Chapter 12 Portfolio Theory with Matrix Algebra

Updated: May 13, 2021

This chapter is laid out as follows. Section 1 describes portfolios with $$N$$ risky assets using matrix algebra. The concept of portfolio risk diversification is elaborated using calculations for large portfolios. Sections 2 through 5 cover the matrix algebra calculations required for determining mean-variance efficient portfolios. Explicit formulas are given for the global minimum variance portfolio, a minimum variance portfolio that achieves a specified target expected return, and the tangency portfolio. A simple algorithm to easily trace out the risky asset only efficient frontier is also presented. Section 6 discusses some practical problems associated with very large portfolios, and section 7 introduces the IntroCompFinR functions for portfolio analysis. Section 9 gives a real-world application of the theory to asset allocation among Vanguard mutual funds.
suppressPackageStartupMessages(library(corrplot))
options(digits=3)