Definition
A convertible bond is a corporate debt security that can be exchanged for a fixed number of the issuer’s common shares. It combines features of a bond (regular interest payments, return of principal at maturity) with an embedded option to convert into equity. The conversion feature gives holders upside if the stock rises while preserving downside protection of a bond when the stock falls.
How it works — core mechanics
– Issue terms set two key numbers: the conversion price (the price per share used for conversion) and the bond’s face (par) value (often $1,000).
– Conversion ratio = par value ÷ conversion price. This is the number of shares each bond converts into.
– Conversion value = current stock price × conversion ratio. This is what the shares received would be worth at market prices.
– If conversion value > bond’s value (market price or redemption value), conversion is economically attractive; otherwise the investor may hold the bond for interest and return of principal.
Important features and variations
– Coupon: Convertible bonds typically pay a lower coupon than comparable straight (nonconvertible) bonds because the conversion option has value.
– Maturity: Like other bonds, they have a maturity date when principal is repaid if not converted.
Call and put provisions
– Call provision (issuer call): The issuer may redeem the convertible early, typically at a specified call price and after a lock-up (no-call) period. Calling forces holders either to convert into equity or accept the call price in cash. Calls limit upside for holders because they can be forced to convert when the stock has risen enough to make conversion attractive to the issuer.
– Put provision (investor put): The holder can require the issuer to buy back the bond at a specified price before maturity. This protects investors if credit or rates move against them.
– Yield-to-worst: When evaluating yield, use the worst-case legal outcome (earliest callable date, put date, or maturity) to avoid overstating prospective return.
Anti-dilution and reset features
– Anti-dilution protection adjusts the conversion ratio (number of shares per bond) if the issuer undertakes stock splits, rights offerings, or certain other corporate actions. This preserves the economic value of the conversion option.
– Reset provisions change the conversion price or ratio under predefined conditions (e.g., if the issuer’s stock falls below a threshold for a set period). Resets can make the bond more equity-like.
Contingent convertibles (CoCos)
– Contingent convertibles are hybrid debt issued mainly by banks. They automatically convert to equity or are written down when a trigger (e.g., regulatory capital ratio) is breached.
– They carry higher complexity and trigger (credit and systemic) risk; valuation and investor protections differ materially from standard convertibles.
Basic valuation concept and formulas
– A convertible bond’s market price ≈ straight-bond value + conversion option value. The conversion option is like a call option on the issuer’s stock embedded in the bond.
– Conversion ratio = par value ÷ conversion price.
– Conversion value = current stock price × conversion ratio.
– Conversion premium (%) = (market price of the convertible − conversion value) ÷ conversion value.
– Parity (bond parity or bond-equivalent value) = conversion value; it is the theoretical bond price if converted immediately.
Worked numeric example
– Given: par value = $1,
000; conversion price = $50; current stock price = $40; coupon = 5% annual; maturity = 5 years; market price of the convertible = $1,050; market yield on a comparable straight (nonconvertible) bond = 6%.
Step 1 — Conversion ratio
– Formula: conversion ratio = par value ÷ conversion price
– Calculation: 1,000 ÷ 50 = 20 shares per bond
Step 2 — Conversion value (bond parity)
– Formula: conversion value = current stock price × conversion ratio
– Calculation: 40 × 20 = $800
– Interpretation: If you converted immediately, the shares received would be worth $800.
Step 3 — Conversion premium (%)
– Formula: conversion premium = (market price of convertible − conversion value) ÷ conversion value
– Calculation: (1,050 − 800) ÷ 800 = 250 ÷ 800 = 0.3125 = 31.25%
– Interpretation: The convertible is trading 31.25% above immediate conversion parity.
Step 4 — Straight-bond value (present value of coupons + principal)
Assumptions: annual coupon payments, market yield = 6% (used as discount rate), par = $1,000, n = 5 years, coupon = 5% → annual coupon = $50.
– PV of coupons (annuity): PVc = C × [1 − (1 + y)^−n] / y
= 50 × [1 − (1.06)^−5] / 0.06
= 50 × [1 − 0.747258] / 0.06
= 50 × 0.252742 / 0.06 = 50 × 4.21237 = $210.62
– PV of principal: PVp = Par ÷ (1 + y)^n = 1,000 × (1.06)^−5 = $747.26
– Straight-bond value = PVc + PVp = 210.62 + 747.26 = $957.88
Step 5 — Implied value of the conversion option
– Formula: conversion option value ≈ market