Beatriz Vaz de Melo Mendes

Copulas: A Review and Recent Developments

In this review paper we outline some recent contributions to copula theory. Several new authors investigations are presented briefly, namely: order statistics copula, copulas with given multivariate marginals, copula representation via a local dependence measure and applications of extreme value copulas.

Robust multivariate modeling in finance

Purpose – Proposes a new covariance matrix robust estimator able to capture the correct orientation of the data and the large unconditional variance caused by occasional high volatility periods. Design/methodology/approach – Derives easy-to-compute estimates for the center and covariance matrix of a data set. The method finds the correct orientation of the data through a robust estimator and the variances through the classical sample covariance matrix. Findings – Simulation experiments confirm the good performance of the proposed estimator under ?-contaminated normal models and multivariate t-distributions. Practical implications – Provides illustrations of the usefulness of this practical tool for the finance industry, in particular when constructing efficient frontiers. Shows that robust portfolios yield higher cumulative returns and possess more stable weights compositions. Originality/value – It provides an alternative estimator for the covariance matrix able to find a good fit for the bulk of the data as well as for the extreme observations, which could be plugged in widely used financial tools.

Robust Fits for Copula Models

In this article, we obtain robust estimators for copula parameters through the minimization of weighted goodness-of-fit statistics. Different weight functions emphasize different regions on the unit square and are able to handle different locations of model violation. The resulting WMDE estimators are compared to the classical maximum likelihood estimators MLE, and to their weighted version WMLE, an estimator obtained in two steps. The weights obtained in the first step by the application of a high breakdown point scatter matrix estimator are used to identify atypical points. All estimators are compared in a comprehensive simulation study. For each ε-contaminated parametric copula family considered, we showed that there is a robust estimator improving over the MLE and able to capture the correct strength of dependence of the data, despite the contamination percentual and location, and the sample size.

Evaluating the Forecast Accuracy of Emerging Market Stock Returns

This paper analyzes the forecast performance of emerging market stock returns using standard autoregressive moving average (ARMA) and more elaborated autoregressive conditional heteroskedasticity (ARCH) models. Our results indicate that the ARMA and ARCH specifications generally outperform random walk models. Models that allow for asymmetric shocks to volatility are better for in-sample estimation (threshold autoregressive conditional heteroskedasticity for daily returns and exponential generalized autoregressive conditional heteroskedasticity for longer periods), and ARMA models are better for out-of-sample forecasts. The results are valid using both U. S. dollar and domestic currencies. Overall, the forecast errors of each Latin American market can be explained by the forecasts of other Latin American markets and Asian markets. The forecast errors of each Asian market can be explained by the forecasts of other Asian markets, but not by Latin American markets. Our predictability results are economically significant and may be useful for portfolio managers to enter or leave the market.

Copula based models for serial dependence

Purpose - This paper aims to statistically model the serial dependence in the first and second moments of a univariate time series using copulas, bridging the gap between theory and applications, which are the focus of risk managers. Design/methodology/approach - The appealing feature of the method is that it captures not just the linear form of dependence (a job usually accomplished by ARIMA linear models), but also the non-linear ones, including tail dependence, the dependence occurring only among extreme values. In addition it investigates the changes in the mean modeling after whitening the data through the application of GARCH type filters. A total 62 US stocks are selected to illustrate the methodologies. Findings - The copula based results corroborate empirical evidences on the existence of linear and non-linear dependence at the mean and at the volatility levels, and contributes to practice by providing yet a simple but powerful method for capturing the dynamics in a time series. Applications may follow and include VaR calculation, simulations based derivatives pricing, and asset allocation decisions. The authors recall that the literature is still inconclusive as to the most appropriate value-at-risk computing approach, which seems to be a data dependent decision. Originality/value - This paper uses a conditional copula approach for modeling the time dependence in the mean and variance of a univariate time series.

Clustering in Emerging Equity Markets

We consider pairwise tail behavior of return series for identifying most important emerging markets clusters. Pairs of markets belonging to the same group present similar type and strength of interdependence during stressful times, represented by a common copula and a statistically equivalent measure of tail dependence. By collapsing data from d markets in a group we overcome the difficult problem of finding their (higher dimensional) d-variate distribution. Results may help portfolio managers to deal out risk due to comovements within clusters. We provide examples on how this can be done. Our study contribute on the discussion about international association among stock markets during turbulent periods, and do not confirm the intuition that the observed association between extremes should be credited to markets drivers.

