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The Impact of Options on Investment Portfolios in the Short-Run and the Long-Run, with a Focus on Downside Protection and Call Overwriting

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  • David Buckle

    (8 Highview, Caterham CR3 6AY, UK)

Abstract

In this article, we analyse the impact of the introduction of options on an investment portfolio. Our first objective is to derive closed-form formulae for the standard measures of portfolio efficiency: risk premium, risk, Sharpe ratio, and beta, of any portfolio containing any combination of options. Using these formulae on three examples of simple option strategies (call overwriting, put protection, and collars), we show how these statistics are altered by the inclusion of an option overlay in a portfolio. Our second objective is to show that if an option strategy is repeated over multiple investment time periods, the long-run return becomes normally distributed. Our motivation is to provide investors with the mathematics to measure the impact of the introduction of options on portfolio efficiency and encourage a potential portfolio rebalance to account for this impact. Then, we highlight that whilst options can create asymmetric non-normal outcomes, their repeated use may not alter the long-run portfolio return in the desired way and thus to encourage investors to assess if an option overlay will deliver the desired long-run outcome.

Suggested Citation

  • David Buckle, 2022. "The Impact of Options on Investment Portfolios in the Short-Run and the Long-Run, with a Focus on Downside Protection and Call Overwriting," Mathematics, MDPI, vol. 10(9), pages 1-56, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1563-:d:809464
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    References listed on IDEAS

    as
    1. Bookstaber, Richard & Clarke, Roger, 1984. "Option Portfolio Strategies: Measurement and Evaluation," The Journal of Business, University of Chicago Press, vol. 57(4), pages 469-492, October.
    2. Sears, R. Stephen & Trennepohl, Gary L., 1982. "Measuring Portfolio Risk in Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(3), pages 391-409, September.
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    Cited by:

    1. Pankaj Agrrawal & Faye W. Gilbert & Jason Harkins, 2022. "Time Dependence of CAPM Betas on the Choice of Interval Frequency and Return Timeframes: Is There an Optimum?," JRFM, MDPI, vol. 15(11), pages 1-18, November.
    2. Kionka, Marlene & Brunckhorst, Henning & Kuethe, Todd H. & Odening, Martin, 2023. "Pricing Derivatives in the Agricultural Land Market," 2023 Annual Meeting, July 23-25, Washington D.C. 335626, Agricultural and Applied Economics Association.
    3. Pankaj Agrrawal, 2023. "The Gibbons, Ross, and Shanken Test for Portfolio Efficiency: A Note Based on Its Trigonometric Properties," Mathematics, MDPI, vol. 11(9), pages 1-19, May.

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