An active learning exercise showing some fundamentals of financial portfolio construction

Abstract

This paper focuses on a key statistical insight, namely, that the statistical variability of a sum of variables may be substantially reduced by combining individual components that have low correlation. We demonstrate this idea on a spreadsheet through the use of simulated data with associated statistics and scatter plots but note that, in addition, these ideas have particular relevance in financial applications. We apply these variability reducing principles in the field of finance to demonstrate, on a spreadsheet, the circumstances under which we may get significant risk reduction in a portfolio of 2 shares, compared to holding only one share. However, rather than simply coming up with a single “true” efficient frontier based on assumed “true” parameters, we suggest using repeated sampling with realistic underlying parameters to simulate sets of share returns and risk and then construct sets of simulated efficient frontiers. These sets of efficient frontiers reflect the underlying uncertainty of future share returns and the variability of the returns. We can then embed the idea in students that far from being an exact optimization problem, portfolio construction requires circumspection and a subtle appreciation of statistical variability. This Excel-based didactic approach has been used to introduce students to the principles of variance reduction and the construction of efficient frontiers in the portfolio paradigm, as a component of Honours level courses in the department of Statistical Sciences at the University of Cape Town. Students in these courses consistently found this spreadsheet-centred approach to be a very useful active learning tool for understanding these principles.