Convertible Bonds as Embedded Options
Convertible Bonds as Embedded Options
Convertible bonds combine debt characteristics with an embedded option to convert into equity at a predetermined price. This hybrid structure provides bond-like downside protection with equity-like upside participation. Understanding convertibles as option structures enables more precise valuation and risk management.
Definition and Key Concepts
Convertible Bond Components
Convertible bond = Straight bond + Call option on stock
| Component | Description |
|---|---|
| Bond value | Present value of coupon and principal |
| Conversion option | Right to convert to equity |
| Call provision | Issuer's right to redeem early |
| Put provision | Holder's right to sell back (sometimes) |
Key Terms
| Term | Definition |
|---|---|
| Conversion price | Price per share implied by conversion |
| Conversion ratio | Shares received per bond (Par / Conversion price) |
| Conversion value | Current stock price × Conversion ratio |
| Parity | Conversion value as % of bond price |
| Premium | Bond price above conversion value |
| Investment value | Bond value without conversion feature |
Convertible Profiles
| Profile | Stock Performance | Bond Behavior |
|---|---|---|
| Equity substitute | Stock up significantly | Trades near conversion value |
| Balanced | Stock near conversion price | Hybrid risk/return |
| Busted | Stock down significantly | Trades like straight bond |
| Distressed | Credit concerns | Credit dominates equity |
How It Works in Practice
Conversion Mechanics
Example:
- Bond par value: $1,000
- Conversion price: $50
- Conversion ratio: $1,000 / $50 = 20 shares
- Current stock price: $55
- Conversion value: 20 × $55 = $1,100
- Bond trading price: $1,150
- Premium: ($1,150 - $1,100) / $1,100 = 4.5%
Investor choice: Convert at maturity if stock > conversion price Otherwise, receive bond principal + coupons
Payoff Profile
At maturity: Convertible payoff = max(Par, Conversion ratio × Stock price)
| Stock Price | Conversion Value | Bond Payoff | Outcome |
|---|---|---|---|
| $30 | $600 | $1,000 | Hold bond |
| $50 | $1,000 | $1,000 | Indifferent |
| $70 | $1,400 | $1,400 | Convert |
| $100 | $2,000 | $2,000 | Convert |
Embedded Option Valuation
Straight bond value: PV of coupons + PV of principal discounted at credit spread
Option value: Convertible price - Straight bond value = Option premium
Example:
- Convertible trading at: $1,150
- Straight bond value: $950 (based on credit spread)
- Embedded option value: $1,150 - $950 = $200
- Implied vol from option value: ~28%
Worked Example
Convertible Bond Analysis
Bond details:
- Issuer: Tech company, BBB rated
- Par: $1,000
- Coupon: 2% annual
- Maturity: 5 years
- Conversion price: $80
- Current stock: $75
- Stock volatility: 35%
- Credit spread: 200 bps
- Risk-free rate: 4%
Step 1: Calculate investment value (straight bond) Annual coupon: $20 PV of coupons: $20 × [1 - (1.06)^-5] / 0.06 = $84.25 PV of principal: $1,000 / (1.06)^5 = $747.26 Investment value: $831.51
Step 2: Calculate conversion value Conversion ratio: $1,000 / $80 = 12.5 shares Conversion value: 12.5 × $75 = $937.50
Step 3: Value embedded option Using Black-Scholes (simplified):
- Stock: $75
- Strike (effective): $64 (= $800 bond value / 12.5 shares)
- Time: 5 years
- Volatility: 35%
- Rate: 4%
Call option value per share: ~$32 Total option value: 12.5 × $32 = $400
Step 4: Fair value estimate Fair value ≈ max(Investment value, Conversion value) + Time value premium Fair value ≈ $937.50 + $150 = $1,087.50
Greeks of Convertibles
| Greek | Equity-Sensitive | Bond-Like |
|---|---|---|
| Delta | 0.7-1.0 | 0.1-0.3 |
| Gamma | High | Low |
| Vega | High | Low |
| Rho (credit) | Low | High |
| Duration | Low | High |
Trading Strategy: Convertible Arbitrage
Classic strategy:
- Long convertible bond
- Short underlying stock (delta hedge)
Position:
- Buy convertible at $1,087.50
- Short 8.75 shares (delta = 0.70)
- Stock at $75: short proceeds = $656.25
P/L scenarios:
| Stock Move | Conv Change | Short Stock P/L | Net P/L |
|---|---|---|---|
| +10% to $82.50 | +$65 | -$65.63 | -$0.63 |
| -10% to $67.50 | -$55 | +$65.63 | +$10.63 |
| Vol spike +5% | +$30 | $0 | +$30.00 |
| Credit tightens | +$20 | $0 | +$20.00 |
Profit sources:
- Gamma (convexity on moves)
- Volatility increases
- Credit improvement
- Coupon income
Risks, Limitations, and Tradeoffs
Credit Risk
Convertibles retain credit exposure:
| Credit Event | Impact |
|---|---|
| Downgrade | Investment value falls, premium expands |
| Default | Potentially total loss (equity worthless, bond recovery low) |
| Spread widening | Bond component loses value |
Call Risk
Issuer call provisions:
| Situation | Issuer Action | Investor Impact |
|---|---|---|
| Stock rallies | Call bond | Forced conversion, lose time value |
| Rates fall | Refinance | Reinvestment risk |
| Near call date | Uncertainty | Price volatility |
Liquidity Risk
| Issue | Description |
|---|---|
| Thin markets | Convertibles less liquid than stock or bonds |
| Wide spreads | Bid-ask can be 1-3% |
| Sizing | Large trades move markets |
| Redemption pressure | Forced selling in credit stress |
Common Pitfalls
| Pitfall | Description | Prevention |
|---|---|---|
| Ignoring credit | Focus only on equity option | Analyze credit quality |
| Wrong delta | Using theoretical vs. trading delta | Observe market sensitivity |
| Call provision | Ignoring issuer call rights | Review prospectus |
| Dilution | Anti-dilution provisions vary | Understand adjustment terms |
| Model risk | Complex structures require sophisticated models | Use appropriate tools |
Advanced Considerations
Mandatory Convertibles
Mandatory convertible:
- Converts to stock at maturity regardless
- Higher coupon than regular convertible
- Downside exposure below threshold
Payoff structure:
- Stock > Upper strike: Fixed shares (capped upside)
- Stock between strikes: Variable shares (participation zone)
- Stock < Lower strike: Fixed shares (full downside)
Contingent Convertibles (CoCos)
CoCo bonds:
- Convert to equity upon trigger event
- Used by banks for regulatory capital
- Triggers: Capital ratio, regulatory discretion
| Trigger Type | Conversion Event |
|---|---|
| High trigger | CET1 < 7% |
| Low trigger | CET1 < 5.125% |
| Discretionary | Regulator intervention |
Checklist and Next Steps
Analysis checklist:
- Calculate investment value (straight bond floor)
- Calculate conversion value
- Assess premium level
- Estimate embedded option value
- Review call provisions
- Analyze credit quality
Trading checklist:
- Determine delta for hedging
- Assess liquidity and bid-ask
- Review borrow availability for shorting
- Understand position sizing limits
- Plan for corporate actions
Risk management checklist:
- Monitor credit spread changes
- Track equity sensitivity (delta drift)
- Watch for call announcements
- Assess funding costs
- Report position Greeks
Related articles:
- For chooser options, see Chooser and Compound Options
- For auto-callables, see Auto-Callable Notes and Yield Enhancers