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