On the Relation between Firm Characteristics and Volatility Dynamics with an Application to the 2007-2009 Financial Crisis

Despite the extensive literature on the analysis of firm equity volatility, relatively little is known about the relation between firm characteristics and volatility dynamics. This is partly due to the lack of an appropriate modelling framework in which these research questions can be addressed adequately. This work proposes a Hierarchical Factor GARCH model for multivariate volatility analysis in large panels of assets. The novelty consists of augmenting the dynamic specification with equations that link the volatility dynamics parameters of each firm to observed and unobserved characteristics. The hierarchical approach has features that are useful for both economic and forecasting applications. It permits one to investigate how variation of firm variables explains variation in volatility dynamics. Moreover, it allows for a parsimonious parameterization of a multivariate system that is independent of its dimension, yet capable of retaining flexibility in the individual series dynamics thanks to the random effect structure. The model is estimated via Maximum Likelihood. The proposed methodology is used to analyse the volatility dynamics of top U.S. financial institutions during the 2007-2009 crisis using a financial index as common factor. Dynamics are a function of firm size, leverage, distance to default and liquidity before the beginning of the credit crunch. Results show that leverage is the most influential variable, and firms with high leverage have high factor exposure, high idiosyncratic volatility as well as high sensitivity to temporary idiosyncratic volatility shocks. Factor exposure in the crisis is also high for firms that are large, have a small distance to default and are illiquid. Overall, the model captures a substantial portion of cross sectional variation in volatility dynamics.

[1]  Disentangling Systematic and Idiosyncratic Risk for Large Panels of Assets , 2010 .

[2]  Andrew J. Patton.  Modelling Asymmetric Exchange Rate Dependence , 2006 .

[3]  C. Brownlees,et al.  A Practical Guide to Volatility Forecasting through Calm and Storm , 2011 .

[4]  F. Diebold,et al.  VOLATILITY AND CORRELATION FORECASTING , 2006 .

[5]  Søren Feodor Nielsen,et al.  On simulated EM algorithms , 2000 .

[6]  L. Bauwens,et al.  Multivariate GARCH Models: A Survey , 2003 .

[7]  Giampiero M. Gallo,et al.  Comparison of Volatility Measures: A Risk Management Perspective , 2009 .

[8]  S. Basu,et al.  The Mean, Median, and Mode of Unimodal Distributions:A Characterization , 1997 .

[9]  George C. Tiao,et al.  Kurtosis of GARCH and stochastic volatility models with non-normal innovations , 2003 .

[10]  Calyampudi Radhakrishna Rao,et al.  Statistical methods in finance , 1996 .

[11]  Paul A. Ruud,et al.  Handbook of Econometrics: Classical Estimation Methods for LDV Models Using Simulation , 1993 .

[12]  S. Satchell,et al.  Forecasting Volatility in Financial Markets : A Review , 2004 .

[13]  H. Bungartz,et al.  Sparse grids , 2004, Acta Numerica.

[14]  Spain,et al.  PANEL DATA MODELS : SOME RECENT DEVELOPMENTS * , 2004 .

[15]  C. Granger,et al.  A long memory property of stock market returns and a new model , 1993 .

[16]  R. Engle,et al.  A Permanent and Transitory Component Model of Stock Return Volatility , 1993 .

[17]  Clive W. J. Granger,et al.  Combining competing forecasts of inflation using a bivariate arch model , 1984 .

[18]  George Tauchen,et al.  Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models , 1991 .

[19]  Samuel Kotz,et al.  Multivariate T-Distributions and Their Applications , 2004 .

[20]  E. Ghysels,et al.  Série Scientifique Scientific Series Predicting Volatility: Getting the Most out of Return Data Sampled at Different Frequencies , 2022 .

[21]  B. M. Pötscher,et al.  MODEL SELECTION AND INFERENCE: FACTS AND FICTION , 2005, Econometric Theory.

[22]  J. Zakoian,et al.  Threshold Arch Models and Asymmetries in Volatility , 1993 .

[23]  Edward I. Altman,et al.  FINANCIAL RATIOS, DISCRIMINANT ANALYSIS AND THE PREDICTION OF CORPORATE BANKRUPTCY , 1968 .

[24]  Enrique Sentana,et al.  Indirect estimation of large conditionally heteroskedastic factor models, with an application to the Dow 30 stocks , 2008 .

[25]  F. Diebold,et al.  The dynamics of exchange rate volatility: a multivariate latent factor ARCH model , 1986 .

[26]  S. Rabe-Hesketh,et al.  Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects , 2005 .

