Carr’s statement is correct. Using historical estimates and market model estimates both involve the implicit assumption that the historical relationship between a stock and the market is indicative of the future relationship. The historical estimate method uses direct historical means, variances, and correlations as inputs to the model. The market model method regresses historical returns against returns for the market and assumes that returns for each asset are correlated with returns to the market. Since both methods use some form of historical data, both assume that history is indicative of the future.

Bocock is also correct. The historical estimate method requires a large number of estimates, especially for computing the covariances between every stock in a portfolio. The market model estimate method simplifies the process significantly (resulting in fewer parameters) since all stock returns are assumed to be correlated with the market.