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Portfolio behaving like a small cap portfolio is not necessarily a small cap portfolio. Your regression shows the appearance, not the fundamentals.


I browsed through the work and this is what I see: the lhs $r_{t+1} + \cdots + r_{t+H}$ is the sum of log-returns after $t$. the rhs is indexed by $t-i, i=0, \ldots, H$ thus this has something to do with the past before (and at) $t$. Thus the regression models the future ($r_{t+1} + \cdots + r_{t+H}$) dependent of the past where only PCA projections of ...

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