A generalized Dynamic Conditional Correlation Model for Portfolio Risk Evaluation

We propose a generalization of the Dynamic Conditional Correlation multivariate GARCH model of Engle (2002) and of the Asymmetric Dynamic Conditional Correlation model of Cappiello et al. (2006). The model we propose introduces a block structure in parameter matrices that allows for interdependence with a reduced number of parameters. Our model nests the Flexible Dynamic Conditional Correlation model of Billio et al. (2006) and is named Quadratic Flexible Dynamic Conditional Correlation Multivariate GARCH. In the paper, we provide conditions for positive definiteness of the conditional correlations. We also present an empirical application to the Italian stock market comparing alternative correlation models for portfolio risk evaluation.Dynamic correlations, Block-structures, Flexible correlation models

Bayesian nonparametric sparse VAR models

High dimensional vector autoregressive (VAR) models require a large number of parameters to be estimated and may suffer of inferential problems. We propose a new Bayesian nonparametric (BNP) Lasso prior (BNP-Lasso) for high-dimensional VAR models that can improve estimation efficiency and prediction accuracy. Our hierarchical prior overcomes overparametrization and overfitting issues by clustering the VAR coefficients into groups and by shrinking the coefficients of each group toward a common location. Clustering and shrinking effects induced by the BNP-Lasso prior are well suited for the extraction of causal networks from time series, since they account for some stylized facts in real-world networks, which are sparsity, communities structures and heterogeneity in the edges intensity. In order to fully capture the richness of the data and to achieve a better understanding of financial and macroeconomic risk, it is therefore crucial that the model used to extract network accounts for these stylized facts.Comment: Forthcoming in "Journal of Econometrics" ---- Revised Version of the paper "Bayesian nonparametric Seemingly Unrelated Regression Models" ---- Supplementary Material available on reques

Portfolio Symmetry and Momentum

This paper presents a theoretical framework to model the evolution of a portfolio whose weights vary over time. Such a portfolio is called a dynamic portfolio. In a first step, considering a given investment policy, we define the set of the investable portfolios. Then, considering portfolio vicinity in terms of turnover, we represent the investment policy as a graph. It permits us to model the evolution of a dynamic portfolio as a stochastic process in the set of the investable portfolios. Our first model for the evolution of a dynamic portfolio is a random walk on the graph corresponding to the investment policy chosen. Next, using graph theory and quantum probability, we compute the probabilities for a dynamic portfolio to be in the different regions of the graph. The resulting distribution is called spectral distribution. It depends on the geometrical properties of the graph and thus in those of the investment policy. The framework is next applied to an investment policy similar to the Jeegadeesh and Titman's momentum strategy. We define the optimal dynamic portfolio as the sequence of portfolios, from the set of the investable portfolios, which gives the best returns over a respective sequence of time periods. Under the assumption that the optimal dynamic portfolio follows a random walk, we can compute its spectral distribution. We found then that the strategy symmetry is a source of momentum.Graph Theory, Momentum, Dynamic Portfolio, Quantum Probability, Spectral Analysis

Dynamic Risk Exposure in Hedge Funds

We measure dynamic risk exposure of hedge funds to various risk factors during different market volatility conditions using the regime-switching beta model. We find that in the high-volatility regime (when the market is rolling-down) most of the strategies are negatively and significantly exposed to the Large-Small and Credit Spread risk factors. This suggests that liquidity risk and credit risk are potentially common factors for different hedge fund strategies in the down-state of the market, when volatility is high and returns are very low. We further explore the possibility that all hedge fund strategies exhibit idiosyncratic risk in a high volatility regime and find that the joint probability jumps from approximately 0% to almost 100% only during the Long-Term Capital Management (LTCM) crisis. Out-of-sample forecasting tests confirm the economic importance of accounting for the presence of market volatility regimes in determining hedge funds risk exposure.Hedge Funds; Risk Management; Regime-Switching Models, Liquidity

Bayesian Inference on Dynamic Models with Latent Factors

In time series analysis, latent factors are often introduced to model the heterogeneous time evolution of the observed processes. The presence of unobserved components makes the maximum likelihood estimation method more difficult to apply. A Bayesian approach can sometimes be preferable since it permits to treat general state space models and makes easier the simulation based approach to parameters estimation and latent factors filtering. The paper examines economic time series models in a Bayesian perspective focusing, through some examples, on the extraction of the business cycle components. We briefly review some general univariate Bayesian dynamic models and discuss the simulation based techniques, such as Gibbs sampling, adaptive importance sampling and finally suggest the use of the particle filter, for parameter estimation and latent factor extraction.Bayesian Dynamic Models, Simulation Based Inference, Particle Filters, Latent Factors, Business Cycle

