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Your interpretation is correct. SMB - size premium - suggest that smaller companies outperform larger companies. HML - value premium - suggest that value stocks outperform growth stocks. Negative loading for SMB indicates that the stock in question is in the large cap category. Positive loading for HML indicates that the stock offers value exposure. However, ...


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Because u = y - b0 - b1x1 - b2x2, by definition. So any derivatives must surely follow from this... I suspect your problem here lies in the econometric distinction of “reality” where the above holds true; versus the model, where you are estimating betas and hoping normally-distributed residuals etc. Seen thus, changing actual-Y will also change your residual ...


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