Where is the distribution tail threshold? A tale on tail and copulas in financial risk measurement

Estimating the market risk is conditioned by the fat tail of the distribution of returns. But the tail index depends on the threshold of this distribution fat tail. We propose a methodology based on the decomposition of the series into positive outliers, Gaussian central part and negative outliers and uses the latter to estimate this cutoff point. Additionally, from this decomposition, we estimate extreme dependence correlation matrix which is used in the measurement of portfolio risk. For a sample consisting of six assets (Bitcoin, Gold, Brent, Standard&Poor-500, Nasdaq and Real Estate index), we find that our methodology presents better results, in terms of normality and volatility of the tail index, than the Kolmogorov–Smirnov distance, and its unnecessary capital consumption is lower. Also, in the measurement of the risk of a portfolio, the results of our proposal improve those of a t-Student copula and allow us to estimate the extreme dependence and the corresponding indexes avoiding the implicit restrictions of the elliptic and Archimedean copulas. •This paper presents a new method for estimating the threshold of the distribution tail.•The returns are decomposed into positive (Good), Gaussian (Usual) and negative (Bad).•Our tail index is more consistent than that using the Kolmogorov–Smirnov distance.•Using our methodology, the estimated market risk is better than other measures.•Also, for a portfolio, our proposal shows better results than the usual copulas.•Using the Bad-to-Bad asset dependency is computationally less intensive than copulas.