\( \newcommand{\bm}[1]{\boldsymbol{#1}} \newcommand{\textm}[1]{\textsf{#1}} \newcommand{\textnormal}[1]{\textsf{#1}} \def\T{{\mkern-2mu\raise-1mu\mathsf{T}}} \newcommand{\R}{\mathbb{R}} % real numbers \newcommand{\E}{{\rm I\kern-.2em E}} \newcommand{\w}{\bm{w}} % bold w \newcommand{\bmu}{\bm{\mu}} % bold mu \newcommand{\bSigma}{\bm{\Sigma}} % bold mu \newcommand{\bigO}{O} %\mathcal{O} \renewcommand{\d}[1]{\operatorname{d}\!{#1}} \)

Chapter 13 Index Tracking Portfolios

“If you have assumed a character beyond your strength, you have both played a part ill, and have fallen in an unbecoming manner: you have gone aground.”

— Epictetus

“I never met another man I’d rather be. And even if that’s a delusion, it’s a lucky one.”

— Charles Bukowski

Can we outsmart the market? The efficient-market hypothesis states that the price of a security already contains all the publicly available information about the future (Fama, 1970), although another line of thought supports precisely the opposite view in favor of inefficient and irrational markets (Shiller, 1981). In any case, beating the market is routinely promised by investment funds, hedge funds, financial experts, but do they keep up their promises? Empirical analysis of data shows that about 95% of funds do not outperform the market (Malkiel, 1973).

This chapter explores the topic of market or index tracking as an alternative to active investment strategies that attempt to beat the market: from heuristic and discretionary approaches, to more sophisticated optimization formulations, and even the most recent techniques to automatically choose the number of active assets in a statistically controlled way.

This material will be published by Cambridge University Press as Portfolio Optimization: Theory and Application by Daniel P. Palomar. This pre-publication version is free to view and download for personal use only; not for re-distribution, re-sale, or use in derivative works. © Daniel P. Palomar 2025.

References

Fama, E. F. (1970). Efficient capital markets: A review of theory and empirical work. The Journal of Finance, 25(2), 383–417.

Malkiel, B. G. (1973). A Random Walk down Wall Street. New York: W. W. Norton.

Shiller, R. J. (1981). Do stock prices move too much to be justified by subsequent changes in dividends? American Economic Review, 71(3), 421–436.