Average stock returns for North America, Europe, and Asia Pacific increase with the book-to-market ratio (B/M) and profitability and are negatively related to investment. For Japan, the relation between average returns and B/M is strong, but average returns show little relation to profitability or investment. A five-factor model that adds profitability and investment factors to the three-factor model of Fama and French (1993) largely absorbs the patterns in average returns. As in Fama and French, 2015, Fama and French, 2016, the model's prime problem is failure to capture fully the low average returns of small stocks whose returns behave like those of low profitability firms that invest aggressively.

A five-factor model directed at capturing the size, value, profitability, and investment patterns in average stock returns performs better than the three-factor model of Fama and French (FF, 1993). The five-factor model׳s main problem is its failure to capture the low average returns on small stocks whose returns behave like those of firms that invest a lot despite low profitability. The model׳s performance is not sensitive to the way its factors are defined. With the addition of profitability and investment factors, the value factor of the FF three-factor model becomes redundant for describing average returns in the sample we examine.

Variables with strong marginal explanatory power in cross-section asset pricing regressions typically show less power to produce increments to average portfolio returns, for two reasons. (1) Adding an explanatory variable can attenuate the slopes in a regression. (2) Adding a variable with marginal explanatory power always attenuates the values of other explanatory variables in the extremes of a regression’s fitted values. Without a restriction on portfolio weights, the maximum Sharpe ratios in the GRS statistic of Gibbons, Ross, and Shanken (1989) provide little information about an incremental variable’s impact on the portfolio opportunity set.

In the four regions (North America, Europe, Japan, and Asia Pacific) we examine, there are value premiums in average stock returns that, except for Japan, decrease with size. Except for Japan, there is return momentum everywhere, and spreads in average momentum returns also decrease from smaller to bigger stocks. We test whether empirical asset pricing models capture the value and momentum patterns in international average returns and whether asset pricing seems to be integrated across the four regions. Integrated pricing across regions does not get strong support in our tests. For three regions (North America, Europe, and Japan), local models that use local explanatory returns provide passable descriptions of local average returns for portfolios formed on size and value versus growth. Even local models are less successful in tests on portfolios formed on size and momentum.

Standard asset pricing models assume that: (i) there is complete agreement among investors about probability distributions of future payoffs on assets; and (ii) investors choose asset holdings based solely on anticipated payoffs; that is, investment assets are not also consumption goods. Both assumptions are unrealistic. We provide a simple framework for studying how disagreement and tastes for assets as consumption goods can affect asset prices.

Valuation theory says that expected stock returns are related to three variables: the book-to-market equity ratio (Bt/Mt), expected profitability, and expected investment. Given Bt/Mt and expected profitability, higher expected rates of investment imply lower expected returns. But controlling for the other two variables, more profitable firms have higher expected returns, as do firms with higher Bt/Mt. These predictions are confirmed in our tests.

Financing decisions seem to violate the central predictions of the pecking order model about how often and under what circumstances firms issue equity. Specifically, most firms issue or retire equity each year, and the issues are on average large and not typically done by firms under duress. We estimate that during 1973–2002, the year-by-year equity decisions of more than half of our sample firms violate the pecking order.

The class of firms that obtain public equity financing expands dramatically in the 1980s and 1990s. The number of new firms listed on major U.S. stock markets jumps from 156 per year for 1973–1979 to 549 per year for 1980–2001. The characteristics of new lists also change. The cross section of profitability becomes progressively more left skewed, and growth becomes more right skewed. The result is a sharp decline in survival rates. We suggest that the changes in the characteristics of new lists are due to a decline in the cost of equity that allows weaker firms and firms with more distant expected payoffs to issue public equity.

The proportion of firms paying cash dividends falls from 66.5% in 1978 to 20.8% in 1999, due in part to the changing characteristics of publicly traded firms. Fed by new listings, the population of publicly traded firms tilts increasingly toward small firms with low profitability and strong growth opportunities – characteristics typical of firms that have never paid dividends. More interesting, we also show that regardless of their characteristics, firms have become less likely to pay dividends. This lower propensity to pay is at least as important as changing characteristics in the declining incidence of dividend-paying firms.

Estimates of the cost of equity for industries are imprecise. Standard errors of more than 3.0% per year are typical for both the CAPM and the three-factor model of Fama and French (1993). These large standard errors are the result of(i) uncertainty about true factor risk premiums and (ii) imp ecise estimates of the loadings of industries on the risk factors. Estimates of the cost of equity for firms and projects are surely even less precise.