a Hypothetical Convertible Applying the Methodology We now illustrate how the model can be applied by valuing a hypotheticalconvertible bond, described in Figure 72. A large credit spread of 500 basispoints is used to make its effect on the credit-adjusted discount rate easilyobservable. In order to display the full tree from valuation date to maturity, thetime steps between periods were taken as one year in length. Although this makesthe distribution of stock prices unrealistically coarse-grained, it makes drawingand interpreting the tree easier. A computer version of the model would use muchsmaller steps in order to achieve greater accuracy.

Figure 72: Hypothetical Terms

Principal $100

Coupon 10% per year

Maturity 5 years

Conversion Ratio 1

Calls $115 in year 2, declining by $5 every yearuntil maturity

Puts put at $120 in year 3

Current stock price $100

Stock dividend rate 0%

Volatility 10% per year

Riskless rate 5% per year

Stock loan rate 5% per year

Credit spread 500 basis points

Note. Bond coupon, stock dividend yield and all interest rates are annually compounded.Source: Goldman Sachs convertible research


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Figure 74 shows the stock and convertible trees with one-year time steps. Eachnode on the stock tree shows the stock price, while each node on the convertibletree shows the convertible value and a letter code to indicate the action that hasbeen taken at that node. Figure 73 explains the letter codes. The conversion probability used to calculatethe credit-adjusted discount rate is also shown at each node.

Figure 73: Letter Codes

X Investor converts to stock

P Investor exercises put

C Issuer exercises call

H Investor holds convertible for one more period

R Issuer redeems convertible at maturity


We now turn to look at some specific nodes and to show how the valuesassociated with them on the trees were obtained. At t=0, the stock has a value of100 and after one year, it either moves up to 115.47 or down to 94.53. Thesemoves correspond to a one year return volatility of 10% and an average price of$105, exactly the forward price of the stock after one year.

Now look at the convertible bond tree. At maturity in year 5, the convertible bondpays out 110 (principal plus accrued interest) if the investor does not convert intostock. Therefore, at each node, the bond is either worth the maximum of the stockprice at the corresponding node on the stock tree or 110. At those nodes wherethe maximum is the stock price, the conversion probability is 1.0. In these cases,the node’s letter code is X to indicate conversion, and the credit-adjusted discountrate is the riskless rate (5%). At those nodes where the maximum is 110, theconversion probability is 0.0, the letter code is R for redemption, and the credit-adjusted rate is the riskless rate (5%) plus the credit spread (500bp), or 10%.

Now look at the stock node with the lowest price (79.87) in year 4. Thecorresponding convertible node in year 4 can evolve into up and down nodes atmaturity that are each worth 110 and have a code R with a conversion probabilityof 0.0. The credit-adjusted discount rate at each of these nodes is 10%.Therefore, the expected present values over these two nodes is (0.5)*(110/1.1)+(0.5)*(110/1.1) = 100. The holding value of the convertible at the lowest stocknode in year 4 is calculated by adding the coupon worth 10 that is paid at the startof the year to give a holding value of 110.


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Figure 74: Binomial Trees for Valuing the Convertible Bond



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Since the call value (including accrued interest in year 4) is 115, the issuer willnot call the bond. There is no applicable put in year 4 and converting to stockyields a value of 79.87. Therefore, the investor maximizes his value by holdingthe convertible. The convertible’s theoretical value at this node is 110 with aletter code H. The conversion probability at this node, at which the bond is notconverted, put or called, is the average of its values at the up- and down-nodes,namely 1.00. The corresponding credit-adjusted discount rate is 10%.

As a final example, look at the stock node with price 103.19 in year 3. On theconvertible tree, the holding value at the corresponding node is given by the sumof: (1) the coupon paid at the start of the year 3 and (2) the expected value of theconvertible at the two connected up- and down-nodes in year 4, each discounted atthe credit-adjusted rate. The up-node in year 4 has a value of 119.15, with aconversion probability of 1.0. The corresponding credit-adjusted rate fordiscounting the up-value is 5%. The present value of 119.15 at this rate is 113.48.Similarly, the down-node’s conversion probability is 0.5.

