Equity Derivatives

Joshua  Coval; Erik   Stafford

Background Note | HBS Case Collection | January 2008

Equity Derivatives

Abstract

The goal of these simulations is to understand the dynamic replication technique behind the Black-Scholes/Merton options model. The simulations focus on a single stock and a risk-free discount bond, which are used to replicate a contingent payoff. The underlying stock and bond prices are randomly generated from the assumptions of the model, so that this simulation is testing the student's understanding and ability to use the model, rather than testing whether the model accurately explains prices. In each of the four simulations that make up this lesson, students are trying to replicate a contingent payoff, which is specified in terms of the closing stock price in one month (European-style derivative). The students are essentially working on an equity derivatives desk at a large bank and are responsible for delivering a derivative payoff to a client. The desk has taken in a premium upfront for guaranteeing the contingent payoff in one month's time. In the Black-Scholes/Merton model, a trader should be able to exactly match the contractual payment at expiration. Therefore, students are penalized based on the absolute difference between their actual ending value and a target ending value (starting value + derivative payoff). In particular, this difference is cumulated across all four simulations and then subtracted from their account.

Keywords: Equity; Bonds; Stocks; Price; Risk Management;

Format: Print

7 pages

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Citation:

Coval, Joshua, and Erik Stafford. "Equity Derivatives." Harvard Business School Background Note 208-117, 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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Equity Derivatives

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