Convertible Bonds & Parity
Overview
Convertible corporate bonds are very similar to convertible preferred stocks, with a few key differences.
Similarities to convertible preferred stock
- Both can be converted into common stock of the same issuer
- Both provide the investor with capital appreciation potential
- Both sets of formulas are essentially the same
The key difference
The biggest difference is the par value. Preferred stock typically has a $100 par value, while bonds usually have a $1,000 par value. Aside from that, the core conversion concepts work the same way.
| Security | Typical par value | Converts into |
|---|---|---|
| Convertible preferred stock | $100 | Common stock of the same issuer |
| Convertible corporate bond | $1,000 | Common stock of the same issuer |
Conversion logistics — the two core numbers
A convertible bond’s conversion terms are usually described using two related numbers.
| Term | Definition | Example |
|---|---|---|
| Conversion ratio (CR) | How many shares you receive if you convert one bond | A 25:1 CR means 1 bond converts into 25 shares of common stock |
| Conversion price (CP) | The effective price per share you’re paying at conversion | A $40 conversion price on a $1,000 par bond implies a 25:1 conversion ratio |
Core formulas
Conversion ratio = Par ÷ conversion price
Conversion price = Par ÷ conversion ratio
Fraction reconstruction note: the source page’s fraction rendering is flattened (it prints the denominator on one line and the numerator on the next). I reconstructed both formulas above from the page’s own worked examples ($1,000 ÷ $40 = 25:1, and $1,000 ÷ 20 = $50), which confirm Par is the numerator.
📌 The conversion ratio is essential for most convertible bond math:
- If a question gives you the conversion price, use the formula above to find the conversion ratio.
- If a question already gives you the conversion ratio, you don’t need to calculate it — you already know how many shares you’ll receive.
Worked example — find the conversion ratio
A convertible bond has a conversion price of $40. What is the conversion ratio?
Conversion ratio= conversion price Par Conversion ratio= $40 $1,000 Conversion ratio=25:1
So the conversion ratio is 25:1, meaning 1 bond can be converted into 25 shares of common stock.
Worked example — find the conversion price
Sometimes you’ll be asked to go the other direction.
A convertible bond has a conversion ratio of 20:1. What is the conversion price?
Conversion price= conversion ratio Par Conversion price= 20 $1,000 Conversion price=$50
This is the same relationship as before — conversion price and conversion ratio simply swap places in the formula.
Conversion cost per share (earning a capital gain by converting)
A corporate bond has a conversion ratio of 20:1 and is purchased for 90*.
*As we learned in a previous chapter, 90 represents a percentage of par quote. This bond is trading at 90% of the bond’s $1,000 par value, or $900.
To see when conversion becomes profitable, convert the bond’s cost into a cost per share.
Conversion cost per share = bond price ÷ conversion ratio
Conversion cost per share= conversion ratio bond price Conversion cost per share= 20 $900 Conversion cost per share=$45
Fraction reconstructed: the page flattens this fraction; $900 ÷ 20 = $45 confirms bond price is the numerator.
This means the investor is effectively paying $45 per share (because $900 buys the right to receive 20 shares). If the common stock rises above $45, conversion creates a profit.
Worked example — profit on conversion
A corporate bond has a conversion ratio of 20:1 and is purchased for 90. After a few years, the common stock price rises to $60. What is the profit if the bond is converted and the common shares are sold?
Step 1: factor in bond purchase
Bond purchase=$900
Step 2: find conversion value
Conversion ratio=20:1
Conversion value=20 shares x $60
Conversion value=$1,200
Step 3: compare conversion value to original purchase
Profit=conv. value - original purchase
Profit=$1,200 - $900
Profit=$300
Convertible bonds offer added return potential because of the conversion feature. Because investors are getting that potential upside, issuers can typically offer lower interest rates, and these bonds tend to trade at lower yields (higher prices) than comparable non-convertible bonds.
Parity prices
How do you know when conversion is attractive? Just like we explored in a previous chapter with preferred stock, parity prices help you compare the bond’s conversion terms to the stock’s market price.
| Parity measure | What it answers | Formula |
|---|---|---|
| Stock parity price (PPoCS) | The effective price per share if you buy the bond at its market price and convert it | Stock PP = bond market price ÷ conversion ratio |
| Bond parity price (BPP) | Based on the stock’s market price, what the bond should be worth based only on its conversion feature | Bond PP = stock price × conversion ratio |
Common confusion: the stock parity price divides by the conversion ratio; the bond parity price multiplies by it.
