Is value premium a proxy for time-varying investment opportunities

"Campbell and Vuolteenaho (2004) and Brennan, Wang, and Xia (2004) recently argue that the value premium co-moves with investment opportunities and thus reflects rational pricing. This paper extends their analysis by showing that the ICAPM interpretation of the value premium also sheds light on the puzzling empirical relation between the stock market risk and return across time. That is, in contrast with many early authors, it is found to be positive and highly significant after controlling for the covariance between the stock market return and the value premium. Moreover, we also document a positive and significant relation between the value premium and its conditional variance over the post-1963 period. Our results, which appear to be robust using both the realized volatility model and the GARCH model, confirm that the value premium cannot be completely attributed to data mining and irrational pricing"--Federal Reserve Bank of St. Louis web site.