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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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No, that's right! One fund has a beta of 81.6% and the other 82.4%, each with a ~90% R^2 to market. Therefore, it makes total sense that the spread between the two should have almost no correlation to the market (which is your very low mkt co-efficient value, and your very low R^2). The >90% P-value on the intercept (of the spread) co-efficients does ...

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It's not entirely clear what your objective is. If you'd like to compare portfolio 1 to portfolio 2 as part of an investment decision, using some standard, or set of, performance metric(s) is probably going to be more useful than regression against manufactured benchmarks. As to the regressions, alpha here is only going to be meaningful in absolute ...

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A simple addendum, that doesn't seek to supplant either the learned question and answer above. The short answer is the initial distinction drawn between ex-ante and ex-post is critical. What do you then want to do with the analysis? Therein lies the answer. Imagine a prosaic reality in which a stock's returns are driven by its beta to market, to value, to ...

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