Estimating Sharpe ratio function in the presence of measurement error

Hongmei Lin, Shaodong Zhang, Wenchao Xu, Tiejun Tong and Riquan Zhang

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 18, 5687-5702

Abstract: In financial econometrics, the Sharpe ratio function serves as a gold standard to measure the return-to-risk ratio for comparing different assets or trading strategies. In the recent literature, several methods have been developed to directly or indirectly estimate the Sharpe ratio function, yet none of them apply to the scenario where the covariates are measured with error. To handle this problem, we propose a new method by incorporating the local polynomial smoothing and SIMEX to simultaneously estimate the Sharpe ratio function and the negative log-volatility function in the presence of measurement error. The asymptotic bias and variance of the proposed estimators are also derived under some regularity conditions. We further conduct Monte Carlo simulations to evaluate the finite sample performance, and apply two real data examples to illustrate the usefulness of our new method.

Date: 2025
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DOI: 10.1080/03610926.2024.2444501

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