Application of Singular Value Decomposition (SVD) in Dimensionality Reduction and Portfolio Risk Forecasting: Evidence from the Vietnamese Stock Market (2016–2024)

ABSTRACT : This study applies Singular Value Decomposition (SVD), a fundamental technique in linear algebra, to reduce data dimensionality and improve portfolio risk estimation in the Vietnamese stock market. Using daily return data of 30 stocks included in the VN30 index over the period 2016–2024, the study employs SVD to extract the principal factors driving market fluctuations and to reconstruct the covariance matrix after noise filtering. Empirical results indicate that the first five principal factors explain more than 90% of total variance, with the leading factor capturing common systemic risk, while subsequent factors are associated with sectoral risk and liquidity effects. When SVD is applied, the average portfolio risk estimation error decreases by approximately 12%, whereas expected returns remain largely unchanged. These findings demonstrate that SVD is an effective tool for financial data analysis, enabling the separation of signal from noise, enhancing the reliability of risk models, and providing practical implications for investors in Vietnam.