The Effect of Mis-Estimating Correlation on Value-at-Risk

This paper examines the systematic relationship between correlation mis-estimation and the corresponding Value-at-Risk (VaR) mis-calculation. To this end, first a semi-parametric approach, and then a parametric approach is developed. Both approaches are based on a simulation setup. Various linear and non-linear portfolios are considered, as well as variance-covariance and Monte-Carlo simulation methods are employed. We find that the VaR error increases significantly as the correlation error increases, particularly in the case of well-diversified linear portfolios. In the case of option portfolios, this effect is more pronounced for short-maturity, in-the-money options. The use of MC simulation to calculate VaR magnifies the correlation bias effect. Our results have important implications for measuring market risk accurately