Measuring Systemic Risk: Common Factor Exposures and Tail Dependence Effects

• Published date: 01 November 2015
• Date: 01 November 2015
• DOI: http://doi.org/10.1111/eufm.12040

European Financial Management, Vol. 19, No. 5, 2013, 887–910

doi: 10.1111/j.1468-036X.2012.00659.x

© 2014 John Wiley & Sons Ltd

© 2014 John Wiley & Sons Ltd

Measuring Systemic Risk: Common

Factor Exposures and Tail

Dependence Effects

Wan-Chien Chiu and Juan Ignacio Peña

Department of Business Administration, Universidad Carlos III de Madrid, c/ Madrid 126,

28903 Getafe, Madrid, Spain

E-mails: wchiu@emp.uc3m.es; ypenya@eco.uc3m.es

Chih-Wei Wang

Chinese Academy of Finance and Development, Central University of Finance and Economics,

39 South College Road, Haidian District, Beijing 100081, China

Department of Business Administration, Universidad Carlos III de Madrid, c/ Madrid 126,

28903 Getafe, Madrid, Spain

E-mail: chwang@emp.uc3m.es; redrum3690@gmail.com

Abstract

We model systemic risk using a common factor that accounts for market-wide

shocks and a tail dependence factor that accounts for linkages among extreme

stock returns. Specifically, our theoretical model allows for firm-specific impacts of

infrequent and extreme events. Using data on the four sectors of the US financial

industry from 1996 to 2011, we uncover two key empirical findings. First,

disregarding the effect of the tail dependence factor leads to a downward bias in

the measurement of systemic risk, especially during weak economic times. Second,

when these measures serve as leading indicators of the St. Louis Fed Financial

Stress Index, measures that include a tail dependence factor offer better

forecasting ability than measures based on a common factor only.

Keywords: systemic risk, tail dependence effects, correlated jumps, predictability

JEL classification: G01, G10, G18, G20, G28

We thank David Martínez Miera, Pablo Ruiz Verdú, Pedro Serrano, Sergio Vicente, Silvia

Stanescu, and Denisa Banulescu, as well as participants in the 3rd Financial Engineering

and Banking Society (FEBS) 2013 Conference on Financial Regulation and Systemic Risk,

the 2013 European Financial Management Association (EMFA) annual conference, and the

Universidad Carlos III finance seminar, for useful comments. We thank the Editor

John A. Doukas for useful suggestions. An anonymous referee provided many astute

comments which considerably improved the paper. The usual disclaimer applies. Peña

acknowledges financial support from MCI grants ECO2009-12551 and ECO2012-35023.

*Correspondence: Wan-Chien Chiu.

European Financial Management, Vol. 21, No. 5, 2015, 833–866

doi: 10.1111/eufm.12040

© 2014 John Wiley & Sons Ltd

Wan-Chien Chiu, Juan Ignacio Peña and Chih-Wei Wang

834

1. Introduction

Multiple published studies document the importance of a stable financial system for not

just the financial industry but the real economy as well. Monitoring the whole financial

system (not just the banking industry) in turn is required, to guarantee its stability. As the

2007–2012 crises (corporate and sovereign) highlighted, a key factor that affects the

stability of the overall financial system, and the real economy, is the level of systemic

risk.

1

An accurate measure of this level should be of crucial importance for regulators

and investors alike.

In response, extensive literature explores a variety of systemic risk measures (e.g.,

Bisias et al., 2012). Most measures refer to the aggregate system or individual firm level;

in the latter case, systemic risk aggregates can be viewed as the aggregation of financial

institutions’risks,

2

which are driven by both common factor exposures to market-wide

shocks and additional exposures to other, observed and unobserved factors. A common

factor accounts for the systematic component of systemic risk (Das and Uppal, 2004) it

cannot capture correlation due to large, infrequent changes (e.g., unexpected failure of a

major bank).

3

Therefore, an alternative approach that includes relevant frailty and

contagion effects, arising from exposure to unobservable covariates (e.g., common latent

factors) is outlined both in Das et al. (2007) and Duffieet al. (2009). In a frailty setting,

the arrival of (bad) news about one firm (extreme negative stock returns) causes a jump in

the conditional distribution of hidden covariates and therefore a (negative) jump in any

firm’s stock returns that depend on the same unobservable covariates.

Unlike previous studies, we use a structural-model approach, rather than a reduced-

form approach, and do not make assumptions about the nature of these common factors.