Crisis and Hedge Fund Risk

We study the effect of financial crises on hedge fund risk. Using a regime-switching beta model, we separate systematic and idiosyncratic components of hedge fund exposure. The systematic exposure to various risk factors is conditional on market volatility conditions. We find that in the high-volatility regime (when the market is rolling-down and is likely to be in a crisis state) most strategies are negatively and significantly exposed to the Large-Small and Credit Spread risk factors. This suggests that liquidity risk and credit risk are potentially common factors for different hedge fund strategies in the down-state of the market, when volatility is high and returns are very low. We further explore the possibility that all hedge fund strategies exhibit a high volatility regime of the idiosyncratic risk, which could be attributed to contagion among hedge fund strategies. In our sample this event happened only during the Long-Term Capital Management (LTCM) crisis of 1998. Other crises including the recent subprime mortgage crisis affected hedge funds only through systematic risk factors, and did not cause contagion among hedge funds.Hedge Fund, Risk Management, High frequency data

A Cross-Sectional Performance Measure for Portfolio Management

Sharpe-like ratios have been traditionally used to measure the performances of portfolio managers. However, they are known to suffer major drawbacks. Among them, two are intricate : (1) they are relative to a peer's performance and (2) the best score is generally assumed to correspond to a "good" portfolio allocation, with no guarantee on the goodness of this allocation. Last but no least (3) these measures suffer significant estimation errors leading to the inability to distinguish two managers' performances. In this paper, we propose a cross-sectional measure of portfolio performance dealing with these three issues. First, we define the score of a portfolio over a single period as the percentage of investable portfolios outperformed by this portfolio. This score quantifies the goodness of the allocation remedying drawbacks (1) and (2). The new information brought by the cross-sectionality of this score is then discussed through applications. Secondly, we build a performance index, as the average cross-section score over successive periods, whose estimation partially answers drawback (3). In order to assess its informativeness and using empirical data, we compare its forecasts with those of the Sharpe and Sortino ratios. The results show that our measure is the most robust and informative. It validates the utility of such cross-sectional performance measure.Performance measure, portfolio management, relative-value strategy, large portfolios, absolute return strategy, multivariate statistics, Generalized hyperbolic Distribution.

Market linkages, variance spillovers and correlation stability: empirical evidences of financial contagion

We propose a simultaneous equation system with GARCH errors to model the contemporaneous relations among Asian and American stock markets. On the estimated residuals, we evaluate the correlation matrix over rolling windows and introduce a correlation matrix distance, which allows both a graphical analysis and the development of a statistical test of correlation movements. Furthermore, we introduce a methodology that can be used for identifying turmoil periods on a data-driven basis. We employ the previous results in the analysis of the contagion issue between Asian and American stock markets. Our results shows some evidence of contagion and the proposed statistics identifies, on a data-driven basis, turmoil periods consistent with the ones currently assumed in the literature.Financial market contagion, Market linkages, Variance spillovers, Dynamic correlations, Rolling correlations, Transformed correlations

Granger-causality in Markov Switching Models

In this paper we propose a new parametrisation of transition probabilities that allows us to characterize and test Granger-causality in Markov switching models by means of an appropriate specification of the transition matrix. Test for independence are also provided. We illustrate our methodology with an empirical application. In particular, we investigate the causality and interdependence between financial and economic cycles using a bivariate Markov switching model. When applied to U.S. data, we find that financial variables are useful for forecasting the direction of aggregate economic activity, and vice versa.Granger Causality, Markov Chains, Switching Models

Business Cycle Analysis with Multivariate Markov Switching Models

The class of Markov switching models can be extended in two main directions in a multivariate framework. In the first approach, the switching dynamics are introduced by way of a common latent factor. In the second approach a VAR model with parameters depending on one common Markov chain is considered (MSVAR). We will extend the MSVAR approach allowing for the presence of specific Markov chains in each equation of the VAR (MMSVAR). In the MMSVAR approach we also explore the introduction of correlated Markov chains which allow us to evaluate the relationships among phases in different economies or sectors and introduce causality relationships, which allow a more parsimonious representation. We apply our model to study the relationship between cyclical phases of the industrial production in the US and Euro zone. Moreover, we construct a MMS model to explore the cyclical relationship between the Euro zone industrial production and the industrial component of the European Sentiment Index.Economic cycles, Multivariate models, Markov switching models, Common latent factors, Causality, Euro-zone