earnings growth with a higher expected return, but that the risk from buying higher expected growth is also higher, particularly in the tails. The final measure in Table 9, the beta with respect to the market portfolio, suggests that the risk observed in the earning outcomes is priced risk . The betas are those actually experienced during the portfolio holding period (not the historical betas). Those estimated under all conditions are higher for the higher expected return portfolios, particularly portfolio ten, though portfolio one has a higher beta that the average. Significantly, the down-market betas (estimated in years when the market return was less than negative ten percent) are considerably higher for portfolios eight to ten, indicating that firms with high expected returns have higher downside risk. Correspondingly, these portfolios exhibit higher up-market betas (estimated in years when the market return was greater than positive ten percent). This exhibits the essence of risk: risk is rewarded with up-side potential. In portfolios one to three, the low down-market betas are consistent with these firms providing a hedge in bad times, a property which, under Merton asset pricing theory, means lower risk and a lower required return. While asset pricing research has had difficulty identifying observable extra-market common factors, there is a general acceptance that the market factor is relevant so these findings have some credibility. results present a higher hurdle for someone attributing “anomalous returns” to “abnormal returns.” More so, given long-standing economic theory that predicts (approximate) efficient markets. As Richardson, Tuna, and Wysocki (2010) point out, anomaly research needs to offer a credible alternative hypothesis to efficient markets. That may well be forthcoming. Credible behavioral conjectures abound and formal models with transactions costs and other limits to arbitrage, noise traders, and investor sentiment have been offered. But the analysis in this paper challenge some of explanations for anomalous returns. For example, the conjecture
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