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VaR estimation using skewed mixture models and various mixtures of factor analyzers
Journal of the Korean Data & Information Science Society 2018;29:769-78
Published online May 31, 2018
© 2018 Korean Data and Information Science Society.

Kwangyee Ko1 · Jangsun Baek2

12Department of Statistics, Chonnam National University
Correspondence to: Professor, Department of Statistics, Chonnam National University, Gwangju 61186, Korea. E-mail:
Received May 15, 2018; Revised May 24, 2018; Accepted May 25, 2018.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
It is very important to estimate VaR (Value-at-Risk) of the portfolio with many returns on investment for risk management. The distribution of returns has often thick tails, skewness or kurtosis. In order to estimate VaR of the total investment return, we consider not only mixture of skewed distributions models such as MSN (Mixtures of skew-normal distribution) and MSt (Mixtures of skew-t distribution), but also various parsimonious mixtures of factor analyzers models of MFA (Mixtures of factor analyzers), MCFA (Mixtures of common factor analyzers) and MCtFA (Mixtures of common skew-t factor analyzers). Application of the models to the KOSPI returns data showed that all models have the similar performance for estimating 1% - 5% VaR, but the estimates of MFA and MCtFA are more close to the empirical VaRs of the data.
Keywords : EM algorithm, mixtures of factor analyzers, portfolio, skewed mixture model, VaR.