R Programming for Actuarial Science

8 Modern Portfolio Theory

Peter McQuire

library(dplyr)

8.1 Introduction

In 1952 Harry Markovitz published his paper “Portfolio Selection” in the Journal of Finance. The paper proposed a methodology which allowed investors to analyse the balance between risk and returns between various asset portfolios. The theory became popularly known as “mean-variance portfolio theory,” “Modern Portfolio Theory (MPT),” “mean-variance optimisation,” or even “Markovitz Portfolio Theory”.

In this chapter we discuss the key aspects of this theory. We proceed to calculate the expected returns and variance of returns from various combinations of assets, comparing our results from portfolios which consist of a range of risky and risk-free assets (we will define exactly what is meant by “risk” under MPT shortly). We will do this by writing our own code rather than use one of the many functions within R already available, which should aid the learning process. An Appendix is included which describes a method to determine efficient portfolios using Lagrange multipliers.

Remark 8.1 There are various packages in R which are related to the material in this chapter, such as fPortfolio and PortfolioAnalytics. The reader may wish to review these in due course.

MPT allows an investor, at least in theory, to choose a particular portfolio of assets which is expected to provide the greatest investment return subject to an acceptable level of risk which the investor is willing to take. Thus our calculations may ...