Therefore, the credit-adjusted rate at the up-node is (0.5)*(5%)+(0.5)*(10%) =7.50%. The present value of 113.64 at this rate is 105.71. The expected presentvalue of the up- and down-nodes is 109.60. The holding value includes a couponworth 10, to give a total of 119.60. However, the investor has the right to put thebond for the put price ($120) plus accrued interest ($10), a total of $130. Sincethis is worth more than holding the bond for one more year, the investor willexercise the put, and the value of the convertible at this node is $130. Theconversion probability here is reset to 0.0 because the convertible was put and thecredit-adjusted rate is 10%.

This procedure can be repeated at all nodes in the tree, working from maturity tothe present, to compute the value of the convertible in year 0 when the stock priceis 100.

Using the Model to Hedge Let us assume a convertible trader finances the purchase of the convertible byborrowing at his cost of funds.

To hedge the convertible’s stock price risk, he maintains a short position of Δshares of the underlying stock, where Δ is the model’s value for the sensitivity ofthe convertible’s value to stock price changes. The funds from the short stockposition are maintained in an escrow account where they earn the stock loan rate.The trader now owns a portfolio consisting of a long position in the convertiblebond and a short position in stock. In theory, this portfolio is hedged againstsmall stock price moves. Any income generated by convertible coupons and theshort stock position after paying for the convertible’s financing is used to reducethe amount of borrowed capital.


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The trader will also need to hedge against changes in interest rates by computingthe value of the convertible’s sensitivity to interest rate changes. There are threeindependent types of interest rates to be considered: the riskless rate, the stockloan rate, and the credit spread.

The riskless rate and the stock loan rate usually move more or less in tandemand can both be hedged using Treasury bonds of maturity comparable to thatof the convertible. For callable convertibles, using Treasuries with maturitiesnear the first call date is more logical.

The issuer’s credit spread can vary independently of Treasury rates. If thereare outstanding straight bonds of the issuer with similar terms, they will havesensitivity to both the Treasury rates and the credit spread; a trader can thencombine them with Treasury bonds to offset the risks due to changes in bothtypes of rates. Unfortunately, such straight bonds often do not exist becausecompanies frequently issue convertibles as a substitute for straight debt. Inthat case, hedging exposure to credit risk is difficult.


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8. Convertibles in the Euromarket

Structure of the Euroconvertible MarketDefinitionForm and TaxationSettlementRegulationGoverning LawTransaction Costs and LiquidityOwnership Restrictions: ‘Seasoning’


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Structure of the Euroconvertible Market Definition The Euroconvertible market is an international, over-the-counter market forconvertible securities. The following features distinguish it from otherconvertible markets:

Securities are offered by an international syndicate to investors in more thanone country;

Securities are denominated in a eurocurrency (a eurocurrency is a liability of abank held outside the country where that currency is legal tender);

Securities are traded on an over-the-counter basis;

Dealers trading in Euroconvertibles are subject to the rules of the ISMA (theInternational Securities Market Association); and

Coupon payments are generally made without deduction of any withholdingtaxes at the source.

Form and Taxation Euroconvertibles are usually available in both bearer and registered form, withbearer form being more common. Interest income from Euroconvertibles inbearer form is generally paid without any withholding tax deductions. There areno stamp duties or other transaction taxes payable on Euroconvertible trades.

Settlement Settlement usually occurs three business days after a transaction via one of thetwo principal clearing houses: Euroclear in Brussels or Cedel in Luxembourg.Physical delivery outside the two houses is possible, although becomingincreasingly rare. Book entry within the registers maintained by the clearinghouses is standard practice.

Regulation Euroconvertible market practices are in the first instance regulated by the Zurich-based International Securities Market Association (ISMA). This is a self-regulatory organization comprised of over 800 international securities housesfrom 40 different countries which imposes a series of regulations on its membersin order to promote an orderly, well-functioning market.

