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The Nobel Foundation asks that the Nobel lecture cover the work for which the Prize is awarded. The announcement of this year's Prize cites empirical work in asset pricing. I interpret this to include work on efficient capital markets and work on developing and testing asset pricing models—the two pillars, or perhaps more descriptive, the Siamese twins of asset pricing. I start with efficient markets and then move on to asset pricing models.

The aggregate portfolio of actively managed U.S. equity mutual funds is close to the market portfolio, but the high costs of active management show up intact as lower returns to investors. Bootstrap simulations suggest that few funds produce benchmark-adjusted expected returns sufficient to cover their costs. If we add back the costs in fund expense ratios, there is evidence of inferior and superior performance (nonzero true α) in the extreme tails of the cross-section of mutual fund α estimates.

The capital asset pricing model (CAPM) of William Sharpe (1964) and John Lintner (1965) marks the birth of asset pricing theory (resulting in a Nobel Prize for Sharpe in 1990). Before their breakthrough, there were no asset pricing models built from first principles about the nature of tastes and investment opportunities and with clear testable predictions about risk and return. Four decades later, the CAPM is still widely used in applications, such as estimating the cost of equity capital for firms and evaluating the performance of managed portfolios. And it is the centerpiece, indeed often the only asset pricing model taught in MBA level investment courses. The attraction of the CAPM is its powerfully simple logic and intuitively pleasing predictions about how to measure risk and about the relation between expected return and risk. Unfortunately, perhaps because of its simplicity, the empirical record of the model is poor - poor enough to invalidate the way it is used in applications. The model's empirical problems may reflect true failings. (It is, after all, just a model.) But they may also be due to shortcomings of the empirical tests, most notably, poor proxies for the market portfolio of invested wealth, which plays a central role in the model's predictions. We argue, however, that if the market proxy problem invalidates tests of the model, it also invalidates most applications, which typically borrow the market proxies used in empirical tests. For perspective on the CAPM's predictions about risk and expected return, we begin with a brief summary of its logic. We then review the history of empirical work on the model and what it says about shortcomings of the CAPM that pose challenges to be explained by more complicated models.

We examine (1) how value premiums vary with firm size, (2) whether the CAPM explains value premiums, and (3) whether, in general, average returns compensate β in the way predicted by the CAPM. Loughran's (1997) evidence for a weak value premium among large firms is special to 1963 to 1995, U.S. stocks, and the book-to-market value-growth indicator. Ang and Chen's (2005) evidence that the CAPM can explain U.S. value premiums is special to 1926 to 1963. The CAPM's more general problem is that variation in β unrelated to size and the value-growth characteristic goes unrewarded throughout 1926 to 2004.

A five-factor model that adds profitability (RMW) and investment (CMA) factors to the three-factor model of Fama and French (1993) suggests a shared story for several averagereturn anomalies. Specifically, positive exposures to RMW and CMA (stock returns that behave like those of profitable firms that invest conservatively) capture the high average returns associated with low market β, share repurchases, and low stock return volatility. Conversely, negative RMW and CMA slopes (like those of relatively unprofitable firms that invest aggressively) help explain the low average stock returns associated with high β, large share issues, and highly volatile returns.

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.

We estimate the equity premium using dividend and earnings growth rates to measure the expected rate of capital gain. Our estimates for 1951 to 2000, 2.55 percent and 4.32 percent, are much lower than the equity premium produced by the average stock return, 7.43 percent. Our evidence suggests that the high average return for 1951 to 2000 is due to a decline in discount rates that produces a large unexpected capital gain. Our main conclusion is that the average stock return of the last half-century is a lot higher than expected.

Value stocks have higher returns than growth stocks in markets around the world. For the period 1975 through 1995, the difference between the average returns on global portfolios of high and low book-to-market stocks is 7.68 percent per year, and value stocks outperform growth stocks in twelve of thirteen major markets. An international capital asset pricing model cannot explain the value premium, but a two-factor model that includes a risk factor for relative distress captures the value premium in international returns.

The anomalous returns associated with net stock issues, accruals, and momentum are pervasive; they show up in all size groups (micro, small, and big) in cross-section regressions, and they are also strong in sorts, at least in the extremes. The asset growth and profitability anomalies are less robust. There is an asset growth anomaly in average returns on microcaps and small stocks, but it is absent for big stocks. Among profitable firms, higher profitability tends to be associated with abnormally high returns, but there is little evidence that unprofitable firms have unusually low 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.