Cristiano Fernandes

Decomposing and Simulating the Movements of Term Structures of Interest Rates in Emerging Eurobond Markets

CRISTIANO AUGUSTO COELHO FERNANDES is with Pontificia Universidade Cat6lica of Rio de Janeiro. e movements of a term structure of interest rates are usually assumed to be driven by three orthogonal factors: parallel shfts, changes in slope, and changes in curvature (see Litterman and Scheinkman [ 19911). Principal components analysis has traditionally been used to obtain the most important factors explaining the dynamics of a term structure (see Mardia, Kent, and Bibby [1992]). The objective is to obtain those orthogonal linear combinations that best explain the covariance matrix of the term structure of interest rates. The approach is simple. Given a data base of term structures, select a set of maturities, estimate the covariance matrix of the yields for this set of maturities and, finally, apply principal components analysis to this covariance matrix to obtain the most important orthogonal factors. Identitjring and simulating the most important factors driving the movements of a term structure of interest rates is important for portfolio managers, risk managers, and derivatives analysts. Fixed-income securities present dfferent exposures to the orthogonal factors driving the movements of a term structure of interest rates. For example, while short-term bonds are basically sensitive to parallel shifts, long-term bonds are more sensitive to parallel shifts and changes in slope. All three orthogonal factors are important when long-term bonds with embedded options are analyzed. A fixed-income portfolio manager should be able to simulate different movements in a term structure to vahdate an investment strategy (see Carino et al. [1994]). A risk manager should be able to estimate the impact of dfferent risk factors on a fixed-income portfolio to suggest optimal hedges (Singh [1997]). A r

A aleatoriedade do passeio na Bovespa: testando a eficiência do mercado acionário brasileiro

We tested two versions of the random walk model for portfolios of Brazilian stocks. We found evidence of persistency in daily and weekly returns, rejecting the random walk models. Those evidences are weaker in recent periods. We also found a Monday effect, other seasonality effects for monthly returns, and asymmetric first order cross correlations on portfolios ranked by sizes. Non-linearities in returns are also detected at several time horizons.

A GENERALIZATION OF PRINCIPAL COMPONENT ANALYSIS FOR NON-OBSERVABLE TERM STRUCTURES IN EMERGING MARKETS

Principal Component Analysis (PCA) has been traditionally used for identifying the most important factors driving term structures of interest rates movements. Once one maps the term structure dynamics, it can be used in many applications. For instance, portfolio allocation, Asset/Liability models, and risk management, are some of its possible uses. This approach presents very simple implementation algorithm, whenever a time series of the term structure is disposable. Nevertheless, in markets where there is no database for discount bond yields available, this approach cannot be applied. In this article, we exploit properties of an orthogonal decomposition of the term structure to sequentially estimate along time, term structures of interest rates in emerging markets. The methodology, named Legendre Dynamic Model (LDM), consists in building the dynamics of the term structure by using Legendre Polynomials to drive its movements. We propose applying LDM to obtain time series for term structures of interest rates and to study their behavior through the behavior of the Legendre Coefficients levels and first differences properly normalized (Legendre factors). Under the hypothesis of stationarity and serial independence of the Legendre factors, we show that there is asymptotic equivalence between LDM and PCA, concluding that LDM captures PCA as a particular case. As a numerical example, we apply our technique to Brazilian Brady and Global Bond Markets, briefly study the time series characteristics of their term structures, and identify the intensity of the most important basic movements of these term structures.

An adaptive robust portfolio optimization model with loss constraints based on data-driven polyhedral uncertainty sets

Robust portfolio optimization models widely presented in the financial literature usually assume that asset returns lie in a parametric uncertainty set with a controlled level of conservatism expressed in terms of the variability of the uncertain parameters. In practice however, it is not clear how investors should choose the conservatism parameter to reflect their own preferences, while considering price dynamics. In this paper, we provide a new perspective on robust portfolio optimization where we impose an intuitive loss constraint for the optimal portfolio considering asset returns in a data-driven polyhedral uncertainty set. Adaptively updated in a rolling horizon scheme, the proposed model captures price dynamics, absorbing new patterns and forgetting old ones, by means of a data-driven polyhedral-based loss constraint and an optimal mixture of asset price signals. We perform a case study to illustrate that it is possible to obtain a loss-controlled portfolio with higher expected returns than chosen benchmark strategies. Considering realistic transaction costs, out-of-sample results, obtained by applying our model for each day of the historical data (2000–2015) and updating with realized returns, indicate that our robust portfolio exhibited an enhanced performance while successfully constraining possible losses.

