This article takes a shrinkage approach to examine the empirical implications of aversion to model uncertainty. The shrinkage approach explicitly shows how predictive distributions incorporate data and prior beliefs. It enables us to solve the optimal portfolios for uncertainty-averse investors. A version to uncertainty about the capital asset pricing model leads investors to hold a portfolio that is not mean-variance efficient for any predictive distribution. However, mean-variance efficient portfolios corresponding to extremely strong beliefs in the Fama-French model are approximately optimal for uncertainty-averse investors. The empirical Bayes approach does not result in optimal portfolios for investors who are averse to model uncertainty.

[Financial institutions around the world expected the millennium date change (Y2K) to cause an aggregate liquidity shortage. Responding to the concern, the Federal Reserve Bank of New York auctioned Y2K options to primary dealers. The options gave the dealers the right to borrow from the Fed at a predetermined interest rate. Using the implied volatilities of Y2K options and the on/off-the-run spread, we demonstrate that the Fed's action eased the fears of bond dealers, contributing to a drop in the liquidity premium of Treasury securities. Our analysis shows the link between the microstructure of government debt markets and the central bank's provision of liquidity. We argue that Y2K options and their effects on liquidity premium broadly conform to the economic theory on public provision of private liquidity.]

Without the assumption of conditional homoskedasticity, a general asymptotic distribution theory for the two-stage cross-sectional regression method shows that the standard errors produced by the Fama–MacBeth procedure do not necessarily overstate the precision of the risk premium estimates. When factors are misspecified, estimators for risk premiums can be biased, and the t-value of a premium may converge to infinity in probability even when the true premium is zero. However, when a beta-pricing model is misspecified, the t-values for firm characteristics generally converge to infinity in probability, which supports the use of firm characteristics in cross-sectional regressions for detecting model misspecification.

Most empirical studies of the static capital asset pricing model (CAPM) assume that betas remain constant over time and that the return on the value-weighted portfolio of all stocks is a proxy for the return on aggregate wealth. The general consensus is that the static CAPM is unable to explain satisfactorily the cross-section of average returns on stocks. The authors assume that the CAPM holds in a conditional sense, i.e., betas and the market risk premium vary over time. They include the return on human capital when measuring the return on aggregate wealth. The authors' specification performs well in explaining the cross-section of average returns.

This paper examines the degree of portfolio inefficiency subject to various constraints on portfolio weights. When portfolio weights are unconstrained, the posterior loss in expected return on the NYSE-AMEX market portfolio is over 20% (annualized). In contrast, when portfolio weights are constrained to be nonnegative, the posterior loss in expected return is only about 4% (annualized). In addition, short-sale constraints greatly reduce uncertainty in inferences about portfolio efficiency.

This article takes a shrinkage approach to examine the empirical implications of aversion to model uncertainty. The shrinkage approach explicitly shows how predictive distributions incorporate data and prior beliefs. It enables us to solve the optimal portfolios for uncertainty-averse investors. Aversion to uncertainty about the capital asset pricing model leads investors to hold a portfolio that is not mean-variance efficient for any predictive distribution. However, mean-variance efficient portfolios corresponding to extremely strong beliefs in the Fama--French model are approximately optimal for uncertainty-averse investors. The empirical Bayes approach does not result in optimal portfolios for investors who are averse to model uncertainty.

The stochastic discount factor (SDF) method provides a unified general framework for econometric analysis of asset‐pricing models. There have been concerns that, compared to the classical beta method, the generality of the SDF method comes at the cost of efficiency in parameter estimation and power in specification tests. We establish the correct framework for comparing the two methods and show that the SDF method is as efficient as the beta method for estimating risk premiums. Also, the specification test based on the SDF method is as powerful as the one based on the beta method.