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Portfolio beta is a linear combination of each asset's beta times the weight of the asset in the portfolio. Thus in general we have $$ \beta = \sum_{i=1}^N w_i \beta_i $$ where $w_i$ is the weight of asset $i$ and $\beta_i$ its beta. If we assume that for stocks the betas are positive then $\beta$ above is positive for positive weights. If you have positive ...

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