Convertible Arbitrage

Joshua  Coval; Erik   Stafford

Background Note | HBS Case Collection | January 2008

Convertible Arbitrage

Abstract

The goal of this simulation is to understand how convertible bonds can be viewed as a portfolio of simpler securities and to introduce an over-the-counter market. The convertible bonds that are available during the simulation are at-the-money and in-the-money so that changing credit risk exposure is not much of an issue. A convertible bond can be viewed as a simple coupon paying corporate bond plus a conversion option. A bond pricing model discounts the promised payments at a rate that compensates for time, risk, and expected loss (maturity matched Treasury yield plus a credit rating matched yield spread). The conversion option can be valued using the Black-Scholes call option pricing formula. The key is to recognize that each conversion option (one per bond) is equivalent to several equity call options (the conversion ratio determines how many equity options are implicit in each bond).

Keywords: Bonds; Investment Portfolio; Price; Risk Management; Mathematical Methods;

Format: Print

5 pages

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Citation:

Coval, Joshua, and Erik Stafford. "Convertible Arbitrage." Harvard Business School Background Note 208-116, January 2008.

We decompose bank activities into passive and active components and evaluate the performance of the active components of the bank business model by controlling for passive maturity transformation strategies that can be executed in the capital market. Over the period 1960–2016, we find that (1) unlevered bank assets underperform passive portfolios of maturity-matched U.S. Treasury bonds; (2) the cost of bank deposits exceeds the cost of bank debt; (3) bank equities have CAPM betas near one, while passive maturity transformation strategies have CAPM betas near zero; and (4) portfolios of bank equities consistently underperform portfolios designed to passively mimic their economic exposures. The very strong investment performance of passive maturity transformation strategies over this period may mask the underperformance of the specialized bank activities.

While we commend the initiative of Snyder and Welch (2017), we lay out in this short reply why we remain highly confident in our results and our interpretation thereof. We welcome authors to continue to explore the data for themselves and look forward to the new questions they can tackle with it.

Private equity funds tend to select relatively small firms with low EBITDA multiples. Publicly traded equities with these characteristics have high risk-adjusted returns after controlling for common factors typically associated with value stocks. Hold-to-maturity accounting of portfolio net asset value eliminates the majority of measured risk. A passive portfolio of small, low EBITDA multiple stocks with modest amounts of leverage and hold-to-maturity accounting of net asset value produces an unconditional return distribution that is highly consistent with that of the pre-fee aggregate private equity index. The passive replicating strategy represents an economically large improvement in risk- and liquidity-adjusted returns over direct allocations to private equity funds, which charge average fees of 6% per year.

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Convertible Arbitrage

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