Should Expected or Most Likely Returns be the Focus in Investment Decisions? Introducing “Most Likely†Versions of Sharpe and Sortino Ratios

For the last 60 years, Expected Utility Theory, Rational Expectations, and a tacit presumption of symmetry in outcome distributions have been the micro and macro foundations of decision-making paradigms which seek optimum risk tempered expected outcomes. The Sharpe ratio, in its use in evaluating portfolio performance and its focus on average returns, epitomizes the practice. When outcome distributions are symmetric unimodal, expected and most likely outcomes coincide, and choices can be construed as being made on the basis of either. However, when outcome distributions are asymmetric or multi-modal, expected outcomes are not the most likely and, in contradiction of rational expectations assumptions, expectations-based choice will engender systematic information laden surprises raising questions as to whether choice should be most likely or expected outcome based. Here, the impact of switching to a Most Likely view of the world is examined and “Most Likely†focused versions of the Sharpe and Sortino Ratios are introduced. Simple exercises performed on commonly used benchmark portfolio and stock returns data demonstrate that portfolio orderings change substantially when the focus is switched to most likely outcomes, all of which gives some pause for thought.