Stock parity price — worked example
A corporate bond has a conversion ratio of 20:1 and is purchased for 90. What is the parity price of the common stock?
Stock PP= conversion ratio bond market price Stock PP= 20 $900 Stock PP=$45
Fraction reconstructed: Stock PP = bond market price ÷ conversion ratio ($900 ÷ 20 = $45).
A $900 bond converted into 20 shares produces an effective cost of $45 per share. If the stock trades above $45, conversion produces a profit. In the earlier example, the stock traded at $60, which is a $15 per share difference.
Stock parity price — practice question
A 10%, $1,000 par convertible corporate bond with a conversion price of $20 is purchased at 110. The common stock is currently trading at $25. What is the parity price of the stock?
Answer = $22
The first step is calculating the conversion ratio.
Conversion ratio= conversion price Par Conversion ratio= $20 $1,000 Conversion ratio=50:1
Now calculate the stock’s parity price using the bond’s market price ($1,100) and the conversion ratio (50:1).
Stock PP= conversion ratio bond market price Stock PP= 50 $1,100 Stock PP=$22
This question does not require two pieces of information: the coupon (10%) and the stock’s market price ($25). The stock price isn’t needed to compute parity, but it does tell you whether immediate conversion would be profitable.
Buying the bond for $1,100 and converting into 50 shares creates an effective cost of $22 per share (the parity price). With the stock trading at $25, there is an arbitrage opportunity: buy the bond, convert, and sell the shares for a $3 per share difference.
Bond parity price — worked example
Bond parity price answers the reverse question: based on the stock’s market price, what should the bond be worth based only on its conversion feature?
A corporate bond has a conversion ratio of 10:1 and is purchased, while the common stock trades at $90. What is the parity price of the bond?
Bond PP=stock price x conversion ratio
Bond PP=$90 x 10
Bond PP=$900
If the bond trades in the market below $900, an investor could buy the bond, convert it, and sell the shares for more than the bond’s purchase price — an immediate arbitrage profit.
Bond parity price — practice question
A 7%, $1,000 par convertible corporate bond with a conversion price of $10 is purchased at 95. The common stock is currently trading at $8. What is the parity price of the bond?
Answer = $800
The first step is calculating the conversion ratio.
Conversion ratio= conversion price Par Conversion ratio= $10 $1,000 Conversion ratio=100:1
Now calculate the bond’s parity price using the stock’s market price ($8) and the conversion ratio (100:1).
Bond PP=stock price x conversion ratio
Bond PP=$8 x 100
Bond PP=$800
Two pieces of information are not required in this question — the coupon (7%) and the bond’s market price ($950). The bond’s market price isn’t needed to compute parity, but it does tell you whether an arbitrage trade exists.
A bond convertible into 100 shares of stock trading at $8 should be worth at least $800 based on conversion value. Since the bond is trading at $950, there is no arbitrage opportunity. Arbitrage would exist only if the bond could be purchased for less than $800, converted, and the shares sold for $800.
Callable convertible bonds
| Term | Definition | Example |
|---|---|---|
| Callable | The issuer can redeem (“call”) the bonds before maturity at a stated call price | A bond callable at 101 |
| Tender | Surrendering the bond to the issuer in exchange for the call price | Bondholders may be asked to tender the bond when it is called |
| Call price | The stated price the issuer pays, quoted as a percentage of par | Callable at 101 = 101% of par = $1,010 for a $1,000 bond |
Investors compare the call price to the bond’s conversion value to determine whether it is better to tender the bond or convert it into common stock.
Anti-dilution covenants
Like convertible preferred stock, convertible bonds are typically issued with anti-dilution covenants.
Setting the baseline (parity)
Assume the following:
- $1,000 par convertible bond
- Convertible bond market price = $1,000
- Conversion ratio = 40:1
- Common stock market price = $25
In this circumstance, the conversion feature is at breakeven (parity). Buying the bond for $1,000, converting into 40 shares, and selling those shares for $1,000 total ($25 x 40) produces no gain or loss.
Conversion becomes profitable if the stock price rises above $25. Issuers and their employees generally don’t like conversions because conversion creates new common shares. That increases the number of shares outstanding and can dilute both ownership percentage and value for existing shareholders (including officers and directors).
