Foundations of Computational Finance with MATLAB

CHAPTER 9Portfolios

9.1 Introduction

This chapter introduces multiple-asset portfolios and the MATLAB® Portfolio object.

Key concepts and tools in this chapter include:

• Basic portfolio theory
• The logic of mean-variance optimization and risk–return trade-off
• MATLAB Portfolio object
• Object-oriented programming
• Calculating and plotting efficient frontiers
• Portfolio constraints
• Portfolio analytic functions

Required software: MATLAB base program; MATLAB Financial Toolbox™

9.2 Finance Background

The analytic and valuation functions covered to this point have focused mainly on single assets. That approach provides useful insights, but many financial decisions involve multiple-asset portfolios. Within the portfolio these assets are grouped into broad classes, such as cash, commodities, equities, and fixed income. A portfolio can hold multiple securities within one class and multiple securities from different asset classes, depending on the desired degree of diversification and available funds.

Investors typically hold diversified portfolios because most investments' returns are unpredictable due to numerous potentially influential factors. Imagine that you knew with certainty an investment's performance one day in advance. You would raise all the funds you could and buy or sell short that investment, depending on whether it was going to increase or decrease in price. Most investors lack such foresight, however, which makes it prudent to diversify a portfolio across and within asset ...