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Imagine a scenario where a beta neutral portfolio comprised being long one very high beta stock and short many low beta stocks. Such a portfolio clearly has extreme concentration of risk. Additionally imposing a 'dollar neutral' constraint, would help to spread the weights more evenly over all the stocks. A further observation is that measuring true 'beta'...


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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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