Skip to content

Convertible Bonds

One-line definition

A bond that can be converted into a fixed number of the issuer's common shares at the holder's option — a straight bond plus an embedded call option on the issuer's stock, priced as a hybrid of the two.

Formula

conversion_value = conversion_ratio * stock_price (also called "parity" — what the bond is worth if converted right now)

conversion_premium = (bond_price - conversion_value) / conversion_value (how much richer the bond trades than immediate conversion is worth)

pm.fixed_income.convertibles.conversion_value and conversion_premium implement both directly.

Why PMs care

A convertible's price behaves like a straight bond when the stock is far below the conversion price (the embedded option is deep out-of-the-money and worthless, so the bond trades on credit and rates like any other bond) and increasingly like the stock itself as the stock price rises past the conversion price (the option moves in-the-money and dominates the bond's value). That means a convertible's effective duration and equity delta both change with the stock price — a genuinely different risk profile from either a plain bond or plain equity position, and exactly the kind of instrument a multi-asset or credit-plus-equity PM uses to get asymmetric exposure: bond-like downside protection with equity-like upside participation.

Worked example

A $1,000-par convertible bond, conversion ratio 20 (20 shares per bond), trading at a price of 950 (95% of par) while the stock trades at $45:

conversion_value = 20 * 45 = $900 conversion_premium = (950 - 900) / 900 ≈ 5.56%

The bond trades 5.56% above its immediate conversion value — investors are paying a premium for the option's remaining time value plus the bond's downside floor (tests/test_munis_and_convertibles.py::test_conversion_premium_hand_example). If the stock instead traded at $47.50, conversion value would exactly equal the bond price and the premium would be zero — the breakeven point where converting immediately and holding the bond are worth the same.

Common mistakes

  • treating conversion premium as pure "overpayment" — some premium is expected and rational, since it reflects the value of the embedded option's remaining optionality (time value), not necessarily mispricing
  • ignoring the straight-bond floor — a convertible shouldn't trade below what an equivalent non-convertible bond from the same issuer would be worth, even if the stock collapses; this repo's conversion_premium is a simplified version of the CFA-standard definition (which compares bond price against max(conversion_value, straight_bond_value), not conversion value alone) — see Limitations
  • assuming conversion ratio is fixed forever — most convertibles have anti-dilution adjustments that change the ratio around stock splits, spin-offs, or large dividends

Why the straight-bond floor isn't implemented in src/pm

Pricing the straight-bond floor requires the same discounted-cash-flow machinery as bond pricing applied to the convertible's coupon/maturity at a market-appropriate credit spread — genuinely doable with functions this repo already has, but combining it correctly with the option-value side (which behaves like the Black-Scholes framework, since a convertible is economically a bond plus a call option) into one coherent convertible-bond valuation model is a larger integration project than this page's two formulas, which only capture the "as-converted" side of the story.

Free resources