We use the cross-section regression approach of Fama and MacBeth (1973) to construct cross-section factors corresponding to the time-series factors of Fama and French (2015). Time-series models that use only cross-section factors provide better descriptions of average returns than time-series models that use time-series factors. This is true when we impose constant factor loadings and when we use time-varying loadings that are natural for time-series factors and time-varying loadings that are natural for cross-section factors.

The book‐to‐market ratio (B/M) is a noisy measure of expected stock returns because it also varies with expected cashflows. Our hypothesis is that the evolution of B/M, in terms of past changes in book equity and price, contains independent information about expected cashflows that can be used to improve estimates of expected returns. The tests support this hypothesis, with results that are largely but not entirely similar for Microcap stocks (below the 20 th NYSE market capitalization percentile) and All but Micro stocks (ABM).

We estimate the internal rates of return earned by nonfinancial firms on (i) the initial market values of their securities and (ii) the cost of their investments. The return on value is an estimate of the overall corporate cost of capital. The estimate of the real cost of capital for 1950–96 is 5.95 percent. The real return on cost is larger, 7.38 percent, so on average corporate investment seems to be profitable. A by‐product of calculating these returns is information about the history of corporate earnings, investment, and financing decisions that is perhaps more interesting than the returns.

Previous work shows that average returns on common stocks are related to firm characteristics like size, earnings/price, cash flow/price, book‐to‐market equity, past sales growth, long‐term past return, and short‐term past return. Because these patterns in average returns apparently are not explained by the CAPM, they are called anomalies. We find that, except for the continuation of short‐term returns, the anomalies largely disappear in a three‐factor model. Our results are consistent with rational ICAPM or APT asset pricing, but we also consider irrational pricing and data problems as possible explanations.

Two easily measured variables, size and book‐to‐market equity, combine to capture the cross‐sectional variation in average stock returns associated with market β , size, leverage, book‐to‐market equity, and earnings‐price ratios. Moreover, when the tests allow for variation in β that is unrelated to size, the relation between market β and average return is flat, even when β is the only explanatory variable.