IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1908.04837.html
   My bibliography  Save this paper

The implied Sharpe ratio

Author

Listed:
  • Ankush Agarwal
  • Matthew Lorig

Abstract

In an incomplete market, including liquidly-traded European options in an investment portfolio could potentially improve the expected terminal utility for a risk-averse investor. However, unlike the Sharpe ratio, which provides a concise measure of the relative investment attractiveness of different underlying risky assets, there is no such measure available to help investors choose among the different European options. We introduce a new concept -- the implied Sharpe ratio -- which allows investors to make such a comparison in an incomplete financial market. Specifically, when comparing various European options, it is the option with the highest implied Sharpe ratio that, if included in an investor's portfolio, will improve his expected utility the most. Through the method of Taylor series expansion of the state-dependent coefficients in a nonlinear partial differential equation, we also establish the behaviour of the implied Sharpe ratio with respect to an investor's risk-aversion parameter. In a series of numerical studies, we compare the investment attractiveness of different European options by studying their implied Sharpe ratio.

Suggested Citation

  • Ankush Agarwal & Matthew Lorig, 2019. "The implied Sharpe ratio," Papers 1908.04837, arXiv.org.
    • Handle: RePEc:arx:papers:1908.04837
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1908.04837
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Louis Eeckhoudt & Christian Gollier & Harris Schlesinger, 1995. "The Risk-Averse (and Prudent) Newsboy," Management Science, INFORMS, vol. 41(5), pages 786-794, May.
    2. Jensen, Michael C, 1969. "Risk, The Pricing of Capital Assets, and the Evaluation of Investment Portfolios," The Journal of Business, University of Chicago Press, vol. 42(2), pages 167-247, April.
    3. Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, vol. 57(1), pages 405-443, February.
    4. Matthew Lorig, 2018. "Indifference Prices And Implied Volatilities," Mathematical Finance, Wiley Blackwell, vol. 28(1), pages 372-408, January.
    5. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    6. Matthew Lorig & Stefano Pagliarani & Andrea Pascucci, 2017. "Explicit Implied Volatilities For Multifactor Local-Stochastic Volatility Models," Mathematical Finance, Wiley Blackwell, vol. 27(3), pages 926-960, July.
    7. Ian Jewitt, 1987. "Risk Aversion and the Choice Between Risky Prospects: The Preservation of Comparative Statics Results," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(1), pages 73-85.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. John H. Cochrane, 1999. "New facts in finance," Economic Perspectives, Federal Reserve Bank of Chicago, vol. 23(Q III), pages 36-58.
    2. Yang Shen, 2020. "Effect of Variance Swap in Hedging Volatility Risk," Risks, MDPI, vol. 8(3), pages 1-34, July.
    3. Matthew Lorig, 2014. "Indifference prices and implied volatilities," Papers 1412.5520, arXiv.org, revised Sep 2015.
    4. Sørensen, Carsten & Trolle, Anders Bjerre, 2006. "Dynamic asset allocation and latent variables," Working Papers 2004-8, Copenhagen Business School, Department of Finance.
    5. Ankush Agarwal & Ronnie Sircar, 2017. "Portfolio Benchmarking under Drawdown Constraint and Stochastic Sharpe Ratio," Working Papers hal-01388399, HAL.
    6. Ankush Agarwal & Christian-Oliver Ewald & Yongjie Wang, 2023. "Hedging longevity risk in defined contribution pension schemes," Computational Management Science, Springer, vol. 20(1), pages 1-34, December.
    7. Matthew Lorig & Ronnie Sircar, 2015. "Portfolio Optimization under Local-Stochastic Volatility: Coefficient Taylor Series Approximations & Implied Sharpe Ratio," Papers 1506.06180, arXiv.org.
    8. Ankush Agarwal & Ronnie Sircar, 2016. "Portfolio Benchmarking under Drawdown Constraint and Stochastic Sharpe Ratio," Papers 1610.08558, arXiv.org.
    9. Kathleen Walsh, 2015. "The investment horizon and asset pricing models," Australian Journal of Management, Australian School of Business, vol. 40(2), pages 277-294, May.
    10. Anne Lavigne, 2006. "Gouvernance et investissement des fonds de pension privés aux Etats-Unis," Working Papers halshs-00081401, HAL.
    11. An Chen & Thai Nguyen & Thorsten Sehner, 2022. "Unit-Linked Tontine: Utility-Based Design, Pricing and Performance," Risks, MDPI, vol. 10(4), pages 1-27, April.
    12. Alan J. Auerbach, 1981. "Evaluating the Taxation of Risky Assets," NBER Working Papers 0806, National Bureau of Economic Research, Inc.
    13. George G. Kaufman, 1980. "Duration, Planning Period, And Tests Of The Capital Asset Pricing Model," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 3(1), pages 1-9, March.
    14. Hong, Claire Yurong & Lu, Xiaomeng & Pan, Jun, 2021. "FinTech adoption and household risk-taking," BOFIT Discussion Papers 14/2021, Bank of Finland Institute for Emerging Economies (BOFIT).
    15. Curatola, Giuliano, 2022. "Price impact, strategic interaction and portfolio choice," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    16. Auffret, Philippe, 2001. "An alternative unifying measure of welfare gains from risk-sharing," Policy Research Working Paper Series 2676, The World Bank.
    17. David A. Volkman, 1999. "Market Volatility And Perverse Timing Performance Of Mutual Fund Managers," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 22(4), pages 449-470, December.
    18. Luca De Gennaro Aquino & Sascha Desmettre & Yevhen Havrylenko & Mogens Steffensen, 2024. "Equilibrium control theory for Kihlstrom-Mirman preferences in continuous time," Papers 2407.16525, arXiv.org, revised Oct 2024.
    19. Mofidi, Seyed Shahab & Pazour, Jennifer A. & Roy, Debjit, 2018. "Proactive vs. reactive order-fulfillment resource allocation for sea-based logistics," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 114(C), pages 66-84.
    20. Chen, An & Hieber, Peter & Sureth, Caren, 2022. "Pay for tax certainty? Advance tax rulings for risky investment under multi-dimensional tax uncertainty," arqus Discussion Papers in Quantitative Tax Research 273, arqus - Arbeitskreis Quantitative Steuerlehre.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1908.04837. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.