ISMA has been in existence since 1969 and has, among other things, beenresponsible for the establishment of uniform market practices which now governnearly all transactions in international securities and for the introduction of astandard method of calculating yields on these instruments.


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Governing Law Euroconvertible indentures (the legally binding agreement between the issuer andthe convertible holders which details the rights and obligations of each party)from US, UK and French issuers are usually governed by the laws of their owncountry. Other Euroconvertible indentures are typically governed by either US(usually State of New York) or English law.

Transaction Costs and Liquidity There are typically no commissions and no centralized collation of prices in theEuroconvertible market. Market makers can set their own spread between theirbid and offer prices and this effectively constitutes the investor’s transactioncosts. Spreads for liquid issuers are typically in the region of one quarter to onepoint.

The liquidity of any convertible will be primarily a function of the followingfactors:

The size of an issue. The larger the size, the greater the market maker’s abilityto make markets for a larger volume of a security.

The ability to hedge risk. The more that a market maker can offset the risksof altering its convertible inventory in response to customer flows (for exampleby shorting stock, fixed income securities or a mixture of the two against along convertible position), the tighter will be the likely bid to offer spread.

The liquidity of the underlying stock. The tighter the bid to offer spread onthe underlying equity, the tighter the spread on the convertible.

The age of an issue. More recent issues usually see the greatest volume oftransactions, whereas older issues are often stored away by long term investorsand traded less frequently.

Ownership Restrictions: ‘Seasoning’Local laws may affect the ability of investors to either own or convertEuroconvertibles, or may restrict these privileges to certain types of investor.Typically, these restrictions apply more to the initial offering rather thansecondary market transactions.

‘Seasoning’ for purposes of compliance with the US Securities Act of l933 (‘Act’)and in particular with the ‘safe harbor’ provisions of Regulation S of theSecurities and Exchange Commission (SEC) refers to the passage of a period oftime following the initial public distribution outside the US of an issue ofsecurities, during which sales of the securities into the US or to US persons arerestricted. Once the restricted period has passed, the offering is deemed to ‘cometo rest’ and thereafter may be sold as a secondary offering into the US and to USpersons, without the need to register the securities under the Act so long as the


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offering is not characterized by extraordinary selling efforts or otherwiseconstitutes a new public distribution in the US market. However, individual state‘blue sky’ laws might restrict the universe of eligible investors.


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9. Convertible Market ProfilesIntroduction to Market ProfilesFurther InformationFranceGermanyHong KongIndiaItalyJapanKoreaPhilippinesSwitzerlandTaiwanThailandUKUSRest of AsiaRest of EuropeAfrica and Eastern Europe


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IntroductionThe diversity of structures, issuers, markets and regulatory environmentscomprising the global convertible market make it impossible to create a fullycomprehensive set of market profiles. In the following pages, however, we haveattempted to offer at least a flavor of the market. For each major market wehave included summary information on the following subjects:

1. Convertible market capitalization broken out by sector.

2. Recent volumes of new issuance (1995-97 Q1).

3. Coupon levels.

4. Time to maturity of outstanding instruments as of end February 1997.

5. Premium levels as of end February 1997.

6. Yield to maturity levels as of end February 1997.

7. The currencies in which convertibles are denominated.

8. The significance of the domestic convertible market versus theEuroconvertible market.

9. Liquidity.

10. Settlement procedures.

11. The convertible instruments most widely issued.

12. The composition of the investor base.

13. Quotation methods.

14. Ease (or otherwise) of conversion.

15. The largest outstanding instruments.

Further InformationCalculation of market capitalization (and new issue volumes) for the convertiblemarket is complicated by the existence of private placements, very small issues,and convoluted definitions. We have confined ourselves in the following pages topublicly traded issues with an issue size (by proceeds) over US$25 million. Thefour market structure charts included for each market (coupon, time to maturity,


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premium, yield to maturity) give a snapshot of the extant market at the end ofFebruary 1997. Each bar represents one issue.

For many of the markets, we have only included information on the verylargest outstanding instruments: in Japan, for example, we have only included300 instruments out of a universe of over 1,000.

