Equity Options

Joshua  Coval; Erik   Stafford

Background Note | HBS Case Collection | January 2008

Equity Options

Abstract

The goal of this simulation is to understand the reliance of option values on volatility. When an investor trades an option, they are essentially trading volatility. Therefore, much of the focus in this lesson is on forecasting volatility. Students are able to use two primary methods for forecasting volatility in this lesson-historical and implied. Students are provided with a historical dataset, from which they can estimate historical volatility of the stock returns. They can also use the dataset to study various statistical relations between the securities. In particular, two of the three securities behave independently of the others. Thus, students are able to analyze the dataset to form views of how the security prices are likely to evolve relative to each other.

Keywords: Volatility; Forecasting and Prediction; Stock Options; Investment Return; Price; Market Transactions; Mathematical Methods; Value;

Format: Print

3 pages

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Citation:

Coval, Joshua, and Erik Stafford. "Equity Options." Harvard Business School Background Note 208-118, January 2008.

Overall, no! We show that the level and time series variation in cash flows for most bank activities are well matched by capital market portfolios with similar interest rate and credit risk to what banks report to hold. Ignoring operating expenses, bank loans earn high returns and transaction deposits pay low interest rates, consistent with these activities having a potential edge. The edge among these activities is insufficient to cover the large operating expenses of banks. A large portion of the aggregate U.S. banking sector closely resembles a tax inefficient passive mutual fund. The residual risks of bank activities, presumably generated by the unique components of the bank business model, generate systematic risks that are uncompensated.

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 Options

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