A robust VaR model under different time periods and weighting schemes

This paper analyses several volatility models by examining their ability to forecast Value-at-Risk (VaR) for two different time periods and two capitalization weighting schemes. Specifically, VaR is calculated for large and small capitalization stocks, based on Dow Jones (DJ) Euro Stoxx indices and is modeled for long and short trading positions by using non parametric, semi parametric and parametric methods. In order to choose one model among the various forecasting methods, a two-stage backtesting procedure is implemented. In the first stage the unconditional coverage test is used to examine the statistical accuracy of the models. In the second stage a loss function is applied to investigate whether the differences between the models, that calculated accurately the VaR, are statistically significant. Under this framework, the combination of a parametric model with the historical simulation produced robust results across the sample periods, market capitalization schemes, trading positions and confidence levels and therefore there is a risk measure that is reliable.

Managing extreme risks in tranquil and volatile markets using conditional extreme value theory

Financial risk management typically deals with low-probability events in the tails of asset price distributions. To capture the behavior of these tails, one should therefore rely on models that explicitly focus on the tails. Extreme value theory (EVT)-based models do exactly that, and in this paper, we apply both unconditional and conditional EVT models to the management of extreme market risks in stock markets. We find conditional EVT models to give particularly accurate Value-at-Risk (VaR) measures, and a comparison with traditional (Generalized ARCH (GARCH)) approaches to calculate VaR demonstrates EVT as being the superior approach both for standard and more extreme VaR quantiles.     

Extremes and Robustness: A Contradiction?

Stochastic models play an important role in the analysis of data in many different fields, including finance and insurance. Many models are estimated by procedures that lose their good statistical properties when the underlying model slightly deviates from the assumed one. Robust statistical methods can improve the data analysis process of the skilled analyst and provide him with useful additional information. For this anniversary issue, we discuss some aspects related to robust estimation in the context of extreme value theory (EVT). Using real data and simulations, we show how robust methods can improve the quality of EVT data analysis by providing information on influential observations, deviating substructures and possible mis-specification of a model while guaranteeing good statistical properties over a whole set of underlying distributions around the assumed one.     

Extreme observations and diversification in Latin American emerging equity markets

In this paper, we focus on the tails of the unconditional distribution of Latin American emerging markets stock returns. We explore their implications for portfolio diversification according to the safety first principle, first proposed by Roy [Econometrica (1952) 20, 431]. We find that the Latin American emerging markets have significantly fatter tails than industrial markets, especially, the lower tail of the distribution. We consider the implication of the safety first principle for a US investor who creates a diversified portfolio using Latin American stock markets. We find that a US investor gains by adding Latin American equity markets to her purely domestic portfolio. For different parameter specifications, we find a more realistic asset allocation than the one suggested by the literature based on the traditional mean-variance framework.