Convertible Bonds

E Q U I T Y R E S E A R C H : I N T E R N A T I O N A LConvertibles February 2002 For enquiries please contact: Christopher Davenport (44-20) 7986-0233 [email protected] Convertible Bonds A Comprehensive Beginner’s Guide London Luke Fletcher (44-20) 7986-0125 [email protected] London International Convertible Bonds – February 2002 Table of Contents Executive Summary ............................................................................................................................... Summary ................................................................................................................................................ The Basics .............................................................................................................................................. 3 4 5 Convertible Bonds, an Investor’s Perspective ........................................................................................ 23 Convertible Bonds, an Issuer’s Perspective ........................................................................................... 30 Convertible Structures............................................................................................................................ 34 Pitfalls and Protection ............................................................................................................................ 44 Convertible Pricing Models.................................................................................................................... 47 Appendix ................................................................................................................................................ 50 Glossary.................................................................................................................................................. 57 2 Convertible Bonds – February 2002 This report1 is primarily intended as an aid to investors who wish to explore opportunities in convertibles and other equity-linked structures and would appreciate more background on the nature of the product. We outline practical and theoretical aspects of the market in six sections. There is also a glossary of terms. The basics A convertible is a hybrid security, offering aspects of both equity and straight bond investment. Using a hypothetical example, the key features of a typical issue are introduced, defined and their importance illustrated. The interpretation of a convertible as a derivative instrument is also explained, together with definitions of such terms as delta and gamma. Convertibles from an investor’s perspective From an equity investor’s point of view, a convertible bond resembles the purchase of a certain number of shares, the purchase of downside protection and possible purchase of additional yield. From a fixed-income investor’s perspective, a convertible bond looks like the purchase of a straight bond and the purchase a right to participate in an element of the appreciation of the underlying equity. The purchase of a convertible is often perceived as a compromise in an uncertain world, as it will typically underperform the underlying share in a rising share price environment and underperform bonds in a falling equity price environment. Convertibles from an issuer’s perspective The same principal of uncertainty applies to issuers of convertibles: with no presumption concerning the direction of share prices, the issuance of a convertible can look an attractive option relative to the issuance of pure equity or pure straight debt. Convertible structures Convertibles can be structured across the pure-bond to pure-equity spectrum to appeal to distinct investor groups. We introduce non-vanilla convertible structures such as mandatory ‘DECs’ in this section. Pitfalls and protections Appreciating the importance of prospectus detail is crucial in convertible analysis; we identify some protection issues. Pricing models We present a brief intuitive description of the nature of the theoretical models most frequently employed to value convertible bonds. 1 We would like to thank Laura Bordigato for her extensive contribution to this publication. 3 the bond will fall due for repayment of principal at maturity.Convertible Bonds – February 2002 Summary A convertible bond is a debt security that can be converted into a fixed number of shares per bond. If a bondholder decides not to exercise the option to exchange bonds for shares. 4 . one can observe that they characteristically display levels of volatility and return greater than straight debt. however. However. convertibles are attractive relative to straight corporate debt as they offer the holder the potential to participate in the appreciation of the underlying equity. Investors should not conclude that convertibles simply provide investors with the best of both worlds. They are corporate bonds that may be exchanged at the option of the holder for a fixed number of ordinary shares. ➤ Downside protection in a declining equity market (thus outperforming straight equity). a convertible is worth whichever is the greater of its cash redemption value and the market value of the shares into which it converts. 5 . Equities will typically outperform convertibles in a rising share price environment. Convertible securities offer a hybrid mix of equity exposure and fixed income defensiveness. but lower than straight equity. An investor would benefit more from investing directly in the underlying shares of a company (in a rising price environment). In analysing the performance of convertibles as a separate asset class. convertible bonds offer the following: ➤ Upside participation in a rising equity market (thus outperforming straight debt). providing an element of downside protection.Convertible Bonds – February 2002 The Basics ➤ ➤ ➤ ➤ ➤ Convertible bonds as hybrid securities The ‘vanilla’ structure Terminology Convertibles as derivatives Convertible price sensitivities — the ‘Greeks’ Convertible bonds as hybrid securities Convertible bonds are hybrid securities. They pay regular coupons and are senior to ordinary share capital. and ➤ Possible income advantage to the underlying shares. At maturity. Convertibles offer some of the defensive characteristics usually associated with fixed income paper. From an investor’s point of view. The uncertain nature of investment returns increases the attraction of convertible securities. To recap. and in its straight debt (if the share price is falling). It is this defensive quality combined with the prospect of participation in the event of share price strength that is fundamental to the product’s appeal. Convertibles are usually redeemable in cash at maturity and typically pay a fixed coupon over their life. while a company’s straight debt is likely to outperform its convertible debt in a falling share price environment. investment returns are not predictable. part debt and part equity. in our opinion. Below are the terms of the bond at issue: Figure 1. 4% 2 (semi-annual) 1 January 2002 1 July 2002 1 January 2007 €1000 100 100 10 shares per bond €100 Hard Call 3 years Soft Call 2 years. Below is an example of a simple callable convertible. as most convertible bonds include call features. Trigger @ 130% 100 €300m As the convertible contains an option on the shares of the company. in favour of ownership of the predetermined number of shares underlying the bond. parity and premium. John Smith Corp — Ordinary Share Data Stock Price Stock Volatility Dividend per Share Dividend Yield Source: Schroder Salomon Smith Barney Convertibles. an investor will wish to monitor the following characteristics of the convertible: convertible price. usually at any time. A convertible differs from straight debt in that the holder has the right to exchange the bond. without any extra payment. The example is used to provide a glossary of terms useful in explaining and valuing convertibles bonds in general. An investor will also monitor the yield of the bond compared to yields on fixed income paper with similar characteristics (maturity. 6 . coupon. for a predetermined number of the company’s ordinary shares (the ‘conversion ratio’). John Smith Corp 4% 2007 — Convertible Data at Issue Coupon Coupon Frequency Issue Date First Coupon Date Maturity Nominal Value Issue Price Redemption Value Conversion Ratio Conversion Price Call Protection Call Price Put Feature Issue Size Source: Schroder Salomon Smith Barney Convertibles. In the event of conversion. issue size).5% During the life of the convertible.Convertible Bonds – February 2002 The ‘vanilla’ structure A convertible in its simplest ‘plain vanilla’ form is essentially a corporate bond with an embedded equity option. the John Smith Corp. We use a hypothetical convertible bond. Convertible EUR 4% 2007. €80 25% €2 2. Figure 2. Plain vanilla structures are rare. The value of these shares will naturally be determined by their prevailing market price. At issue. the investor pays an up-front amount (the ‘issue price’) to receive annual or semi-annual coupon payments and a cash redemption value at maturity (as with straight corporate debt). however. the investor will renounce title to the corporate bond and any future income streams from it (including the final redemption payment). the investor will want to remain aware of the price and other details of the underlying. though this may be abbreviated to issuer name. coupon and maturity. will pay the ‘clean price2’ of the bond.000 CouponPaymentPerYear = € 40 As the John Smith Corp Convertible EUR 4% 2007 pays coupons semi-annually. plus the interest accrued on the bond since the last coupon payment date (1 January 2003).88 2 The clean price is the one conventionally used for quoting the price of both straight-bonds and the convertibles. The interest accrued on the John Smith Corp Convertible EUR 4% 2007 for the above purchase would be calculated as follows: æ ActualNumberofDays ö ÷ * (Coupon * NomValue ) AccruedInterest = ç ç ÷ 365 Days è ø æ 154 ö AccruedInterest = ç ÷ * (4% * € 1.Convertible Bonds – February 2002 John Smith Corp Convertible EUR 4% 2007 has the following characteristics: Figure 3. the coupon payments are calculated as follows: Coupon CouponPaymentPerYear = Coupon * No min alValue CouponPaymentPerYear = 4% * € 1. The coupon payments are typically fixed at issue and are a percentage of the bond’s nominal value. to the date they purchase the bond. For the John Smith Corp Convertible EUR 4% 2007. It is expressed as a percentage of nominal value and exclusive of accrued interest. half of this €40 amount will be paid to investors in the bond on each coupon date (1 July and 1 January each year). John Smith Corp 4% 2007 — Convertible Data at Issue Convertible Price Parity Premium Current/Running Yield Yield To Maturity Source: Schroder Salomon Smith Barney Convertibles. An investor buying the John Smith Corp Convertible EUR 4% 2007 for settlement 4 June 2003. Accrued interest Interest accrues between coupon payment dates. 100 80 25% 4% 4% Terminology Quotation Convertible bonds are usually identified by issuer name (John Smith Corp). coupon (4%) and maturity date 2007. Purchasers of convertible bonds generally have to compensate the seller for the interest accrued from the time of the last coupon payment date. Coupons are the interest payments made on a bond by the issuer.000 ) è 365 ø AccruedInterest = € 16. 7 . currency (EUR). Convertible Bonds – February 2002 If we assume that the convertible’s ‘clean price’ on 4 June 2003 is 102, an investor purchasing the bond would pay: Purchase Pr ice = (Clean Pr ice * No min alValue ) + AccruedInterest Purchase Pr ice = (102% * € 1,000) + € 16.88 Purchase Pr ice = € 1,036.88 The convertible price inclusive of accrued interest is also referred to as the convertible’s ‘dirty price’. It is worth noting the following points: ➤ According to the prevailing market convention, the ratio that expresses the time over which interest accrues is given by the actual number of days between the last coupon and the settlement date, divided by 365 days (in the year). Some older bonds specify calculation of accrued interest with respect to a 30-day month and 360-day year, however. ➤ By historical convention, French convertible bond prices are quoted in ‘dirty price’ format (inclusive of accrued interest) and in nominal terms, not as a percentage of the nominal value. Maturity The maturity date is the date on which the issuer must redeem unconverted bonds at the redemption price. The John Smith Corp Convertible EUR 4% 2007 would mature on 1 January 2006 at 100% of its nominal value or €1,000 per bond. However, it would be rational for holders of the bonds to convert them prior to the final maturity date if the market value of the shares into which they convert exceeds the cash redemption value of the bond. Nominal value A convertible’s nominal value may also be referred to as its face value. Each John Smith Corp Convertible EUR 4% 2007 convertible has a nominal value of €1,000. A nominal value of 1,000 (in the relevant bond currency) is often the market standard in the Euroconvertible markets, though it is typically ¥1,000,000 in the Japanese domestic and Euroyen markets. As described above, the convertible’s price, issue price and redemption value are all expressed as a percentage of the bond’s nominal value; French convertibles are an exception to this rule, however, being quoted in unit form. Convertible price The convertible price is the price at which it trades in the market. It is generally quoted as a percentage of its par amount. The major influences on the convertible price are as follows: ➤ Movements in the underlying stock price; ➤ Underlying stock volatility perceptions; ➤ Changes in the credit perception of the issuer; ➤ Movements in interest rates on risk-free securities; ➤ Prospective dividends; and ➤ The passage of time. 8 Convertible Bonds – February 2002 Issue price When the issue price of the convertible is equal to the bond’s nominal value, we say that the convertible has been issued at ‘par’. The term ‘par’ is often used to represent 100% of the face value of a bond. The John Smith Corp Convertible EUR 4% 2007 was issued at par, as its issue price (€1,000) was equal to 100% of the convertible’s nominal value. If a bond is issued at a price below its nominal value, it is referred to as an ‘original issue discount’ (OID) bond. The influence of market forces will cause the price of a convertible bond to deviate from its nominal or face value over its life. Redemption value At maturity, a convertible’s redemption price is often equal to its issue price, implying redemption at the bond’s nominal value. Where the redemption value of a bond is above its nominal value, it is said to redeem at a premium to par and is a ‘premium redemption’ structure. In this case, the redemption price of the convertible is normally expressed as a percentage of its original issue price (and nominal value). The John Smith Corp Convertible EUR 4% 2007 was issued at 100% of face value and will redeem at 100% of face value. Conversion ratio The number of shares a convertible can be exchanged for is represented by its ‘conversion ratio’. Though this ratio is determined initially at issue, it will usually be adjusted to account for stock splits, special dividends and other dilutive events. The John Smith Corp Convertible EUR 4% 2007 has a conversion ratio of 10. This means that each John Smith Corp bond of €1,000 nominal can be converted for 10 John Smith Corp ordinary shares. The conversion ratio is calculated by dividing a convertible’s nominal value by its conversion price. ConversionRatio = Conversion price No min alValue Conversion Pr ice The price at which underlying shares are indirectly purchased, assuming conversion takes place and the convertible has been purchased at par, is shown by the ‘conversion price’. Although no cash changes hands upon conversion, we can determine the price at which a convertible investor initially buys shares by dividing the face value of the bond by its conversion ratio. Conversion Pr ice = No