For ease of comparison, summary market capitalization and issuance data is allincluded in US$. The sectoral breakdown of the convertible universe is alsoincluded using a series of generic sector definitions.

Fully comprehensive (and up-to-date) market profiles are available on requestfrom Goldman Sachs Global Convertible Securities Research Group.


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10. Glossary of Convertible Terms

Absolute call

The right of the issuer to redeem the bond at any time, under any circumstance (ie,without precondition).

Accrued interest

The interest earned since the last coupon payment.

ACES (Automatically Convertible Equity Securities)

A type of convertible security which is mandatorily convertible into commonstock at maturity. Also known as DECS and PRIDES.

Anti-dilution clause

An investor protection measure which provides for the adjustment of theconversion ratio in the event of stock dividends or stock splits.

At the money convertible

See balanced convertible.

Balanced convertible

A convertible which offers some (at least 25%) upside participation with theunderlying shares and only a part (no more than 75%) of the downside of theunderlying shares.

Bond premium

The difference between the market price of the convertible and its bond value.

Bond with warrant (Bond cum warrant)

Instruments created by combining a straight bond with an option or a warrant.Analytically, a bond with warrant package offers similar but not identical featuresto a convertible bond.

Bond value

The value of the ‘straight’ fixed income element of the convertible alone, withoutregard to the value of the convertible's equity option.


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Breakeven

The number of years it takes for an investor to recover the conversion premiumfrom the convertible's higher income relative to an investment of an equivalentcash amount in stock.

Purchase price Market value ofof convertible underlying shares

Breakeven =Annual income Annual income from equivalent

from convertible amount of stock

(Convertible price - Parity)=

(Bond coupon - (Stock dividend yield *Convertible price))

Busted convertible

A convertible bond whose conversion price is so far above the actual stock pricethat it trades close to its bond value.

Call feature

The right of the issuer to redeem the convertible prior to maturity at a stated price.

Clean (or net) price

Convertible bond price quoted exclusive of accrued interest. Most convertiblebonds are quoted clean.

Conversion premium

The difference between the market value of the convertible and its parity value,usually expressed as a percentage of parity value.

Conversion price

The price per share at which the convertible can be converted into common stock.

Conversion ratio

The number of shares of common stock into which each bond can be converted.


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Conversion value

See parity value.

Convertible bonds

Debt securities issued by a company that are convertible at the investor's optioninto common stock of that company.

Convertible debentures

See convertible bonds.

Convertible preferreds

Preferred shares issued by a company that are convertible at the investor's optioninto common stock of that company.

Convertible QUIPS

A type of convertible security which is similar to convertible preferred for theinvestor but offers the issuer tax and rating advantages.

Current yield

The yield that the investor receives based on the current price of the convertible.Calculated as coupon divided by current convertible price

Denomination

The minimum size in which a convertible may be traded.

Dirty (or gross) price

Convertible bond price quoted inclusive of accrued interest. SomeEuroconvertibles (especially in France) which have domestically traded tranchesmay be quoted on this basis.

Discounted income advantage

The present value of the difference between the convertible's coupon and theunderlying stock's dividend. The dividend is assumed to grow annually. Thedifference between coupon and dividend payments is discounted over the perioduntil the dividend exceeds the coupon for the first time.


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Exchangeable

A convertible issued by a company that can be converted into another company'sshares rather than its own. In the US, exchangeable can have another meaning,namely the right of an issuer, if so stated, to exchange its existing convertiblepreferred for convertible debentures with identical terms.

Fixed exchange rate

The exchange rate on a cross-currency bond at which the redemption value(typically in US$) is calculated at maturity. These features are most prevalent inThailand.

Flexible put convertible

A rolling put convertible in which the issuer establishes the price and date of justthe first put option at the convertible's original issue date. The terms of eachsucceeding put are established just prior to the preceding put, in order to give theissuer maximum flexibility to reflect changes in market conditions between putdates.

