Convertible arbitrage

What Is Convertible Arbitrage?

Convertible arbitrage is a sophisticated hedge fund strategy within the broader category of alternative investments that seeks to profit from pricing inefficiencies between a company's convertible securities and its underlying common stock. It typically involves taking a long position in a convertible bond or convertible preferred stock while simultaneously taking a short position in the issuer's common equity. The goal of this strategy is to create a market-neutral position, aiming to generate returns largely independent of overall market movements¹⁷, ¹⁸. By exploiting the embedded call option within the convertible security, convertible arbitrageurs attempt to capture profits from the bond's fixed-income characteristics and the equity's potential price movements, while hedging out a significant portion of market risk.

History and Origin

The concept of convertible securities, which form the basis of convertible arbitrage, dates back centuries. Convertible bonds, instruments combining features of both debt and equity, emerged in English capital markets as early as 1798 when the Ashton-under-Lyne Canal Company issued five-year convertible loans¹⁶. This financial innovation later spread to the United States through canal and railroad companies seeking to raise capital¹⁴, ¹⁵.

The modern practice of convertible arbitrage as a distinct arbitrage strategy gained prominence with the evolution of financial markets and the increasing complexity of convertible instruments. Its rise as a significant hedge fund strategy occurred particularly in the late 20th and early 21st centuries, as sophisticated investors sought ways to generate returns with lower correlation to traditional equity and bond markets¹², ¹³. Managers began systematically exploiting what they perceived as consistent underpricing of the embedded equity call option component of convertible bonds, particularly at their issuance¹¹.

Key Takeaways

• Convertible arbitrage is a market-neutral strategy involving a long position in a convertible security and a short position in the underlying common stock.
• Its primary aim is to exploit pricing discrepancies between the debt and equity components of a convertible instrument.
• The strategy typically employs delta hedging to minimize exposure to the underlying stock price movements.
• Returns from convertible arbitrage are generally uncorrelated with traditional equity and fixed income markets, making it an attractive diversification tool.
• The strategy faces risks such as liquidity constraints, credit deterioration of the issuer, and changes in implied volatility.

Formula and Calculation

The core of convertible arbitrage involves assessing the fair value of a convertible bond, which can be viewed as a traditional bond plus an embedded call option. The strategy aims to profit when the market price of the convertible bond deviates from its theoretical value.

The theoretical value of a convertible bond ((CB_{value})) can be approximated as the sum of its straight bond value ((Bond_{value})) and the value of the embedded call option ((Option_{value})):

Where:

• (Bond_{value}): The present value of the convertible bond's future coupon payments and its principal repayment, discounted at a rate appropriate for a non-convertible bond of similar risk and maturity. This value is influenced by prevailing interest rates and the issuer's credit risk.
• (Option_{value}): The value of the embedded call option, which gives the holder the right to convert the bond into a specified number of common shares. This is typically valued using an option pricing model, such as the Black-Scholes model, considering factors like the underlying stock price, strike price (implied by the conversion ratio), time to maturity, volatility, and risk-free interest rate.

A key calculation in managing a convertible arbitrage position is the delta, which represents the sensitivity of the convertible bond's price to changes in the underlying stock price. For hedging purposes, the number of shares to short is determined by multiplying the number of convertible bonds held by the conversion ratio and the bond's delta.

Interpreting Convertible Arbitrage

Interpreting convertible arbitrage involves understanding its objective: generating returns from mispricings while largely neutralizing market exposure. Success is often measured by the strategy's ability to produce consistent positive returns regardless of whether the broader stock or bond markets are rising or falling. This "market-neutral" characteristic is achieved through the careful balancing of the long convertible position with a short selling position in the underlying equity.

Arbitrageurs interpret opportunities by identifying convertible bonds that are trading below their theoretical fair value, particularly when the implied volatility of the embedded option is low compared to the historical or expected future volatility of the underlying stock¹⁰. A high-quality convertible arbitrage strategy would demonstrate low correlation to traditional asset classes and a relatively stable return profile, ideally with limited drawdowns during periods of market stress. Conversely, underperformance might indicate issues with trade selection, risk management, or a lack of suitable mispricing opportunities in the market.

Hypothetical Example

Consider "Tech Growth Inc." which has issued a convertible bond. The bond has a face value of $1,000, a coupon rate of 2%, and is convertible into 20 shares of Tech Growth Inc.'s common stock. The current stock price is $45 per share.

An arbitrageur identifies that the convertible bond is trading at $980, while its calculated theoretical value (considering the straight bond component and the embedded call option) is $1,010. This indicates a potential underpricing.

To execute a convertible arbitrage trade, the investor would:

1. Long the Convertible Bond: Purchase 100 Tech Growth Inc. convertible bonds for $98,000 (100 bonds * $980/bond).
2. Short the Common Stock: Calculate the delta of the convertible bond. Let's assume the delta is 0.50 (meaning for every $1 change in the stock price, the convertible bond changes by $0.50). Each bond can be converted into 20 shares. So, for 100 bonds, the equivalent shares are 2,000 (100 bonds * 20 shares/bond). The number of shares to short would be 1,000 shares (2,000 equivalent shares * 0.50 delta). The investor sells 1,000 shares of Tech Growth Inc. common stock short at $45 per share, generating $45,000.

