Although the single-factor expected return–beta relationship has not been confirmed by scientific standards, its use is already commonplace in economic life.

Early tests of the single-factor CAPM rejected the SML, finding that nonsystematic risk was related to average security returns.

Later tests controlling for the measurement error in beta found that nonsystematic risk does not explain portfolio returns but also that the estimated SML is too flat compared with what the CAPM would predict.

Roll's critique implied that the usual CAPM test is a test only of the mean-variance efficiency of a prespecified market proxy and therefore that tests of the linearity of the expected return–beta relationship do not bear on the validity of the model.

Tests of the mean-variance efficiency of professionally managed portfolios against the benchmark of a prespecified market index conform with Roll's critique in that they provide evidence on the efficiency of the market index. Empirical evidence suggests that most professionally managed portfolios are outperformed by market indexes, which corroborates the efficiency of those indexes and hence the CAPM.

Tests of the single-index model that account for human capital and cyclical variations in asset betas are far more consistent with the single-index CAPM and APT. These tests suggest that extra-market macroeconomic variables are not necessary to explain expected returns. Moreover, anomalies such as effects of size and book-to-market ratios disappear once these variables are accounted for.

The dominant multifactor models today are variants of the Fama-French model, incorporating market, size, value, momentum, and sometimes liquidity factors. Debate continues on whether returns associated with these extra-market factors reflect rational risk premia or behaviorally induced mispricing.

The equity premium puzzle originates from the observation that equity returns exceeded the risk-free rate to an extent that is inconsistent with reasonable levels of risk aversion—at least when average rates of return are taken to represent expectations. Fama and French show that the puzzle emerges primarily from excess returns over the last 50 years. Alternative estimates of expected returns using the dividend growth model instead of average returns suggest that excess returns on stocks were high because of unexpected large capital gains. The study suggests that future excess returns will be lower than realized in recent decades.

Early research on consumption-based capital asset pricing models was disappointing, but more recent work is far more encouraging. In some studies, consumption betas explain average portfolio returns as well as the Fama-French three-factor model. These results support Fama and French's conjecture that their factors proxy for more fundamental sources of risk.