ORIGINAL ARTICLE
Self-similarity in long-horizon returns
Dilip B. Madan,
Wim Schoutens,
Corresponding Author
Dilip B. Madan
Robert H. Smith School of Business, University of Maryland, College Park, Maryland
Correspondence
Dilip B. Madan, Robert H. Smith School of Business, University of Maryland, College Park, MD 20742.
Email: dbm@rhsmith.umd.edu
Search for more papers by this authorWim Schoutens
Department of Mathematics, K.U. Leuven, Leuven, Belgium
Search for more papers by this authorDilip B. Madan,
Wim Schoutens,
Corresponding Author
Dilip B. Madan
Robert H. Smith School of Business, University of Maryland, College Park, Maryland
Correspondence
Dilip B. Madan, Robert H. Smith School of Business, University of Maryland, College Park, MD 20742.
Email: dbm@rhsmith.umd.edu
Search for more papers by this authorWim Schoutens
Department of Mathematics, K.U. Leuven, Leuven, Belgium
Search for more papers by this authorAbstract
Asset returns incorporate new information via the effects of independent and possibly identically distributed random shocks. They may also incorporate long memory effects related to the concept of self-similarity. The two approaches are here combined. In addition, methods are proposed for estimating the contribution of each component and evidence supporting the presence of both components in both the physical and risk-neutral distributions is presented. Furthermore, it is shown that long-horizon returns may be nonnormal when there is a self-similar component. The presence of a self-similar component also questions positive equity biases over the longer term.
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