Convertible Bond Arbitrage: Profiting from Debt-Equity Mispricing

Key Takeaways

• Convertible arbitrage is a relative-value strategy that goes long convertible bonds and hedges equity exposure by shorting the underlying stock to isolate mispricing between debt and converted equity.
• The core risks are credit, interest rate, dividend and financing cost exposure, plus model risk from delta and vega hedging; dynamic rebalancing and stress testing are essential.
• You manage equity risk by delta-hedging the embedded option and manage volatility exposure with options or variance trades; financing terms and repo rates materially affect returns.
• Practical P/L comes from coupon carry, convergence of credit spread or option price, and exploiting transient volatility or liquidity dislocations, not pure directional bets on the stock.
• Common failures come from underestimating event risk, using static hedges, poor repo management, and mispricing of conversion features; contingency planning prevents forced liquidations.

Introduction

Convertible bond arbitrage is a hedged, relative-value trading strategy that profits from mismatches between a convertible security's debt characteristics and its embedded equity option. In simple terms, you buy the convertible bond and short the underlying stock to neutralize directional equity exposure while capturing carry and expected convergence.

This matters because convertibles sit at the intersection of fixed income, equity derivatives, and credit markets, creating opportunities when one leg is mispriced relative to the others. If you want to exploit volatility dislocations or credit spread tightening without a pure equity bet, this strategy can be attractive, but it requires precision in hedging, financing, and risk management.

You'll learn the mechanics of hedging the embedded option, the drivers of returns, practical P/L examples with numbers, and how to manage the credit, financing, and volatility risks that break convertible arbitrage funds.

How Convertible Bonds Work and Why They Misprice

Convertible bonds are corporate debt instruments that can be converted into a fixed number of shares. They pay coupon and have credit risk like regular bonds, but they also include an embedded equity call option. That hybrid nature creates multiple pricing inputs: interest rates, credit spreads, stock price, dividend expectations, and implied volatility.

Mispricing arises when one market — say corporate credit or equity options — moves faster than the other, or liquidity dries up in one leg. For instance, a sudden widening in credit spreads may drop bond prices, while option values embedded in convertibles do not fall proportionally because equity markets remain calm. That gap is the arbitrage opportunity.

Core Mechanics of the Arbitrage Trade

At its simplest, the trade is long one convertible bond and short the delta-equivalent number of shares. You keep the bond's coupon and potential upside in conversion, while the short equity hedge limits your exposure to stock declines. Over time, you rebalance to maintain a neutral delta as the stock moves and as option greeks change.

Key quantities you must compute

• Conversion ratio: shares per bond, usually par divided by the conversion price.
• Delta: sensitivity of the convertible to a small move in the underlying stock, often derived from option models times the conversion ratio.
• Vega: sensitivity to implied volatility changes, which drives option value and can create directional P/L when volatility moves.
• Credit spread and interest rate sensitivity, which affect the straight bond component.

Dynamic delta hedging

Delta is not static. As the stock price or implied volatility changes, the convertible's delta changes and you must rebalance your short position. Many funds rebalance intraday for large moves and daily for routine drift. You have to balance transaction costs against hedging error, so choose a rebalance rule that fits your liquidity profile.

Sources of Return and How They Add Up

There are three principal return sources: carry, convergence, and volatility capture. Carry comes from coupon income minus the financing cost of your net position. Convergence is the profit realized when bond yields and option prices realign. Volatility capture earns you returns when implied volatility mean-reverts or when you capture mispriced vega.

At the end of the day, successful convertible arbitrage generates positive expected returns with limited directional equity exposure, but you must actively manage financing and credit exposures that can erode or reverse those returns.

Example components with numbers

• Coupon carry: a 3% coupon on a $1,000 bond yields $30 annually before financing.
• Financing cost: if you short shares and borrow funds at 4% annual, that reduces carry.
• Expected convergence: if the convertible currently trades 5% cheap relative to model fair value, you expect to capture that gap over time if nothing adverse happens.

Worked Numerical Example

Walk through a concrete, realistic scenario to make things tangible. Suppose a convertible with $1,000 face value converts at $50 per share, so conversion ratio is 20 shares. The underlying stock trades at $40. The convertible trades for $930. The conversion value is 20 times $40, or $800, so the convertible trades with $130 of option and bond spread value above conversion value.

Assume the option delta per convertible equates to 6 shares, so you short 6 shares to be delta neutral for each bond. You receive coupon payments of 3% on the bond, $30 annually. Your net financing cost for the hedge and bond funding, including repo and borrowing fees, totals 4% annual, or $40 on $1,000 par. Your starting carry is negative $10 per year before other P/L sources.

Now suppose implied volatility drops and the option component falls by $100 while credit spreads remain stable, reducing the convertible price to $830. Your bond loses $100 in value but your short stock position gains because the effective delta exposure was hedged. If your short 6 shares P/L offsets most of the bond decline, you net a gain from the option contraction minus financing and transaction costs. Conversely, if credit spreads widen, the bond could fall with little offset from the equity hedge and you incur losses.

Risk Management: What Breaks Convertible Arbitrage

Convertible arbitrage failures are usually not from small model errors, they come from large, correlated shocks. You need frameworks for liquidity risk, event risk, and financing stress. That means stress-testing worse-case scenarios and planning for rapid rebalancing or orderly exit.

