In this paper we present a rigorous, yet easy to apply method that substitutes those tedious techniques and error prone procedures that are currently used in finding optimal portfolios. Our work is not to support or dispute the applicability of the Mean-Variance optimization method in finance; we simply offer a robust approach to find all the characteristics of any efficient portfolios, with or without bonds. We show that one matrix multiplication provides all the characteristics of all efficient portfolios including risk and return of these optimal portfolios and their corresponding Lagrange multipliers as well as the proportions invested in each asset. The rest is just a few simple elementary arithmetic operations. | Portfolio optimization is one multiplication, the rest is arithmetic
