IDEAS home Printed from https://ideas.repec.org/a/ris/jofitr/0937.html
   My bibliography  Save this article

Risk and Return Measures for a Non-Gaussian World

Author

Listed:
  • Powers, Michael R.

    (Temple University, Tsinghua University)

  • Powers, Thomas Y.

    (Yale University)

Abstract

We propose new measures of both risk and anticipated return that incorporate the effects of skewness and heavy tails from a financial return’s probability distribution. Our cosine-based analysis, which involves maximizing the marginal Shannon information associated with the Fourier transform of the distribution’s probability density function, also facilitates the use of Lévy-stable distributions for asset prices, as suggested by Mandelbrot (1963). The new measures generalize the concepts of standard deviation and mean in the sense that they simplify to constant multiples of these widely used parameters in the case of Gaussian returns.

Suggested Citation

  • Powers, Michael R. & Powers, Thomas Y., 2009. "Risk and Return Measures for a Non-Gaussian World," Journal of Financial Transformation, Capco Institute, vol. 25, pages 51-54.
    • Handle: RePEc:ris:jofitr:0937
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    More about this item

    Keywords

    Risk; anticipated return; portfolio theory; Gaussian distribution; skewness; heavy tails; Lévy-stable family; Shannon information; Fourier transform; characteristic function;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

    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:ris:jofitr:0937. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Prof. Shahin Shojai (email available below). General contact details of provider: http://www.capco.com/ .

    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.