Practical Financial Optimization: Decision Making for Financial Engineers

Chapter 7

Index Funds

They also serve who only sit and hold.

Paul A. Samuelson

7.1 Preview

Broadly defined market indices are comprehensive measures of market trends. Passive strategies that manage index funds to mimic market trends are prevalent among portfolio managers. In this chapter we develop optimization models for structuring index funds. We start with a review of the basics of market indices and then discuss two broad model classes for structuring indexed portfolios. Models for creating index funds for international and corporate bond markets help to clarify the issues. The use of multi-period stochastic optimization models is also discussed for this broad problem class, and empirical results with several applications illustrate the uses of the models and establish their efficacy.

7.2 Basics of Market Indices

An index is a single statistic that summarizes the relative changes in a set of variables, such as stock or bond or commodity prices. An index can be broad in scope and include variables based on value, growth rate, or geographical region, or it can take a narrow view of the market and focus on a single economic sector or an industry.

As international institutions change location and invest funds outside their domestic market they need tools to guide investment analysis, asset allocation, and performance measurement in diverse markets. Investors quite often evaluate their portfolio choices with respect to overall market trends. Indices provide comprehensive measures ...