VaRCVaR

VaRCVaR is a risk measure used in finance to evaluate potential portfolio losses by combining the traditional Value at Risk (VaR) with the Conditional Value at Risk (CVaR). It is described in various sources as a hybrid that aims to leverage VaR’s thresholding with CVaR’s emphasis on tail risk, providing a single framework for risk assessment.

Value at Risk (VaR) at level alpha represents the loss threshold that is not exceeded with probability alpha over a given horizon. CVaR at level alpha, also known as Expected Shortfall, is the expected loss given that losses exceed VaR_alpha. VaRCVaR integrates these concepts, with common formulations including a weighted blend VaRCVaR_alpha = w * VaR_alpha + (1 - w) * CVaR_alpha, where w is a weight in [0,1]. Some approaches instead treat VaRCVaR as a two-stage measure: report VaR as the threshold and report CVaR for the tail beyond VaR.

Calculation methods for VaRCVaR include parametric models, historical simulation, and Monte Carlo simulation. Each method requires estimating the tail behavior of the loss distribution and selecting the confidence level alpha. The chosen weight or structural definition influences sensitivity to extreme outcomes and the interpretability of the metric.

Applications of VaRCVaR span risk reporting, capital allocation, and stress testing. The measure seeks to address VaR’s limitations—such as non-coherence and insensitivity to tail losses—by incorporating CVaR information. However, VaRCVaR introduces additional model assumptions and a weighting parameter, which can create model risk and complexity in interpretation.

See also Value at Risk, Conditional Value at Risk, Expected Shortfall, and Risk management.