Gamma

The sensitivity of the delta of a convertible to changes in the stock price isreferred to as the gamma. It is the ratio of the change in the convertible’s delta tothe (small) corresponding percentage change in the stock price that produced it.

Hard call protection

A period during which a convertible is not callable for early redemption by theissuer under any circumstances (except in cases of force majeure).

In the money

Stock price is above the conversion price.

Investment value

See bond value.

Junk convertible

A convertible of a low credit quality company, typically trading on a very highyield to maturity.


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Mandatory convertible

A convertible bond which the holder is obliged to convert into equity at maturity.

Out of the money

Stock price is well below the conversion price. The embedded warrant has nointrinsic value.

Original issue discount

A convertible bond which is issued at a discount to par value and pays a nominalor no coupon. The value of the bond appreciates to par through the life of theconvertible at a rate equal to the yield to maturity.

Par

The face value of the convertible. For non premium put convertibles this is alsothe redemption value at final maturity.

Par put convertible

A convertible in which the investor has a put option prior to final maturity, andthe strike price of the put is at par.

Parity value

The market value of the shares of common stock into which the convertible can beconverted. Calculated by multiplying the stock price by the conversion ratio.

Payback

See breakeven.

Points premium

The market price of a convertible minus its parity value.

Preferred Equity Redemption Cumulative Stock (PERCS)

See Yield Enhanced Stock (YES).

Premium put convertible

A convertible in which the investor has a put option prior to final maturity, andthe strike price of the put is at a premium to par.


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Premium redemption convertible

A type of discount convertible where the security is issued at par but redeemsabove par.

Provisional (or soft) call

A feature that allows a convertible to be called for early redemption by the issuerbut only if the issuer's share price is above a predetermined premium to theconversion price.

Put

An option, exercisable by the investor, to redeem the convertible prior to finalmaturity for a given amount.

Rho

The sensitivity of the convertible to changes in interest rates is referred to as rho.It is the ratio of the change in the convertible price to the (small) change ininterest rates that produced it.

Risk premium

The market price of a convertible minus its investment value, expressed as apercentage of par.

Rolling premium put convertible

A premium put convertible with several premium put options. Typically, each putis structured in such a way that on any put date, the terms of the next put aresufficiently attractive that the investor has an economic incentive to continueholding the convertible until the next put date, rather than exercise the put. In thisway the convertible should remain outstanding until final maturity or until it isconverted.

Theta

The sensitivity of the convertible to changes in time to expiration is referred to astheta. It is the ratio of the change in the convertible price to the (small) change inthe time to expiration that produced it.

Useable bond with warrant

Variation on traditional bond with warrant, where the bond element can be used toexercise the warrant as an alternative to cash. In practice, this combinationbehaves like a vanilla convertible.


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Vega

The sensitivity of the option price to changes in volatility is referred to as vega. Itis the ratio of the change in the convertible’s price to the (small) correspondingpercentage change in the stock’s volatility that produced it.

Yield advantage

Difference between the current yield on the convertible and the stock dividendyield.

Yield Enhanced Stock (YES)

A type of mandatory convertible. This security is characterized by a zero issuepremium, high yield advantage over the common stock and a predetermined capon capital appreciation.

Yield pickup

See yield advantage.

Zero coupon convertible

A convertible without an annual coupon which is issued at a deep discount to, andmatures at, par. Typically, this structure will also have several put options inyears prior to maturity.


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11. Figures in TextFigure 1: Securities Market Capitalization Comparisons (US$) 5

Figure 2: The Equity-linked Financing Spectrum 5

Figure 3: The Equity Perspective on Convertibles 7

Figure 4: The Fixed Income Perspective on Convertibles 7

Figure 5: Basic Convertible Price Behavior 8

Figure 6: Calculating Parity 9

Figure 7: Market Terminology 10

Figure 8: Introducing Premium 11

Figure 9: Calculating Premium over Parity 12

Figure 10: Calculating Risk Premium 13

Figure 11: Calculating Breakeven 15

Figure 12: Cookson 7% 2004 - Anatomy of a Balanced Convertible 20

Figure 13: Michelin 2.5% 2001 - Anatomy of an In the MoneyCallable Convertible 21

