The building blocks of the Sharpe ratio—expected returns and volatilities— are unknown quantities that must be estimated statistically and are, therefore, subject to estimation error. This raises the natural question: How accurately are Sharpe ratios measured? To address this question, I derive explicit expressions for the statistical distribution of the Sharpe ratio using standard asymptotic t...

We prove that the Omega measure, which considers all moments when assessing portfolio performance, is equivalent to the widely used Sharpe ratio under jointly elliptic distributions of returns. Portfolio optimization of the Sharpe ratio is then explored, with an active-set algorithm presented for markets prohibiting short sales. When asymmetric returns are considered, we show that the Omega mea...

many performance measures, such as the classical sharpe ratio have difficulty in evaluating the performance of investment companies whose return distributions are skewed. common causes for skew ness are the use of options in the portfolio or superior market timing skills of the portfolio managers. in this article, we examine the ability of the downside risk and the upside potential ratio (upr) ...

This paper uses the concept of possibilistic risk aversion to propose a new approach for portfolio selection in fuzzy environment. Using possibility theory, the possibilistic mean, variance, standard deviation and risk premium of a fuzzy number are established. Possibilistic Sharpe ratio is defined as the ratio of possibilistic risk premium and possibilistic standard deviation of a portfolio. T...

In this research, performance of portfolios formed by use of grid strategy based on new variables (aggressive, indifference and defensive stocks) presented by Rahnamaye Roodposhti (1388), and traditional ones (growth, growth-value and value stocks), calculated with Sharpe and Treynor performance measures and tested by an Active portfolio management approach to identify the portfolios by perform...

We evaluate the probability that an estimated Sharpe ratio exceeds a given threshold in presence of non-Normal returns. We show that this new uncertainty-adjusted investment skill metric (called Probabilistic Sharpe ratio, or PSR) has a number of important applications: First, it allows us to establish the track record length needed for rejecting the hypothesis that a measured Sharpe ratio is b...