Roll's critique

Roll's critique makes two statements regarding the market portfolio: 1.

[1]) Mean-variance efficiency of the market portfolio is equivalent to the CAPM equation holding.

This statement is a mathematical fact, requiring no model assumptions.

The market portfolio is unobservable: The market portfolio in practice would necessarily include every single possible available asset, including real estate, precious metals, stamp collections, jewelry, and anything with any worth.

From statement 1, validity of the CAPM is equivalent to the market being mean-variance efficient with respect to all investment opportunities.

The mean-variance tautology argument applies to the arbitrage pricing theory and all asset-pricing models of the form where

If the factors are returns on a mean-variance portfolio, the equation holds exactly.

It is always possible to identify in-sample mean-variance efficient portfolios within a dataset of returns.

Many researchers and practitioners interpret Roll's critique as stating only that "the market portfolio is unobservable".