Calculating the misspecification in beta from using a proxy for the market portfolio

This study investigates the effects of the market portfolio being unknown on the estimation of beta in the CAPM. Providing an analysis of the impact of using a proxy for the market portfolio when the market portfolio is known. This allows one to ask and answer 'if what' questions, such as if portfolio A is the true market portfolio, what happens to beta if one uses portfolio B as a proxy for A. It is shown that for a given universe of investible assets, frequently used equally weighted and value weighted portfolios are far from the Markowitz market portfolio and thus the betas calculated with the equally weighted and value weighted portfolios are quite different from those obtained with the Markowitz portfolio. These calculations are based on sequential assumptions that one portfolio is a proxy whilst another is the actual market.