The Capital Asset Pricing Model implies that (i) the market portfolio is efficient and (ii) expected returns are linearly related to betas. Many do not view these implications as separate, since either implies the other, but we demonstrate that either can hold nearly perfectly while the other fails grossly. If the index portfolio is inefficient, then the coefficients and from an ordinary least squares regression of expected returns on betas can equal essentially any values and bear no relation to the index portfolio's mean‐variance location. That location does determine the outcome of a mean‐beta regression fitted by generalized least squares.

The capital asset pricing model implies that the market portfolio is efficient and expected returns are linearly related to betas. Many do not view these implications as separate, since either implies the other, but the authors demonstrate that either can hold nearly perfectly while the other fails grossly. If the index portfolio is inefficient, then the coefficient and R[squared] from an ordinary least squares regression of expected returns on betas can equal essentially any values and bear no relation to the index portfolio's mean-variance location. That location does determine the outcome of a mean-beta regression fitted by generalized least squares.

[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.]

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.