Why a stock split would dilute the bondholder
A forward stock split increases the number of shares outstanding and lowers the market price per share. If the conversion terms didn’t adjust, the conversion feature could lose value.
Assume the following:
- $1,000 par convertible bond
- Convertible bond market price = $1,000
- Conversion ratio = 40:1
- Common stock market price = $25
- 2:1 stock split
| Common stock price | Conversion value (at CR 40:1) | |
|---|---|---|
| Pre-split | $25.00 | $1,000 ($25.00 x 40) |
| Post-split | $12.50 | $500 ($12.50 x 40) |
A 2:1 stock split doubles the number of shares outstanding, and each share trades at half its prior price. If the conversion ratio stayed at 40:1, the conversion value would drop from $1,000 to $500. That’s dilution from the convertible bondholder’s perspective.
Anti-dilution covenants are designed to prevent this by requiring the issuer to adjust the conversion terms.
Anti-dilution — full worked example
An investor purchases a $1,000 par, 5% convertible bond with a conversion price of $50. The common stock is currently trading at $40. The issuer performs a 4:1 stock split on the common stock. What are the conversion price and ratio adjustments if the bond contains an anti-dilution covenant?
Start by finding the original conversion ratio.
CR= Conversion price Par CR= $50 $1,000 CR=20:1
Initially, the bond converts into 20 shares. With the stock at $40, the conversion feature is worth $800 ($40 x 20).
After a 4:1 stock split, the stock price adjusts downward.
New common stock price= Stock split factor Current market price New common stock price= 4 $40 New common stock price=$10
Fraction reconstructed: New common stock price = current market price ÷ stock split factor ($40 ÷ 4 = $10).
If the conversion terms didn’t change, the bond would still convert into 20 shares, now worth $10 each, for a total of $200. The anti-dilution covenant requires adjustments so the conversion feature keeps the original $800 value.
To adjust the conversion ratio, multiply the original conversion ratio by the stock split factor.
New conversion ratio=20 x 4
New conversion ratio=80
Now the bond converts into 80 shares. At $10 per share, the conversion value is back to $800 (80 x $10).
Do you know what the new conversion price would be? Answer = $12.50
You can find this two ways.
Method 1: use the stock split factor — divide the original conversion price ($50) by the stock split factor (4).
New conversion price= 4 $50 New conversion price=$12.50
Method 2: use the new conversion ratio — if you already have the new conversion ratio (80), use the conversion price formula.
CP= Conversion ratio Par CP= 80 $1,000 CP=$12.50
🔑 Anti-dilution adjustment direction on a stock split:
| Item | Direction | 4:1 split example |
|---|---|---|
| Conversion ratio | Goes UP (× split factor) | 20:1 → 80:1 |
| Conversion price | Goes DOWN (÷ split factor) | $50 → $12.50 |
| Common stock price | Goes DOWN (÷ split factor) | $40 → $10 |
| Conversion value | Unchanged | $800 → $800 |
Key points
Convertible bonds
- Converts to common stock of the same issuer
- Investors eligible to make capital gains on stock
- Sold with lower dividend rates (vs. non-convertible)
- Higher prices & lower yields
Conversion ratio
CR= conversion price Par
Conversion price
CP= conversion ratio Par
Common stock parity price
- Price paid per common share based on convertible security market price
PPoCS= Conversion ratio Convertible bond market price
Bond parity price
- Value of bond based only on the conversion feature
BPP=stock price x conv. ratio
Anti-dilution covenant
- Prevents issuer from performing dilution actions without adjusting the conversion feature
- Involved when stock splits occur
- Conversion ratio goes up
- Conversion price goes down
Fraction reconstruction reminder — the Key points fractions above are reproduced verbatim from the flattened page text. Correctly read, they are: CR = Par ÷ conversion price, CP = Par ÷ conversion ratio, and PPoCS = convertible bond market price ÷ conversion ratio.
Sources
Primary/official references for the material in this chapter. Every link was fetched and returned HTTP 200 on 2026-08-15.
| # | Source | Publisher |
|---|---|---|
| 1 | Bonds — coupon, maturity, price/yield, credit risk | SEC / Investor.gov |
| 2 | Stocks — common vs preferred, dividends, voting | SEC / Investor.gov |
| 3 | Securities Act 1933 — definition of security, issuer | Cornell LII (15 U.S.C. 77b) |
| 4 | Achievable Series 65 — chapter 1.2.5 | Achievable (course text) |