According to conventional wisdom, annualized volatility of stock returns is lower over long horizons than over short horizons, due to mean reversion induced by return predictability. In contrast, we find that stocks are substantially more volatile over long horizons from an investor's perspective. This perspective recognizes that parameters are uncertain, even with two centuries of data, and that observable predictors imperfectly deliver the conditional expected return. Mean reversion contributes strongly to reducing long‐horizon variance but is more than offset by various uncertainties faced by the investor. The same uncertainties reduce desired stock allocations of long‐horizon investors contemplating target‐date funds.

We develop a framework for estimating expected returns—a predictive system —that allows predictors to be imperfectly correlated with the conditional expected return. When predictors are imperfect, the estimated expected return depends on past returns in a manner that hinges on the correlation between unexpected returns and innovations in expected returns. We find empirically that prior beliefs about this correlation, which is most likely negative, substantially affect estimates of expected returns as well as various inferences about predictability, including assessments of a predictor's usefulness. Compared to standard predictive regressions, predictive systems deliver different expected returns with higher estimated precision.

A long return history is useftil in estimating the current equity premium even if the historical distribution has experienced structural breaks. The long series helps not only if the timing of breaks is uncertain but also if one believes that large shifts in the premium are unlikely or that the premium is associated, in part, with volatility. Our framework incorporates these features along with a belief that prices are likely to move opposite to contemporaneous shifts in the premium. The estimated premium since 1834 fluctuates between four and six percent and exhibits its sharpest drop in the last decade.

Costs of equity for individual firms are estimated in a Bayesian framework using several factor‐based pricing models. Substantial prior uncertainty about mispricing often produces an estimated cost of equity close to that obtained with mispricing precluded, even for a stock whose average return departs significantly from the pricing model's prediction. Uncertainty about which pricing model to use is less important, on average, than within‐model parameter uncertainty. In the absence of mispricing uncertainty, uncertainty about factor premiums is generally the largest source of overall uncertainty about a firm's cost of equity, although uncertainty about betas is nearly as important.

This study investigates whether marketwide liquidity is a state variable important for asset pricing. We find that expected stock returns are related cross-sectionally to the sensitivities of returns to fluctuations in aggregate liquidity. Our monthly liquidity measure, an average of individual-stock measures estimated with daily data, relies on the principle that order flow induces greater return reversals when liquidity is lower. From 1966 through 1999, the average return on stocks with high sensitivities to liquidity exceeds that for stocks with low sensitivities by 7.5 percent annually, adjusted for exposures to the market return as well as size, value, and momentum factors. Furthermore, a liquidity risk factor accounts for half of the profits to a momentum strategy over the same 34-year period.

A Bayesian approach is used to investigate a sample’s information about a portfolio’s degree of inefficiency. With standard diffuse priors, posterior distributions for measures of portfolio inefficiency can concentrate well away from values consistent with efficiency, even when the portfolio is exactly efficient in the sample. The data indicate that the NYSE–AMEX market portfolio is rather inefficient in the presence of a riskless asset, although this conclusion is justified only after an analysis using informative priors. Including a riskless asset significantly reduces any sample’s ability to produce posterior distributions supporting small degrees of inefficiency.

Green assets delivered high returns in recent years. This performance reflects unexpectedly strong increases in environmental concerns, not high expected returns. German green bonds outperformed their higher-yielding non-green twins as the “greenium” widened, and U.S. green stocks outperformed brown as climate concerns strengthened. Despite that outperformance, we estimate lower expected returns for green stocks than for brown, consistent with theory. We estimate expected returns in two ways: ex ante, using implied costs of capital, and ex post, using realized returns purged of shocks from climate concerns and earnings. A theoretically motivated green factor explains much of value stocks’ recent underperformance.

We model investing that considers environmental, social, and governance (ESG) criteria. In equilibrium, green assets have low expected returns because investors enjoy holding them and because green assets hedge climate risk. Green assets nevertheless outperform when positive shocks hit the ESG factor, which captures shifts in customers’ tastes for green products and investors’ tastes for green holdings. The ESG factor and the market portfolio price assets in a two-factor model. The ESG investment industry is largest when investors’ ESG preferences differ most. Sustainable investing produces positive social impact by making firms greener and by shifting real investment toward green firms.

We study tradeoffs among active mutual funds’ characteristics. In both our equilibrium model and the data, funds with larger size, lower expense ratio, and higher turnover hold more-liquid portfolios. Portfolio liquidity, a concept introduced here, depends not only on the liquidity of the portfolio’s holdings but also on the portfolio’s diversification. We also confirm other model-predicted tradeoffs. Larger funds are cheaper. Larger and cheaper funds are less active, based on our new measure of activeness. Better-diversified funds hold less-liquid stocks; they are also larger and cheaper, and they trade more. These tradeoffs provide novel evidence of diseconomies of scale in active management.

We empirically analyze the nature of returns to scale in active mutual fund management. We find strong evidence of decreasing returns at the industry level. As the size of the active mutual fund industry increases, a fund׳s ability to outperform passive benchmarks declines. At the fund level, all methods considered indicate decreasing returns, though estimates that avoid econometric biases are insignificant. We also find that the active management industry has become more skilled over time. This upward trend in skill coincides with industry growth, which precludes the skill improvement from boosting fund performance. Finally, we find that performance deteriorates over a typical fund׳s lifetime. This result can also be explained by industry-level decreasing returns to scale.