Rethinking risk and return: part 2 – some felicitous Fourier frequencies

Michael R. Powers

Journal of Risk Finance, 2009, vol. 10, issue 3, 205-209

Abstract: Purpose - This editorial, the second of a two‐part series, proposes a new measure of risk for analyzing highly non‐normal (i.e. asymmetric and long‐tailed) random variables in the context of both investment and insurance portfolios. The proposed measure replaces thep‐norm‐based definition of “risk” – found wanting in Part 1 – with a cosine‐based alternative. Design/methodology/approach - Just asp‐norm‐based risk measures were derived as generalizations of the standard deviation in Part 1, the paper now extend this approach to a cosine‐based risk measure. This involves computing the Fourier transform of the underlying random variable for a given frequency value. Methods for selecting an appropriate frequency are then discussed. Findings - The cosine‐based risk measure provides an effective alternative top‐norm‐based measures because the Fourier transform is always well defined, even for long‐tailed random variables. The frequency parameter necessary for the Fourier transform may be computed according to several interesting criteria, including the maximization of marginal Shannon information, as well as consideration of “Planck boundaries” in human cognition. Originality/value - The editorial explores the use of cosine‐based measures in constructing a general definition of “risk” that is equally applicable to asymmetric and long‐tailed random variables as to normal random variables.

Keywords: Risk management; Portfolio investment; Insurance; Normal distribution; Random variables; Fourier transforms (search for similar items in EconPapers)
Date: 2009
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.emerald.com/insight/content/doi/10.110 ... d&utm_campaign=repec (text/html)
https://www.emerald.com/insight/content/doi/10.110 ... d&utm_campaign=repec (application/pdf)
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eme:jrfpps:15265940910959348

DOI: 10.1108/15265940910959348

Access Statistics for this article

Journal of Risk Finance is currently edited by Nawazish Mirza

More articles in Journal of Risk Finance from Emerald Group Publishing Limited
Bibliographic data for series maintained by Emerald Support ().