The Effect of Misestimating Correlation on Value at Risk

Value at risk (VaR) is an estimate of the worst loss over a target horizon with a given level of confidence. Despite its shortcomings, the Basel Committee on Banking Supervision has chosen it as the standard method to measure the market risk of a portfolio of financial assets. This measure of risk is widely used by practitioners and regulators because of its conceptual simplicity and flexibility. This article examines the systematic relationship between correlation misestimation and the corresponding value-at-risk miscalculation. 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. Results show 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. These results have important implications for measuring market risk accurately.