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.

中文翻译：

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长期收益中的自相似性

资产收益通过独立且可能相同分布的随机冲击的影响吸收新信息。它们也可能包含与自相似性概念有关的长记忆效应。这两种方法结合在一起。此外，提出了估算各成分贡献的方法，并提出了支持两种成分在自然分布和风险中性分布中均存在的证据。此外，它表明，当存在自相似成分时，长期投资回报可能是不正常的。自相似成分的存在还对长期的正股偏倚提出了质疑。