Applying Spectral Decomposition in Value-at-Risk: Empirical Evidence from the Taiwan Stock Market

Abstract

Controlling financial risk is an important issue for financial institutions. Value-at-risk is commonly used by practitioners to quantify risk and the Monte Carlo simulation is a popular method to calculate value-at-risk. Generally, the correlation matrix is decomposed by Cholesky decomposition in order to compute the value-at-risk of portfolio. However, it cannot be used to decompose a non-positive correlation matrix. This paper uses the spectral decomposition to solve the limitation of Cholesky method. The simulation results show that the Cholesky decomposition and the spectral decomposition have consistent results in the positive correlation case. For the non-positive case, the results of Monte Carlo simulation by spectral decomposition and other approaches are identical. Thus, we recommend that spectral decomposition is a better method to adopt in the value-at-risk approach for risk management.