The Distribution of Returns at Longer Horizons

20 Pages Posted: 28 Jan 2010 Last revised: 30 Jan 2011

Ernst Eberlein

University of Freiburg

Dilip B. Madan

University of Maryland - Robert H. Smith School of Business

Date Written: January 9, 2010

Abstract

Longer horizon returns are constructed from data on daily returns. Observed drawbacks of a Lévy process are a sharp decrease in skewness and excess kurtosis. Drawbacks to scaling are a flat term structure of skewness and excess kurtosis. A strategy that combines some exposure to independent increments and some exposure to scaling is developed in the context of self decomposable daily return distributions. Estimations are conducted on 400 stocks and we report that a good strategy for constructing longer horizon returns can be that of accumulating as i.i.d. half the daily return while scaling the remainder at rate one half.

Keywords: self similarity, independent increments, term structure of moments

JEL Classification: G1, G11, G12

Suggested Citation

Eberlein, Ernst and Madan, Dilip B., The Distribution of Returns at Longer Horizons (January 9, 2010). Robert H. Smith School Research Paper No. RHS 06-146. Available at SSRN: https://ssrn.com/abstract=1540777 or http://dx.doi.org/10.2139/ssrn.1540777

Ernst Eberlein

University of Freiburg ( email )

Department of Mathematical Stochastics
Eckerstrasse 1
D-79104, Freiburg
Germany
++49 761 203 5660 (Phone)
++49 761 203 5661 (Fax)

Dilip B. Madan (Contact Author)

University of Maryland - Robert H. Smith School of Business ( email )

College Park, MD 20742-1815
United States
301-405-2127 (Phone)
301-314-9157 (Fax)

Paper statistics

Downloads
128
Rank
182,321
Abstract Views
872