Convertible bond

Underwriters have been quite innovative and provided several variations of the initial convertible structure. Although no formal classification exists in the financial market it is possible to segment the convertible universe into the following sub-types:

• Coupon: Periodic interest payment paid to the convertible bond holder from the issuer. Could be fixed or variable or equal to zero.
• Maturity/redemption date: The date on which the principal (par value) of the bond (and all remaining interest) are due to be paid. In some cases, for non-vanilla convertible bonds, there is no maturity date (i.e. perpetual), this is often the case with preferred convertibles (e.g. US0605056821).
• Final conversion date: Final date at which the holder can request the conversion into shares. Might be different from the redemption date.
• Yield: Yield of the convertible bond at the issuance date, could be different from the coupon value if the bond is offering a premium redemption. In those cases the yield value would determine the premium redemption value and intermediary put redemption value.
• Bond floor: Also known as straight bond value, this is the value of a convertible bond's fixed income elements (regular interest payments, payment of principal at maturity and a superior claim on assets compared to common stock) excluding the ability to convert into equities.[5]
• The issuance prospectus will state either a conversion ratio or a conversion price. The conversion ratio is the number of shares the investor receives when exchanging the bond for common stock. The conversion price is the price paid per share to acquire the shares when exchanging the bond for common stock.[6]
• Market conversion price: The price that the convertible investor effectively pays for the right to convert to common stock. It is calculated as shown below. Once the actual market price of the underlying stock exceeds the market conversion price embedded in the convertible, any further rise in the stock price will drive up the convertible security's price by at least the same percentage. Thus, the market conversion price can be thought of as a "break-even point."[7]

Market conversion price = market price of convertible bond / conversion ratio

• Market conversion premium: the difference between the market conversion price and the current market price of the underlying stock. Convertible bond buyers accept a conversion premium in exchange for the downside protection provided by a convertible bond's fixed income characteristics. As the stock price declines, the price of the convertible bond will not drop below its bond floor value. Usually expressed as on a per-share basis, the market conversion premium is calculated as follows:[8]

Market conversion premium per share = market conversion price - current market price

• Parity: Immediate value of the convertible if converted, typically obtained as current stock price multiplied by the conversion ratio expressed for a base of 100. May also be known as Exchange Property.

Convertibles may have other features, such as:

• Call features: The ability of the issuer (on some bonds) to call a bond early for redemption. This should not be mistaken for a call option. A Softcall would refer to a call feature where the issuer can only call under certain circumstances, typically based on the underlying stock price performance (e.g. current stock price is above 130% of the conversion price for 20 days out of 30 days). A Hardcall feature would not need any specific conditions beyond a date: that case the issuer would be able to recall a portion or the totally of the issuance at the Call price (typically par) after a specific date.
• Put features: The ability of the holder of the bond (the lender) to force the issuer (the borrower) to repay the loan at a date earlier than the maturity. These often occur as windows of opportunity, every three or five years and allow the holders to exercise their right to an early repayment.
• Contingent conversion (aka CoCo): Restrict the ability of the convertible bondholders to convert into equities. Typically, restrictions would be based on the underlying stock price and/or time (e.g. convertible every quarter if stock price is above 115% of the conversion price).[9] Reverse convertibles in that respect could be seen as a variation of a Mandatory bearing a contingent conversion feature based. More recently some CoCo's issuances have been based on Tier-1 capital ratio for some large bank issuers.
• Reset: Conversion price would be reset to a new value depending on the underlying stock performance. Typically, would be in cases of underperformance (e.g. if stock price after a year is below 50% of the conversion price the new conversion price would be the current stock price).
• Change of control event (aka Ratchet): Conversion price would be readjusted in case of a take-over on the underlying company. There are many subtype of ratchet formula (e.g. Make-whole base, time dependent...), their impact for the bondholder could be small (e.g. ClubMed, 2013) to significant (e.g. Aegis, 2012). Often, this clause would grant as well the ability for the convertible bondholders to "put" i.e. ask for the early repayment of their bonds.
• Non-dilutive: The non-dilutive feature has been popularised with the lower interest rates (e.g. in Euro) in order to make convertible issuance still attractive for issuers already benefitting from low interest charges in the straight bond market. In a non-dilutive placement, the issuer would simultaneously enter in an OTC option agreement with the underwriter (or a third party). This option would often match the strike of the convertible as well as its maturity. This would result in cancelling out the dilution in case of a conversion of the convertible at maturity if the stock price is above the strike. Typically, in order to fully prevent dilution the convertible prospectus would constraint possibility of early conversion.[10]

The global convertible bond market is relatively small, with about 400 bn USD (as of Jan 2013, excluding synthetics). As a comparison, the straight corporate bond market would be about 14,000 bn USD. Among those 400 bn, about 320 bn USD are "Vanilla" convertible bonds, the largest sub-segment of the asset class.

