Christian T. Brownlees

Volatility, Correlation and Tails for Systemic Risk Measurement

We introduce SRISK to measure the systemic risk contribution of a financial firm. SRISK measures the capital shortfall of a firm conditional on a severe market decline, and is a function of its size, leverage and risk. We use the measure to study top financial institutions in the recent financial crisis. SRISK delivers useful rankings of systemic institutions at various stages of the crisis and identifies Fannie Mae, Freddie Mac, Morgan Stanley, Bear Stearns, and Lehman Brothers as top contributors as early as 2005-Q1. Moreover, aggregate SRISK provides early warning signals of distress in indicators of real activity.Received June 7, 2011; accepted April 18, 2016 by Editor Geert Bekaert.

SRISK: A Conditional Capital Shortfall Measure of Systemic Risk

We introduce SRISK to measure the systemic risk contribution of a financial firm. SRISK measures the capital shortfall of a firm conditional on a severe market decline, and is a function of its size, leverage and risk. We use the measure to study top financial institutions in the recent financial crisis. SRISK delivers useful rankings of systemic institutions at various stages of the crisis and identifies Fannie Mae, Freddie Mac, Morgan Stanley, Bear Stearns, and Lehman Brothers as top contributors as early as 2005-Q1. Moreover, aggregate SRISK provides early warning signals of distress in indicators of real activity.Received June 7, 2011; accepted April 18, 2016 by Editor Geert Bekaert.

NETS: Network Estimation for Time Series

This work proposes novel network analysis techniques for multivariate time series. We define the network of a multivariate time series as a graph where vertices denote the components of the process and edges denote non zero long run partial correlations. We then introduce a two step LASSO procedure, called NETS, to estimate high dimensional sparse Long Run Partial Correlation networks. This approach is based on a VAR approximation of the process and allows to decompose the long run linkages into the contribution of the dynamic and contemporaneous dependence relations of the system. The large sample properties of the estimator are analysed and we establish conditions for consistent selection and estimation of the non zero long run partial correlations. The methodology is illustrated with an application to a panel of U.S. bluechips.

Multiplicative Error Models

Financial time series analysis has focused on data related to market trading activity. Next to the modeling of the conditional variance of returns within the GARCH family of models, recent attention has been devoted to other variables: first, and foremost, volatility measured on the basis of ultra-high frequency data, but also volumes, number of trades, durations. In this paper, we examine a class of models, named Multiplicative Error Models, which are particularly suited to model such non-negative time series. We discuss the univariate specification, by considering the base choices for the conditional expectation and the error term. We provide also a general framework, allowing for richer specifications of the conditional mean. The outcome is a novel MEM (called Composite MEM) which is reminiscent of the short- and long-run component GARCH model by Engle and Lee (1999). Inference issues are discussed relative to Maximum Likelihood and Generalized Method of Moments estimation. In the application, we show the regularity in parameter estimates and forecasting performance obtainable by applying the MEM to the realized kernel volatility of components of the S&P100 index. We suggest extensions of the base model by enlarging the information set and adopting a multivariate specification.

SRISK: A Conditional Capital Shortfall Index for Systemic Risk Measurement

We introduce SRISK to measure the systemic risk contribution of a financial firm. SRISK measures the capital shortfall of a firm conditional on a severe market decline, and is a function of its size, leverage and risk. We use the measure to study top financial institutions in the recent financial crisis. SRISK delivers useful rankings of systemic institutions at various stages of the crisis and identifies Fannie Mae, Freddie Mac, Morgan Stanley, Bear Stearns, and Lehman Brothers as top contributors as early as 2005-Q1. Moreover, aggregate SRISK provides early warning signals of distress in indicators of real activity.Received June 7, 2011; accepted April 18, 2016 by Editor Geert Bekaert.

Empirical risk minimization for heavy-tailed losses

The purpose of this paper is to discuss empirical risk minimization when the losses are not necessarily bounded and may have a distribution with heavy tails. In such situations, usual empirical averages may fail to provide reliable estimates and empirical risk minimization may provide large excess risk. However, some robust mean estimators proposed in the literature may be used to replace empirical means. In this paper, we investigate empirical risk minimization based on a robust estimate proposed by Catoni. We develop performance bounds based on chaining arguments tailored to Catonis mean estimator.

Shrinkage Estimation of Semiparametric Multiplicative Error Models

Within models for nonnegative time series, it is common to encounter deterministic components (trends, seasonalities) which can be specified in a flexible form. This work proposes the use of shrinkage type estimation for the parameters of such components. The amount of smoothing to be imposed on the estimates can be chosen using different methodologies: Cross-Validation for dependent data or the recently proposed Focused Information Criterion. We illustrate such a methodology using a semiparametric autoregressive conditional duration model that decomposes the conditional expectations of durations into their dynamic (parametric) and diurnal (flexible) components. We use a shrinkage estimator that jointly estimates the parameters of the two components and controls the smoothness of the estimated flexible component. The results show that, from the forecasting perspective, an appropriate shrinkage strategy can significantly improve on the baseline maximum likelihood estimation.

A Bayesian approach for capturing daily heterogeneity in intra-daily durations time series

Intra-daily financial durations time series typically exhibit evidence of long range dependence. This has motivated the introduction of models able to reproduce this stylized fact, like the Fractionally Integrated Autoregressive Conditional Duration Model. In this work we introduce a novel specification able to capture long range dependence. We propose a three component model that consists of an autoregressive daily random effect, a semiparametric time-of-day effect and an intra-daily dynamic component: the Mixed Autoregressive Conditional Duration (Mixed ACD) Model. The random effect component allows for heterogeneity in mean reversal within a day and captures low frequency dynamics in the duration time series. The joint estimation of the model parameters is carried out using MCMC techniques based on the Bayesian formulation of the model. The empirical application to a set of widely traded US tickers shows that the model is able to capture low frequency dependence in duration time series. We also find that the degree of dependence and dispersion of low frequency dynamics is higher in periods of higher financial distress.

Credit Risk Interconnectedness: What Does the Market Really Know?

We analyze the relation between market-based credit risk interconnectedness among banks during the crisis and the associated balance sheet linkages via funding and securities holdings. For identification, we use a proprietary dataset that has the funding positions of banks at the bank-to-bank level for 2006-13 in conjunction with investments of banks at the security level and the credit register from Germany. We find asymmetries both cross-sectionally and over time: when banks face difficulties to raise funding, the interbank lending affects market-based bank interconnectedness. Moreover, banks with investments in securities related to troubled classes have a higher credit risk interconnectedness. Overall, our results suggest that market-based measures of interdependence can serve well as risk monitoring tools in the absence of disaggregated high-frequency bank fundamental data.

Back to the Future: Backtesting Systemic Risk Measures during Historical Bank Runs and the Great Depression

We evaluate the performance of two popular systemic risk measures, CoVaR and SRISK, during eight financial panics in the era before FDIC insurance. Bank stock price and balance sheet data were not readily available for this time period. We rectify this shortcoming by constructing a novel dataset for the New York banking system before 1933. Our evaluation exercise focuses on two challenges: the ranking of systemically important financial institutions (SIFIs) and financial crisis prediction. We find that CoVaR and SRISK meet the SIFI ranking challenge, i.e. help identifying systemic institutions in periods of distress beyond what is explained by standard risk measures up to six months prior to panics. In contrast, aggregate CoVaR and SRISK are only somewhat effective at predicting financial crises.