The regression-based efficient frontier

The standard mean–variance analysis employs quadratic optimization to determine the optimal portfolio weights and to plot the mean–variance efficient frontier (MVEF). It then indirectly evaluates the mean–variance efficiency test (MVET) by considering the maximum Sharpe ratios of the tangency portfolio within the MVEF framework, which assumes a risk-free rate. This paper integrates these procedures without considering the risk-free rate by transitioning to a regression-based efficient frontier (RBEF). The RBEF estimates the optimal portfolio weights and simultaneously implements the MVET based on an OLS F-test, offering a simpler approach to portfolio optimization.