The Distribution of Returns at Longer Horizons
University of Freiburg
Dilip B. Madan
University of Maryland - Robert H. Smith School of Business
January 9, 2010
Robert H. Smith School Research Paper No. RHS 06-146
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.
Number of Pages in PDF File: 20
Keywords: self similarity, independent increments, term structure of moments
JEL Classification: G1, G11, G12
Date posted: January 28, 2010 ; Last revised: January 30, 2011
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