Self‐similarity in long‐horizon returns

Dilip B. Madan and Wim Schoutens

Mathematical Finance, 2020, vol. 30, issue 4, 1368-1391

Abstract: 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.

Date: 2020
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