min alValue ConversionRatio The conversion ratio on the John Smith Corp Convertible EUR 4% 2007 is calculated as follows: 9 Convertible Bonds – February 2002 No min alValue ConversionRatio € 1,000 Conversion Pr ice = 10 Conversion Pr ice = € 100 Conversion Pr ice = The €100 conversion price can be thought of in option terminology as the convertible’s ‘strike price’. An investor may convert the bond into the underlying shares at any time. The investor will receive 10 shares having theoretically paid €100 for each of them, regardless of the prevailing stock price at the time of conversion. An investor in a convertible bond estimates the likelihood of (eventual) conversion by monitoring the course of the stock price. If the share price > conversion price, the convertible is said to be in-the-money If the share price < conversion price, the convertible is said to be out-of-the-money If the share price is reasonably close the conversion price, the convertible is said to be at-the-money The share price of John Smith Corp at the time of the convertible issue is €80 (see Figure 3 above). As the conversion price on the John Smith Corp Convertible EUR 4% 2007 (€100) is above the share price of the stock, the convertible is said to be out-of-the-money. If the stock price were to approach and rise above €100, the John Smith Corp Convertible EUR 4% 2007 would gradually become classified as more at-the-money and then in-the-money. Parity Parity is the market value of the shares into which a convertible bond may be converted. Parity is expressed in terms of the bond currency and is normally quoted as a percentage of par, except in the case of French bonds where it is quoted relative to a bond’s nominal value. Parity = (ConversionRatio * CurrentShare Pr ice) No min alValue For the John Smith Corp Convertible EUR 4% 2007, parity is calculated as follows: Parity = (ConversionRatio * CurrentShare Pr ice) No min alValue (10 * € 80) Parity = € 1,000 Parity = 80% 10 Yield advantage3 Yield advantage is another justification for paying a premium (in cases where the current yield on the convertible is greater than the dividend yield of the common stock). Premium is expressed as a percentage of parity. while waiting for the optimal moment to convert. ConvertibleYieldAdvantage = ConvertibleRunningYield − EquityDividendYield Breakeven ‘Breakeven’ on a convertible may be thought of as the length of time (in years) that it takes for a convertible’s premium to be made up by the yield advantage of the convertible. we can see that the underlying stock has a dividend of €2 per share. Premium Premium on a convertible is the difference between the bond’s price and its equity value or parity. 11 . Convertible investors will receive €20 more in income than investors who bought the equivalent number of John Smith Corp shares will. It is the difference between the two and represents how much more the investor is paying to control a given number of shares via the convertible. Additionally. Pr emium = (Convertible Pr ice − Parity ) Parity The premium on the John Smith Corp Convertible EUR 4% 2007 is: Pr emium = Pr emium = (Convertible Pr ice − Parity ) (100 − 80) Parity 80 Pr emium = 25% A convertible’s premium will change with movements in convertible price and parity. From Figure 3. In our example. see Current or running yield below. an investor receives extra income from investment in the convertible.Convertible Bonds – February 2002 Parity on the convertible will move in line with changes in the underlying share price. The shares underlying the convertible would return only €20 a year. movements in the exchange rate between the stock and bond will influence parity on a cross-currency bond (where the bond currency differs to that of the underlying equity). over the life of the bond. the John Smith Corp Convertible EUR 4% 2007 will pay €40 in income per annum. ‘Breakeven’ is a crude measure that makes no adjustment for the present value of future monetary cash flows. A convertible investor retains the option to receive the redemption value of the bond at maturity instead of converting into the underlying shares (which may fall in price). 3 For a definition of Convertible Running Yield and Equity Dividend Yield. In many cases. One justification for the payment of a premium is the downside protection offered by a convertible. DividendPerShare CurrentShare Pr ice Coupon RunningYield = CurrentConvertible Pr ice DividendYield = At issue. Convertible EUR 4% 2007: Absolute Pr emium [Coupon − (DividendPerShare * ConversionRatio )] € 200 Breakeven = [€ 40 − (€ 2 *10)] 200 Breakeven = 20 Breakeven = 10 years Breakeven = We argue above that the yield advantage of a convertible relative to its underlying share is a justification for a convertible’s premium. the running yield on the John Smith Corp Convertible EUR 4% 2007 was: Coupon CurrentConversion Pr ice € 40 RunningYield = € 1. adjusted for the unit size. The John Smith Corp Convertible EUR 4% 2007 only has a five-year maturity.000 RunningYield = 4% RunningYield = A convertible’s current or running yield will change over the life of a bond as the convertible price varies. For convertibles that are by convention quoted with accrued interest included in the price. it is common to see the current yield expressed as the coupon divided by the quoted price.Convertible Bonds – February 2002 Breakeven = Absolute Pr emium [Coupon − (DividendPerShare * ConversionRatio )] For the John Smith Corp. in some cases analysts will use a notional clean price. 12 . As this is inconsistent with the use of the term in relation to the majority of convertibles that are quoted in clean price form. In this case it would take 10 years for the extra income on the bond to offset the premium on the convertible. Current or running yield The current yield on a convertible is similar to the dividend yield on a stock. However yield advantage is seldom the only justification. both are defined below. This is the same calculation that would be applied to a normal fixed income security to determine its value. However an investor should be aware that a dramatic fall in the share price of a company can affect the perception of the correct credit level for that issuer. which will tend to lower the perceived level of the bond floor. the convertible should be worth at least its bond floor. expressed as a percentage of the bond floor. which measures the credit quality of the issuer5. In theory. Please refer to the Appendix for a more detailed breakdown of this calculation. or swap curve (for the relevant underlying currency) is conventionally used in the Euroconvertible market as a proxy for the risk-free rate6. (its coupons and redemption value). For example the Treasury yield curve should be used for US dollar bonds. or investment value). Though swap rates are higher than Treasury rates. plus a credit spread. Risk Pr emium = (Convertible Pr ice − BondFloor ) BondFloor 4 This is a somewhat simplistic definition as it ignores the reinvestment of coupon interest. is calculated by considering the fixed income attributes of a convertible security alone. or investment value Risk Premium A convertible’s risk premium is calculated as the difference between its price and bond floor. 6 Ideally sovereign debt of the nation associated with the currency in question should be used. by inspecting the credit spread on corporate bonds for similarly rated issuers. The credit spread assumption is fundamental to the valuation of a convertible as it can significantly affect the measures used to judge the merits of a bond. or investment value. The bond floor should provide the convertible price with a minimum price floor. other things being equal. there is a compensatory effect in that the spread over swaps for a given corporate bond will be tighter than the spread over Treasuries. please see the Appendix. Using the risk-free rate plus credit spread method described above. A convertible’s YTM is inversely correlated to movements in its price: the higher the convertible price. For a more complete definition of YTM. The Libor.Convertible Bonds – February 2002 Yield to maturity (YTM) A bond’s yield to maturity (YTM) is the rate of return that an investor will receive if the bond is held to maturity4. Bond floor. for example. the investment value on the John Smith Corp Convertible EUR 4% 2007 bond at issue was 89. independent of the performance of the underlying share price. one is forced to make an assumption on the credit quality of the issuer. When choosing a credit spread. 5 An alternative method for calculating the bond floor considers the spot yield curve and discounts each future payment using the appropriate spot rate plus credit spread. subject to prevailing interest rates and the credit of the issuer. the lower its YTM and vice-versa. 13 . A convertible’s bond floor. The discount rate generally applied to a bond’s cash flows is the risk-free rate relevant for the maturity of the bond. a convertible would be worth no more than its fixed income value (its bond floor. The investment value of a convertible is found by discounting to present value the cash flows of the convertible. Without its embedded conversion option.91% of its par value. The risk premium measures how much of a ‘premium’ to the bond floor a fixed-income investor is required to pay for an option on the underlying shares. or at the accreted value of the bond. The issuer can only call the bond if the stock trades at 130% of the initial conversion price. must also be satisfied. or 100% of its nominal value. HNC protection has value to a convertible investor. in the case of an OID or premium redemption security. however. or €130.91) Risk Pr emium = 89. It guarantees the holder of the bond exposure to the underlying share and to any yield advantage that this may imply for an identifiable period of time.22% The difference between a convertible’s price and its bond floor can be seen as the value that the market places on the option to convert. The conditions of the bond’s ‘soft call’ (sometimes referred to as its provisional call). it cannot be called for at least three-years (the bond has three-years of ‘hard non-call’ (HNC) protection). The John Smith Corp Convertible EUR 4% 2007 cannot be called unconditionally until after this initial three-year. for at least 20 days. 14 . as shown in Figure 2. In addition to the call price. Our notional bond has two years of ‘soft call’ protection following its three years of HNC protection.Convertible Bonds – February 2002 The risk premium on the John Smith Corp. However. HNC period has expired. Convertible EUR 4% 2007 at issue was: BondFloor (100 − 89. A call feature gives the issuer the right to redeem a convertible before maturity (from the call date) at a predetermined price (the call price). The John Smith Corp Convertible EUR 4% 2007 can be called at par. A ‘soft call’ usually requires the price of the shares underlying a convertible to trade above a predetermined percentage of the initial conversion price.91 Risk Pr emium = 11. The call price of a bond is typically at par. Call protection Risk Pr emium = (Convertible Pr ice − BondFloor ) Many convertibles have call features. the company issuing a call notice will generally have to pay investors the amount of interest that has accrued on the security between the previous coupon payment date and the call date. for a specified period of time (often 20 of 30 consecutive business days). in effect. A put feature gives the holder of the convertible the right to require the issuer to redeem a convertible on a predetermined date or dates prior to maturity at a fixed price. an investor should compare the value of the call price plus accrued interest with the current market value of the shares they would receive on conversion. some convertibles give the issuer the option of delivering shares. If parity is greater than the call price plus accrued interest. If forcing equity conversion is the company’s ultimate goal. investors have the right to choose whether to accept the call price plus accrued interest7. In making this investment decision. the issuer’s decision to call the bond back will. Similarly. The issuer is usually required to redeem the convertible for cash. a fixed income investor will consider the risk premium on a convertible as the cost of owning it. Calls for cash redemption are much rarer than calls forcing conversion. investors normally forfeit any accrued interest). 15 . Put features While many convertibles have call features. or to convert into the underlying shares. as long as the market value of the shares issued or mix paid is at least equivalent to the predetermined cash value of the put. Sometimes it may be rational for an issuer to call a bond even if parity is well below the call price. We can think of parity as the equity component of a convertible and the bond floor as its fixed-income component.Convertible Bonds – February 2002 When a bond is called. In instances where the call date falls on a coupon payment date. The issue size is the nominal amount of convertible bonds sold by the issuing firm. This is to ensure that movements of the share price during the required notice period of the call (typically between 30 and 90 days). the issuer may delay calling the bond until parity is well above the call plus accrued interest price. This may be the case either if interest rates have fallen or if the company’s credit has improved and so that it may be able to refinance on more attractive terms. the premium to parity of a convertible represents the cost to an equity investor of owning the bond. or a mix of cash and shares. investor put options are less common. parity. (note that on conversion. this issue does not arise. This being the case. However. force investors to convert into shares. The intention behind most call decisions is to force conversion. Issue size Convertibles as derivatives A convertible is a hybrid instrument. 7 Assuming the call notice specifies payment of accrued interest. will not affect the result of the call (investors will make their decision to convert or redeem their bonds during the notice period). the investor can choose not to convert and instead to receive a cash redemption amount at maturity. In terms of value. the investor pays a premium to own this embedded put option.Convertible Bonds – February 2002 The different views taken by fixed income and equity investors on the make up of a convertible is consistent with the very different views each have on the value underlying a convertible. Equity investor viewpoint Equity investors tend to view a convertible as a combination of: ➤ Equity — a convertible holder has control over a fixed number of shares. the investor will pay a premium to own this embedded dividend swap. but if the stock price falls. The converting bondholder ‘gives up’ the straight bond he controlled until the moment of conversion though has paid a premium to own the embedded call option (the risk premium). Assuming there is an income advantage for the convertible holder. there is no cash payment on exercise. Unlike a conventional option. usually at any time. This is equivalent to owning a call option that gives the fixed-income investor the right to buy shares by giving up the convertible. ➤ A dividend swap — a convertible holder indirectly owns a certain number of shares but receives coupons instead of dividends until the earlier of maturity or conversion. At maturity this is equivalent to a call with a strike price approximately equal to the conversion price (for a single currency bond). A convertible’s bond floor represents this straight bond value. ➤ A put option — a convertible holder has control over the underlying shares. The rational investor will exercise this right if the redemption value is greater than parity. if one imagines the investor automatically being delivered the fixed number of shares at maturity and then having the (notional) right to sell the package of shares back again at the cash redemption amount. This is equivalent to owning a dividend swap that gives the equity investor coupons in exchange for dividends. It is sometimes easier to think of the right not to convert as a put option. Fixed income investor viewpoint Fixed income investors tend to view convertibles as a combination of: ➤ A straight bond — a convertible holder owns a straight corporate bond that pays coupons and has a cash redemption value at maturity. ➤ A call option — a convertible holder has the right to exchange his corporate bond for a predetermined number of the company’s ordinary shares. an investor ‘owns’ parity. We can show graphically how the value of a convertible and its debt and equity vary with the share price: 16 . Convertible We note that: ➤ The bond floor of a convertible tends not to be correlated with movements in the share price. 