Which portfolio is better? A discussion of several possible comparison criteria

TL;DR

This paper examines various criteria for comparing portfolio performance, analyzing their implications in different market scenarios to clarify why certain portfolios may outperform others, especially when heuristic methods seem superior.

Contribution

It provides a detailed analysis of different portfolio comparison criteria and their effects in single-asset and no-risk-free-asset markets, clarifying reasons for apparent outperformance.

Findings

Comparison criteria influence perceived portfolio performance.

In single-asset markets, certain comparisons are straightforward.

The absence of a risk-free asset affects portfolio comparison outcomes.

Abstract

During the last few years, there has been an interest in comparing simple or heuristic procedures for portfolio selection, such as the naive, equal weights, portfolio choice, against more "sophisticated" portfolio choices, and in explaining why, in some cases, the heuristic choice seems to outperform the sophisticated choice. We believe that some of these results may be due to the comparison criterion used. It is the purpose of this note to analyze some ways of comparing the performance of portfolios. We begin by analyzing each criterion proposed on the market line, in which there is only one random return. Several possible comparisons between optimal portfolios and the naive portfolio are possible and easy to establish. Afterwards, we study the case in which there is no risk free asset. In this way, we believe some basic theoretical questions regarding why some portfolios may seem to outperform others can be clarified.