Three Methods to Calculate the Financial Risk Measurement: Value-At-Risk and Expected Shortfall

Liu Yulin(University of Leeds)

Abstract

This paper analyzes the relationship between the risk factor of each stock and the portfolio’s risk based on a small portfolio with four U.S. stocks, and the reason why these risk factors can be regarded as a market invariant. Then, it evaluates the properties of the convex and coherent risk indicators of the capital requirement index composed of VaR and ES, and use three methods(the historical estimation method, boudoukh’s mixed method and Monte Carlo method) to estimate the risk measurement indicators VaR and ES respectively based on the assumption of multivariate normal distribution’ risk factors and multivariate student t-copula distribution’s one, finally it figures out that these three calculation results are very close.

Keywords

Value at risk, Expected shortfall, Risk factors, Student’s t-copula

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DOI: http://dx.doi.org/10.26549/jfr.v4i2.5510