Sobre a precisão das estimativas de máxima verossimilhança nas distribuições bivariadas de valores extremos

The non-degenerated limit distributions of normalized maxima are the so called bivariate extreme value distributions. When modeling the asymptotic probabilistic behavior of extremes the objective is to obtain good approximations for the bivariate extremes distributions allowing the investigation of simultaneous extreme events. Typically the sample sizes are small, and this raises questions related to the quality and accuracy of the maximum likelihood estimates of the parameters and other quantities derived from the models. In this article we use bootstrap resampling schemes and Monte Carlo simulations to assess the variability and to construct confidence intervals for these estimates, in order to establish how reliable are the conclusions drawn from the analyzes based on these models. Critical values for the tests proposed in Tawn (1988) are obtained through simulations.

LOCAL ESTIMATION OF DYNAMIC COPULA MODELS

It has been empirically verified that the strength of dependence in stock markets usually rises with volatility. In this paper we exploit this stylized fact combined with local maximum likelihood estimation of copula models to analyze the dynamic joint behavior of series of financial log returns. Explanatory variables based on the estimated GARCH volatilities are considered as potential regressors for explaining the dynamics in the copula parameters. The proposed model can assess and discriminate how much of the strength of dependence is due just to the time-varying volatility. The final local-parametric estimates may be used to compute risk measures, to simulate portfolio behavior, and so on. We illustrate our methods using two American indexes. Results indicate that volatility does affect the strength of dependence. The in-sample Value-at-Risk based on the dynamic model outperforms those based on the empirical estimates.

The Risk-Return Relationship of Pension Funds With Investments in Hedge Funds

ABSTRACT This article investigates if investing in local hedge funds improves the risk-return relationship of Brazilian pension funds. Investment in hedge funds by pension funds is growing elsewhere, with an increasing utilization of a multiplicity of hedge funds specialized in specific strategies or niches. We analyzed the performance of a typical pension fund allocation in Brazil as well as alternate allocations that included hedge funds. We used robust estimates of the covariance matrix to mitigate the errors in variables that are problematic in the inputs of the optimization. The results show that hedge funds improve the risk-return relationship of the typical pension fund allocation, contribute to a higher accumulated return at the end of a one-year period, and reduce portfolio rebalancing. Investments in hedge funds ease reaching the typical 6% annual return target with less risk exposure.

Foreign Exchange Volatility and Trading Volume of Derivatives Instruments: Evidence from the Brazilian Market

ABSTRACT The main objective of this work is to investigate the empirical relationship between trading volume and volatility. The understanding of foreign exchange market microstructure can provide better understanding of its volatility, which may be useful to support market intervention decisions made by the authorities responsible for conducting macroeconomic policies. Results show a positive contemporaneous relationship between unexpected volume and volatility, suggesting simultaneous influence at the arrival of relevant information. Moreover, they support the idea of market inefficiency, meaning that expected volume also reveals a positive correlation with volatility. RESUMEN. O objetivo principal deste trabalho é investigar a relação empírica entre volume de comercialização e volatilidade. A compreensão da microestrutura do mercado de divisas pode fornecer uma compreensão melhor de sua volatilidade, que pode ser útil para respaldar decisães de intervenção no mercado pelas autoridades responsáveis por conduzir as políticas macoeconômicas. Os resultados mostram uma relação con-temporânea positiva entre volume inesperado e volatilidade, sugerindo uma influência simultânea na chegada de informações relevantes. Além disso, eles reforçam a idáia da ineficiência do mercado, significando que o volume esperado tambám revela uma correlação positiva com a volatilidade. RESUMO. El objetivo principal de este trabajo consiste en investigar la relación empírica entre el volumen de transacciones y la volatilidad. La comprensión de la microestructura del mercado cambiario puede brindar un entendimiento mejor sobre su volatilidad, lo que a su vez puede ser de utilidad para respaldar las decisiones tomadas por las autori-dades responsables por la conducción de las políticas macroeconómicas, de intervenir en el mercado. Los resultados muestran una relación contempor