A Row-Wise Stacking of the Runoff Triangle: State Space Alternatives for IBNR Reserve Prediction

This work deals with prediction of IBNR reserve under a different data ordering of the noncumulative runoff triangle. The rows of the triangle are stacked, resulting in a univariate time series with several missing values. Under this ordering, two approaches entirely based on state space models and the Kalman filter are developed, implemented with real data, and compared with a well-established IBNR estimation method – the chain ladder. The remarks from the empirical results are: (i) computational feasibility and efficiency; (ii) accuracy improvement for IBNR prediction; and (iii) flexibility regarding IBNR modeling possibilities. Key-words: IBNR, Kalman filter, mean square error, missing values, state space model. JEL codes: C22, C53, G22. IME codes: IM10, IM42. ∗Department of Electrical Engineering of the Pontifical Catholic University of Rio de Janeiro. †Corresponding author. Financial and Actuarial Risk Management Institute of the Pontifical Catholic University of Rio de Janeiro (IAPUC). E-mail: adrianhpster@gmail.com ‡Department of Electrical Engineering of the Pontifical Catholic University of Rio de Janeiro. 1

Credit Spread Arbitrage in Emerging Eurobond Markets

In the corporate emerging Eurobond fixed-income market there are two main sources of credit risk: sovereign risk and the relative credit quality of issuers of the eurobonds. This article presents a model to estimate, in a one-step procedure, both the term structure of interest rates and the credit spread function of a diversified international portfolio of Eurobonds with different credit ratings. The estimated term structures can be used to analyze credit spread arbitrage opportunities in Eurobond markets. Numerical examples in the Argentinean, Brazilian, and Mexican Eurobond markets illustrate the practical use of the methodology.

Interest rate risk measurement in Brazilian sovereign markets

Fixed income emerging markets are an interesting investment alternative. Measuring market risks is mandatory in order to avoid unexpected huge losses. The most used market risk measure is the Value at Risk, based on the profit-loss probability distribution of the portfolio under consideration. Estimating this probability distribution requires the prior estimation of the probability distribution of term structures of interest rates. An interesting possibility is to estimate term structures using a decomposition of the spread function into a linear combination of Legendre polynomials. Numerical examples from the Brazilian sovereign fixed income international market illustrate the practical use of the methodology.

Forecasting Longevity Gains for a Population with Short Time Series Using a Structural SUTSE Model: An Application to Brazilian Annuity Plans

In this article, a multivariate structural time series model with common stochastic trends is proposed to forecast longevity gains of a population with a short time series of observed mortality rates, using the information of a related population for which longer mortality time series exist. The state space model proposed here makes use of the seemingly unrelated time series equation and applies the concepts of related series and common trends to construct a proper model to predict the future mortality rates of a population with little available information. This common trends approach works by assuming the two populations’ mortality rates are affected by common factors. Further, we show how this model can be used by insurers and pension funds to forecast mortality rates of policyholders and beneficiaries. We apply the proposed model to Brazilian annuity plans where life expectancies and their temporal evolution are predicted using the forecast longevity gains. Finally, to demonstrate how the model can be used in actuarial practice, the best estimate of the liabilities and the capital based on underwriting risk are estimated by means of Monte Carlo simulation. The idiosyncratic risk effect in the process of calculating an amount of underwriting capital is also illustrated using that simulation.

Forecasting Surrender Rates Using Elliptical Copulas and Financial Variables

A multistage stochastic model to forecast surrender rates for life insurance and pension plans is proposed. Surrender rates are forecasted by means of Monte Carlo simulation after a sequence of GLM, ARMA-GARCH, and copula fitting is executed. The model is illustrated by applying it to age-specific time series of surrender rates derived from pension plans with annuity payments of a Brazilian insurer. In the GLM process, the only macroeconomic variable used as an explanatory variable is the Brazilian real short-term interest rate. The advantage of such a variable is that we can take future market expectation through the current term structure of interest rates. The GLM residuals of each age/gender group are then modeled by ARMA-GARCH processes to generate i.i.d. residuals. The dependence among these residuals is then modeled by multivariate Gaussian and Students t copulas. To produce a conditional forecast on a stock market index, in our application we used the residuals of an ARMA-GARCH model fitted to the Brazilian stock market index (Ibovespa) returns, which generates one of the marginal distributions used in the dependence modeling through copulas. This strategy is adopted to explain the high and uncommon surrender rates observed during the recent economic crisis. After applying known simulation methods for elliptical copulas, we proceeded backwards to obtain the forecasted distributions of surrender rates by application, in the sequel, of ARMA-GARCH and GLM models. Additionally, our approach produced an algorithm able to simulate multivariate elliptical copulas conditioned on a marginal distribution. Using this algorithm, surrender rates can be simulated conditioned on stock index residuals (in our case, the residuals of the Ibovespa returns), which allows insurers and pension funds to simulate future surrender rates assuming a financial stress scenario with no need to predict the stock market index.

Estimação do Impacto do El Niño/La Niña na Intensidade dos Ventos do Nordeste Brasileiro

Wind energy is now one of the most promising energy sources of the world for being clean and abundant. The study of phenomena that are related to changes in atmospheric circulation, such as El Nino, are extremely important for its ability to affect wind generation. In order to explore the possible effect of such phenomena in the winds of the Northeast region of Brazil, a statistical analysis to quantify this effect through the model Generalized Autoregressive Score (GAS) is performed. This allows the modeling of time series for different probability distributions. Thus, the GAS is applied to the wind speed series from the Gamma distribution. The model results showed that El Nino has influence on the behavior of the wind, even though it is small in magnitude.