Refinements to the Sharpe ratio: Comparing alternatives for bear markets

In recent years, various proposals have been published and discussed on overcoming the problems in evaluating fund performance based on ex post Sharpe ratios during periods of declining markets. In particular, it has frequently been debated whether negative Sharpe ratios, which naturally occur in bear markets, reliably measure fund performance. This paper presents refinements to the Sharpe ratio and compares them with the original Sharpe ratio. We show that only the so-called normalised Sharpe ratio produces meaningful results, not only for bear markets, but for any other market period as well. Our findings are derived from theoretical analyses based on a factor model and checked for plausibility against economic fundamentals. The practical relevance of our theoretical results is confirmed by a subsequent empirical study based on sample data from US equity mutual funds.