17 . Parity Convertible Figure 5. Risk Premium against Share Price Risk premium Bond Floor Source: Schroder Salomon Smith Barney Convertibles. Convertible Price. unless a fall in the stock price is perceived to affect the credit quality of the issuer (shown in the extreme left of Figures 4 and 5 above). Parity and Bond Floor against Share Price Premium Share Price Bond Floor Source: Schroder Salomon Smith Barney Convertibles.Convertible Bonds – February 2002 Figure 4. the more the convertible price is supported by and trades increasingly in line with its bond floor. both the value of the put option and the value of the dividend swap decrease. The put value decreases as it becomes less likely that investors will exercise the option to ‘sell’ shares for cash redemption at maturity. Longer options also tend to be more valuable than shorter ones.Convertible Bonds – February 2002 ➤ Parity varies proportionally with the share price (in non-cross currency bonds). ➤ Volatility of the underlying stock — the higher the volatility of the underlying share. the lower the credit spread over Libor or the benchmark government yield curve required to discount a bond’s coupon payments and redemption value. ➤ The difference between the convertible price and the bond floor (the risk premium) represents the value of the embedded call option to a fixed income investor. the premium narrows to a point where the convertible derives its value from the equity component only. as it becomes more likely that the issuer will call the bond back and investors expect the period of yield advantage to shorten. ➤ Call protection — the longer the call protection on a bond. When the share price rises. ➤ Figure 4 shows how investors purchasing shares via a convertible forfeit a degree of equity appreciation. so the greater the value of the convertible. the higher its bond floor and the greater its value. the longer the guaranteed period of yield advantage and the greater the value of the convertible’s embedded dividend swap. In single currency bonds the slope of the parity line represents the conversion ratio. Convertible price sensitivities — the Greeks A convertible’s price is positively correlated with: ➤ The underlying stock price — the higher the underlying stock price. Simultaneously the dividend swap value may decrease in a callable bond. so the greater the value of the convertible. as the equity price rises. as the convertible price is less sensitive to share price variations than pure equity. The lower the discount factor applied to a bond’s cash flows. the greater the value of the convertible’s embedded option (put or call. 18 . so the greater the value of the convertible. according to the equity or the fixed-income investor’s perspective). the premium expands. ➤ Figure 4 illustrates how. as it is equal to the share price (expressed in the bond currency) multiplied by the conversion ratio. ➤ Issuer credit quality —the better the credit quality of the issuer. the greater the value of parity (the equity component of a convertible). ➤ When the equity price declines. ➤ The difference between the convertible price and parity (premium) represents the value of the embedded put option (downside protection) and the dividend swap (yield advantage) to an equity investor. The more the share price falls. the lower the yield advantage of the convertible over the share. a 40% delta means that if parity rises by 1 point. the greater the value of the convertible’s embedded call and so the greater the convertible’s value. Further comments on delta from a theoretical perspective are available in the Appendix. the higher the convertible’s delta. It is the equity sensitivity of the convertible. For material share price moves. Conventionally. Thus. It is also true that the higher the interest rate. it is expressed as the change in delta for a one-point change in parity. We can describe the impact of various factors on the price of a convertible using the following concepts. Delta changes along the convertible price curve. delta can be a poor guide to the sensitivity of the convertible to a move in parity. the ‘Greeks’ are outputs of convertible pricing models.4 points (40% of the one-point change in parity). in absolute terms. Thus a convertible’s price is less sensitive to interest rates movements than an otherwise identical straight-bond.Convertible Bonds – February 2002 A convertible’s price is negatively correlated with: ➤ Stock dividends — the higher the dividend. the higher the discount rate for coupon payments and redemption value. The higher the value of parity. the convertible price will rise by 0. Gamma Gamma is the rate of change in delta for movements in the underlying share price. delta is expressed as the change in convertible price for a one-point change in parity. its delta will increase as the convertible’s equity component becomes more significant. ➤ Interest rates — the higher the prevailing interest rate. which are more commonly referred to as the ‘Greeks’. Gamma is the measure of the intensity of this effect. The range of delta along the convertible curve varies between 0% and 100%. In general the convertible is more equity sensitive in rising markets and less sensitive in falling markets than the delta would suggest. As the convertible’s price moves from out-of-the-money to in-the-money (due to a rise in the underlying share price and therefore parity). Conventionally. the lower the bond floor and convertible’s value. 19 . ➤ ➤ ➤ ➤ ➤ Delta — measures the sensitivity of the convertible price to changes in parity Gamma — measures the sensitivity of delta to changes in parity Vega — measures the sensitivity of the convertible price to changes in underlying stock volatility Rho — measures the sensitivity of the convertible price to changes in interest rates Theta — measures the sensitivity of the convertible price to the passage of time Delta Delta measures the sensitivity of a convertible’s price to changes in parity. vega is expressed as the change in the fair value of the convertible for a one percentage point increase in the assumption for stock volatility. and ➤ A volatility assumption for the underlying stock. all other things being equal. Vega measures the sensitivity of fair value to changes in the assumed level of stock volatility. In approximate terms the closer the convertible is to being at-the-money. There are no short names in common use for the dividend and spread sensitivity. Conventionally. to maturity. Theta Theta is the change in convertible price with the passage of time. Rho Rho measures the sensitivity of a convertible price to movements in interest rates. 20 . Rho is the fixed income sensitivity of the convertible just as delta was defined as the equity sensitivity. it is necessary to input assumptions to a convertible pricing model: ➤ A credit spread (or spread over Libor). Delta increases as parity (the equity component of the convertible) increases. Conventionally. The convertible price curve is set for an assumed level of stock volatility: it shows how the convertible price changes when parity changes.Convertible Bonds – February 2002 This topic will be covered later when discussing ‘gamma trading’. In order to find a theoretical value for a convertible (its theoretical ‘fair value’). A chart of vega against parity is available in the Appendix. For a near-the-money convertible. the more sensitive the convertible price is to changes in assumed volatility. A more thorough treatment of Rho is to be found in the Appendix. Vega Vega is the sensitivity of the convertible price to changes in the volatility of the underlying stock. ➤ Dividends on the underlying share. A theoretical treatment of gamma and a chart of its sensitivity to the share price level are available in the Appendix. given the assumed volatility. Conversely. it is expressed as the percentage change in convertible price for the passage of one day. the passage of time is normally negative for the value of a convertible. or as the convertible starts trading more on its fixed interest characteristics. used to establish the rate for discounting the bond’s coupon payments and its redemption value. rho increases when parity decreases. the time decay of the option element outweighing any upward drift in the bond floor (see Figure 23 in the Appendix). it is expressed as the change in convertible price for a given one basis point move in interest rates (a parallel shift in the whole yield curve). Conventionally. the convertible is said to trade at a discount9 to parity 8 The phrase ‘busted debt’ or ‘busted convertible’ has no precise definition. the convertible is said to be in-the-money If the share price < conversion price. 21 . the convertible is said to be at-the-money We add here two other. To reiterate our earlier comment. It is used here to generate a simple classification system for convertibles in different share price zones. Figure 6. or a high yield convertible If the share price rises dramatically and parity is greater than the convertible price (ie a negative premium).Convertible Bonds – February 2002 Convertible bonds. The classification refers to the relationship of the stock price to the conversion price. Many will not apply the description unless there has been a deterioration of the credit as well as a fall in parity. Arbitrage opportunities from exploiting any anomaly are frequently hindered by market inefficiencies. it is sometimes referred to as busted debt8. leaving the convertible trading at a price so deeply out-of-the-money that its equity component becomes immaterial. 9 A discount convertible trades at a negative premium to parity. If the share price > conversion price. more extreme classifications: If the share price falls dramatically. the convertible is said to be out-of-the-money If the share price is reasonably close the conversion price. a simple classification Figure 6 reproduces the chart showing convertible behaviour for different share price levels. Behaviour of Convertible in Different Share Price Zones Busted OTM ATM Share Price Parity ITM Discount Bond Floor Convertible Source: Schroder Salomon Smith Barney Convertibles. convertibles in each category outlined above will tend to have certain premium. It indicates the level of exposure an investor wishes to have to the equity market. ➤ Since gamma is a measure of how responsive the equity sensitivity of a convertible is to share price movements. Holders of such bonds are likely to be mainly interested in their straight-bond component.Convertible Bonds – February 2002 At issue a convertible is. Thus it is possible to draw conclusions about a bondholder’s investment objective from the characteristics of the securities owned. Figure 7 gives a description of each category in terms of the typical value of the parameters for a basic convertible: Figure 7. delta. priced slightly out-of-the-money. ➤ Rho represents the interest rate sensitivity of a convertible. 22 . gamma and rho characteristics. It is possible to draw conclusions about an investor’s priorities from the nature of the convertibles owned: ➤ A high premium over parity may indicate that the investor attaches particular importance to downside protection and yield advantage. However. A high level of rho indicates that the convertible is trading predominantly as a debt instrument. ➤ Delta represents the equity sensitivity of a convertible. generally speaking. high gamma bonds are natural holdings for those anticipating dramatic share price movements (in either direction). Typical Characteristics of Convertible Bonds Categories Busted OTM ATM ITM Discount Premium Delta Gamma Rho >100% 0-10% None High 100-40 10-40% Varied High 40-10 40-80% High Low <10% >80% Low None <0% 100% None None Source: Schroder Salomon Smith Barney Convertibles. We identify the objectives and strategies of different investor types and analyse their preference for different types of convertible below. Some equity investors are attracted by the income characteristics of certain convertibles. This is particularly so if the premium paid is quickly made up for by an income advantage over the underlying shares. This right will be exercised if parity on the bond is less than the cash redemption value (the strike price of the notional put) at maturity. Whatever other attributes an equity investor looks for in a convertible. it is likely that they will maintain a preference for bonds whose risk and return characteristics do not deviate radically from equities themselves. From our notional example earlier. if John Smith Corp shares are trading at €125. Convertibles that trade on very low premiums are obvious candidates for equity investors. assuming the convertible stands on a premium. Such convertibles typically have high deltas and a relatively distant investment value (ie a high-risk premium).000 shares has a cash investment of €5 million.Convertible Bonds – February 2002 Convertible Bonds. The yield advantage can be characterised as an embedded dividend swap. Instances in which the premium is amortised before the first call date of the convertible will have obvious appeal (see the definition of ‘breakeven’ on page 13 for more details). for example. which gives the investor coupons in exchange for dividends until the convertible bond is converted or redeemed. 