Matteo Bonato

Forecasting Realized (Co)Variances with a Block Structure Wishart Autoregressive Model

In modelling and forecasting volatility, two main trade-offs emerge: mathematical tractability versus economic interpretation and accuracy versus speed. The authors attempt to reconcile, at least partially, both trade-offs. The former trade-off is crucial for many financial applications, including portfolio and risk management. The speed/accuracy trade-off is becoming more and more relevant in an environment of large portfolios, prolonged periods of high volatility (as in the current financial crisis), and the burgeoning phenomenon of algorithmic trading in which computer-based trading rules are automatically implemented. The increased availability of high-frequency data provides new tools for forecasting variances and covariances between assets. However, there is scant literature on forecasting more than one realised volatility. Following Gourieroux, Jasiak and Sufana (Journal of Econometrics, forthcoming), the authors propose a methodology to model and forecast realised covariances without any restriction on the parameters while maintaining economic interpretability. An empirical application based on variance forecasting and risk evaluation of a portfolio of two US treasury bills and two exchange rates is presented. The authors compare their model with several alternative specifications proposed in the literature. Empirical findings suggest that the model can be efficiently used in large portfolios.

Robust Estimation of Skewness and Kurtosis in Distributions with Infinite Higher Moments

This paper studies the behavior of the conventional measures of skewness and kurtosis when the data generator process is a distribution which does not possess variance or third or fourth moment and assesses the robustness of the alternative measures for these particular cases. It is first shown that for symmetric fat-tailed distribution skewness is far from being a valid indicator of the presence of asymmetry. Secondly, a Monte Carlo simulation is performed to investigate the behavior of the alternative measures of skewness and kurtosis when applied to distributions which do not possess finite higher moments. Finally, an application to the series of daily returns on a large cap US stock is presented to explain why alternative measures are a better tool to describe the distribution of financial returns.

Does Geopolitical Risks Predict Stock Returns and Volatility of Leading Defense Companies? Evidence from a Nonparametric Approach

Abstract We use the k-th-order nonparametric causality test at monthly frequency over the period of 1985:1 to 2016:06 to analyze whether geopolitical risks can predict movements in stock returns and volatility of 24 global defense firms. The nonparametric approach controls for the existing misspecification of a linear framework of causality, and hence, the mild evidence of causality obtained under the standard Granger tests cannot be relied upon. When we apply the nonparametric test, we find that there is no evidence of predictability of stock returns of these defense companies emanating from the geopolitical risk measure. However, the geopolitical risk index does predict realized volatility in 50% of the companies. Our results indicate that while global geopolitical events over a period of time is less likely to predict returns, such global risks are more inclined in affecting future risk profile of defense firms.

Risk spillovers in international equity portfolios

We define risk spillover as the dependence of a given asset variance on the past covariances and variances of other assets. Building on this idea, we propose the use of a highly flexible and tractable model to forecast the volatility of an international equity portfolio. According to the risk management strategy proposed, portfolio risk is seen as a specific combination of daily realized variances and covariances extracted from a high frequency dataset, which includes equities and currencies. In this framework, we focus on the risk spillovers across equities within the same sector (sector spillover), and from currencies to international equities (currency spillover). We compare these specific risk spillovers to a more general framework (full spillover) whereby we allow for lagged dependence across all variances and covariances. The forecasting analysis shows that considering only sector- and currency-risk spillovers, rather than full spillovers, improves performance, both in economic and statistical terms.

Estimating the Degrees of Freedom of the Realized Volatility Wishart Autoregressive Model

In this paper an in-depth analysis of the estimation of the realized volatility Wishart Autoregressive model is presented. We focus in particular on the estimation of the degrees of freedom. A new estimator is proposed. Monte Carlo simulations show that this novel estimator is more efficient when compared to the standard estimator proposed in literature. We also studied the effect of extreme observation in the variance-covariance process. Analytically and relying on simulation, we show that extreme observations in the variance-covariance process induce a bias toward zero of the estimated degrees of freedom, no matter which estimator one uses. However, the new proposed estimator is more robust compared to the standard one. An empirical application to the S&P 500 - NASDAQ 100 futures realized variance-covariance series confirms that the estimated degrees of freedom result sensitively lower when extremely high values in the volatility process are present and they increase with the sampling frequency.

A forecast-based comparison of restricted Wishart autoregressive models for realized covariance matrices

Models for realized covariance matrices may suffer from the curse of dimensionality as more traditional multivariate volatility models (such as GARCH and stochastic volatility). Within the class of realized covariance models, we focus on the Wishart specification introduced by C. Gourieroux, J. Jasiak, and R. Sufana [2009. The Wishart autoregressive process of multivariate stochastic volatility. Journal of Econometrics 150, no. 2: 167–81] and analyze here the forecasting performances of the parametric restrictions discussed in M. Bonato [2009. Estimating the degrees of freedom of the realized volatility Wishart autoregressive model. Manuscript available at http://ssrn.com/abstract=1357044], which are motivated by asset features such as their economic sector and book-to-market or price-to-earnings ratios, among others. Our purpose is to verify if restricted model forecasts are statistically equivalent to full-model specification, a result that would support the use of restrictions when the problem cross-sectional dimension is large.

A Forecast Based Comparison of Restricted Realized Covariance Models

Models for realized covariance matrices may suffer for the curse of dimensionality as more traditional multivariate volatility models(such as GARCH and stochastic volatility). Within the class of realized covariance models we focus on the Wishart specification introduced by Gourieroux et al. (2009) and analyze here the forecasting performances of the parametric restrictions discussed in Bonato et al. (2009) which are motivated by asset features such as their economic sector, book-to-market or price-earnings ratios, among others. Our purpose is to verify if restricted model forecasts are statistically equivalent to full model specification, a result that would support the use of restrictions when the problem cross sectional dimension is large.

Comovement and the financialization of commodities

We investigate how the correlations amongst commodity futures have changed since the early 2000s. Using data from 1998 to 2011, we examine differences in the dependence structure of index and off-index commodities, and three major commodities indexes. We find that non-energy commodities included in the index exhibit an increase in comovement with the respective index, whereas commodities off the index do not. We interpret our findings as providing some evidence in support of post-2005 commodity financialization. We show that our results are robust to alternative explanations – non-trading effects and common fundamental characteristics. Finally, our results are supported by the analysis of high-frequency returns dynamics by means of the so called realised beta.

Realized Correlations, Betas and Volatility Spillover in the Commodity Market: What Has Changed?

This papers adopts the recently proposed realized Beta GARCH model of Hansen et al. (J. Appl. Econ. (2014)) to examine the changes in price and return dynamics that affected the commodity market during the 2007-2008 boom and bust. We provide evidence that, starting from2006, realized correlations between agricultural commodities within the same group significantly increased. Moreover, the observed increase in correlations between agriculturals and oil was greater still. The dynamics of the volatility spillover across commodities are also investigated. It is found that spillover effects became more evident prior to the commodity price crash. However, this increase in volatility transmission tended to anticipate the increase in correlations. To conclude, it is shown that the size of a short position in oil required to hedge a long agricultural commodity position , given by the realized beta, therefore increased significantly.