Marcelo Brutti Righi

Shortfall Deviation Risk: An Alternative for Risk Measurement

We present the Shortfall Deviation Risk (SDR), a risk measure that represents the expected loss that occurs with certain probability penalized by the dispersion of results that are worse than such an expectation. SDR combines Expected Shortfall (ES) and Shortfall Deviation (SD), which we also introduce, contemplating two fundamental pillars of the risk concept, the probability of adverse events and the variability of an expectation, and considers extreme results. We demonstrate that SD is a generalized deviation measure, whereas SDR is a coherent risk measure. We achieve the dual representation of SDR, and we discuss issues such as its representation by a weighted ES, acceptance sets, convexity, continuity and the relationship with stochastic dominance. Illustrations with real and simulated data allow us to conclude that SDR offers greater protection in risk measurement compared with VaR and ES, especially in times of significant turbulence in riskier scenarios.

Individual and Flexible Expected Shortfall Backtesting

In this paper we propose an expected shortfall (ES) backtesting approach that uses the dispersion of a truncated distribution by the estimated value-at-risk (VaR) upper limit, does not limit the approach to the Gaussian case and allows us to test if each individual VaR violation is significantly different from the ES. Moreover, we present a Monte Carlo simulation algorithm to determine the significance of the backtest. We provide an empirical illustration that demonstrates the advantages that our backtests provide, especially the fact that there is no need to wait for a whole backtest period in order to prove the prediction that the ES test is inefficient.

A fuzzy hybrid integrated framework for portfolio optimization in private banking

Abstract Decision-making processes in private banking must comply with standards for risk management and transparency enforced by banking regulations. Therefore, investors must be supported throughout a risk-informed decision process. This paper contributes to the literature by presenting a hybrid integrated framework that considers personal features of the investor and additional characteristics imposed by regulations, for which linguistic evaluations are used with regard to risk exposure. The proposed approach for personal investment portfolios considers legal aspects and investor’s preferences as an input to the novel fuzzy multiple-attribute decision making approach for sorting problems proposed in this paper, called FTOPSIS-Class. Then, the next step of the proposed framework uses the sorting results for a fuzzy multi-objective optimization model that considers the risk and return associated with the investor’s profile over three objectives. The contributions of this paper are illustrated and validated by using a numerical application in line with a new trend for modern portfolio theory which enables a real world investor’s characteristics to be considered throughout the decision-making process.

A composition between risk and deviation measures

The intuition of risk is based on two main concepts: loss and variability. In this paper, we present a composition of risk and deviation measures, which contemplate these two concepts. Based on the proposed Limitedness axiom, we prove that this resulting composition, based on properties of the two components, is a coherent risk measure. Similar results for the cases of convex and co-monotone risk measures are exposed. We also provide examples of known and new risk measures constructed under this framework in order to highlight the importance of our approach, especially the role of the Limitedness axiom.

Emerging Market Return Pricing: An Intertemporal and Interquantile Approach

The objective of this study is to analyze the return pricing dynamics in six Latin American countries based on the ICAPM model of (Merton, 1973; Bekaert & Harvey, 1995). We analyze Argentina, Brazil, Chile, Colombia, Mexico and Peru market return and a world market proxy return as a measure of systematic risk. However, instead of traditional covariance, we used the Dynamic Conditional Correlation (DCC) model of Engle (2002) to measure the volatility correlation between each Latin market and the world market. We based the DCC model on marginal volatilities estimated by the GJR-GARCH model (Glosten et al., 1993), using a copula function. The copula-DCC-GARCH model was proposed with a financial application by (Jondeau & Rockinger, 2006). The univariate volatility and an autoregressive vector were also included as independent variables in the model, which coefficients were estimated by quantile regression. The results reveal a breakthrough because the model can capture relationships that were previously masked by the coefficients steadiness and by the lack of consideration over the differences in extreme quantiles pricing. In the lower quantile, negative risk premium was found, reflecting the leverage effect. Furthermore, we found that the quantile correlation coefficients between each market return proxy and the world return proxy were not significant, i.e, only the market own risk is priced, what indicates that Latin markets may present a good diversification opportunity. DOI: http://dx.doi.org/10.5755/j01.ee.25.4.5205

WORLD FINANCIAL RELATIONS: UNDERSTANDING THE CREDIT DERIVATIVE SWAPS (CDS) DEPENDENCE STRUCTURE

This study investigates the copula model that best fit to model the dependence structure of Credit Derivative Swaps (CDS) spreads. For the analysis, we consider daily data from the period of January 1, 2009 to December 31, 2014. Regarding the models, we considered Vine copulas and Hierarchical Archimedean copulas, and different families of copulas. Our results indicate that C-Vine copulas, as well Student t family, demonstrated better performance, according to the criteria used to get the dependence structure. The best fit of the dependence structure can avoid the model risk, from the use of an incorrect model.

Performance comparison of scenario-generation methods applied to a stochastic optimization asset-liability management model

In this paper, we provide an empirical discussion of the differences among some scenario tree-generation approaches for stochastic programming. We consider the classical Monte Carlo sampling and Moment matching methods. Moreover, we test the Resampled average approximation, which is an adaptation of Monte Carlo sampling and Monte Carlo with naive allocation strategy as the benchmark. We test the empirical effects of each approach on the stability of the problem objective function and initial portfolio allocation, using a multistage stochastic chance-constrained asset-liability management (ALM) model as the application. The Moment matching and Resampled average approximation are more stable than the other two strategies.

Mispricing in the Odd Lots Market in Brazil

We study the case of mispricing in the odd lots equity market in Brazil. Contrary to expectation, odd lot investors are paying higher prices than round lot investors. The pricing difference between markets is affected by market returns, volatility and spreads. Our main hypothesis is that; once the assets traded in the odd lot market are more illiquid than their counterparts, the mispricing is driven by liquidity factors. We propose regulators to review the market design for odd lots in Brazil. We argue that reducing the minimal trading unit in the round lots market would benefit investors.

Numerical Comparison of Multivariate Models to Forecasting Risk Measures

We evaluated the performance of multivariate models for forecasting Value at Risk (VaR), Expected Shortfall (ES) and Expectile Value at Risk (EVaR). We used Historical Simulation (HS), Dynamic Conditional Correlation-Generalized Autoregressive Conditional Heteroskedastic (DCC-GARCH) and copula methods: Regular copulas, Vine copulas and Nested Archimedean copulas. We assessed the performance of the models using Monte Carlo simulations, considering different scenarios, with regard to the marginal distributions, correlation and number the assets of portfolio. Numerical results evidenced that the accuracy forecasting risk measure is associated with marginal distributions. For a data generating process where the marginal distribution is Gaussian, Regular and Vine copulas demonstrated better performance. For data generated with Students t distribution, we verified a better performance by Nested Archimedean copulas. In addition, we identified the superiority of copula methods over Historical Simulation and DCC-GARCH, which reduces the model risk.

Risk Parity in the Brazilian Market

Using sectorial indices of the Brazilian market, we compare the portfolio optimization approach known as risk parity with minimum variance and equally weighted approaches. We apply various estimators for the covariance matrix to each portfolio strategy, since portfolio variance is considered as risk measure. Empirical results demonstrate that the risk parity approach provides more diversified portfolios and stable weights in the out-of-sample than the other two approaches, thereby avoiding the dangers of excessive concentration and reducing transaction costs. Furthermore, the results demonstrate that different estimators of the covariance matrix had little influence on the results obtained through the risk parity approac