The Variance Drain and Jensen's Inequality
AbstractThe well-known approximation of the difference between the arithmetic average and geometric average returns as one-half of the variance of the underlying returns is reexamined using Jensen’s Inequality. The ”defect” in Jensen’s Inequality, is given an exlicit formula in terms of the variance following some ideas put forward by Holder. A new form of the AM-GM Inequality follows and is is applied to financial returns. Both exact, and approximate relations between the arithmetic average, geometric average, and variance of returns are discussed. The mathematical formulation of these relations are free of distributional assumptions governing the underlying returns process.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington in its series Caepr Working Papers with number 2012-004.
Length: 14 pages
Date of creation: Mar 2012
Date of revision:
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-04-03 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Hirshleifer,Jack & Riley,John G., 1992. "The Analytics of Uncertainty and Information," Cambridge Books, Cambridge University Press, number 9780521283694.
- Goetzmann, William N. & Ibbotson, Roger G., 2006. "The Equity Risk Premium: Essays and Explorations," OUP Catalogue, Oxford University Press, number 9780195148145, September.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Heather Steele).
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 references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.