the ideal size of the investment, which when adjusted by the period and expected rate of return per unit, gives a rate of return. The accuracy of Sharpe ratio estimators hinges on the statistical properties of returns, and these properties can vary considerably among strategies, portfolios, and over time. Drawback as fund selection criteria Bailey and López de Prado (2012) show that Sharpe ratios tend to be overstated in the case of hedge funds with short track records. These authors propose a probabilistic version of the Sharpe ratio that takes into account the asymmetry and fat-tails of the returns' distribution. With regards to the selection of portfolio managers on the basis of their Sharpe ratios, these authors have proposed a Sharpe ratio indifference curve This curve illustrates the fact that it is efficient to hire portfolio managers with low and even negative Sharpe ratios, as long as their correlation to the other portfolio managers is sufficiently low. Goetzmann, Ingersoll, Spiegel, and Welch (2002) determined that the best strategy to maximize a portfolio's Sharpe ratio, when both securities and options contracts on these securities are available for investment, is a portfolio of selling one out-of-the-money call and selling one out-of-the-money put. This portfolio generates an immediate positive payoff, has a large probability of generating modestly high returns, and has a small probability of generating huge losses. Shah (2014) observed that such a portfolio is not suitable for many investors, but fund sponsors who select fund managers primarily based on the Sharpe ratio will give incentives for fund managers to adopt such a strategy. See also Bias ratio Calmar ratio Capital asset pricing model Coefficient of variation Hansen–Jagannathan bound Information ratio Jensen's alpha List of financial performance measures Modern portfolio theory Omega ratio Risk adjusted return on capital Roy's safety-first criterion Signal-to-noise ratio Sortino ratio Sterling ratio Treynor ratio Upside potential ratio V2 ratio Z score References . Further reading Lo, Andrew W. "The statistics of Sharpe ratios." Financial analysts journal 58.4 (2002): 36-52 https://doi.org/10.2469/faj.v58.n4.2453 Bacon Practical Portfolio Performance Measurement and Attribution 2nd Ed: Wiley, 2008. Bruce J. Feibel. Investment Performance Measurement. New York: Wiley, 2003. External links The Sharpe ratio Generalized Sharpe Ratio All Hail the Sharpe Ratio - Uses and abuses of the Sharpe Ratio What is a good Sharpe Ratio? - Some example calculations of Sharpe ratios What is a good Sharpe Ratio? - Some example calculations of Sharpe