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Convertible bond

A convertible bond combines a debt claim with a conversion right. Follow a USD100 bond into four shares worth USD120, and separate that exchange from a full valuation.

A convertible bond is debt that carries a contractual right to convert into equity, usually the issuer’s common shares, or to receive an equity-linked settlement specified by its terms. For a quant, the important consequence is that one security combines credit risk with equity exposure: neither a plain bond yield nor a share-price view describes the whole position.

The ordinary optional-conversion structure lets the holder retain the debt claim until conversion, redemption or another contractual event. Interest may be payable along the way. The conversion right gives an alternative way to settle that investment; it does not ordinarily add the full share value on top of a separate principal repayment.

Follow one bond through conversion

Consider a fictional contract with face value F=100F=100 USD per bond and a fixed conversion ratio q=4q=4 shares per bond. At a share price S=30S=30 USD per share, its conversion value, also called parity, is
qS=4×30=120USD per bond.qS=4\times30=120\quad\text{USD per bond}.

That is the market value of the specified shares. It is neither a quoted convertible price nor a profit calculation: we have not said what the investor paid for the bond.

To make the choice concrete, place the example at maturity, assume the issuer pays its obligations, and stipulate a choice between redemption for USD100 cash and surrendering the bond for four shares. Conversion is freely available, with no coupons, accrued interest, fees or taxes at this terminal date. Under precisely these assumptions,
terminal value per bond=max⁡(F,qS)=max⁡(100,120)=120.\text{terminal value per bond}=\max(F,qS)=\max(100,120)=120.
A fictional USD100 face convertible can be redeemed for USD100 or surrendered for four shares worth USD30 each, USD120 total; the chosen terminal value is USD120, not USD220.
A fictional USD100 face convertible can be redeemed for USD100 or surrendered for four shares worth USD30 each, USD120 total; the chosen terminal value is USD120, not USD220.
One stipulated solvent maturity decision. Redemption and share conversion are alternative outcomes for the same bond; the diagram does not price it before maturity.

The holder who converts receives four shares and gives up the debt being converted. Adding USD100 face to USD120 conversion value would count the debt twice and invent a USD220 receipt. Coupons already received before conversion are separate historical cashflows; whether any accrued interest is paid at conversion depends on the contract.

The implied conversion price is F/q=100/4=25F/q=100/4=25 USD per share. This translates the face amount into a share-price threshold in the simple example. It is not an additional cash exercise payment that this holder must make when surrendering the bond.

Read the rights before drawing a payoff

The ratio is only the beginning. A term sheet or indenture also determines:

  • Conversion eligibility: the dates, share-price tests or other events that allow conversion. A large conversion value does not itself prove that conversion is available today.
  • Issuer call and holder put rights: an issuer call can shorten the time left to choose; a holder put may permit early repayment at a specified amount. Notice periods, prices and conditions matter.
  • Settlement: shares, cash or a combination may satisfy the conversion obligation. Cash settlement may use a contractual averaging period rather than the single spot price in our illustration.
  • Adjustments and dilution: stock splits, dividends or other corporate events can change conversion terms. Issuing shares can dilute existing shareholders; fixed-ratio and market-price-based conversion formulas have different effects.
  • Credit and ranking: redemption and coupon promises remain exposed to issuer default and the bond’s priority in the capital structure. An estimated bond floor is not guaranteed principal protection.
Settlement variation is observable in actual documents. Southwest Airlines’ 27 January 2025 notice changed the default settlement method for its specified convertible notes to cash settlement. That historical notice illustrates why “convertible” alone does not tell you what will be delivered; it is not a statement about a currently outstanding trade.

From an exchange rule to a price

Before maturity, a convertible’s value depends on remaining coupons, rates, issuer credit, the share price and its dynamics, dividends, liquidity, and the exact exercise and settlement rights. Conversion can sacrifice future coupons and remaining optionality. A positive difference between conversion value and face therefore does not, on its own, establish the best exercise decision today.

“Bond plus call option” is a useful starting description. The simple terminal identity max⁡(F,qS)=F+max⁡(qS−F,0)\max(F,qS)=F+\max(qS-F,0) adds only the excess over face, rather than adding the full conversion value. Turning that identity into a valuation requires consistent credit, cashflows and exercise assumptions; attaching a generic Black–Scholes call to a corporate bond does not automatically price the contract.
For a fuller treatment of ratios, calls, puts and the limits of the simplified payoff, read Convertible Terminology and Payoff (public preview; full lesson requires membership). Convertible arbitrage then adds hedging and relative-value questions to these contract mechanics.

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