Risk measures are statistical measures that are historical predictors of investment risk and volatility, and they are also major components in modern portfolio theory (MPT). MPT is a standard financial and academic methodology for assessing the performance of a stock or a fund as compared to its benchmark index. The most popular risk measure has been Value at Risk (VaR).

Recent development about VaR

The chapter reviews recent developments on VaR, including general properties, parametric estimation methods for value at risk based on well-known univariate distributions, time series models, approximations, copulas, principal components, quantile regression, Bayesian methods and Brownian motion; nonparametric estimation methods for value at risk based on historical methods, bootstrapping, importance sampling and kernel density estimation; semiparametric estimation methods for value at risk based on the extreme value theory method, the generalized Pareto distribution and M-estimation methods; computer software for value at risk based on the R platform and other platforms.

Further ressearch

The chapter can be used as a source of reference and can also encourage further research with respect to measures of financial risk.

Related contributions

• Extreme value theory: an introductory overview by Isabel Fraga Alves and Claudia Neves
• On the estimation of the distribution of aggregated heavy tailed risk by Marie Kratz
• Measures of financial risk by Serguei Novak