23 . The cash for cash switching strategy An investor selling shares to buy a bond convertible into the same underlying shares on a cash for cash basis is reducing the number of shares he controls. Convertible = Equity + Downside Pr otection + YieldAdvantage The downside protection over the life of the convertible can be seen as an embedded European put option to sell shares at the redemption price at maturity. the purchase of downside protection and the purchase of possible yield advantage. an Investor’s Perspective ➤ ➤ ➤ ➤ Convertibles for equity investors Convertibles for fixed income investors Convertibles for hedge funds Change in the investor base over the life of the convertible Convertibles for equity investors We stated above that equity investors perceive the purchase of a convertible as equivalent to the purchase of a certain number of shares. an equity investor with 40. Intuitively. but by less than parity. Thus the cash-for-cash switching strategy suggests: Impact of a share price fall ➤ Equity investors should consider selling shares and switching into convertibles when the premium is very low because of the asymmetrical nature of prospective returns If the share falls and the premium widens. Though the convertible may underperform the underlying shares. (the €5 million proceeds divided by the clean price of the bond (129%)).2%.Convertible Bonds – February 2002 If the John Smith Corp Convertible EUR 4% 2007 is trading at 129% (clean) on a premium of 3. low premium) ➤ ➤ 24 . the value of the downside protection will decrease and the risk of losing the yield advantage will increase due to increased call risk. because the premium is so low (its delta will be tending towards 100%). bearing in mind that a rally in the share price could wipe out his gain This strategy may outperform simple ‘buy and hold’ strategies for either shares or convertibles in a range-bound but volatile market.876. the equity investor’s €5 million potential sale proceeds would purchase €3. As each bond converts into 10 shares (the conversion ratio of the bond). The premium is actually the amount that an equity investor stands to lose when switching into a convertible if the share price rises. ignoring accrued interest effects. a convertible will tend to outperform the underlying shares. Impact of a share price rise From an equity investor’s perspective. the convertible price will tend to rise. the convertible will fall but the decline will be softened by expansion of the bond’s premium. the convertible price will tend to fall. When the underlying share price falls. Equity investors switching into convertibles at very low premium levels (and consequently.000 nominal of the convertible bond. investors following this strategy will tend to buy in-the-money convertibles (high delta. the investor in reality ‘buys’ control of only 38. ➤ If the underlying shares fall. this underperformance should be slight.760 shares (from 40. but by less than parity because the premium expands on the downward move. investors should consider switching back into shares to crystallise a profit. Thus convertibles will tend to outperform the underlying shares because of premium expansion. when the share price underlying a convertible rises.000 above). high delta levels) often get a highly asymmetric risk/return profile: ➤ If the underlying shares keep rallying the convertible price will rise on almost a 1:1 basis. In such a scenario. Thus convertibles will typically underperform the underlying share because the premium contracts. The premium expansion is actually the amount that equity investors stand to gain from switching into a convertible if the share price falls. fixed income investors may be tempted to lock in their profit and sell the convertible. if the underlying share price falls. The straight-bond component is the bond floor and upside participation comes from the embedded call option to purchase the underlying shares. Despite offering only a small element of equity sensitivity. The position of convertibles as a ‘halfway house’ between fixed income and straight equity is especially relevant for the many institutional investors who are bound by a requirement to invest only in bonds. the risk premium contracts. but as long as the fall in the underlying share price does not affect the credit quality of the issuer. Implications of share price moves When the underlying share price (and consequentially. Conversely. or to keep a large proportion of their portfolio in fixed-income securities. fixed-income investors may use them to inject equity elements into their portfolios without losing the support offered by the bond floor. The convertible price will fall. they will have paid almost nothing for this option. The risk premium is the premium to the bond floor a fixed-income investor pays in order to gain access to participation in upward moves in the underlying shares. the convertible price) rises. it will respond to movements in interest rates and credit spreads in a similar fashion to a straight bond. the risk premium on the convertible will expand. As convertibles are often classified as bonds. Out-of-the-money convertibles Traditionally. so they will lose little if the underlying share price falls. Since rho is high on an out-of-the-money convertible. if the underlying share price rises. On the other hand. the purchase of a convertible is equivalent to the purchase of a straight bond plus the purchase of upside participation in any underlying share price appreciation. due to the expansion of the risk premium.Convertible Bonds – February 2002 Convertibles for fixed income investors For a fixed income investor. the risk premium can be seen as the amount that a fixed income investor stands to lose from switching by a straight bond into a convertible. 25 . Risk premium expansion is the potential advantage that a fixed income investor stands to gain by switching from a straight bond into a convertible. fixed-income investors with a low risk profile have preferred to buy out-of-the-money convertibles since they trade close to their bond floor and can offer inexpensive call options on the price performance of the underlying shares. When the underlying share price (and convertible price) falls. on account of the low delta that typifies an out-of-the-money convertible security). As the underlying share price rises. an out-of-the-money call still gives an investor the chance to participate in any appreciation of the underlying stock (even if only moderately. moving the convertible more into the money. the convertible’s bond floor (its fixed interest value) should support its price. as the call becomes more in-the-money. as the call becomes more out-of-the-money. In order to hedge the long convertible position against changes in the underlying share price. The cash amount corresponds to the value of the convertible’s bond floor. Convertibles for hedge investors It is possible to construct a portfolio that is theoretically insulated from share price movements. by retaining an option to buy back the convertible in future. 26 . for example.Convertible Bonds – February 2002 In some cases. The credit spread at which a fixed income investor can buy the bond element of a convertible in a callable asset swap. This portfolio is based on a long convertible position and a short position in the underlying share. In this case they will buy deep out-of-the-money convertibles. This floor is calculated at a given credit spread over Libor. The value of this option is reflected in the higher credit spread (and therefore. but at an advantageous yield. has attempted to isolate and dispose of the straight bond part of the convertible. Moreover the relative coupon structure and sometimes the subordination of the convertible can differentiate it from other debt of the issuer. The number of underlying shares per bond necessary to hedge a convertible position is given by the bond’s delta multiplied by its conversion ratio. under certain circumstances. Predictably. Often the convertible will present a higher risk/higher reward profile than other corporate debt. but a contract in which the option investor physically sells the convertible to the bond investor who becomes the beneficial owner of the security and receives the coupon payments and the redemption value on maturity. yield advantage plays a key role. This type of investor may find a yield advantage in convertibles compared to their related straight-bonds due to anomalies in the secondary market in which convertibles are traded. making it attractive to certain investors. fixed income investors may not be motivated at all by upside participation in underlying share appreciation and may only be interested in the bond component of the convertible. Callable asset swaps A callable asset swap is a contract between two counterparties. which seeks to repackage the convertible so that one counterparty owns only the fixed income component of the convertible and the other owns just the call option on the underlying shares. while retaining the right to repurchase the convertible should they want to convert. a fixed-income investor may have the chance to buy a straight bond proxy with the same apparent level of risk. Thus. higher yield). In reality a ‘callable asset swap’ is not an asset swap at all. This lower spread. The terms of the contract specify the cash amount due for selling the convertible and the formula for calculating the price at which the convertible may be bought back. The option investor. calculated using a lower credit spread. the number of shares that must be sold is indicated by the convertible’s delta or ‘hedge ratio’. termed the ‘recall spread’. The price at which the convertible may be repurchased is worked out as another bond floor. We explain below why a fixed income investor should enter into an asset swap agreement instead of just buying a straight bond. may be higher than the credit spread implied in the price of a straight-bond with the same profile. We say apparently because in reality the bond investor is short a credit option to the option investor. is also specified in the contract. as they will be reluctant to pay any premium to the perceived bond floor. 27 . the effect of convexity (gamma) on the convertible price cannot be ignored. When the move in the underlying shares is not small.Convertible Bonds – February 2002 Delta hedging and gamma trading If the delta — the change in the convertible price for a one-point change in parity — of a convertible was 40%. Convertible EUR 4% 2007 Long Convertible Position Convertible Price Conversion Ratio Underlying Share Price Delta Gamma Source: Schroder Salomon Smith Barney Convertibles. the hedged portfolio will return a positive amount regardless of the direction of the underlying price move. as the shares rise. all other things (including the effects of time decay) being equal. This causes the hedge ratio to increase meaning that more shares need to be sold to keep the portfolio delta neutral.5% In order to hedge the long position of one bond against changes in the underlying share price. However. used above: Figure 8. €1000 10 €80 40% 0. This means that the convertible should participate in a greater proportion of any future share price appreciation. it is possible to compensate for small share price moves on the long position in the convertible. to hedge it successfully. As the share price underlying a convertible rises. Figure 8 below uses the details of the notional John Smith Corp. As a result of this. the convertible’s delta also rises. Providing the correct hedge ratio is employed. it would be necessary to sell a number of shares equal to 40% of the number into which the bond may be converted. on an upward move in the underlying stock price. The net position from the trade will be a profit. the profit on the long convertible position should be greater than the loss suffered on the short position in the underlying stock. the convertible’s delta falls and some shares must be bought back in order to re-hedge the portfolio. John Smith Corp. The positive gamma effect ensures that hedged investors are always buying shares after a price fall and selling after a price rise: this is one mechanism through which hedge investors generate profits from their portfolios. the convertible’s delta will also rise. Convertible EUR 4% 2007 issue. As the underlying share price falls. (the effect of gamma). we need to take a short position in four shares: DeltaShortShareSale = ConversionRatio * Delta DeltaShortShareSale = 10 * 40% DeltaShortShareSale = 4 shares When the underlying share price rises. Delta hedging insulates convertibles against small movements in the underlying stock price. the short position in the underlying share has not been altered. despite the convertible’s higher delta. For significant movements in the underlying share. Theoretical fair value depends on several variables including the assumed volatility of the underlying shares. The short position in the underlying share remains based on the original. hedge investors using this strategy to trade their convertible portfolios. if it trades above fair value. 28 . however. ➤ Stock volatility is a measure of the propensity of the underlying share to move sharply. if it trades below theoretical fair value and ‘theoretically rich’. due to the effect of gamma. ➤ The gamma trading strategy works by adjusting the stock short necessary (by buying back or selling shares) for changes in the share price (and therefore delta) level. higher delta (40%). The loss on the convertible long position should be smaller than the profit on the short sale of the underlying stock. Naturally. The leverage comes from their ability to create the necessary stock short by borrowing the underlying shares at a reasonable fee. ➤ To conclude. according to a bond’s theoretical delta. Again. the bond will participate in a diminishing proportion of the decline. Hedged investors will be natural buyers and sellers of shares as they maintain the portfolio hedge. ➤ Delta hedging is most effective when a convertible is theoretically cheap — an investor will expect to capture more volatility than he has ‘paid for’. It is also worth considering the following: ➤ The greater the move in the underlying share price. due to supply and demand. the greater the potential profits from the hedged convertible position. The loss of value as a result of time decay (theta) can prove the more important factor. Shares do not always exhibit sufficient volatility for the strategy to make money. An investor will estimate the level of underlying stock volatility and input this in to a convertible pricing model. Hedge funds are often highly leveraged and can produce a substantial profit for a low initial investment. A convertible is defined as ‘theoretically cheap’. Gamma trading is not infallible. as the underlying share price falls (causing the delta of the convertible to fall). The higher the underlying stock volatility. the net position from the trade will be a profit. hedge funds will prefer convertibles with underlying shares that are both highly volatile and easily borrowable. Convertibles trade at prices that can be higher or lower than theoretical fair value. the greater the chance of significant gamma trading profits. ‘Implied volatility’ is the stock volatility that is theoretically implied in the convertible price. The size of any profit on this type of trade is dependent on both the move in the underlying stock and on the bond’s gamma profile. are employing a technique known as ‘gamma trading’.Convertible Bonds – February 2002 Conversely. Convertible Bonds – February 2002 Changes in the investor base over the life of the convertible At issue. An in-the-money convertible is likely to be purchased by an equity investor who will consider selling the bond as it begins to move out-of-the-money and its delta starts to fall. Such bonds typically attract a wide range of investors including mixed funds and hedge funds. An out-of-the-money convertible is more likely to be purchased by a fixed-income investor. however. The investor base will change as the underlying share price moves up or down. This chapter has explained how a convertible may be viewed from several different angles and may fulfil differing investment objectives for different investor bases. and Buying convertibles perceived as ‘theoretically cheap’ for hedge funds 29 . We have identified key valuation elements and trading strategies including: ➤ ➤ ➤ Buying high delta convertibles as a substitute for equity. who will consider selling his position to lock in a profit as the convertible becomes more in the money. moving the convertible more in or out-of-the-money. a convertible can normally be classified as one of the following: ➤ An equity alternative — a low premium and a relatively low bond floor. or ➤ A total return alternative — incorporating a medium premium to parity and investment value (risk premium). The majority of new issues will naturally fall into the third ‘balanced’ or ‘total return’ category. Buying high yielding convertibles as a substitute for corporate bonds. ➤ A yield alternative — a high premium and a relatively high bond floor. In theory. On a share price fall 30 . the company will in effect sell its stock at a discount to the prevailing market price. We said that in general. an investor cannot know whether the share price will rise or fall. The issue price of this equity will be at a premium to the stock price on the date of issue. when the underlying share price falls than they would owing a convertible. one could also argue that the convertible will have proved a better form of financing than straight equity. However. made a (deferred) sale of equity at issue date. on conversion. On a share price rise If the underlying share price of a convertible were to rise above the conversion price. In the same way. it is equivalent to a debt issue at a lower coupon. the issuer may have been better off economically issuing straight debt since. In the weak share price scenario. investors would do better investing directly in shares. an Issuer’s Perspective ➤ ➤ ➤ Convertible financing Financing objectives and prospective issuers To call or not to call? Convertible financing We have looked at the idea of investing in a convertible as an alternative to investing in either equity or straight debt.Convertible Bonds – February 2002 Convertible Bonds. If the underlying share price were to fall and conversion fails to take place. We concluded that much of the appeal of convertible securities (from an investor’s viewpoint) is their ability to achieve high expected returns with low volatility. in effect. However. investors would (eventually) convert into equity. as with the investor at the time of purchase. Assuming eventual conversion the issuer has. We also pointed out the limitation of this argument: at the time of the investment. the issuer cannot know in advance whether the share price will rise or fall. when the underlying share price rises and would do better owning straight debt. one can consider an issuer’s choice of financing using a convertible rather than equity or straight debt. a convertible will have been a better form of financing than straight debt — if the bond is not converted. the company would theoretically have done better selling straight equity. A company that believes the market is undervaluing its shares and expects the share price to rise. Thus convertible debt financing is generally more tax efficient than equity issuance. 