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You don't 'find' factors. Factors are systematic sources of risk the market rewards investors for holding. They're based in research done by academics over the years and include things like value, momentum and quality. You don't generate alpha from factors. In fact, using the APT framework, with a given set of factors, if your model suggests the ...


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At a minimum, because there's more ambiguity in 'market return'. What constitutes the market? In the US, LC or SC? For LC, S&P 500 or Russell 1000? And even though they're both meant to represent broad-based LC US equities, S&P skews larger than the R1, so the R1 will show a tilt to small cap, slightly impacting your size factor exposures if you ...


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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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Preliminary/Warning: A correlation test is not an appropriate method for analyzing potential risk-factors! Let's (very precisely) recall, what a risk-factor is (see Bali/Engle/Murray (2016), p.173f.), by using the size-anomaly (Banz (1981)) as an example: The difference in expected returns between small and big stocks is due to exposures towards a ...


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This is a quite broad question, but as requested, i would like to provide you four recommendations. First, testing any portfolio sorting-strategy, it is common in academics to account for autocorrelation and heteroscedascitiy in portfolio returns, i.e. applying Newey/West (1987) adjusted standard errors. As you seem to use the R-statistical language, this ...


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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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