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The maximum attainable return is unbounded as in the model you can borrow without limit. However, what matters in that model is what is the maximum sharpe ratio you can attain. That has bounds, which are given by the Hansen-Jagannathan distance. Let me show you what the JH distance looks like. From the law of one price: \begin{equation} 1 = E [R_{i,t+1} ...


Betas aren't traditionally used in creating MV optimal portfolios. Insofar as beta is a proxy for risk, as is vol, there's probably some relationship between your betas and the covariance matrix that IS used in MV optimization, but there's not really any guide to give you that shows how betas are used, because they aren't.


In a factorial model, such as CAPM / APT, you have a linear relationship describing the process generating expected returns. Therefore, expected returns depend on betas. Therefore, since both the Covariance matrix and expected return vector depend on returns, they will also depend on betas under the assumptions of a factorial model.

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