Monica Billio

Value-at-Risk: a multivariate switching regime approach

Abstract This paper analyses the application of a switching volatility model to forecast the distribution of returns and to estimate the Value-at-Risk (VaR) of both single assets and portfolios. We calculate the VaR value for 10 Italian stocks and a number of portfolios based on these stocks. The calculated VaR values are also compared with the variance–covariance approach used by JP Morgan in RiskMetrics™ and GARCH(1,1) models. Under backtesting, the VaR values calculated using the switching regime beta model are preferred to both other methods. The Proportion of Failure and Time Until First Failure tests [The Journal of Derivatives (1995) 73–84] confirm this result.

Flexible Dynamic Conditional Correlation multivariate GARCH models for asset allocation

This paper introduces the Flexible Dynamic Conditional Correlation (FDCC) multivariate GARCH model which generalizes the Dynamic Conditional Correlation (DCC) multivariate GARCH model proposed by Engle (2002). The FDCC model relax the assumption of common dynamics among all assets used in the DCC model. In fact, we cannot impose that the correlation dynamics of, say, European sectorial stock indexes are identical to the corresponding US ones. We thus extend the DCC model introducing a block-diagonal structure; in the FDCC the dynamics are constrained to be equal among groups of variables. We present an application to a sectorial asset allocation problem.

Contagion and interdependence in stock markets: Have they been misdiagnosed?

Abstract We discuss different methods proposed in the literature to analyse the propagation mechanism of a crisis and to verify the presence of contagion. We consider the propagation mechanisms of the Hong Kong index on the Eurostoxx, Nikkei and Dow Jones indexes during the Asian financial crisis. We show that the methodologies proposed by Forbes and Rigobon [J. Finance 57 (2002) 2223] and by Corsetti et al. [Some contagion, some interdependence more pitfalls in tests of financial contagion, CEPR Discussion Paper No. 3310, London, 2002] are highly affected by the windows used and by the presence of omitted variables: we propose some analyses to strengthen the robustness of these tests. Concerning the DCC test, we show that it is unable to cope with some kinds of heteroskedasticity.

Volatility and shocks spillover before and after EMU in European stock markets

Abstract This paper analyzes whether deregulation, globalization, recent financial crises, the convergence of European economies and the introduction of the euro have produced some effects on the return distribution of the world market index and on the volatility spillover from the world index to European stock markets. Using multivariate switching regime models we test these issues for the world equity index and some European capital market indexes. Our results suggest that in the last 5 years the world index volatility has increased as has the idiosyncratic German risk factor. Moreover, the volatility spillovers from both the world index and the German market have increased after EMU for most European stock markets.

Multivariate Markov Switching Dynamic Conditional Correlation GARCH representations for contagion analysis

Abstract.This paper provides an extension of the Dynamic Conditional Correlation model of Engle (2002) by allowing both the unconditional correlation and the parameters to be driven by an unobservable Markov chain. We provide the estimation algorithm and perform an empirical analysis of the contagion phenomenon in which our model is compared to the traditional CCC and DCC representations.

Dynamic risk exposures in hedge funds

A regime-switching beta model is proposed to measure dynamic risk exposures of hedge funds to various risk factors during different market volatility conditions. Hedge fund exposures strongly depend on whether the equity market (S&P 500) is in the up, down, or tranquil regime. In the down-state of the market, when market volatility is high and returns are very low, S&P 500, Small-Large, Credit Spread, and VIX are common risk factors for most of the hedge fund strategies. This suggests that hedge fund exposures to the market, liquidity, credit, and volatility risks change depending on market conditions, and these risks are potentially common factors for the hedge fund industry in the down-state of the market.

Market linkages, variance spillovers, and correlation stability: Empirical evidence of financial contagion

To model the contemporaneous relationships among Asian and American stock markets, a simultaneous equation system with GARCH errors is introduced. In the estimated residuals, the correlation matrix is analyzed over rolling windows and using a correlation matrix distance, which allows a graphical analysis and the development of a statistical test of correlation movements. Furthermore, a methodology that can be used to identify turmoil periods on a data-driven basis is presented. The previous results are applied in the analysis of the contagion issue between Asian and American stock markets. The results show some evidence of contagion, and the proposed statistics identify, on a data-driven basis, turmoil periods consistent with the ones currently assumed in the literature.

A generalized Dynamic Conditional Correlation model for portfolio risk evaluation

We propose a generalization of the Dynamic Conditional Correlation multivariate GARCH model of Engle [R.F. Engle, Dynamic conditional correlation: a simple class of multivariate generalized autoregressive conditional heteroskedasticity models, Journal of Business and Economic Statistics 20 (2002) 339-350] and of the Asymmetric Dynamic Conditional Correlation model of Cappiello et al.[L. Cappiello, R.F. Engle, K. Sheppard, Asymmetric dynamics in the correlations of global equity and bond returns, Journal of Financial Econometrics 25 (2006) 537-572]. 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. [M. Billio, M. Caporin, M. Gobbo, Flexible dynamic conditional correlation multivariate GARCH for asset allocation, Applied Financial Economics Letters 2 (2006) 123-130] 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.

Crises 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.

Bayesian estimation of switching ARMA models

Abstract Switching ARMA processes have recently appeared as an efficient modelling to nonlinear time-series models, because they can represent multiple or heterogeneous dynamics through simple components. The levels of dependence between the observations are double: at a first level, the parameters of the model are selected by a Markovian procedure. At a second level, the next observation is generated according to a standard time-series model. When the model involves a moving average structure, the complexity of the resulting likelihood function is such that simulation techniques, like those proposed by Shephard (1994, Biometrika 81, 115–131) and Billio and Monfort (1998, Journal of Statistical Planning and Inference 68, 65–103), are necessary to derive an inference on the parameters of the model. We propose in this paper a Bayesian approach with a non-informative prior distribution developed in Mengersen and Robert (1996, Bayesian Statistics 5. Oxford University Press, Oxford, pp. 255–276) and Robert and Titterington (1998, Statistics and Computing 8(2), 145–158) in the setup of mixtures of distributions and hidden Markov models, respectively. The computation of the Bayes estimates relies on MCMC techniques which iteratively simulate missing states, innovations and parameters until convergence. The performances of the method are illustrated on several simulated examples. This work also extends the papers by Chib and Greenberg (1994, Journal of Econometrics 64, 183–206) and Chib (1996, Journal of Econometrics 75(1), 79–97) which deal with ARMA and hidden Markov models, respectively.