Now, imagine the stock price rises to $50 per share.

• The value of the 100 convertible bonds would increase. Due to the delta of 0.50, the bond value might increase by approximately $0.50 for every $1 increase in stock price. The bond's price would rise, but by less than the proportional increase in the stock, as the bond component provides a floor.
• The short selling position in the stock will incur a loss as the stock price rises.

If the stock price falls to $40 per share:

• The convertible bond's value would decrease, but the bond floor would limit the downside.
• The short selling position in the stock will generate a profit as the stock price falls.

The arbitrageur's profit comes from the initial mispricing they identified. They profit if the convertible bond converges to its fair value, or if the delta hedging allows them to capture the spread while minimizing market exposure. The key is to constantly adjust the delta hedging position as the stock price and the bond's delta change, a process known as rebalancing.

Practical Applications

Convertible arbitrage finds its primary application within the realm of hedge funds and sophisticated institutional investment strategies. Fund managers utilize convertible arbitrage to:

• Generate Absolute Returns: The strategy aims to produce positive returns regardless of the direction of the broader equity or bond markets, making it a valuable component for investors seeking non-correlated returns in their portfolio diversification efforts.
• Exploit Market Inefficiencies: By simultaneously holding a long position in a convertible bond and a short position in the underlying equity, managers exploit perceived underpricing or overpricing between the two linked securities⁹.
• Capitalize on Volatility: While often viewed as market-neutral, convertible arbitrage can benefit from volatility in the underlying stock, as the embedded call option gains value with increased price swings. However, extreme volatility or "gamma" exposure needs careful management.
• Manage Capital Structure Arbitrage: Convertible arbitrage is a specific form of capital structure arbitrage, where traders exploit mispricings between different securities issued by the same company (e.g., debt and equity), particularly in situations like mergers, acquisitions, or restructurings that might affect the company's capital structure.
• Regulatory Framework: The trading of convertible debt, like other securities, is subject to regulatory oversight. For example, in the United States, the SEC approved new trade reporting requirements for convertible debt transactions listed on Nasdaq in 1993, requiring real-time reporting for surveillance purposes⁸. The Financial Industry Regulatory Authority (FINRA) also provides guidance on the reporting of convertible bond conversions⁷. The convertible bond market experienced significant issuance in 2020 and 2021 as companies utilized them for capital raising, indicating their continued relevance in corporate finance⁶.

Limitations and Criticisms

While convertible arbitrage aims for market neutrality, it is not without limitations and criticisms. One significant drawback is the potential for liquidity risk. Convertible bonds, especially those issued by smaller companies, can sometimes be less liquid than their underlying common stocks, making it difficult to execute or unwind positions efficiently⁵. This can lead to wider bid-ask spreads and impact profitability.

Another challenge lies in managing the dynamic nature of the hedge. The delta of a convertible bond changes as the underlying stock price moves, requiring constant rebalancing of the short selling position. This rebalancing incurs transaction costs and can be difficult to execute precisely in highly volatile markets. Furthermore, unexpected changes in implied volatility can negatively impact the strategy's profitability, as the value of the embedded call option is highly sensitive to this factor⁴.

Credit risk is also a consideration. While the strategy often emphasizes market neutrality, a sharp deterioration in the issuer's credit risk can significantly impact the value of the convertible bond component, potentially overwhelming the gains from the short equity position. During periods of significant market stress, such as the 2008 financial crisis, convertible arbitrage strategies faced challenges due to increased credit spreads, reduced liquidity, and difficulties in maintaining hedges³. Indeed, the strategy has seen periods of declining returns, partly due to a shift towards more debt-like convertibles by issuing companies and increased competition among arbitrageurs².

Convertible Arbitrage vs. Arbitrage

Convertible arbitrage is a specialized form of arbitrage, which is a broader financial concept.

The confusion often arises because both involve exploiting price discrepancies. However, convertible arbitrage focuses specifically on the hybrid nature of convertible securities and the relationship between their debt and equity components, employing continuous hedging to maintain its market-neutral stance. General arbitrage, on the other hand, simply refers to the act of profiting from any discrepancy in prices for the same asset.

FAQs

What is a convertible bond?

A convertible bond is a type of debt security that can be converted into a predetermined number of shares of the issuing company's common stock at specified times during its life. It combines features of both a bond (paying fixed income interest) and an equity option.

How do arbitrageurs make money in convertible arbitrage?

Arbitrageurs typically make money by simultaneously buying a convertible bond (going long) and short selling the underlying common stock. They profit from perceived underpricing of the convertible bond relative to its components, or from the sophisticated management of the combined position, particularly through delta hedging, which seeks to neutralize the directional risk from the stock's price movements.

Is convertible arbitrage a risky strategy?

While convertible arbitrage aims for "market neutrality" to reduce exposure to overall market swings, it is not risk-free. Risks include liquidity risk (difficulty buying or selling the securities), credit risk (the possibility of the issuer defaulting on the bond), and the complexities of managing the dynamic hedge, especially changes in implied volatility¹. Incorrect assumptions in pricing models or significant market dislocations can also lead to losses.