Figure 14: Daimler 4.125% 2003 - Anatomy of an In the Money NonCallable Convertible 22

Figure 15: KEPCO 5% 2001 - Anatomy of an Out of the MoneyConvertible 23

Figure 16: Junk Convertibles – The Investment Floor ‘Disappears’ 24

Figure 17: Anatomy of a Junk Convertible - NTS Steel 4.0% 2008 25

Figure 18: ACES Terms at Issuance 32

Figure 19: Dole Food ACES Payoff Profile at Maturity 33

Figure 20: Total Return Analysis for Dole Food ACES if Held to Maturity 34

Figure 21: Valuing ACES 35


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Figure 22: Breaking Down a Convertible Quips 38

Figure 23: Convertible QUIPS Terms at Issuance 38

Figure 24: Simplified Annual Cost to Issuer of Normal Convertible 40

Figure 25: Simplified Annual Cost to Issuer of CrEDITS 41

Figure 26: (Bankgesellschaft Berlin) Metro Exchangeable Terms andValuation at Issue 42

Figure 27: Summary Issue Terms for the (Italian Government) INA PENs 44

Figure 28: Issue Terms for Marriott International, Inc. 0% 2011 45

Figure 29: Pay Off Profile at Maturity for a Mandatory Convertible withReset Feature 48

Figure 30: Negative Gamma Illustrated 49

Figure 31: YES Terms at Issuance 52

Figure 32: SunAmerica PERCS Payoff Profile at Maturity 53

Figure 33: Valuing YES 54

Figure 34: Total Return Analysis for SunAmerica PERCS if Held toMaturity 55

Figure 35: Convertible Valuation Influences 59

Figure 36: Illustration of Convertible Asymmetry 61

Figure 37: Nedlloyd Group 4.5% 2001 63

Figure 38: Quintiles Transnational 4.25% 2000 Premium (%) 64

Figure 39: Royal Sun Alliance 7.25% 2008 65

Figure 40: Ashanti 5.5% 2003 66

Figure 41: VLSI 8.25% 2005 66

Figure 42: Bangkok Bank 1.5% 2006 67

Figure 43: Aegon 4.75% 2004 68

Figure 44: Banamex 7% 1999 69


209

Figure 45: Anatomy of a Convertible Strip (Part 1) 73

Figure 46: Anatomy of a Convertible Strip (Part 2) 73

Figure 47: Anatomy of a Convertible Strip (Summary) 74

Figure 48: Convertible Stripping in the ‘Real World’ 75

Figure 49: Growth of $1 Invested at Year-End 1956 in Convertibles 79

Figure 50: Growth of $1 Invested at Year-End 1973 80

Figure 51: Summary Statistics Since 1956 80

Figure 52: Summary Statistics Since 1972 81

Figure 53: Risk and Return - 5 Year Increments 1957-1995 81

Figure 54: Risk and Return - 5 Year Increments 1957-1995 82

Figure 55: Convertible, Long-term and Intermediate-term Bonds:Calculation of Jensen’s Alpha and Beta 1973-1995 82

Figure 56: Convertible Bonds and S&P 500 Yearly Total Returns1973-1995 83

Figure 57: Analysis of Monthly Total Returns in Up and Down Markets1973-1995 84

Figure 58: Correlation of Convertible Bonds with Other Major US AssetClasses 85

Figure 59: Estimates of the Long-Run Expected Return and StandardDeviation for Convertible Bonds and Major US Asset Classes 86

Figure 60: Correlation Matrix for Convertible Bonds and Major AssetClasses 87

Figure 61: Relative Cost of Capital of Differing Financing Alternatives 93

Figure 62: A Broader Cost of Capital Comparison 94

Figure 63: Issuer Checklist for ACES* 98

Figure 64: Issuer Checklist for YES 98

Figure 65: Issuer Checklist for Convertible Preferreds 99


210

Figure 66: Issuer Checklist for Vanilla Convertible Debt 99

Figure 67: Issuer Checklist for Discount Convertible Debt 100

Figure 68: Issuer Checklist for Zero Coupon Convertible Debt 100

Figure 69: New Issue Summary Information 101

Figure 70: One-period Stock Tree 105

Figure 71: One-period Convertible Tree 105

Figure 72: Hypothetical Terms 110

Figure 73: Letter Codes 110

Figure 74: Binomial Trees for Valuing the Convertible Bond 111


211

12. Select Bibliography

Altman, EL ‘The Convertible Bond Market: Are Returns Worth the Risk?’Financial Analysts Journal, July-August 1989.

