Market neutral funds are commonly advertised as alternative investments that offer returns which are uncorrelated with the broad market. Utilizing recent advances in financial econometrics, we demonstrate that using standard forecasting methods to construct market (beta) neutral funds is often very inaccurate. Our findings demonstrate that the econometric methods that are commonly employed for forecasting the beta (systematic) risk typically lack sufficient accuracy to permit the successful construction of market neutral portfolios. The results in this paper also highlight the need for higher frequency returns data to be utilized more commonly. Using daily returns over the past year, we demonstrate an approach that is easy to implement and delivers a substantial improvement, relative to other methods, when attempting to construct a market neutral portfolio.