Convertibles are not spread equally and some slight differences exist between the different regional markets:

• North America: About 50% of the global convertible market, mostly from the USA (even if Canada is well represented in the Material sector). This market is more standardised than the others with convertible structures being relatively uniform (e.g. Standard Make-Whole take over features, Contingent Conversion @ 130%). Regarding the trading, the American convertible market is "centralised" around TRACE which helps in terms of price transparency. One other particularity of this market is the importance of the Mandatory Convertibles and Preferred especially for Financials (about 10–20% of the issuances in the US regional benchmarks). Most of the trading operation are based in New-York.
• EMEA: European, Middle Eastern and African issuances are trading usually out of Europe, London being the biggest node followed by Paris and to a lesser extent Frankfurt and Geneva. It represents about 25% of the global market and shows a greater diversity in terms of structures (e.g. from CoCoCo's to French OCEANE). Because of that lack of standardisation, it is often considered to be more technical and unforgiving than the American market from a trading perspective. A very tiny amount of the volumes is traded on exchange while the vast majority is done OTC without a price reporting system (e.g. like TRACE). Liquidity is significantly lower than on the Northern American market. Trading convention are NOT uniform: French Convertibles would trade dirty in units while the others countries would trade clean in notional equivalent.
• Asia (ex Japan): This region represents about 17% of the total market, with an overall structure similar to the EMEA market albeit with more standardisation across the issuances. Most of the trading is done in Hong-Kong with a minor portion in Singapore.
• Japan: This region represents about 8% of the total market as of January 2013 in spite of being in the past comparable in size to the Northern American market. It mostly shrunk because of the low interest environment making the competitive advantage of lowering coupon payment less appealing to issuers. One key specificity of the Japanese market is the offering price of issuance being generally above 100, meaning the investor would effectively bear a negative yield to benefit from the potential equity underlying upside. Most of the trading is done out of Tokyo (and Hong-Kong for some international firms).

Convertible bond investors get split into two broad categories: Hedged and Long-only investors.

• Hedged/Arbitrage/Swap investors: Proprietary trading desk or hedged-funds using as core strategy Convertible Arbitrage which consists in, for its most basic iteration, as being long the convertible bonds while being short the underlying stock. Buying the convertible while selling the stock is often referred to as being "on swap". Hedged investors would modulate their different risks (e.g. Equity, Credit, Interest-Rate, Volatility, Currency) by putting in place one or more hedge (e.g. Short Stock, CDS, Asset Swap, Option, Future). Inherently, market-makers are hedged investors as they would have a trading book during the day and/or overnight held in a hedged fashion to provide the necessary liquidity to pursue their market making operations.
• Long-only/Outright Investors: Convertible investors who will own the bond for their asymmetric payoff profiles. They would typically be exposed to the various risk. Global convertible funds would typically hedged their currency risk as well as interest rate risk in some occasions, however Volatility, Equity & Credit hedging would typically be excluded from the scope of their strategy.

The splits between those investors differ across the regions: In 2013, the American region was dominated by Hedged Investors (about 60%) while EMEA was dominated by Long-Only investors (about 70%). Globally the split is about balanced between the two categories.

In theory, the market price of a convertible debenture should never drop below its intrinsic value. The intrinsic value is simply the number of shares being converted at par value times the current market price of common shares.

The 3 main stages of convertible bond behaviour are:

• In-the-money: Conversion Price is < Equity Price.
• At-the-money: Conversion Price is = Equity Price.
• Out-the-money: Conversion Price is > Equity Price.

From a valuation perspective, a convertible bond consists of two assets: a bond and a warrant. Valuing a convertible requires an assumption of

1. the underlying stock volatility to value the option and
2. the credit spread for the fixed income portion that takes into account the firm's credit profile and the ranking of the convertible within the capital structure.

Using the market price of the convertible, one can determine the implied volatility (using the assumed spread) or implied spread (using the assumed volatility).

