# Market Model vs. Historical estimation, need clarification

Will explain my conundrum in an example… Suppose we have 1000 assets and want to create a mean-variance frontier. We need “n” variance forecasts, so 1000 forecasts We need “n” expected return forecasts, 1000 as well We need [n(n-1)]/2 covariance forecasts, so 499,500 covariance forecasts Therefore, we need 501,500 forecasts. Using traditional historical estimation for these inputs, we need to get the equivalent number of parameters. So we’ll need 501,500 parameters to get 501,500 forecasts for these inputs. BUT: Market model is much more efficient in terms of gathering the number of required parameters. For 1000 assets, we only need 3n+2 parameters to get the the same 501,500 forecasted inputs for the calculations. Thus, we only need 3002 parameters for the same number of inputs. Thus, the market model is simply a more efficient way to get the parameter inputs for the forecasts needed for the mean variance calculations. Are my conclusions here correct? Any clarification would be much appreciated.

“Market Portfolio” is kind of hard to ascertain , and we can only assume some proxy for it. Otherwise your idea is 100 % correct. Cov(A,B) = BetaofA * BetaofB * varianceOfMarketPortfolio . So we measure Betas to the market ( if we can find that elusive creature) and that way we get order n terms and no need of order n^2 terms