The Variance Drain and Jensen's Inequality
The 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.
|Date of creation:||Mar 2012|
|Date of revision:|
|Contact details of provider:|| Postal: 812-855-1021|
Web page: http://www.iub.edu/~caepr
More information through EDIRC
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.:
- Goetzmann, William N. & Ibbotson, Roger G., 2006. "The Equity Risk Premium: Essays and Explorations," OUP Catalogue, Oxford University Press, number 9780195148145, July.
When requesting a correction, please mention this item's handle: RePEc:inu:caeprp:2012-004. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Center for Applied Economics and Policy Research)
If references are entirely missing, you can add them using this form.