Measuring Systemic Risk: Common Factor Exposures and Tail Dependence Effects

Published date01 November 2015
Date01 November 2015
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
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
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. Specically, our theoretical model allows for rm-specic impacts of
infrequent and extreme events. Using data on the four sectors of the US nancial
industry from 1996 to 2011, we uncover two key empirical ndings. 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
1. Introduction
Multiple published studies document the importance of a stable nancial system for not
just the nancial industry but the real economy as well. Monitoring the whole nancial
system (not just the banking industry) in turn is required, to guarantee its stability. As the
20072012 crises (corporate and sovereign) highlighted, a key factor that affects the
stability of the overall nancial system, and the real economy, is the level of systemic
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 rm level;
in the latter case, systemic risk aggregates can be viewed as the aggregation of nancial
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).
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 Dufeet al. (2009). In a frailty setting,
the arrival of (bad) news about one rm (extreme negative stock returns) causes a jump in
the conditional distribution of hidden covariates and therefore a (negative) jump in any
rms 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 nancial 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,
we can
address the rm-specic impact of infrequent and extreme events. When a jump occurs,
its impact occurs at the same time and in the same direction for all rms (positive or
Rajan (2006) highlights the importance of the exposure of the real economy to shocks
stemming from the nancial sector.
An alternative approximation relies on Lehars (2005) and Suhs (2012) portfolio approach,
which measures systemic risk in the nancial sector according to groups of nancial rms
risks. Altman and Rijken (2011) similarly assess sovereign default risk by aggregating the
Altmans z-scores of non-nancial corporations.
Literature on default risks suggests that default times concentrate around periods in which
the probability of default of all rms increases. However, this increase cannot be totally, or
even partially, explained by rmscommon dependence on systematic macroeconomic
factors (see Giesecke, 2004; Giesecke and Goldberg, 2004; Elsinger et al., 2006a, 2006b).
Adding a correlated jumps factor allows to capture the stylized fact that default correlations
may increase when an inuential event (e.g. a major bankruptcy), affecting many rms
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 rms
extending the traditional rst-passage-time model.
© 2014 John Wiley & Sons Ltd
Measuring Systemic Risk 835
negative), but its size and volatility is specic to each rm. We also rene 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 nancial
industry: (1) DD, or the average distance-to-default in a given sector; (2) NoD,denedas
the number of joint defaults in a given sector; and (3) PIR, which is the ratio of the price
of insurance against nancial 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 nancial 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 rms and the whole stock market, and
In an empirical application, we rely on stock market data, which has a leading role in
the price discovery process.
Specically, we focus on the US nancial 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 rms reects
their crucial contribution to systemic risk.
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 nancial 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 nancial stress
index, namely, the St. Louis Fed Financial Stress Index (STLFSI).
The results show that
our measures provide extra forecasting power.
In contrast, measures of systematic risk (e.g. CAPM beta) only take into one of these
characteristics, namely the correlation between a rms stock returns and aggregate market
stock returns.
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 afrm 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).
Acharya et al. (2010) show that the top six rms 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 nancial institutions track with the level of systemic
risk. Pais and Stork (2013) suggest that a high stress level in large banks signicantly drives
systemic instability.
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 nancial conditional
indexes (Aramonte et al., 2013).

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