Main risks explained

1. Credit/Event risk: A credit downgrade or covenant breach can collapse the bond while the equity may not compensate. This is a tail risk that can overwhelm hedges.
2. Financing and repo risk: Shorting requires borrowing stock and funding the position. If repo rates spike or you face recall on a borrow, costs or forced cover can destroy returns.
3. Dividend and corporate actions: Unexpected dividends, special dividends, or calls change the convertible's economics and force hedge adjustments.
4. Model risk and gamma: Aggressive gamma exposure requires frequent rebalancing, increasing transaction costs. A gap move during low liquidity can create large losses.
5. Concentration and liquidity: Large positions in a single issuer or in illiquid convertibles increase execution risk if you need to exit quickly.

How to mitigate these risks

• Set position limits by issuer and sector and stress-test for credit events and rapid implied volatility moves.
• Maintain multiple financing lines and a diversified set of securities available for rehypothecation and margin calls.
• Use options or variance swaps to hedge vega exposure when the convertible's option sensitivity is material and costly to hedge by delta alone.
• Implement liquidity-adjusted rebalance triggers that balance P/L risk against transaction costs, and use limit orders around earnings and known corporate action dates.

Practical Execution: Trading, Financing, and Operations

Execution quality matters. You need tight execution on both bond and equity legs to capture small pricing anomalies. The typical toolkit includes a convertible pricing model, real-time greeks, a robust repo desk, and automated rebalancing rules to manage intraday flows.

Financing nuance

Financing costs vary by security and over time. Hard-to-borrow equities can add substantial borrow fees. Bonds used as collateral may receive favorable repo rates, but haircuts and margin calls can change under stress. Always price your trade at likely funded rates, not theoretical overnight rates.

Operational controls

• Pre-trade risk checks that validate conversion ratios and corporate terms, including call or put provisions.
• Automated P&L attribution that separates coupon, carry, delta-hedge P/L, and credit spread movements.
• Regular reconciliation of borrow positions and contingency plans for shares recalled by lenders.

Real-World Examples and Scenarios

Consider a hypothetical fund long a $1,000 par convertible from $TSLA with a conversion price implying 10 shares per bond, and short the delta-equivalent shares. If $TSLA announces a sudden rights offering or a credit event, the convertible could reprice dramatically while the stock response is ambiguous. The fund may face a margin call if the bond sells off faster than the short gains, forcing deleveraging at the worst time.

Another scenario: during market-wide volatility spikes, implied vol jumps and convertible prices rise more than the underlying stocks. If you had shorted the equity without dynamically adjusting delta, you could be exposed to losses as equity rallies on re-risking. Using options to hedge vega could have limited that exposure.

Common Mistakes to Avoid

• Under-hedging delta and ignoring gamma risk, which leads to large losses on gaps. Avoid by setting disciplined rebalance rules and simulating gap scenarios.
• Ignoring financing liquidity and single-lender concentration. Maintain multiple borrow sources and model repo-run scenarios to avoid forced covers.
• Relying on static models without recalibrating implied vol and credit parameters. Recalibrate models frequently and use market-implied inputs when available.
• Assuming dividend timing and amounts are fixed. Monitor corporate calendars and treat unexpected distributions as scenario risks to be hedged or sized accordingly.
• Overconcentrating in illiquid convertibles to chase yield. Enforce issuer and liquidity limits and plan exits before you need them.

FAQ

Q: How frequently should I delta-hedge a convertible position?

A: There is no one-size-fits-all schedule. Many funds rebalance intraday for large moves and daily for routine drift. Choose a rule based on liquidity, transaction cost estimates, and your tolerance for hedge error. Backtest rebalance frequency against historical volatility to find a balance between cost and risk.

Q: Can convertible arbitrage be replicated with options alone?

A: Not easily. Convertibles combine bond and option characteristics plus issuer credit terms that options do not replicate precisely. Options can hedge vega or add synthetic positions, but the credit and carry of the bond are central to the strategy and are not captured by plain vanilla equity options.

Q: What financing metrics should I monitor daily?

A: Track repo and borrow rates, borrow availability and recall risk, funding spreads for the bond and any collateral, and margin utilization. Also monitor intraday moves that could trigger margin increases under bilateral agreements.

Q: How do events like a convertible being called affect the arbitrage trade?

A: A call compresses optionality and typically forces conversion or early redemption, often at a disadvantageous price for the convertible holder. You must model call features up front and maintain a contingency plan to unwind or adjust hedges when call risk increases, especially near call-protection expiration dates.

Bottom Line

Convertible bond arbitrage is a sophisticated relative-value strategy that requires integrated expertise in fixed income, equity derivatives, and financing. The strategy can deliver attractive risk-adjusted returns, but only with disciplined hedging, diversified financing, and rigorous stress testing.

If you trade or allocate to this strategy, focus on execution quality, model calibration, and contingency planning for credit and funding shocks. Start with small, well-understood positions, monitor live greeks and financing metrics, and build repeatable processes before you scale up your exposure.

Convertible arbitrage rewards careful preparation and dynamic risk management. If you want to pursue it, refine your hedging rules, simulate extreme scenarios, and treat financing as a core part of your trade thesis, not an afterthought.