We examine (i) how value premiums vary with firm size, (ii) whether the CAPM explains value premiums, and (iii) whether in general average returns compensate beta in the way predicted by the CAPM. Loughran's (1997) evidence for a weak value premium among large firms is special to 1963-1995, U.S. stocks, and the book-to-market value-growth indicator. Ang and Chen's (2003) evidence that the CAPM can explain U.S. value premiums is special to 1926-1963. The CAPM's general problem is that variation in unrelated to size and value-growth goes unrewarded throughout 1926-2004. This produces rejections of the model for 1926-1963 and 1963-2004.