10 For more information on ‘exchangeables’. creating a cash-flow advantage. If the company is sure that the share price will rise. 31 . even if the equity placing were not issued at a discount to the prevailing market price. will prefer to sell equity forward at a fairer price via a convertible than to sell shares immediately at the current undervalued price. The issue of a convertible avoids the stigma sometimes associated with a rights issue or other pure equity issuance. The premium to the current share price also means that the issuer receives greater proceeds than would be received in the case of an equity issue (of the same number of shares). the issuer will retain dividend distributions on the underlying shares until conversion. in the case of exchangeable bonds. see page 41. as the full beneficial ownership of the underlying shares transfers to the investors only on conversion.Convertible Bonds – February 2002 Financing objectives and prospective issuers Issuing a convertible may fulfil different financing objectives: Potential deferred sale of equity forward at a premium The issuer of a convertible typically locks in a conditional sale price for the underlying shares that is higher than the market price of those shares in the market. Thus the issuer will be able to fund the coupon/yield obligations partly through the continued receipt of dividends on the underlying shares. no cash interest is actually paid. dividends are paid out of after-tax income. it should issue debt to raise money. They are convertible bonds issued by one company that can be converted into the shares of a different company. In the case of zero coupon convertibles. issuers are allowed to defer the crystallisation of tax liabilities on the sale of shares under many tax regimes. Securing low-cost funding Any company that cannot or does not want to pay high coupons will find convertibles a cheaper source of debt financing. Additionally. Monetising equity investments ‘Exchangeable10’ structures can permit issuers to monetise stakes they hold in other companies at attractive funding rates. only interest payments on debt are tax-deductible. at the time of the issue. In the case of exchangeable bonds. but in most tax regimes the company can deduct the interest implied by the accretion rate of the convertible. such as a start-up company or a company that is already highly geared. It sends a relatively positive signal to the market about the company’s view of its own share price prospects. but some companies may have difficulty doing that. Tax/cash-flow advantages Under most tax jurisdictions. ➤ A high probability of conversion corresponds to the objective of deferring the sale of the stock at a premium. conversion is unlikely to be forced and the company would end up redeeming the security for cash. For example: ➤ A low coupon corresponds to the objective of lowering the cost of financing. however. This is particularly true in cases where the probability of conversion is low. A company that wishes to raise finance via a straight debt issue. If parity falls under the redemption value between the date investors are notified of the call and the call date itself. as analysts will typically employ undiluted EPS calculations. The convertible investor base may be more inclined to accept a greater range of credits since much of an issue’s appeal derives from its option component. while those wishing to increase gearing will be more likely to issue a convertible bond. The suitability of a convertible to meet to an issuer’s objectives will depend to some extent on how it is structured. Moreover convertible investors do not have voting rights. Call features allow the issuer to precipitate conversion by sending out a call notice. Speed of execution is a key advantage of convertible bond issuance. but which has a weak credit rating. To call or not to call? Often the ultimate goal of a convertible issuer is for their convertible bond to be converted into shares. may have a particular interest in raising equity capital via convertibles. whereas an equity issue typically takes several weeks. allowing a company to maximise issue proceeds. The company has a dilemma when deciding whether or not to issue a call notice. and due to the wide investor base. for whom the issuance of voting shares may compromise control. Exploiting market conditions One advantage of issuing a convertible is that it can be completed as an ‘overnight’ transaction. Closely held companies. the size of a convertible issue can sometimes even exceed that of equity or straight debt issue. Targeting a diverse and distinct investor base The diversification of the convertible investor base enables issuers to access a wider investment audience than they might via solely the equity market or fixed interest market alone. For example a company that has recently completed an equity issue may find it easier to raise further capital via a convertible rather than returning to the equity market. 32 . Some companies issue convertibles to widen their shareholder base and increase visibility.Convertible Bonds – February 2002 Delaying dilution Compared with the immediate issuance of equity. so the issuance of a convertible defers the dilution of voting rights in the company. and ➤ A company wishing to keep the debt/equity ratio low will be more inclined to issue a convertible preferred share. Due to the speed with which large convertible issues are allocated and priced. the issuance of a convertible may be beneficial for earnings per share. might find it easier to target the convertible investor. 33 .Convertible Bonds – February 2002 Companies rarely call their convertibles at the optimum moment (which will depend on complex income and options considerations). The decision not to call a convertible may be the result of: ➤ The uncertain course of the share price during the call period. ➤ The desire to avoid dilution. or ➤ Other balance sheet and profit and loss account considerations. Figure 9.Convertible Bonds – February 2002 Convertible Structures ➤ ➤ ➤ ➤ ➤ ➤ ➤ ➤ ➤ ➤ Equity-linked financing Zero coupon and Original Issue Discount (OID) convertibles A plain vanilla convertible compared with a bond + warrant Convertible preferreds Mandatory convertibles DECs PERCs Exchangeables Default swaps Reset features Equity-linked financing Convertibles are hybrid securities with both fixed income and equity characteristics. Zero coupon and Original Issue Discount (OID) convertibles In the wide range of convertible structures. The Convertible Structure Range – From Debt to Equity Straight Debt Zero Coupon Convertible Original Issue Discount Convertible Plain Vanilla Convertible Convertible Preferred Mandatory Convertible Straight Equity Source: Schroder Salomon Smith Barney Convertibles. Original Issue Discount (OID) convertibles (including most 0% coupon bonds) are the closest to the straight debt end of the spectrum. We will show here that it is possible to structure convertible securities such that they bear a greater resemblance to an equity-alternative instrument. or to a straight debt-alternative instrument. We have shown how convertibles can present investment opportunities for both equity and fixed-income investors and how convertible securities can present attractive financing opportunities for issuers. satisfying the demand of investors and issuers alike. 34 . such as to give a certain rate of return (usually the yield to maturity at issue) if held to maturity and redeemed. It is normally calculated as the price at a given date. Some OID convertibles pay a low coupon. the convertible price will also tend to accrete towards its redemption value. A similar structure is obtained when a convertible is issued at par and redeems at a premium. The yield to maturity reflects the accretion from the discount issue price to par. Generally the bond floor will accrue to the redemption value. OID and Premium Redemption Structures Price Redemption Value CB Price CB Bond Floor Maturity Time Note: The course of the convertible price is affected by many factors. which are deferred until final redemption. the remaining value of the interest payments is reflected in the difference between the initial issue price and the redemption price at maturity. taking into account the value of the coupon payments received. Source: Schroder Salomon Smith Barney Convertibles. on specified dates. Figure 10.Convertible Bonds – February 2002 Deferred interest payments Zero coupon convertibles are typically issued at a deep discount to par value and are redeemable at par. Even if the share price is weak. 35 . The performance of a ‘premium redemption’ structure and an OID structure will be similar. Like zero-coupon OID’s. Accretion of Bond Floor and Convertible Price to Redemption Value — Zero Coupon. The difference between the par value and the initial issue price can be viewed as the value of notional interest payments over the life of the convertible. Put features Zero coupon and OID convertibles often carry put options allowing the investor to sell the convertible back to the issuer at a pre-determined price. The graph above shows a regular rate of price accretion over time. This price will typically be equal to the accreted price of the security. The accreted price can be thought of as the issue price plus the value of unpaid notional coupons from issue. The yield to maturity reflects the accretion of the convertible price from the issue price to par. European zero-coupon and OID issues have typically had maturities of between five and 10-years. 100 0% 117 4 years 4% 14 shares per bond Figure 12. Figures 11 and 12 compare a notional zero coupon. From the investor’s perspective Zero coupon and OID bonds are frequently more defensive instruments than coupon convertibles because of the deep discount or premium redemption feature that they generally possess. A contingent conversion feature limits the investor’s ability to convert. Zero Coupon Bond with Premium Redemption Structure Issue Price Coupon Redemption Value Maturity YTM Conversion Ratio Source: Schroder Salomon Smith Barney Convertibles. Maturity Recent US zero coupon convertibles have had final maturities of 20-years or more. Contingent features Contingent features typically relate to restrictions on either conversion or on interest payments: contingent conversion features and contingent interest payment features. it will probably be in the issuer’s interest to force the investor to choose between redeeming the bonds or converting them.Convertible Bonds – February 2002 Call protection Zero coupon and OID convertibles frequently offer investors periods of both hard and soft call protection. Contingent interest payment features allow the payment of a small amount of interest to the convertible bondholder and is dependent on the average market price of the convertible reaching a specified level. Plain Vanilla Convertible Structure Issue Price Coupon Redemption Value Maturity YTM Conversion Ratio Source: Schroder Salomon Smith Barney Convertibles. If it is not in the investor’s interest to exercise the put option forcing early redemption of the convertible. This date can be thought of as the effective maturity date of the bond. This point is illustrated most clearly when one considers a convertible that has a put and a call at the same price and on the same date. However. in both cases. Even if the bond does survive the date without being put or called. Figure 11. 100 4% 100 4 years 4% 14 shares per bond 36 . The incorporation of such a clause in the terms of an issue is generally against the investor’s interest. it can be that the important date from an investor’s perspective is the first put date. premium redemption convertible and a notional conventional convertible with the same yield to maturity (YTM). it is unlikely to attract a significant premium. further enhancing the attraction of the structure to fixed interest investors and reducing its equity sensitivity. However. the ‘effective conversion price’. In other words.00% 5. 190 1 10 19 28 37 46 55 64 73 82 91 37 . premium redemption convertible than on the coupon-convertible. Coupon Convertible and Zero Coupon. In practice. is much higher on the zero coupon. From the issuer’s perspective Major motives for issuing zero coupon and OID bonds lie in the tax and cash-flow advantages of the structure. the coupon-bond will be converted into the underlying shares as the redemption price of 100 is below parity.00% 100 109 118 127 136 145 154 163 172 181 parity zero Source: Schroder Salomon Smith Barney Convertibles. the issuer can normally deduct the notional accretion on the convertible from taxable profits for tax purposes. on the other hand. the coupon-bond has a higher probability of being converted at maturity. put features in a zero coupon bond tend to increase the value of the bond floor. the zero coupon. the zero coupon. If at maturity parity is 106. the price at which the investor is indifferent between redemption and conversion. premium redemption structure has a lower delta. Figure 13 shows the payoff of the two structures: Figure 13.00% rate of return 15. investors must pay taxes on the accretion. Premium Redemption Convertible — Rate of Return Assuming Held to Maturity 25. Even in circumstances in which the tax is recoverable. The zero coupon bond.00% 20. will be redeemed at 117 in this instance. the cash flow implications of this can constitute a negative feature of zeros for certain investors. Although no cash interest is actually paid.00% 10.00% 0. conventional The pay-off analysis demonstrates that given the same YTM.Convertible Bonds – February 2002 Given the same YTM. premium redemption issue offers inferior upside participation to appreciation in the underlying share price. convertible preferreds are not redeemable. As with a traditional convertible security. The instrument is a preferred stock that pays a fixed dividend (usually quarterly) and carries rights of conversion into the issuer’s ordinary shares. Convertible preferreds Convertible preferreds are a common structure in the US convertible market. ➤ Investors in a bond cum warrant can typically exercise their option by subscribing cash instead of bonds leaving the bond portion in existence. Mandatory preferred stocks DECs DECs stands for ‘Dividend Enhanced Common Stock’ (or sometimes ‘Debt Exchangeable for Common Stock’). but will have the obligation to pay the dividend indefinitely. The issue price of a DECs is sometimes the price of the share at issue though many now have an issue price of US$50. however. In many cases. the coupon and premium are set at issue. this is not the case. A DECs will automatically convert into the underlying ordinary shares of the issuer at maturity. in some cases a DECs can also be converted prior to maturity. There is however a difference between buying a convertible and buying a ‘bond cum warrant’ issue (a bond issued with a long maturity call option attached): ➤ A bond cum warrant package can be usually stripped into its components and traded separately in the secondary market. Owners of convertible preferreds have a lower claim on the assets of the issuer than convertible holders. The term ‘conversion premium’ has a different meaning for a DECs. For simplicity. The minimum conversion price is normally the share price at issue and the maximum conversion price is typically some 25% higher. For a convertible. The ‘true’ premium is a moving target. at the time of conversion. The yield at issue is invariably higher than the current yield of the underlying common stock. the premium quoted is that based on the lowest conversion ratio (or highest conversion price) that could apply. however. Adjusted conversion ratio The number of shares received upon conversion depends on the price of the underlying shares at maturity or in cases where early conversion is possible. The issuer is not obliged to return any principal value back to the holder. DECs typically have a maturity of three to four years. A convertible is a ‘package’ and the call is embedded in the instrument so that investors can only own the embedded option by buying the whole instrument. both with the same maturity.Convertible Bonds – February 2002 A plain vanilla convertible compared with a bond + warrant We have described how a convertible can be considered a combination of a straight bond and a call option. A DECs is typically structured as a convertible preferred share that pays a fixed quarterly dividend. 