A Comparison of Ranking Criteria: an Application to Asset Class Indices of Europe, US, Russia and China

The main purpose of this work is the ex post comparison of the performances of three macro asset class indices for Europe, United States, Russia and China during the period 2003-2015. The analysis is based on six different ranking criteria, starting with the well-known Sharpe index and its VaR and CVaR modifications, then considering the Omega and Sortino ratios which employ higher partial moments, and at last the Rachev ratio which changes the profitability index. All the previous performance indices give substantially the same ranking; they all show supremacy of Chinese fixed income and both European and American real estate in the years 2003-2008; they indicate US and European stock indices as the worst performers in 2008, and American, Russian and Chinese fixed income indices from 2012 to 2015 again as the worst performers. A visual display of the six different rankings is also provided, highlighting the adequacy of the Sharpe ratio against its more refined alternatives.