Comparing value-at-risk methodologies

In this paper, we compare four different Value-at-Risk (V aR) methodologies through Monte Carlo experiments. Our results indicate that the method based on quantile regression with ARCH effect dominates other methods that require distributional assumption. In particular, we show that the non-robust methodologies have higher probability to predict V aRs with too many violations. We illustrate our findings with an empirical exercise in which we estimate V aR for returns of S˜ao Paulo stock exchange index, IBOVESPA, during periods of market turmoil. Our results indicate that the robust method based on quantile regression presents the least number of violations.

Modeling and predicting the CBOE market volatility index

This paper performs a thorough statistical examination of the time-series properties of the daily market volatility index (VIX) from the Chicago Board Options Exchange (CBOE). The motivation lies not only on the widespread consensus that the VIX is a barometer of the overall market sentiment as to what concerns investors' risk appetite, but also on the fact that there are many trading strategies that rely on the VIX index for hedging and speculative purposes. Preliminary analysis suggests that the VIX index displays long-range dependence. This is well in line with the strong empirical evidence in the literature supporting long memory in both options-implied and realized variances. We thus resort to both parametric and semiparametric heterogeneous autoregressive (HAR) processes for modeling and forecasting purposes. Our main ndings are as follows. First, we con rm the evidence in the literature that there is a negative relationship between the VIX index and the S&P 500 index return as well as a positive contemporaneous link with the volume of the S&P 500 index. Second, the term spread has a slightly negative long-run impact in the VIX index, when possible multicollinearity and endogeneity are controlled for. Finally, we cannot reject the linearity of the above relationships, neither in sample nor out of sample. As for the latter, we actually show that it is pretty hard to beat the pure HAR process because of the very persistent nature of the VIX index.

Cálculo do Value at Risk (VaR) para o Ibovespa, pós crise de 2008, por meio dos modelos de heterocedasticidade condicional (GARCH) e de volatilidade estocástica (Local Scale Model - LSM)

O objetivo deste estudo é propor a implementação de um modelo estatístico para cálculo da volatilidade, não difundido na literatura brasileira, o modelo de escala local (LSM), apresentando suas vantagens e desvantagens em relação aos modelos habitualmente utilizados para mensuração de risco. Para estimação dos parâmetros serão usadas as cotações diárias do Ibovespa, no período de janeiro de 2009 a dezembro de 2014, e para a aferição da acurácia empírica dos modelos serão realizados testes fora da amostra, comparando os VaR obtidos para o período de janeiro a dezembro de 2014. Foram introduzidas variáveis explicativas na tentativa de aprimorar os modelos e optou-se pelo correspondente americano do Ibovespa, o índice Dow Jones, por ter apresentado propriedades como: alta correlação, causalidade no sentido de Granger, e razão de log-verossimilhança significativa. Uma das inovações do modelo de escala local é não utilizar diretamente a variância, mas sim a sua recíproca, chamada de “precisão” da série, que segue uma espécie de passeio aleatório multiplicativo. O LSM captou todos os fatos estilizados das séries financeiras, e os resultados foram favoráveis a sua utilização, logo, o modelo torna-se uma alternativa de especificação eficiente e parcimoniosa para estimar e prever volatilidade, na medida em que possui apenas um parâmetro a ser estimado, o que representa uma mudança de paradigma em relação aos modelos de heterocedasticidade condicional.

We're Chained: an analysis of systemic risk in finance

This dissertation presents two papers on how to deal with simple systemic risk measures to assess portfolio risk characteristics. The first paper deals with the Granger-causation of systemic risk indicators based in correlation matrices in stock returns. Special focus is devoted to the Eigenvalue Entropy as some previous literature indicated strong re- sults, but not considering different macroeconomic scenarios; the Index Cohesion Force and the Absorption Ratio are also considered. Considering the S&P500, there is not ev- idence of Granger-causation from Eigenvalue Entropies and the Index Cohesion Force. The Absorption Ratio Granger-caused both the S&P500 and the VIX index, being the only simple measure that passed this test. The second paper develops this measure to capture the regimes underlying the American stock market. New indicators are built using filtering and random matrix theory. The returns of the S&P500 is modelled as a mixture of normal distributions. The activation of each normal distribution is governed by a Markov chain with the transition probabilities being a function of the indicators. The model shows that using a Herfindahl-Hirschman Index of the normalized eigenval- ues exhibits best fit to the returns from 1998-2013.

Valuing emerging markets companies : new approaches to determine the effective exposure to country risk

The aim of this paper is to propose new methods to measure the effective exposure to country risk of emerging-market companies. Starting from Damodaran (2003), we propose seven new approaches and a revised CAPM for emerging markets companies. The “Prospective Lambda” represents the effective exposure according to analysts’ estimates of growth. The “Relative Lambda” relies on the firm value estimated through a relative valuation. The “Retrospective Lambda” represents the ex-post effective exposure to country risk. The “Company Effective Risk Premium” is a generalization of the Retrospective Lambda, and expresses the premium effectively requested by investors to invest in that specific company in the past year. “The Actual Lambda” and the “Company Actual Risk Premium” represent, respectively, the actual exposure to country risk of a company and the actual premium requested by investors to invest in that specific company. The “Industry Lambda” reflects the median exposure to country risk of the industry in which the company belongs. We tested our new measures of exposure to country risk on the Latin American emerging markets companies according to the classification of the MSCI Emerging Markets Latin America Index. The results confirm that the new approaches can be effectively applied by financial analysts to stable-growth companies that operate in emerging markets and to mature markets companies that operate in emerging markets, providing with a more reliable estimate of both the premium effectively requested by investors in the past and the actual premium. Applying the new approaches, the cost of equity reflects the effective exposure of a company to country risk without being over- or underestimated, as is the case with other existing approaches.