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See Chris and Almgren "portfolios from sorts"


You can actually show by construction that the beta of the portfolio is the weighted sum of all the underlyings betas. Assume the return of the benchmark and some asset $a$ at time $t$ are respectively denoted $r_{b,t}$ and $r_{a,t}$, then the beta of a given asset is defined by: $$r_{a,t} = \alpha_a + \beta_a r_{b,t} + \epsilon_{a,t}$$ Let's assume you ...

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