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

Wenchao Xu1, Hongmei Lin2, Tiejun Tong3

  • 1Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, People's Republic of China.

Journal of Applied Statistics
|January 5, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces a direct local maximum likelihood method for estimating the Sharpe ratio function and volatility, improving upon traditional two-step approaches in financial econometrics. The new method simultaneously estimates key risk/return measures and their derivatives, offering enhanced accuracy and applicability.

Keywords:
Direct methodSharpe ratio functionheteroscedastic non-parametric regressionjoint limiting distributionlocal polynomial smoothing

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Area of Science:

  • Financial econometrics
  • Quantitative finance

Background:

  • The Sharpe ratio function is a critical risk/return measure in finance.
  • Existing estimation methods often use a two-step plug-in approach, which can be suboptimal.

Purpose of the Study:

  • To propose a direct local maximum likelihood method for simultaneous estimation of the Sharpe ratio and negative log-volatility functions.
  • To extend the method for multivariate Sharpe ratio estimation.
  • To evaluate the performance of the new method and compare it with existing techniques.

Main Methods:

  • Direct local maximum likelihood estimation.
  • Simultaneous estimation of Sharpe ratio and negative log-volatility functions and their derivatives.
  • Establishment of joint limiting distribution for estimators.
  • Application to multivariate Sharpe ratio estimation.

Main Results:

  • The proposed direct method simultaneously estimates the Sharpe ratio and negative log-volatility functions and their derivatives.
  • The joint limiting distribution of the estimators is established.
  • The method is successfully extended to multivariate settings.
  • Numerical simulations and real-data analysis (US Treasury bill data) demonstrate the method's effectiveness and capture covariate-dependent effects.

Conclusions:

  • The direct local maximum likelihood method provides an efficient and accurate approach for estimating the Sharpe ratio function and related volatility measures.
  • This method offers advantages over traditional two-step procedures, particularly in capturing complex financial dynamics.
  • The findings have practical implications for risk management and investment strategy analysis in financial econometrics.