Performance measurement is an integral part of investment analysis and risk management. The Sharpe ratio is one of the most prominently used measures of performance of an investment with respect to return and risk. While most of the literature has addressed the large sample properties of the Sharpe ratio, it is important to compare the performance of these methods when only a small sample of observations is available. We propose a third-order asymptotic likelihood-based method to obtain highly accurate inference for the Sharpe ratio when returns are assumed to follow a Gaussian autoregressive process. Through real life examples, we show that results can vary vastly according to the methods used to obtain them. Results from simulation studies illustrate that our proposed method is superior to the existing methods used in the literature even with a very small number of observations.
Mathematics Subject Classification: 62P05
Keywords: Performance measurement; likelihood based method; Sharpe ratio