This volatility/credit dichotomy is the standard practice for valuing convertibles. What makes convertibles so interesting is that, except in the case of exchangeables (see above), one cannot entirely separate the volatility from the credit. Higher volatility (a good thing) tends to accompany weaker credit (bad). In the case of exchangeables, the credit quality of the issuer may be decoupled from the volatility of the underlying shares. The true artists of convertibles and exchangeables are the people who know how to play this balancing act.

A simple method for calculating the value of a convertible involves calculating the present value of future interest and principal payments at the cost of debt and adds the present value of the warrant. However, this method ignores certain market realities including stochastic interest rates and credit spreads, and does not take into account popular convertible features such as issuer calls, investor puts, and conversion rate resets. The most popular models for valuing convertibles with these features are finite difference models as well as the more common binomial trees[11] and trinomial trees. However, also valuation models based on Monte Carlo methods are available.[12]

Since 1991–92, most market-makers in Europe have employed binomial models to evaluate convertibles. Models were available from INSEAD, Trend Data of Canada, Bloomberg LP and from home-developed models, amongst others. These models needed an input of credit spread, volatility for pricing (historic volatility often used), and the risk-free rate of return. The binomial calculation assumes there is a bell-shaped probability distribution to future share prices, and the higher the volatility, the flatter is the bell-shape. Where there are issuer calls and investor puts, these will affect the expected residual period of optionality, at different share price levels. The binomial value is a weighted expected value, (1) taking readings from all the different nodes of a lattice expanding out from current prices and (2) taking account of varying periods of expected residual optionality at different share price levels.[13] The three biggest areas of subjectivity are (1) the rate of volatility used, for volatility is not constant, and (2) whether or not to incorporate into the model a cost of stock borrow, for hedge funds and market-makers. The third important factor is (3) the dividend status of the equity delivered, if the bond is called, as the issuer may time the calling of the bond to minimise the dividend cost to the issuer.

Convertible bonds are mainly issued by start-up or small companies. The chance of default or large movement in either direction is much higher than well-established firms. Investors should have a keen awareness of significant credit risk and price swing behavior associated with convertible bonds.  Consequently, Valuation models need to capture credit risk and handle potential price jump.

• Convertible bonds are usually issued offering a higher yield than obtainable on the shares into which the bonds convert.
• Convertible bonds are safer than preferred or common shares for the investor. They provide asset protection, because the value of the convertible bond will only fall to the value of the bond floor: however in reality if stock price falls too much the credit spread will increase and the price of the bond will go below the bond floor. At the same time, convertible bonds can provide the possibility of high equity-like returns.
• Also, convertible bonds are usually less volatile than regular shares. Indeed, a convertible bond behaves like a call option. Therefore, if C is the call price and S the regular share then

${\displaystyle \Delta ={\frac {\delta C}{\delta S}}\Rightarrow \delta C=\Delta \times \delta S.}$

In consequence, since ${\displaystyle 0<\Delta <1}$ we get ${\displaystyle \delta C<\delta S}$, which implies that the variation of C is less than the variation of S, which can be interpreted as less volatility.

• The simultaneous purchase of convertible bonds and the short sale of the same issuer's common stock is a hedge fund strategy known as convertible arbitrage. The motivation for such a strategy is that the equity option embedded in a convertible bond is a source of cheap volatility, which can be exploited by convertible arbitrageurs.
• In limited circumstances, certain convertible bonds can be sold short, thus depressing the market value for a stock, and allowing the debt-holder to claim more stock with which to sell short. This is known as death spiral financing.

Source: Bloomberg

• Contingent convertible bond
• Preferred stock
• Convertible security
• Equity-linked note
• Exchangeable bond
• Liquidation preference

• FinPricing. Bond valuation practical guide and calculator tool.
• Max, Kevin. Future Returns: The Case for Convertible Bonds. Barron's. December 3, 2019.
• Xiao, Tim. A simple and precise method for pricing convertible bonds with credit risk. Journal of Derivatives & Hedge Funds, volume 19, issue 4. Pages 259–277.

• Convertible Note Term Sheet Generator from Wilson Sonsini Goodrich & Rosati
• Pricing Convertible Bonds using Partial Differential Equations – by Lucy Li
• Pricing Inflation-Indexed Convertible Bonds – by Landskroner and Raviv
• Harvard i-lab | Foundations of Financings and Capital Raising for Startups. Explains both plain convertible debt and a simplified form of convertible debt called SAFE (Simple Agreement for Future Equity)