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

Wenchao Xu, Hongmei Lin*, Tiejun Tong, Riquan Zhang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

Abstract

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

Original languageEnglish
Pages (from-to)34-52
Number of pages19
JournalJournal of Applied Statistics
Volume51
Issue number1
Early online date9 Oct 2022
DOIs
Publication statusPublished - 2 Jan 2024

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Direct method
  • heteroscedastic non-parametric regression
  • joint limiting distribution
  • local polynomial smoothing
  • Sharpe ratio function

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