Black F, and M Scholes ‘The Pricing of Options and Corporate Liabilities’Journal of Political Economy 81, 1973.

Brennan, MJ, and ES Schwartz ‘The Case for Convertibles’ Continental BankJournal of Applied Corporate Finance, Summer 1988.

Brennan, MJ, and ES Schwartz ‘Convertible Bonds: Valuation and OptimalStrategies for Calls and Conversion’ Journal of Finance, December 1977.

Ingersoll, JE, Jr. ‘A Contingent-Claims Valuation of Convertible Securities’Journal of Fixed Income, September 1993.

Lummer, SL, and MW Reipe ‘Convertible Bonds as an Asset Class: 1957 - 1992’The Journal of Fixed Income Vol 3 No.2 September 1993.

McGuire, SR The Handbook of Convertibles New York: Simon & Schuster, 1991.

Mikkelson, WH ‘Convertible Calls and Security Returns’ Journal of FinancialEconomics 9, 1981.


213

13. Appendices

Appendix 1: Convertible Bond Total Returns (%) 1957-95

Appendix 2: Convertible Market Acronyms


214

Appendix 1: US Convertible Bond Total Returns (%) 1957-95

Year Total Return1957 -12.571958 28.401959 3.751960 -1.171961 17.441962 -10.531963 7.031964 10.181965 22.791966 -9.531967 19.421968 10.121969 -26.111970 -0.621971 21.601972 2.881973 -8.201974 -10.851975 26.101976 27.981977 4.871978 5.431979 16.981980 26.121981 3.691982 31.021983 11.251984 3.751985 28.011986 17.251987 -2.961988 13.421989 12.471990 -3.701991 26.861992 11.151993 15.451994 -1.901995 22.36

Source: Ibbotson Associates


215

Appendix 2: Convertible Market Acronyms

Acronym Bank Full NameACES Goldman Sachs Automatically Convertible Equity Securities

CHIPS Bear Stearns Common-Linked Higher Income ParticipationSecurities

CrEDITS Goldman Sachs Credit Enhanced Debt Indexed to Stock

DECS Salomon Brothers Dividend Enhanced Convertible Stock

ELITES BZW Equity Linked Income Tilted Euro Securities

Convertible MIPS Goldman Sachs Convertible Monthly Income PreferredSecurities

ConvertibleQUIPS

Goldman Sachs Convertible Quarterly Income PreferredSecurities

ConvertibleTOPrS

Merrill Lynch Convertible Trust Originated PreferredSecurities

LYONS Merrill Lynch Liquid Yield Option Notes

NEWS Goldman Sachs Notes with Equity Warrant Securities

OSCARs Goldman Sachs Obligations Subordonnées Convertibles enActions ou Remboursables

PENs Goldman Sachs Privatization Exchangeable Notes

PEPS Morgan Stanley Premium Exchangeable Participating Shares

PERCS Morgan Stanley Preferred Equity Redemption CumulativeStock

PERQS Morgan Stanley Preferred Equity Redeemable Quarterly-PaidShares

PRIDES Merrill Lynch Provisionally Redeemable Income DebtExchangeable for Stock

TOPrS Merrill Lynch Trust Originated Preferred Shares

SAILS CS First Boston Stock Appreciation Income Linked Securities

STRYPES Merrill Lynch Structured Yield Product Exchangeable forStock

TECONS JP Morgan Term Convertible Securities

YES Goldman Sachs Yield Enhanced Stock


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