AbstractPurpose: This study aims to explore the application of the discrete Hilbert transform (DHT) in measuring asset return risk within a portfolio, emphasizing its potential for enhancing risk evaluation in the field of financial mathematics.Methodology/approach: The research utilized a quantitative approach with data sourced from publicly available historical stock prices. Analysis was conducted using software MATLAB to implement the discrete Hilbert transform, which transforms time-series data into phase and amplitude components. The portfolio risk was calculated based on the transformed data, and the results were compared against traditional risk metrics such as variance and Value at Risk (VaR).Results/findings: The findings indicate that the discrete Hilbert transform provides additional insights into portfolio risk by capturing frequency-domain characteristics of asset returns. It complements traditional measures, offering a novel perspective on risk analysis. Specifically, the discrete Hilbert transform was effective in identifying subtle changes in risk patterns that were not apparent in time-domain analyses alone.Conclusion: This study investigates the application of the discrete Hilbert transform (DHT) in measuring the risk of asset returns within investment portfolios, specifically focusing on Indonesian stocks. TheLimitations: This study is limited by its focus on a small sample of stocks within a single financial market, which may restrict the generalizability of the findings. Additionally, the research does not account for macroeconomic factors that could influence asset returns.Contribution: This study contributes to the field of financial risk management by introducing the discrete Hilbert transform as a supplementary tool for risk analysis. It offers practical implications for portfolio managers, actuaries, and financial analysts seeking innovative methods to enhance risk assessment and decision-making processes.