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A Relative Value Strategy: Convertible Arbitrage

Hedge funds deploying relative value strategies seek to take advantage of “discrepancies” in price between securities or the overall market. Within the relative value category, there are sub-strategies, and convertible arbitrage is an important form of relative value strategy where hedge fund managers exploit pricing inefficiencies between convertible securities and the underlying stocks.

Under normal market conditions, convertible arbitrage fund managers expect the combined position to be insensitive to any small fluctuations in the price of such underlying stock. From other risk-management perspectives, convertible arbitrage funds are expected to hedge away credit risk and interest rate risk. The ultimate goal is to isolate underpriced options embedded in convertible bonds. The attractiveness of convertible arbitrage strategy is that its performance does not rely on market directions, rather, it is based on an expected return to fair value of securities.

Convertible arbitrage was one of the most successful hedge fund strategies at the end of the 1990s and the beginning of the 2000s. The Lehman Brothers Event of 2008 pushed investors to withdraw and liquidate from convertible arbitrage funds, and returns turned sharply negative. Since early 2009, a number of firms successfully starting new dedicated convertible arbitrage funds, and the price of such strategy began to rise again. Today, many convertible arbitrage funds of both the developed world and emerging markets continue to outperform the global hedge fund aggregate.

Convertible Securities Valuation

There are Monte Carlo simulations that consider numerous interest rate and equity price scenarios to derive a probability distribution for convertible security values. Although these academic approaches are theoretically more sounds, most convertible arbitrage managers use either the component approach or the binomial model to value convertible securities.

  1. The component approach views the convertible bond as a bundle made up of a plain vanilla fixed rate bond and an option that captures the convertibility dimension. The bond component is valued via a discounted cash flow model (DCF), and the option component is valued using a derivative pricing formula such as Black and Scholes model.
  2. Compared with the component approach, the binomial model is better-known and has been applied in the industry in many different functions. The binomial option model uses a tree approach to valuation. It allows for easier mathematical adjustments, non-continuous motions in price movements, stochastic interest rates and volatility levels, and credit spreads that both vary stochastically and are correlated to the underlying stock. The binomial model performs well in such complexities.

The Use of Leverage

Historically, convertible arbitrage and fixed-income arbitrage hedge funds have used a much greater degree of leverage than have many other hedge fund strategies. Ineichen (2003) estimates that convertible bond arbitrage funds routinely use leverage between two and ten times fund assets, while fixed-income arbitrage strategies may employ more than 20 times leverage. Prior to the crash of 2008, overall convertible arbitrage market was on average four to six times leveraged. The use of overly high leverage made convertible arbitrage funds far too vulnerable to the effects of forced liquidation in a depressed market.

Different approaches to convertible arbitrage, e.g., cash-and-carry trading, volatility trading, and credit trading, differ in the degree of hedging and the leverage used. Ideally, the amount of leverage used in a strategy should be positively related to the degree of liquidity of the assets underlying the strategy.

Convertible Arbitrage Due Diligence

In hiring asset managers in any asset class, it is essential to understand the strengths, weakenesses, and uniqueness and to align the potential risks with them. In the case of convertible arbitrage, the due diligence process should address factors specific to the approach, the manager’s pricing model, and communications to investors.

  • It is essential to understand what the specific strategy of the convertible arbitrage fund is, whether to exploit the mispricing of the bond, or focus on opportunities in trading volatility, trading credit, or trading gamma. Different arbitrage strategies have different risk-return profiles, and more importantly, they require a different set of skill.
  • Another uniqueness in convertible arbitrage is that the success of the convertible arbitrage strategy is highly dependent on the quality of the model. Therefore, it is a must for investors to assess the quality of manager’s pricing and hedging model. Additionally, the quality of the model inputs, a model is only as good as its inputs. Furthermore, what kind of stress tests will run on the portfolio? A well-specified stress test framework should incorporate variations on the shape of the yield curve, the credit risk premium, and the volatility of bond and stock markets.
  • One more concern related to the manager’s model is how much of the portfolio is marked to market versus marked to model. A fund manager may decide to mark to model in situations where he may find it difficult to obtain recent market quote, thus there is a gap in the fund’s valuation between the two prices, especially when the position has to be liquidated very quickly.
  • Moreover, investors need to question what procedure is used to mark the portfolio, and the level of oversight the manager will exercise over portfolio pricing. In convertible arbitrage, it is true that the use of discretionary marks from independent brokers is unavoidable, but they should represent only a very small portion of the total value of the portfolio.
  • Last but foremost, investors should consider whether the manager is dedicated to effective communication. The transparency in convertible arbitrage assets is different in that the Greeks supplied by managers are subject to their interpretation with regard to implied volatility, credit spreads, call provisions, interest rate volatility, time to convergence, etc., which impact the true meaning of the information.


  1. BarclayHedge Alternative Investment Databases
  2. Investing in Hedge Funds: A Guide to Measuring Risk and Return by Turan Bali, Yigit Atilgan, and Ozgur Demirtas
  3. Convertible Arbitrage: Insights and Techniques for Successful Hedging by Nick P. Calamos 2011

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