Multistep stochastic mirror descent for risk-averse convex stochastic programs based on extended polyhedral risk measures

We consider risk-averse convex stochastic programs expressed in terms of extended polyhedral risk measures. We derive computable con dence intervals on the optimal value of such stochastic programs using the Robust Stochastic Approximation and the Stochastic Mirror Descent (SMD) algorithms. When the objective functions are uniformly convex, we also propose a multistep extension of the Stochastic Mirror Descent algorithm and obtain con dence intervals on both the optimal values and optimal solutions. Numerical simulations show that our con dence intervals are much less conservative and are quicker to compute than previously obtained con dence intervals for SMD and that the multistep Stochastic Mirror Descent algorithm can obtain a good approximate solution much quicker than its nonmultistep counterpart. Our con dence intervals are also more reliable than asymptotic con dence intervals when the sample size is not much larger than the problem size.

Nonparametric tail risk, macroeconomics and stock returns: predictability and risk premia

This paper proposes a new novel to calculate tail risks incorporating risk-neutral information without dependence on options data. Proceeding via a non parametric approach we derive a stochastic discount factor that correctly price a chosen panel of stocks returns. With the assumption that states probabilities are homogeneous we back out the risk neutral distribution and calculate five primitive tail risk measures, all extracted from this risk neutral probability. The final measure is than set as the first principal component of the preliminary measures. Using six Fama-French size and book to market portfolios to calculate our tail risk, we find that it has significant predictive power when forecasting market returns one month ahead, aggregate U.S. consumption and GDP one quarter ahead and also macroeconomic activity indexes. Conditional Fama-Macbeth two-pass cross-sectional regressions reveal that our factor present a positive risk premium when controlling for traditional factors.

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.

Cópulas: uma alternativa para a estimação de modelos de risco multivariados

Dentre os principais desafios enfrentados no cálculo de medidas de risco de portfólios está em como agregar riscos. Esta agregação deve ser feita de tal sorte que possa de alguma forma identificar o efeito da diversificação do risco existente em uma operação ou em um portfólio. Desta forma, muito tem se feito para identificar a melhor forma para se chegar a esta definição, alguns modelos como o Valor em Risco (VaR) paramétrico assumem que a distribuição marginal de cada variável integrante do portfólio seguem a mesma distribuição , sendo esta uma distribuição normal, se preocupando apenas em modelar corretamente a volatilidade e a matriz de correlação. Modelos como o VaR histórico assume a distribuição real da variável e não se preocupam com o formato da distribuição resultante multivariada. Assim sendo, a teoria de Cópulas mostra-se um grande alternativa, à medida que esta teoria permite a criação de distribuições multivariadas sem a necessidade de se supor qualquer tipo de restrição às distribuições marginais e muito menos as multivariadas. Neste trabalho iremos abordar a utilização desta metodologia em confronto com as demais metodologias de cálculo de Risco, a saber: VaR multivariados paramétricos - VEC, Diagonal,BEKK, EWMA, CCC e DCC- e VaR histórico para um portfólio resultante de posições idênticas em quatro fatores de risco – Pre252, Cupo252, Índice Bovespa e Índice Dow Jones

Dominância fiscal e suas implicações sobre a política monetária no Brasil: uma análise do período 1999 - 2005

O grau de liberdade da política monetária é uma questão muito relevante em um país que decide adotar um regime de metas inflacionárias e câmbio flutuante. Caso a autoridade monetária desse país não tenha liberdade para atuar, o regime de metas pode ser ineficiente. Em especial, caso esse país se encontre numa situação de Dominância Fiscal, a política monetária pode ter efeitos perversos sobre a relação dívida/PIB, aumentando seu prêmio de risco soberano e causando um aumento na probabilidade de default implícita em seus títulos soberanos. O intuito desse trabalho é realizar o teste de dominância a partir de um modelo proposto por Olivier Blanchard em 2004, e testar primeiro se o país se encontrava em dominância em 2002, 2003 e depois analisar o resultado desse modelo até novembro de 2005. Algumas modificações de variáveis utilizadas, medidas de risco e taxa de juros são propostas e é acrescido ao modelo um teste de estabilidade de coeficientes e a incerteza causada no período eleitoral em 2002. Além disso, é analisada a reação do Banco Central no período, para identificar se sua reação compartilhava da visão de dominância que o modelo original apresentava ou não. A conclusão é que o Brasil, mesmo após as alterações sugeridas, ainda se encontra numa situação de dominância fiscal segundo a descrição do modelo. Porém, o resultado final é cerca de 20% do originalmente observado em 2004, resultando em uma liberdade de atuação significativamente maior para a autoridade monetária no Brasil em 2002 e 2003. O Banco Central parece ter reagido a mudanças de expectativa de inflação e não parecia compartilhar um diagnóstico de dominância fiscal ao longo de 2002. As eleições foram significativas para explicar aumento da probabilidade de default, mas não alteram significativamente o resultado do teste após as mudanças de variáveis. A medida de risco proposta resulta em um modelo melhor para medir dominância no Brasil. A mensagem final é que o Brasil ainda precisa se preocupar com as restrições fiscais, mas elas são menores que o modelo original propunha.

