Quick Answer
A convertible bond lets the holder, at the holder's option, exchange the bond for a fixed number of common shares. It pays a lower coupon in exchange for that conversion privilege. Conversion ratio, parity price, arbitrage, and forced conversion are the calculation-heavy concepts the exam tests most on this topic.
With your understanding of bond types in place, you're ready to tackle convertible bonds, a hybrid security that combines features of both debt and equity. This is one of the most calculation-heavy topics in the corporate bonds unit.
What Are the General Characteristics of a Convertible Bond?
A convertible bond gives the bondholder the right to convert the bond into a fixed number of shares of the issuer's common stock.
Key features:
- Conversion is at the bondholder's option (not the issuer's)
- Convertible bonds pay a lower coupon rate than comparable non-convertible bonds because the conversion feature has value
- Once converted, the bondholder gives up the bond (and future interest payments) in exchange for stock
- The conversion feature is an advantage to the investor; they get to choose if and when to convert
Exam Tip: Gotchas
- Conversion is the bondholder's choice, NOT the issuer's. The exam may phrase this as "at the option of the holder."
- Convertible bonds pay LOWER coupons than comparable non-convertible bonds (not higher) because the conversion privilege has value.
How Do Conversion Ratio and Conversion Price Work?
The two key terms are inversely related:
| Term | Formula | Example |
|---|---|---|
| Conversion price | Stated in the indenture | $50 per share |
| Conversion ratio | Par Value / Conversion Price | $1,000 / $50 = 20 shares |
- The conversion ratio is fixed at issuance and does not change
- Exception: adjusted for stock splits or stock dividends to prevent dilution
- Higher conversion price = lower conversion ratio (inverse relationship)
Exam Tip: Gotchas
- The conversion ratio is fixed at issuance and only adjusted for stock splits or stock dividends. Market price changes do NOT affect it.
How Do You Calculate Parity Price?
The parity price is the price at which the bond and the stock have equal value upon conversion.
| Calculation | Formula |
|---|---|
| Parity price of the stock | Bond Market Price / Conversion Ratio |
| Parity price of the bond | Stock Market Price x Conversion Ratio |
Worked example (Bond at $1,100, conversion ratio = 20):
| Stock Price | Conversion Value | Relationship | Conversion Comparison |
|---|---|---|---|
| $55 | $55 x 20 = $1,100 | At parity (bond = conversion value) | Equal market value before costs |
| $60 | $60 x 20 = $1,200 | Bond below parity ($1,100 < $1,200) | Conversion gives $100 more in market value before costs |
| $45 | $45 x 20 = $900 | Bond above parity ($1,100 > $900, a conversion premium) | Conversion gives up $200 in market value before costs |
- Stock parity = $1,100 / 20 = $55 per share
- If stock trades at $55, the bond and stock are at parity
Think of it this way: Parity compares the bond's current market price with the value of the shares received on conversion. At parity, those market values are equal before costs. Below parity, conversion gives shares worth more than the bond; above parity, conversion gives up the bond's premium over those shares. Coupon income and the investor's objective also matter when deciding whether to convert.
Exam Tip: Gotchas
- A stock price above the conversion price puts conversion value above the bond's par value, not necessarily above its market price. A convertible can track an appreciated stock while still trading above parity. For a current-income investor, converting into non-dividend-paying shares ends the coupon income; if the bond is above parity, it also sacrifices the conversion premium.
How Do You Compare Income Before Converting?
Compare dollars per year, not percentages:
- Bond income = coupon rate x $1,000 par value. A 5% coupon pays $50 a year.
- Share income = dividend per share x conversion ratio. This is the dividend on the shares received.
A coupon rate is a percentage of par value. A dividend yield is a percentage of the stock price. The two use different bases, so a dividend yield above a coupon rate does not prove the shares pay more.
Worked example (5% coupon, conversion ratio = 20, stock at $45, bond at parity):
| Item | Calculation | Annual income |
|---|---|---|
| Bond | 5% x $1,000 | $50.00 |
| Shares | 5.5% dividend yield x $45 x 20 shares | $49.50 |
The 5.5% dividend yield beats the 5% coupon rate, yet the shares pay $0.50 less in dollars. Conversion also ends the bond's claim on the issuer and its price floor.
Exam Tip: Gotchas
- Before you pick "convert for more income," compare the bond's annual interest in dollars with the annual dividends on the shares received. Two percentages on different bases do not settle it.
How Does Convertible-Bond Arbitrage Work?
When the conversion value exceeds the bond's market price, an arbitrage opportunity exists:
- Buy the underpriced bond
- Convert to stock
- Sell the stock at market price for a profit
Arbitrage activity quickly eliminates pricing discrepancies and brings the bond back to parity.
What Factors Influence Conversion?
How a convertible bond trades depends on where the stock price is relative to the conversion price:
| Condition | Bond Behavior | Driven By |
|---|---|---|
| Stock price well above conversion price | Trades like equity | Stock price movements |
| Stock price well below conversion price | Trades like a bond | Yield and credit quality |
| Stock price near conversion price | Hybrid behavior | Both factors |
- The bond's investment value (what it would be worth as straight debt without the conversion feature) provides a price floor against a stock-driven decline. That value changes with interest rates and issuer credit quality; it is not guaranteed par value.
Exam Tip: Gotchas
- The investment value (straight-bond value) acts as a price floor when the stock falls. The floor can fall too if the issuer's ability to pay deteriorates.
What Is Forced Conversion?
Forced conversion is an economic mechanism, not a direct mandate:
- The issuer calls the bond at the call price (e.g., $1,050)
- If the conversion value exceeds the call price (e.g., stock at $60 x 20 shares = $1,200), the bondholder is economically compelled to convert
- A rational investor takes $1,200 in stock rather than accepting $1,050 in cash
Exam Tip: Gotchas
- "Forced conversion" does NOT mean the issuer directly forces conversion. The issuer calls the bond at, say, $1,050. If conversion value is $1,200, a rational bondholder converts rather than accepting $1,050. The exam tests whether you understand this economic incentive mechanism.
What Is the Difference Between Fixed and Variable Conversion?
| Type | Description | Frequency |
|---|---|---|
| Fixed conversion | Conversion ratio stays constant throughout the bond's life | Most common |
| Variable conversion | Conversion ratio changes over time per a schedule in the indenture | Less common; may decrease over time to incentivize early conversion |
What Should You Check on Exam Day?
- Confirm conversion is always the bondholder's choice, and that convertibles pay a lower coupon than comparable non-convertible bonds.
- Recalculate the conversion ratio from Par Value / Conversion Price rather than assuming it from memory.
- Match the parity formula to what you are solving for: stock parity divides the bond price by the ratio; bond parity multiplies the stock price by the ratio.
- Work through forced conversion as an economic comparison between the call price and the conversion value, not a literal mandate.
- Remember that straight-bond value can support the convertible even if the stock price falls to zero; issuer credit risk still matters.