Mark to market value at risk

Abstract

Financial risk management has been overwhelmed by applications and research of value at risk (VaR) in daily practice mainly due to its simple form and easily interpretable feature. Yet, its serious drawback of underestimating an asset’s market risk has been noticed in numerous applications, and many alternative risk measures have been proposed in the literature. Among all existing alternative risk measures, it is hard to find one that a financial institution whose portfolio has multiple settlements before the end of holding period uses to internally perform risk assessment. We propose a new risk measure termed mark to market value at risk (MMVaR) for settlement being taken daily during the holding period. MMVaR is a natural alternative risk measure to VaR as it is a direct generalization of VaR. It not only maintains easily interpretable feature held by VaR, but also better computes an asset’s market risk in a financial institution having daily account settlements. We show that MMVaR is superior to VaR using simulation examples and real data. In real data analysis, we find that risks calculated using MMVaR are about 20% higher than risks calculated using classical VaR, which provides an evidence proof of Basel III’s new capital adequacy ratio requirement, and hence it can become an implementable daily risk measure.