38 . but a senior claim to ordinary shareholders. By convention. the example below assumes the issue price is the share price at issue. The conversion terms (ie conversion ratio) of a DECs vary according to the level of the underlying share price at the date of conversion. the applicable conversion ratio will be twice that in the table above. The post facto performance characteristics of a DECs are as follows: 39 . the conversion ratio no longer falls and is fixed at the minimum level set at issuance. Figure 14. Total Return Analysis on a DECs Total Return Equity DECs Dividend Advantage Straight-Debt Cap Issue Price Max Conversion Price Com m on Share Price Source: Schroder Salomon Smith Barney Convertibles. Conversion Ratio and Value of Share Received on a DECs Issued at Share Price at Issue Stock Price Number of Shares Received Value of the Shares Received Stock Price < Issue Price Issue Price < Stock Price < Conversion Price Stock Price > Conversion Price Source: Schroder Salomon Smith Barney Convertibles.Convertible Bonds – February 2002 The conversion price will be set according to the following rule: ➤ When the underlying share price is at or below the share price at issue. the conversion ratio calculated needs to be multiplied by a factor given by the ratio of 50 to the share price at issue. 1 Stock Price at conversion Issue Price/ Current Stock Price Issue Price Minimum Conversion Ratio Conversion Ratio * Stock Price (issue price/maximum conversion price) at conversion Where the issue price of the DECs is US$50 rather than the share price at issue. Total return analysis Figure 15. the conversion ratio is adjusted downwards and a preferred share becomes convertible into less than one ordinary share. The figure quoted for premium at issue is based on this conversion ratio. one preferred share is convertible into one ordinary share. The ratio is set such that the value of the shares delivered on conversion equals the share price at issue. ➤ As the share price moves between the price at issue and the maximum conversion price. the conversion ratio is 1:1. ➤ Above the maximum conversion price. This rule is summarised in Figure 14. For example if the share price at issue is US$25. one preferred share is convertible into one underlying share so that the equity participation is 100%. so that the equity participation is limited.Convertible Bonds – February 2002 Below the issue price: ➤ Conversion ratio = 1:1. Many investors perceive a DECs as a form of ordinary share where an element of equity participation is sacrificed in exchange for a higher yield. The conversion ratio is calculated as: Figure 16. keeping the total return payoff constant. a PERCs becomes convertible into fewer and fewer underlying shares. ➤ The DECs outperforms the underlying share due to its yield advantage. As the underlying share price rises above a pre-set cap level. ➤ The DECs underperforms the underlying common stock. Between the issue price and the maximum conversion price: ➤ The conversion ratio decreases towards the minimum. A DECs is usually non-callable for life. A PERCs structure offsets a higher yield against lower upside participation. the conversion ratio is below 1:1. ➤ The total return of the DECs can still exceed that of the share due to the dividend advantage Above the maximum conversion price: ➤ Conversion ratio set to minimum. ➤ There is positive upside participation. One preferred share is convertible into less than one share of the underlying. ➤ No equity participation. ➤ Above the cap level. 40 . Conversion Ratio on a PERCs Stock Price Shares of Common Stock Received Stock price > Cap Price Stock Price < Cap Price Source: Schroder Salomon Smith Barney Convertibles. Adjusted conversion ratio The number of shares received upon conversion depends on the underlying share price at conversion relative to the ‘cap level’ set at issue. ➤ Equity participation = 100%. Cap Price / Stock Price at Conversion 1 ➤ Under the cap level. PERCs PERCs (Preferred Equity Redemption Cumulative Stock) are typically structured as mandatory preferred convertibles with a maturity of three to four years. the justification for issuance bears a strong resemblance to that for any convertible. the issuer will have secured low cost funding. Not surprisingly. If the issue remains unconverted. so above a certain level the share will deliver a superior return. The appeal is not only the ability to manage privatisations when equity markets are unreceptive. From the issuer’s perspective Exchangeable bonds can permit a company to dispose of or monetise a shareholding in another company. Above the cap level: The total return of the PERCs is kept constant. Governments have also considered exchangeables as an effective way of monetising shareholdings as part of privatisation programmes. but also to lock in low cost efficient funding. 41 . Exchangeables Exchangeables are bonds issued by one company that exchange into the shares of a different company. the issuer will have succeeded in disposing of the non-core stake at a premium to the price that ruled at the time of issue. regarded as a non-core asset.Convertible Bonds – February 2002 Figure 17. in spite of the PERCs’ dividend advantage. In many tax jurisdictions the disposal of a stake by means of an exchangeable bond enables the issuer to defer the crystallisation of tax liabilities on the sale. Payoff analysis Under the cap level: PERCs outperform the underlying common stocks due to the dividend advantage. They can be issued in both mandatory and non-mandatory form. Payoff Analysis for a PERCs Total Return Equity Cap Dividend Advantage PER Cs Straight-Debt C ap Level C om m on Share Price Source: please add source. If it ends up being converted. The PERCs no longer has sensitivity to the rising share price. A default swap contract usually specifies what constitutes a default event. Reset features allow for a change to the conversion price of a convertible in the event of share price depreciation (downward reset) or appreciation (upward reset) on a certain pre-specified date or dates. Default swaps As with any other bond. In most cases the average is adopted as the new conversion price. given the dual exposures. usually every three months. though could also potentially lead to a doubling of credit and performance risk. and ➤ Restructuring of the debt. To gain protection. though reset clauses can be included in the terms and conditions of many convertible structures. on the principal amount of the swap (the total nominal being hedged).Convertible Bonds – February 2002 From an investor’s perspective Exchangeable bonds have potential credit advantages and disadvantages for the investor. a convertible investor may enter into a default swap. ➤ Failure to pay. 42 . The new conversion price is typically based on the average share price level over a specified period shortly before the reset date. Reset features A convertible in which the terms of conversion are subject to adjustment based on the behaviour of the price of the underlying share is termed a reset convertible. ➤ Repudiation/moratorium. and assuming the average is not below the minimum conversion price discussed below. In a default swap. the investor has exposure to the default risk of the issuer. the single contingent payment in the event of default is replaced by the payment of the principal amount against the delivery of the bond itself. The dislocation of credit risk and underlying share price performance risk can be a potential benefit for the holder of the exchangeable. Increasingly in modern default swap contracts. parity is set at 100%. They will make a single contingent payment to the investor if the issuer of the security defaults. Disregarding movements in the share price between the averaging period and the reset date. These will normally include events such as: ➤ Bankruptcy. The counterparty to the transaction assumes the risk of default. Downward reset clauses allow for an increase of the conversion ratio in the event that the underlying share price is below the initial conversion price on (or shortly before) the specified reset dates: the investor will be given more shares on conversion as their value has declined. the credit seller pays a premium quoted as a fixed interest rate (in basis points). ➤ Obligation acceleration/default. however. delta on a resettable convertible security rises as the underlying share price falls below the minimum reset level and therefore gamma will be negative. Share price falls increase the theoretical hedge necessary to remain delta neutral. the level of the conversion price set at issue will be the cap for an upward reset. In effect. 43 . This feature can create substantial pressure on the share price as arbitrageurs continue to sell shares to cover their increasing exposure (increasing delta) to the underlying share price. Such structures are unusual. (mandatory reset convertibles were popular in Japan during the 1990s particularly). In the proximity of the reset floor. Generally. Sometimes there is also the possibility of an upward reset of the conversion price in the event that the underlying share price is above the ruling conversion price on (or shortly before) specified reset dates: an investor will be given fewer shares on conversion as they have appreciated in value. which is the minimum level to which the conversion price may be reset: even if the average share price goes below this level. selling stocks as the share price falls: so they will be ‘short’ volatility. When the share price is close to the reset floor.Convertible Bonds – February 2002 A reset clause specifies a reset floor. accelerating the share price decline in the process. the reset feature mechanism will make them do the opposite. These features are interesting for their implications on delta and gamma. (the number of shares a resettable convertible security can be exchanged for increases as the share price falls). It is a mandatory reset convertible with one reset at maturity. even for bonds where the conversion price can be reset up or down. Arbitrageurs capture volatility by selling shares as the share price rises and buying shares as the share price falls: they are ‘long’ volatility. the adjustment of the conversion price will be limited by this floor. The DECs structure mentioned above falls under the general heading of a reset convertible. the expected number of shares that will be delivered on mandatory conversion rises. in a situation that is unfavourable and unexpected. These include many covenants regarded as standard in the terms and conditions of straight bonds. and convertible models will give a lower fair value for the convertible. However. they rely on the terms and conditions outlined in the bond’s Prospectus and Trust Deed (or Indenture) for protection. In some cases. Some prospectuses define a capital distribution as one that pushes the annual yield on the underlying shares above a specified level. Convertibles are vulnerable to certain actions over and above those of straight bonds. unless there is some form of compensation to convertible holders. which prevent the issuers undertaking certain courses of action which are detrimental to the interests of bondholders. Whether this yield is set in relation to the previous year’s dividend or some absolute level. One example of this would be a takeover for cash that leaves the bondholder with rights of conversion into cash. Most modern convertible prospectuses contain language designed to protect holders against capital distributions. such as rights issues. however. Events. convertible bondholders may be forced into early conversion in order to participate in the distribution. or near cash. 44 . The convertible price reduction will be approximately equal to the amount of the distribution expressed in parity terms multiplied by the delta of the convertible. Unanticipated capital distributions such as special dividends however. The sensitivity of the value of the convertible to common dividends is well known. the definition of a capital distribution can vary in its generosity. the higher the dividend assumptions. will put convertible bondholders that are not protected by anti-dilution provisions. These fall into two general categories: 1 Events that would tend to lower the fair premium of the convertible. Convertible pitfalls and protection Special distributions to shareholders Distributions that cause the underlying share price to fall (on announcement or ex-date) reduce the value of the convertible. that tend to have a dilutive effect on the underlying share price. investors generally regard these clauses as acceptable.Convertible Bonds – February 2002 Pitfalls and Protection ➤ ➤ The prospectus Convertible pitfalls and protection The prospectus As convertible investors do not physically own the shares into which they have rights of conversion. The prospectus will also provide information on the dividend and coupon entitlements of a convertible bond. 2 These matters are dealt with in more detail below. The intention is generally to increase the conversion ratio such that parity (that is the equity value of the convertible) is left unchanged. Sometimes the takeover language also includes an investors put at par. the treatment of the convertible bondholder will depend on the conditions of the prospectus or trust deed. if necessary. It will depend. on the volatility of the new company relative to that of the old. a measure of standardisation now exists on the question of dividend entitlement. the stock-split. If the stock-split were on a one-for-one basis for example. the conversion ratio would be doubled. a number of exceptions to this rule. the dividend policies of the new company and its credit status. only distributions that exceed net earnings since the issue of the convertible count as a special distribution. and the formula for any such adjustment. there is a distinction in treatment of a bid (mainly) for cash and one that is (mainly) for shares. Anti-dilution provisions Anti-dilution provisions cover a range of situations that can result in dilution of the underlying share price (and therefore the number of shares underlying the convertible). In some convertibles there is a ‘ratchet’ mechanism in which the conversion ratio is adjusted by a specified amount if the takeover takes place within a given time frame. after accounting for the fall in the share price resulting from the dilutive event. The general rule is that accrued interest is not paid on a convertible on conversion and the shares delivered on conversion will rank pari passu with existing shares. Stock-split Conversion ratios are almost always adjusted in case of the most straightforward of dilutive events. In general. the lack of potential movement in the exchange property would extinguish the premium. There are. or some other value. 