Pricing the option adjust spread of Brazilian Eurobonds

This paper presents results of a pricing system to compute the option adjusted spread ("DAS") of Eurobonds issued by Brazilian firms. The system computes the "DAS" over US treasury rates taktng imo account the embedded options present on these bonds. These options can be calls ("callable bond"), puts ("putable bond") or combinations ("callable and putable bond"). The pricing model takes into account the evolution of the term structure along time, is compatible with the observable market term structure and is able to compute risk measures such as duration and convexity, and pricing and hedging of options on these bonds. Examples show the ejJects of the embedded options on the spread and risk measures as well as the ejJects on the spread due to variations on the volatility parameters ofthe short rate.

Public debt management, monetary policy and financial institutions

Despite the large size of the Brazilian debt market, as well the large diversity of its bonds, the picture that emerges is of a market that has not yet completed its transition from the role it performed during the megainflation years, namely that of providing a liquid asset that provided positive real returns. This unfinished transition is currently placing the market under severe stress, as fears of a possible default from the next administration grow larger. This paper analyzes several aspects pertaining to the management of the domestic public debt. The causes for the extremely large and fast growth ofthe domestic public debt during the seven-year period that President Cardoso are discussed in Section 2. Section 3 computes Value at Risk and Cash Flow at Risk measures for the domestic public debt. The rollover risk is introduced in a mean-variance framework in Section 4. Section 5 discusses a few issues pertaining to the overlap between debt management and monetary policy. Finally, Section 6 wraps up with policy discussion and policy recommendations.

Essays on regulation and risk

In this thesis, we investigate some aspects of the interplay between economic regulation and the risk of the regulated firm. In the first chapter, the main goal is to understand the implications a mainstream regulatory model (Laffont and Tirole, 1993) have on the systematic risk of the firm. We generalize the model in order to incorporate aggregate risk, and find that the optimal regulatory contract must be severely constrained in order to reproduce real-world systematic risk levels. We also consider the optimal profit-sharing mechanism, with an endogenous sharing rate, to explore the relationship between contract power and beta. We find results compatible with the available evidence that high-powered regimes impose more risk to the firm. In the second chapter, a joint work with Daniel Lima from the University of California, San Diego (UCSD), we start from the observation that regulated firms are subject to some regulatory practices that potentially affect the symmetry of the distribution of their future profits. If these practices are anticipated by investors in the stock market, the pattern of asymmetry in the empirical distribution of stock returns may differ among regulated and non-regulated companies. We review some recently proposed asymmetry measures that are robust to the empirical regularities of return data and use them to investigate whether there are meaningful differences in the distribution of asymmetry between these two groups of companies. In the third and last chapter, three different approaches to the capital asset pricing model of Kraus and Litzenberger (1976) are tested with recent Brazilian data and estimated using the generalized method of moments (GMM) as a unifying procedure. We find that ex-post stock returns generally exhibit statistically significant coskewness with the market portfolio, and hence are sensitive to squared market returns. However, while the theoretical ground for the preference for skewness is well established and fairly intuitive, we did not find supporting evidence that investors require a premium for supporting this risk factor in Brazil.

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.

An SDF approach to hedge funds’ tail risk: evidence from Brazilian funds

The main purpose of this paper is to propose a methodology to obtain a hedge fund tail risk measure. Our measure builds on the methodologies proposed by Almeida and Garcia (2015) and Almeida, Ardison, Garcia, and Vicente (2016), which rely in solving dual minimization problems of Cressie Read discrepancy functions in spaces of probability measures. Due to the recently documented robustness of the Hellinger estimator (Kitamura et al., 2013), we adopt within the Cressie Read family, this specific discrepancy as loss function. From this choice, we derive a minimum Hellinger risk-neutral measure that correctly prices an observed panel of hedge fund returns. The estimated risk-neutral measure is used to construct our tail risk measure by pricing synthetic out-of-the-money put options on hedge fund returns of ten specific categories. We provide a detailed description of our methodology, extract the aggregate Tail risk hedge fund factor for Brazilian funds, and as a by product, a set of individual Tail risk factors for each specific hedge fund category.