A new method for estimating Sharpe ratio function via local maximum likelihood

The Sharpe ratio function is a commonly used risk/return measure in financial econometrics. To estimate this function, most existing methods take two-step procedure that first estimates the mean and volatility functions separately then applies plug-in method. In paper, we propose direct method via local maximum likelihood to simultaneously negative log-volatility as well their derivatives. We establish joint limiting distribution of proposed estimators, moreover extend multivariate function. also evaluate numerical performance estimators through simulation studies, compare them with methods. Finally, apply three-month US Treasury bill data captures well-known covariate-dependent effect on ratio.