This study examines the relationship between portfolios and regressions, which is desirable for educational, mathematical, and theoretical reasons. Educationally, understanding this relationship simplifies the teaching and learning of both procedures. Mathematically, portfolio optimization and regression systems are abstractly, algebraically, topologically, and structurally equivalent. One is obtained from the other as if modeling clay, without tears or discontinuities, and what one learns in one system can be applied to the other. We show portfolios and regressions are equivalent at a theoretical level as well. In the economic-financial context, this theoretical equivalence means that mean-variance, efficient portfolios are in fact optimal predictors, which is necessary for arbitrage-based investment valuation and for the study of arbitrage-based market adjustment. We use linear algebra and study the characteristics of Lagrange methods to make our point. We also provide specialized procedures to facilitate portfolio optimizations.
M. Tarrazo, Portfolios and Regressions, Journal of Financial Education, 35, (2009), 56-74.