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One general representation of the CAPM model is to suggest that it is the solution of: $$ \min_w f(w) = \alpha \frac{1}{2}w^T(2\Sigma)w - (1-\alpha)\mu^t w $$ $$ s.t. \quad \delta^T w = 1$$ and different $\alpha$ determine different points on the efficient frontier. Note that this form allows short selling and the solution is closed form. The reformulated ...

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