Instead, we direct our attention to tail dependence effects that result from simultaneous,

extreme equity returns across financial institutions. Furthermore, we focus on the impact

of these shocks on systemic risk measures. By adding a correlated jumps factor (as a

proxy for tail dependence effects) to the standard Merton (1974) framework,

4

we can

address the firm-specific impact of infrequent and extreme events. When a jump occurs,

its impact occurs at the same time and in the same direction for all firms (positive or

1

Rajan (2006) highlights the importance of the exposure of the real economy to shocks

stemming from the financial sector.

2

An alternative approximation relies on Lehar’s (2005) and Suh’s (2012) portfolio approach,

which measures systemic risk in the financial sector according to groups of financial firms’

risks. Altman and Rijken (2011) similarly assess sovereign default risk by aggregating the

Altman’s z-scores of non-financial corporations.

3

Literature on default risks suggests that default times concentrate around periods in which

the probability of default of all firms increases. However, this increase cannot be totally, or

even partially, explained by firms’common dependence on systematic macroeconomic

factors (see Giesecke, 2004; Giesecke and Goldberg, 2004; Elsinger et al., 2006a, 2006b).

4

Adding a correlated jumps factor allows to capture the stylized fact that default correlations

may increase when an influential event (e.g. a major bankruptcy), affecting many firms

simultaneously, happens. In this vein, Liu et al. (2013) link default correlation to equity return

correlation in the context of the structural framework An alternative view is formulated in

Zhou (2001a) which develops a model to compute simultaneous defaults for multiple firms

extending the traditional first-passage-time model.

© 2014 John Wiley & Sons Ltd

Measuring Systemic Risk 835

negative), but its size and volatility is specific to each firm. We also refine the

methodology proposed by Das and Uppal (2004) to capture joint tail risk behaviour over

time. Based on our model, we develop three indicators of systemic stress in the financial

industry: (1) DD, or the average distance-to-default in a given sector; (2) NoD,definedas

the number of joint defaults in a given sector; and (3) PIR, which is the ratio of the price

of insurance against financial distress to the aggregate asset value in a given sector.

Given that systemic risk is a multidimensional concept, measures of systemic risk

should be based on several relevant characteristics (Bisias et al., 2012) such as size,

interconnectedness, substitutability, leverage, herd effects (clone property), correlation

with other sectors of the of the financial industry and correlation with the real economy.

Our three measures are attractive because they summarise many of these characteristics,

in particular: size, leverage, dependence between firms and the whole stock market, and

interconnectedness.

5

In an empirical application, we rely on stock market data, which has a leading role in

the price discovery process.

6

Specifically, we focus on the US financial industry and the

stock returns of ten largest institutions in four major sectors: depositories, broker-

dealers, insurance companies, and others. This concentration on the biggest firms reflects

their crucial contribution to systemic risk.

7

The sample period runs from January 1996 to

December 2011. The contribution of this article is threefold. First, our model captures the

stylised fact that extreme negative co-movements for large financial institutions are

stronger and more frequent in bear than in bull markets. Second, disregarding the impact

of tail dependence effects leads to underestimates of the systemic risk level, especially

during weak economic times. Third, we analyse whether our systemic risk measures

offer leading indicators of alternative measures, using a comparison with a model that

includes only common factor effects and a measure based on a public financial stress

index, namely, the St. Louis Fed Financial Stress Index (STLFSI).

8

The results show that

our measures provide extra forecasting power.

5

In contrast, measures of systematic risk (e.g. CAPM beta) only take into one of these

characteristics, namely the correlation between a firm’s stock returns and aggregate market

stock returns.

6

This leading role might entail anticipating trends in subsequent failures (Lehar, 2005) or

changes in supervisory ratings four quarters in advance (Krainer and Lopez, 2001). Several

articles affirm that equity market information leads the credit risk price discovery process.

Zhang et al. (2009) observe that credit default swaps are sensitive to jumps in equity returns.

Previous paper document that the equity market leads both the CDS and bond market in the

price discovery process (see Forte and Peña (2009), and Norden and Weber (2009).

7

Acharya et al. (2010) show that the top six firms in terms of contributions to systemic risk

also rank among the top seven in terms of total assets. Patro et al. (2013) reveals that daily

stock return correlations among large financial institutions track with the level of systemic

risk. Pais and Stork (2013) suggest that a high stress level in large banks significantly drives

systemic instability.

8

This index is constructed from 18 weekly data series: 7 interest rate series, 6 yield spreads,

and 5 other indicators. We chose the STLFSI for three reasons. It is publicly available, spans

the whole sample period, and offers the best indicator among US public financial conditional

indexes (Aramonte et al., 2013).