45 . The provisions will stipulate the situations in which convertible holders are compensated for a dilutive event by receiving an improvement in the conversion terms. In these cases. In others there is an adjustment to the conversion ratio. Income entitlement In the European convertible market. In this situation. Merger or takeover In the case of a merger or takeover of the issuing company by another company. There is no presumption as to whether such a turn of events will be advantageous for convertible holders. accreted price. where there are provisions for a merger or takeover event. it is generally considered reasonable for the rights of conversion to be transferred into the shares of the new entity on a basis equivalent to the terms of the deal (the ‘see through’ basis). The bidder would also assume responsibility for the coupons and repayment of the convertible. A number of devices can be applied to address this situation. which is based on the average premium of the convertible over a specified time period. In some cases there is no protection.Convertible Bonds – February 2002 In some prospectuses. there is generally more scope for disadvantgeous treatment of the convertible bondholder. however. In an all-share bid by a quoted company. The danger in the event of a cash bid is that the exchange property of the convertible becomes cash. inter alia. Convertible Bonds – February 2002 In particular. if holders are ‘forced’ to convert by the sending out of a call notice. the entitlement to dividends may be based on the financial year in which conversion takes place. The percentage will be often set at around 90% of the convertible issue size. For example. there is often language giving protection against the ‘unfair’ scenario in which a long period has passed since a convertible coupon has been paid yet converting bondholders have just missed a dividend payment. Clean-up calls If a certain percentage of the bond has already been converted into shares. 46 . the issuer may be entitled to call any remaining bonds thus forcing conversion. Some transactions specify dividend entitlement that amount to delivery of ordinary shares that are ineligible for one or more dividends. but also calls. Models have been developed to allow more variables to be modelled incorporating stochastic bond yields and bond yields that are correlated to equity prices. dividends and FX rates as being either predetermined or dependant on the share price. puts and other characteristics. the technique will tend to overstate the value of the convertible. and ➤ A volatility assumption for the underlying stock. however. Additionally. such as bond yields. With a two-factor model the number of assumptions increases. but would have no intuition as to the appropriate bond volatility and correlation. A one-factor model varies just underlying stock prices. The major limitation of the binomial tree approach is that it allows the share price to follow a stochastic path. In a one-factor model. These ‘shadow’ probabilities are referred to as ‘risk neutral probabilities’.Convertible Bonds – February 2002 Convertible Pricing Models ➤ ➤ Recursive techniques Approximations using European options Recursive techniques Most convertible pricing models are based on the binomial tree approach. It is easy to misunderstand the nature of these probabilities. Building a binomial tree As with other options models. They do not relate to the chance of certain events occurring in the real world. rather than expectations. but treats all other inputs. but are set such that the expected price of the share at any given date is constrained to equal the theoretical forward price at that date. the lack of a random element in the interest rate assumption is particularly significant limitation. The number of factors in a model refers to how many variables are modelled. The major disadvantage of a two-factor model is its complicated nature and lack of transparency. whereas a two-factor model takes account of movements in interest rates as well. Of these. Generally they employ recursive procedures similar to those of simple binomial trees. the credit spread assumption). This employs a recursive procedure in a manner similar to that employed in valuing American options. ➤ Dividends on the underlying share until maturity. it is necessary to input the following: ➤ An assumption of the Libor spread (or spread to Treasuries. binomial trees deal with probabilities. An investor may have a feel for the volatility assumptions they wish to employ for a share. This approach can deal with most of the common features found in convertibles — it can capture not only the value of the early conversion right. if bonds and equities are positively correlated. 47 . The forward price is based on arbitrage considerations and driven by interest rates and dividend assumptions. the probability of a down and the drift rate per period are based on simple algebra and can be found in options text books. with a range of convertible prices considered for each. Thus the model is set for a plain vanilla European put exercisable only at maturity. The put is interpreted as the right to sell a parity number of shares at the redemption price. The relationship between the price and the two prices from which it is composed being given by the volatility of the share and a drift factor. then all observations under 100 at this date will simply be replaced with 100. In general. ➤ The income advantage value is calculated as the present value of the income advantage. Formulae for the share price outcomes at maturity. with the period length being determined by the term of the convertible and the number of steps chosen. crude adjustments to estimate the value of the put will be necessary. Approximations using European options From an equity investor’s perspective We have established that the value of a convertible to an equity investor can be summarised as: Convertible Pr ice = Parity + PutOptionValue + ValueofIncomeAdvantage In simple. ➤ The put option value can be calculated using the Black Scholes model (the derivative pricing model based on the binomial tree approach). One starts by associating a value for the convertible with each share price level at the maturity date of the bond. the probability of an up. One now simply works backward through the tree. non-callable convertibles we can thus calculate the theoretical value by establishing valuations for the components: ➤ Parity is simply the conversion ratio multiplied by the current stock price expressed in the bond currency. A new distribution for this stage is established and a value is assigned to a range of outcomes. If the adopted horizon is some other date. This process continues until one arrives at the present day with a fair value for the bond. For example if the bond is puttable at 100 on a certain date. Apart form the final (maturity date) range each price is calculated from two prices from the chronologically succeeding range.Convertible Bonds – February 2002 The tree works by dividing the life of the bond into specific moments in time. The next stage will be one period nearer the present day. In some cases the value for the convertible associated with each node calculated in this manner will need to be replaced if some feature of the bond makes this appropriate. 48 . for share price levels above the conversion price the value is parity and for share price levels below the conversion price it is 100%. an adjustment is necessary to approximate for the impact of this feature. If the bond is callable. an adjustment to the effective strike price. the approach is deficient in that it ascribes zero value to the early exercise option. Where there is a provisional call period. is available. based on the forward bond floor. However where there is a significant income advantage in the convertible. even approximations in which the first call date is treated as the effective horizon are unreliable. discounted at the relevant Libor spread plus a credit spread. The extent of the potential error depends on how different the terms of the convertible in question are to this basic description. In the case of callable bonds. however. When the call is provisional. the application of the European option methodology breaks down. ➤ The call option value can be calculated using the Black Scholes model set for a vanilla European call. The problem is that the approach is only theoretically correct if the bond happens to be non-convertible and non-callable for life.Convertible Bonds – February 2002 By adopting this approach. exercisable at maturity. the approach fails when there is a good chance of voluntary early conversion or when there is a period in which the bond is callable. an equity investor can obtain a very clear impression of what they are paying for when they buy a convertible at a premium. If the bond is convertible at any time. From a fixed income investor’s perspective We showed that the value of a convertible to a fixed income investor can be summarised as: Convertible Pr ice = BondFloor + CallOptionValue We can find the theoretical value of a non-callable convertible by calculating the values of its components: ➤ The bond floor value is calculated as the present value of the future coupon payments and the cash redemption value. However. 49 . Again the major advantage of this approach is its transparency for investors. the early exercise right is of little or no value anyway. the coupon and the redemption amount in a simplified case where there is an exact number of years until maturity and the bond and coupons are paid annually. ConvertibleBondFloor = å i =1 m C R + i (1 + d ) (1 + d )m Where: m = years to maturity. the YTM of the issue is that which solves the equation: € 1. gamma. and fugit. the (annual) YTM.000 = å i =1 5 € 40 € 1. bond floor. C = coupon. vega. In the case of the John Smith Corp Convertible EUR 4% 2007. 50 . though the principal of finding the discounted present value of the fixed payments is the same. The formula below shows the relationship between the bond price. Yield to maturity (YTM) YTM can only be calculated through a process of iteration. we need to deduct the accrued interest and to express the result as a percentage of par.000 + = 4% i (1 + YTM ) (1 + YTM )5 Bond floor One formula that can be used to calculate a convertible’s bond floor bears a strong resemblance to the YTM formula above. rho. delta. A somewhat more complex formulation is required when there are fractional periods.Convertible Bonds – February 2002 Appendix Introduction This appendix contains additional information on the following subjects referred to previously: yield to maturity (YTM). When there are fractional periods. C = coupon. Convertible Pr ice = å i =1 m C R + i (1 + YTM ) (1 + YTM )m Where: m = years to maturity. In order to quote it. theta. R = redemption value d = discount rate (the risk free rate (m) + a credit spread) The formula applies where there is a whole number of years to maturity. and R = redemption value. the value is ‘dirty’. the appropriate discount rate for the John Smith Corp Convertible EUR 4% 2007 is 6. Delta Figure 18 displays the sensitivity of the price of the convertible to changes in parity.423% and appropriate credit spread for John Smith Corp is 100bp. this is 89.91% (€899.098 i (1 + 0. Another method calculates the spot yield curve and discounts each future payment using the appropriate spot rate plus the credit spread. Solving for the bond floor on the John Smith Corp Convertible EUR 4% 2007 at issue gives: ConvertibleBondFloor = å i =1 5 € 40 € 1. If the euro-Libor rate (the risk-free rate) for the five-year. euro-denominated John Smith Corp convertible is 5. It is necessary to make an assumption on the credit quality of the issuer. In Europe.1/€1. plus a credit spread that reflects the credit quality of the issuer.Convertible Bonds – February 2002 The discount rate is calculated using the risk-free rate for the maturity of the bond.423%. Convertible Price against Parity CB1 CB0 Convertible Parity P0 P1 Source: Schroder Salomon Smith Barney.000). 51 . Figure 18. It shows that in geometric terms.6423) (1 + 0.000 + = € 899. it is common to adopt the swap rate (Libor) in the currency in which the convertible is denominated as the risk-free rate. delta is the slope of the tangent drawn on the convertible price curve at the level of the current share price (parity).06423)5 Expressed as a percentage of par. Gamma Gamma is the rate of change of delta for movements in the underlying share price: Gamma = d ( Delta) d ( Parity ) Conventionally. ➤ Gamma as the second partial derivative of the convertible price curve with respect to parity.Convertible Bonds – February 2002 Figure 18 shows how the tangent can be an accurate representation of convertible price movements only for small share price movements. it measures the slope of the tangent drawn on the convertible price curve at the current level of parity. d. We can interpret: ➤ Delta as the first partial derivative of the convertible price curve with respect to parity. then (P1 − P0) * Delta ≈ CB1 − CB0 If we consider infinitesimal changes. If parity moves from P0 to P1. then d ( Parity ) * Delta = d (Convertible Pr ice) Delta = Figure 19. gamma is expressed as the change in delta for a one-unit increase in parity. 52 . it measures the degree of convexity of the convertible price curve at the current level of parity. Delta against Parity Delta 100 90 80 70 60 50 40 30 20 10 0 Parity d (Convertible Pr ice) d ( Parity ) Source: Schroder Salomon Smith Barney. Adjusting for the effect of gamma is particularly important for larger share price movements.Convertible Bonds – February 2002 Gamma = Gamma = d ( Delta) d ( Parity ) d 2 (Convertible Pr ice) d ( Parity 2 ) We can isolate an approximate formula to estimate the change in the price of a convertible for a given absolute change in parity: Convertible Pr iceMove = Delta * ParityMove + 1 Gamma * ParityMove 2 2 This is a simple approximation by linear interpolation. For small stock price fluctuations. as the effect of convexity on the convertible price can be significant. if the initial delta is D1. 53 . the final delta is approximately D2: D2 = (D1 + Gamma * ParityMove) So the average delta over the whole move is: D1 + D2 2 D + (D1 + Gamma * ParityMove) DA = 1 2 Gamma D A = D1 + * ParityMove 2 DA = The formula above shows the convertible price move is the average delta multiplied by the parity move: Gamma æ ö 2 ParityMove ç D1 + * * ParityMove = Delta* ParityMove 1 Gamma ParityMove + * ÷ 2 2 è ø It can also be derived from a simple Taylor series expansion. delta multiplied by the parity move can be a good approximation for changes in the convertible price. It can be expressed as follows: Vega = Figure 21.2 0.2 1 0. Vega Vega is the sensitivity of the convertible price to changes in the volatility of the underlying stock.45 0. Gamma against Parity Gamma 1.2 0 Parity Source: Schroder Salomon Smith Barney. 