Convertible Bond

Also known as: Convert, CB

A bond with an escape hatch into shares: downside of a bond, upside of a stock — priced in between.

3 min read · 574 words · Updated

1 · SnapshotThe one idea to remember
Key intuition: convert = bond + call option. At low share prices it behaves like credit; at high prices like equity; in between it is the market's most famous hybrid.
2 · BeginnerWhat is it, really?

A convertible bond starts life as a normal corporate bond — fixed coupons, principal back at maturity — but carries a golden ticket: the holder may swap the bond for a fixed number of shares whenever that's more attractive.

If the stock soars, you convert and ride the equity. If it stagnates or falls, you keep collecting coupons and get your principal back like any bondholder. Downside cushioned, upside open — you pay for this via a lower coupon than a plain bond would offer.

Issuers — often growth companies with expensive debt and volatile shares — like converts because the embedded option lets them borrow cheaply, betting that conversion (dilution) is a happy problem to have.

Convertible value vs. share price: bond floor at low prices, tracking parity at high prices.
ConvertibleBond floorParityShare priceConvertible value

Point at a line to pick it out from the others.

A bond with an exit into shares
The holderlends, and may convertThe companythe issuer1The face amount, lent2A coupon, below theplain-bond rate3The bond, surrendered4Newly issued shares5Face value, at maturity

a paymentonly if a condition is met

Two instruments in one document, and the holder chooses which one it turns out to have been.

At issue

  1. The holder → The company The company receives the money and owes it back, exactly as with any bond.

Every period

  1. The company → The holder The holder accepts less interest because the conversion right is worth something. That discount is what the company is really selling.

If the shares do well

  1. The holder → The company The holder converts at the agreed ratio rather than waiting for repayment.
  2. The company → The holder The company issues shares instead of repaying cash. Existing shareholders are diluted — the price of the cheap coupon.

If they do not

  1. The company → The holder The conversion right expires unused and the holder is repaid as an ordinary creditor, ranking above shareholders.
Asset class
Hybrid (credit + equity)
Instrument type
Bond with embedded call option
Traded
OTC (institutional)
Typical users
Convert arb funds, income investors, growth companies

Which risks decide the outcome

Not how risky this is, and not a rating — there is deliberately no total. It says which of five failure modes drives what happens here, in the same order on all 129 products so they can be compared. This publication's own reading; see the notice below.

  • Marketdecides it
  • Creditdecides it
  • Liquiditymatters
  • Fundingmatters
  • Operationalbarely applies

What decides it here. Two risks in one document. Below the conversion price it is a bond and the issuer's solvency decides; above it, the share price does.

What the five mean, and which one decides where →

3 · IntermediateHow it works in practice

The vocabulary

  • Conversion ratio: shares received per bond. Conversion price = face / ratio.
  • Parity = ratio × share price — the bond's value if converted right now.
  • Bond floor = value as a straight bond (coupons + principal discounted at the issuer's credit spread).
  • Premium = convert price − parity: what you pay for the option and the floor.

Issuer options complicate life

  • Call provisions: after a period, the issuer may redeem early (usually if the stock trades above a trigger ≈ 130% of conversion price) — forcing holders to convert and capping the option's life.
  • Puts: holders sometimes may sell back at par on set dates — a valuable floor-raiser.

Convertible arbitrage

The classic hedge-fund trade: buy the convert, short delta shares against it, and capture the embedded option cheaply (converts often issue "cheap" to vol). The book earns from gamma trading and coupon carry, and suffers when credit gaps or borrow disappears.

Worked example: €1,000 face, ratio 20 (conversion price €50), stock at €40. Parity = €800; bond floor ≈ €920; convert trades at €980. You pay a 22.5% premium to parity for downside protection plus optionality.
4 · AdvancedPricing & valuation

Pricing: a contingent claim on two risk factors

A convert depends on the share price (equity risk) and the issuer's survival (credit risk) — inseparably, since default crushes both bond and shares. The standard framework is a PDE/lattice with an equity-dependent default intensity \(\lambda(S)\):

$$ \frac{\partial V}{\partial t} + \tfrac{1}{2}\sigma^2 S^2 \frac{\partial^2 V}{\partial S^2} + \big(r + \lambda(S)\big) S \frac{\partial V}{\partial S} - \big(r + \lambda(S)\big)V + \lambda(S)\,R(S) + c = 0 $$
What the symbols mean
  • Va value
  • ta point in time
  • sigmavolatility, the standard deviation of returns
  • Sthe price of the underlying today
  • rthe interest rate, per year
  • lambdaan intensity, usually of defaults per year

with recovery \(R\), coupon flow \(c\), and free-boundary conditions at each node: \(V \ge \text{parity}\) (holder converts), \(V \le \max(\text{call price}, \text{parity})\) (issuer calls), \(V \ge \text{put price}\) on put dates. Typically \(\lambda(S) = \lambda_0 (S_0/S)^{\alpha}\) — spreads blow out as the stock falls, generating the realistic "credit cliff".

Greeks worth naming

  • Delta rises from ~0 (busted convert) to ~ratio (deep ITM); gamma peaks near the conversion price.
  • Rho/credit DV01: dominant when busted — the convert is then a distressed bond.
  • Vega: converts are long equity vol; issuance waves cheapen listed vol via arb hedging.

Market conventions

Desks quote implied vol given a credit-spread assumption (or vice versa) — the "vol-credit smile" of the convert market. Documentation details (dividend protection via ratio adjustments, takeover ratchets) materially move value and are priced explicitly.

The formulas above are standard textbook formulations, simplified for teaching. They explain the mechanism — they are not a valuation tool, and they will not reproduce a dealer’s price.

5 · Desk notesHow practitioners think about it
Practitioner note: the same convert can be an equity trade, a vol trade or a credit trade depending on moneyness — know which one you own today.

Now say it back

Close the page and give Convertible Bond in four sentences. It takes a minute and it is the only way to find out whether reading it was enough.

  1. Who wants what — two parties wanted opposite things badly enough to write it down.
  2. What the contract obliges, and when — not the payoff; the obligation.
  3. Where the money comes from — name the source, or you have described a hope.
  4. What makes it lose — the ordinary way, not the dramatic one.

Do it with a clock → · why these four

Put Convertible Bond beside any other instrument →

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Where this instrument shows up elsewhere

  • EasyThe Bond vs. the Share of the Same CompanyCompareOne company, two claims on it, and almost nothing else in common
  • EasyVenture CapitalIndustryFunding companies that mostly will not work, in sizes chosen so that the ones that do can pay for all of them
  • MediumEcmDeskHow a company lists and raises equity: the bookbuild, the price range, allocation, the greenshoe and the lock-up —…
  • MediumWhich Desk Trades WhatPrepEleven trading seats and six that sit next to them: what each one actually touches, the single number it lives by,…
  • HardConvertible bond issueDealA bond that can become shares
  • HardRelative ValueIndustryTwo things that should cost the same and do not — a small difference, held in size, financed by somebody else

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