<p>Bi-objective portfolio optimization, which simultaneously seeks to minimize risk and maximize expected return, has been a central topic in financial research for several decades. This problem is typically formulated as a parametric quadratic programming model, whose set of optimal solutions defines the efficient frontier and its construction remains a major challenge, particularly in large-scale scenarios. To address this issue, we propose the parametric direct support method (PDSM) to solve the bi-objective portfolio selection problem under linear constraints. By adapting the support concept to the special structure of the problem, the novel approach computes iteratively and efficiently all the pivot points and traces out the entire efficient frontier. In contrast to classical approaches, our PDSM method takes into account the sparsity structure of the solutions when dealing with large-scale problems. This provides a key advantage to the proposed approach, which operates on small linear systems at each iteration, thereby significantly accelerating computation and reducing CPU time. We provide a theoretical analysis of the algorithm, establish its finite termination, and evaluate its computational complexity. Extensive numerical experiments on financial datasets and randomly generated instances demonstrate the scalability and superior performance of PDSM in solving large-scale portfolio optimization problems.</p>