54 . Vega against Parity d (Convertible Pr ice) d ( StockVolatility ) Vega 0.1 0.05 0 Parity Source: Schroder Salomon Smith Barney. or at-the-money. and it is at a maximum when the convertible is close to.Convertible Bonds – February 2002 Figure 20.4 0.15 0.35 0. Gamma changes along the convertible price curve.4 0.8 0. Gamma is always positive in conventional convertibles (as delta increases for increases in parity).6 0.25 0.3 0. it is expressed as the percentage change in the convertible price for the passage of one day. or at-the-money. Theta = d (Convertible Pr ice) d (Time) 55 . Rho is always a negative number in conventional convertibles. Conventionally. all other things being equal. A change in the stock volatility assumption may not have a material impact on fair value if the convertible is out-of-the-money or deep in-the-money. than it does a positive impact on the value of the embedded call option. Rho can be expressed as follows: Rho = d (Convertible Pr ice) d ( InterestRate) Figure 22. Rho against Parity Rho 0.8 0.Convertible Bonds – February 2002 As can be seen from Figure 21. the sensitivity of the convertible price to changes in interest rates increases.9 0. vega is always positive on a standard convertible and is greatest when the convertible is close to.5 0.1 0 Parity Source: Schroder Salomon Smith Barney. Rho Rho measures the sensitivity of the convertible price to movements in interest rates.4 0. Theta Theta is the change in convertible price with the passage of time.7 0. As the bond floor becomes the most important component of a convertible’s valuation (the convertible is out-of-the-money). as an increase in interest rates has a greater negative impact on the value of the bond floor.3 0.6 0.2 0. so there is a natural upward drift in the bond floor in both cases. and the line marked OOM parity is 80 throughout. 4 3. Time Decay for At-The-Money and Out-Of-The-Money Convertibles 108 106 104 102 value 100 98 96 94 92 90 0. and ➤ The bond floor trends towards the redemption value over time. For the line marked ATM. 4 0. Figure 23 shows the effect of the passage of time on a notional four-year convertible. 2 0. Convertibles trading below redemption value will rise towards this value over time. OOM 56 4 . 6 3.Convertible Bonds – February 2002 As a convertible approaches final maturity. parity is 100 throughout. Figure 23. 6 0. 6 1. with theta being a negative number. 2 2. 2 3. 8 0 1 2 3 time ATM Source: Schroder Salomon Smith Barney. 2 1. we see two opposite effects on the convertible price: ➤ The value of the embedded call option decreases and so the convertible price decreases. 4 1. 4 2. 8 3. 8 1. At-the-money convertibles will usually suffer from the first of these effects. 6 2. 8 2. the drag to redemption of the bond element can be the more potent force. Out-of-the-money convertibles (including original issue discount bonds. The notional bonds both have 1% coupons in a 5% interest rate environment. for which the effective strike price is considerably in excess of the share price). the bond’s method of accrual needs to be known.7. stock splits or other corporate events that can result in the dilution of the underlying share price. Different methods predominate in different markets. Adaptations of the approach are commonly applied to convertible bonds. A call feature gives a convertible issuer the right to redeem a convertible bond prior to maturity at a price determined at issue. This is the value of the accrued portion of the coupon on a convertible bond. The bond floor should support the price of a convertible if the underlying equity falls. thus a call option can frequently be interpreted as required early conversion. multiplied by the number of days since the last coupon was paid. These provide for an adjustment in the conversion terms in the event of special stock dividends. At that price the bond would yield 7.2%. for example. thereby allowing holders of the bond to outperform holders of the equity.2% to maturity at 100 after a further five years. after five years the accreted value would be 70. The bond cum warrant can be stripped and traded separately in the secondary market. This is a straight bond issued with a long maturity call option attached. They take account of events such as puts and calls that take place during the life of the instrument. A binomial tree option-pricing model estimates the theoretical value for an option. If. it is the coupon amount divided by the number of days in a year. It is a simple measure that takes no account of dividend growth projections or discounting for present value. To calculate accrued interest accurately. This type of option allows the holder to exercise into the underlying asset at any time during the life of the option. A convertible is said to be at-the-money if the current share price is close to the conversion price. Generally. a 10-year zero-coupon bond were issued at a price of 50 to yield 7. Accrued interest American-style option Anti-dilution provisions At-the-money Balanced convertible Binomial tree Black-Scholes optionpricing model Bond floor (or investment value) Bond with/cum warrant Breakeven Call feature (or call option) 57 . A balanced convertible is a convertible that trades at a price where it is neither a pure equity substitute nor trading on its bond floor. Holders of convertibles who receive a call notice will generally have time to exercise their rights of conversion before repayment takes place. The breakeven calculation for a convertible measures the time taken for the bond’s income or yield advantage to offset the cost to the investor of a bond’s conversion premium. but is balanced between the two.Convertible Bonds – February 2002 Glossary Accreted value The accreted value is the price at which an OID or premium redemption bond yields the same as it did when it was issued. The bond floor is the value of the straight fixed income element of the convertible if rights of conversion are ignored. The option-pricing model derived by Fischer Black and Myron Scholes is used to estimate the theoretical fair value of option contracts based on a range of inputs and assumptions. Clean-up call Contingent conversion Contingent interest payment Conversion premium Conversion price Conversion ratio Convertible preferreds Convertible price Coupon Credit spread Cross currency convertible Current (or running) yield DECs Delta Denomination Dirty price 58 . These are preferred shares issued by a company that are convertible at the option of the investor into the common shares of that company. At issue. This is the minimum size in which the bond can be traded. The percentage is often set at around 90% of the convertible issue size. The conversion ratio is the number of shares into which each bond can be converted. It is normally quoted as a percentage of the face value. It is generally quoted as a percentage of par (the face value of the bond). the conversion price is the price at which shares are effectively ‘bought’ upon conversion. Most convertibles are quoted this way. They pay a fixed dividend and are often issued in perpetual form so therefore may not be redeemable. When an issuer is entitled to call any remaining bonds if a certain percentage of the bond issue has already been converted into shares. if the convertible is purchased at the issue price. The dirty price is the clean price of a convertible bond plus its accrued interest. The credit spread is the spread over the swaps curve (or sometimes Government bond curve) at which the issuer is assumed able to issue a straight bond that is otherwise identical to the convertible. It is the actual price an investor will pay for a bond. DECs are mandatory convertibles. it is termed a ‘clean-up call’. See premium. It is defined as the expected change in the convertible price for a small absolute change in parity. This is the price at which the convertible is traded in the market. Current yield is the income per unit of currency invested. It is calculated by dividing the issue price of the bond by the conversion ratio. typically issued as preferred stock paying quarterly fixed dividends. A convertible that is denominated in a different currency to that of the underlying shares. It is calculated by dividing the coupon by the current convertible price. The coupon is the interest payment per bond. Contingent interest payment features allow the payment of a small amount of interest to the convertible bondholder if the average market price of the convertible falls to a specified level. Delta is a measure of the sensitivity of the convertible bond price to share price movements. DECS stands for Dividend Enhanced Convertible Securities or Debt Exchangeable for Common Stock. A contingent conversion feature makes a convertible investor’s ability to convert contingent upon some factor such as the share price attaining a specified level.Convertible Bonds – February 2002 Clean price The clean price is the price of a convertible bond quoted without accrued interest included. A convertible issued at a discount to par is termed an original issue discount convertible. European option Exchangeable bond Gamma Greenshoe Hard call protection Hedge ratio High-yield convertible Implied volatility In-the-money Issue price Mandatory convertible Maturity Nominal value Original issue discount (OID) Out-of-the-money Par Par put convertible 59 . Gamma measures the sensitivity of the convertible bond’s delta to share price movements.Convertible Bonds – February 2002 Dividend yield The dividend yield is an indication of the income generated by each share.000 of the relevant currency in the Euroconvertible market and ¥1. A convertible in which the investor has a put option prior to final maturity at par. This is the face value of the bond. A period of time specified in the indenture of a bond during which the issuer is not allowed to call the bond from the investor under any circumstances. The hedge ratio shows the equity sensitivity of a convertible bond and enables an investor to calculate how many shares they would need to sell to hedge their equity exposure. leaving the convertible so deeply out-of-themoney that its equity component becomes immaterial. A convertible is said to be in-the-money if the current share price is greater than the conversion price. The Greenshoe is an over-allotment option that allows an underwriter to increase the number of bonds issued. This is a convertible in which the bondholder is obliged to convert into the underlying equity at maturity. Issues for sub-investment grade companies are also referred to as high-yield convertibles. The current price. A convertible is said to be out-of-the-money if the current share price is below the conversion price. It is calculated by dividing the annual dividend per share by the share price. This type of option gives the holder the right to exercise an option only on the maturity date. This is a convertible bond issued by one company that can be converted into the shares of a different company.000. it is sometimes referred to as a high-yield convertible. It is often 1. issue price and redemption price of most convertibles are expressed as a percentage of the nominal value. Par is the face value of a bond. when there is strong demand for an initial offering. It is the change in delta for a one-point change in parity.000 in the Japanese and Euroyen markets. The maturity date is the final redemption date of the bond. typically by 10%-15%. A convertible bond’s hedge ratio is also referred to as ‘delta’. Implied volatility is the convertible pricing model volatility input used that brings the fair value of a convertible into line with its market price. If the share price falls dramatically. The issue price is the price at which convertible bonds are sold to investors at issue. The call trigger is often stated as a percentage of the conversion price. It is normally expressed as a percentage of a bond’s nominal value. Rho measures the sensitivity of the convertible price to movements in interest rates. This describes a convertible bond that is issued at par but redeems at a premium to par. PERCs are a mandatory convertible bond structure that caps upside participation in a stock’s performance. In some convertibles there is a ratchet mechanism in which the conversion ratio is adjusted by a specified amount if a takeover takes place within a given time frame. PERCs Premium Premium put convertible Premium redemption structure Put feature Ratchet Redemption price Reset date Reset features Reset floor Reset period Rho Risk premium Soft call (or provisional call) 60 . The risk premium is the difference between the convertible price and the bond floor expressed as a percentage of the bond floor. The redemption price is the price at which the issuer must redeem bonds at maturity. The limit below which the conversion price on a reset convertible cannot fall. the share price upon which the new conversion price is based is calculated by reference to the average share price observed in a specified reset period. The date on which a change of conversion terms takes place on a reset convertible is termed the reset date. In most reset convertibles. A put gives investors the option to sell back the convertible bond to the issuer at a fixed price on a given date or dates. thus ‘subject to a 140% trigger’ means that the call trigger is 140% of the conversion price. It is calculated by subtracting parity from the convertible price and is expressed as a percentage of parity. It represents the extra cost an investor must pay to buy the shares a bond converts into via a convertible. Reset features allow for a change in the conversion price of a convertible in the event of share price depreciation (downward reset) or appreciation (upward reset) on certain specified dates. It is expressed as the change in the convertible price for a one basis point move in interest rates (a parallel shift in the yield curve). A convertible in which the investor has a put option prior to final maturity with a put price above par. This predetermined premium is known as the call trigger. A convertible’s premium is the percentage by which the market price of the convertible bond exceeds parity. PERCs stands for Preferred Equity Redemption Cumulative Stock. It is calculated by multiplying the conversion ratio by the current share price expressed in bond currency terms. This is a period of time during which the issuer may only call the bond if the share price has traded above a predetermined premium to the conversion price for a set period of time.Convertible Bonds – February 2002 Parity Parity is the market value of the shares into which the bond may be converted. It is expressed as the change in the convertible price for the passing of one day. It is defined as the annualised standard deviation of returns. The extent to which the underlying share price has fluctuated over a certain period determines the historical or observed volatility. The yield advantage is the difference between the current yield on the convertible bond and the stock dividend yield. Vega is the change in the fair value of the convertible for a one percentage point change in the assumption for stock volatility. Theta is the change in the convertible price with the passage of time. The assumption for future share price volatility is an input for convertible valuation. Vega is the sensitivity of the convertible price to changes in the volatility of the underlying stock. Theta Vega Volatility Yield advantage Yield to maturity 61 . other things being equal.Convertible Bonds – February 2002 Step-up coupon This is where the coupon level increases at a future date. Yield to maturity (YTM) is the discount rate that equates the current market price of a straight bond to the present value of its future cash flows. Share price volatility is a measure of the dispersion of share price returns. a credit rating downgrade. This can be a contingent event on for instance. Convertible Bonds – February 2002 Notes 62 . Convertible Bonds – February 2002 Notes 63 . S.S. or be subject to. as defined by the rules of the Financial Services Authority. a licensed Dealer and Investment Advisor. including its parent. A thorough explanation of the ratings system is available upon request. may entail certain risks. Tel: (44-20) 7986-4000 .S. Securities recommended. has acted as manager or co-manager of a public offering of the securities of this company. suitable for average equity investors. suitable for conservative investors. Schroders is a trademark of Schroders Holdings plc and is used under license. is being so distributed under license. Investing in non-U. 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