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The extreme points of Vandermonde determinants when optimized on surfaces like spheres and cubes have various applications in random matrix theory, electrostatics and financial mathematics. In this study, we apply the extreme points of Vandermonde determinant when optimized on various surfaces to risk minimization in financial mathematics. We illustrate this by constructing the efficient frontiers represented by spheres, cubes and other general surfaces as applies to portfolio theory. The extreme points of Vandermonde determinant lying on such surfaces as efficient frontier would be used to determine the set of assets with minimum risk and maximum returns. This technique can also applied in optimal portfolio selection and asset pricing.