[27]  G. Robinson.  That BLUP is a Good Thing: The Estimation of Random Effects , 1991 .

[28]  Viktor Winschel,et al.  Solving, Estimating, and Selecting Nonlinear Dynamic Models Without the Curse of Dimensionality , 2010 .

[29]  René M. Stulz,et al.  The Credit Crisis Around the Globe: Why Did Some Banks Perform Better? , 2011 .

[30]  C. Brownlees,et al.  On Variable Selection for Volatility Forecasting: The Role of Focused Selection Criteria , 2008 .

[31]  Ser-Huang Poon,et al.  Practical Issues in Forecasting Volatility , 2005 .

[32]  Neil Shephard,et al.  Nuisance parameters, composite likelihoods and a panel of GARCH models , 2009 .

[33]  Yacine Ait-Sahalia,et al.  How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise , 2003 .

[34]  Fulvio Corsi,et al.  A Simple Approximate Long-Memory Model of Realized Volatility , 2008 .

[35]  Marshall F Chalverus,et al.  The Black Swan: The Impact of the Highly Improbable , 2007 .

[36]  B. Ripley,et al.  Semiparametric Regression: Preface , 2003 .

[37]  Florian Heiss,et al.  Likelihood approximation by numerical integration on sparse grids , 2008 .

[38]  Nassim Nicholas Taleb,et al.  The Black Swan: The Impact of the Highly Improbable , 2007 .

[39]  W. Distaso,et al.  Tailing Tail Risk in the Hedge Fund Industry , 2012 .

[40]  Jean-François Richard,et al.  Methods of Numerical Integration , 2000 .

[41]  Hannes Leeb,et al.  Performance Limits for Estimators of the Risk or Distribution of Shrinkage-Type Estimators, and Some General Lower Risk-Bound Results , 2002 .

[42]  A. Gallant,et al.  Which Moments to Match? , 1995, Econometric Theory.

[43]  Neil Shephard,et al.  Realising the future: forecasting with high frequency based volatility (HEAVY) models , 2010 .

[44]  L. Glosten,et al.  On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks , 1993 .

[45]  W. Newey,et al.  Large sample estimation and hypothesis testing , 1986 .

[46]  R. Engle,et al.  A Multiple Indicators Model for Volatility Using Intra-Daily Data , 2003 .

[47]  Viral V. Acharya,et al.  Regulating Wall Street: The Dodd-Frank Act and the New Architecture of Global Finance , 2010 .

[48]  Wenjiang J. Fu,et al.  Asymptotics for lasso-type estimators , 2000 .

[49]  Luc Bauwens,et al.  Bayesian Clustering of Many Garch Models , 2003 .

[50]  Luc Laeven,et al.  Bank Governance, Regulation, and Risk Taking , 2008 .

[51]  Jeffrey R. Russell,et al.  Separating Microstructure Noise from Volatility , 2004 .

[52]  Robert F. Engle,et al.  Volatility, Correlation and Tails for Systemic Risk Measurement , 2010 .

[53]  L. Pedersen,et al.  Measuring Systemic Risk , 2010 .

[54]  S. Laurent,et al.  Modelling Daily Value-at-Risk Using Realized Volatility and Arch Type Models , 2001 .

[55]  Dennis Kristensen,et al.  Estimation of Dynamic Models with Nonparametric Simulated Maximum Likelihood , 2005 .

[56]  M. Rothschild,et al.  Asset Pricing with a Factor Arch Covariance Structure: Empirical Estimates for Treasury Bills , 1988 .

[57]  W. Greene,et al.  Fixed and Random Effects in Nonlinear Models , 2001 .

[58]  P. Hansen,et al.  Realized GARCH: A Complete Model of Returns and Realized Measures of Volatility ∗ , 2010 .

[59]  Francis X. Diebold,et al.  Modeling and Forecasting Realized Volatility , 2001 .

[60]  Jean-David Fermanian,et al.  A NONPARAMETRIC SIMULATED MAXIMUM LIKELIHOOD ESTIMATION METHOD , 2004, Econometric Theory.

[61]  N. Shephard,et al.  Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise , 2006 .

[62]  Nikolaus Hautsch,et al.  Capturing Common Components in High-Frequency Financial Time Series: A Multivariate Stochastic Multiplicative Error Model , 2008 .

[63]  Yi Lu,et al.  Forecasting realized volatility using a long-memory stochastic volatility model : estimation, prediction and seasonal adjustment , 2006 .

[64]  Enrique Sentana,et al.  Volatiltiy and Links between National Stock Markets , 1990 .