Applying CoV aR to Measure Systemic Market
Risk: the Colombian Case∗
Juan Carlos Mendoza
David P´ erez-Reyna†
In Colombia, the exposition to market risk has increased significantly since 2009.
Nonetheless, the risk codependence among agents has not been analyzed yet from the
perspective of this risk. Therefore, this paper presents an approach to estimate such
relevance based on CoV aR and quantile regressions. This methodology is flexible
enough to allow the estimation of the systemic market risk contribution of banks,
pension funds, and between different types of financial institutions. Results suggest
that risk codependence among entities increases during distress periods.
JEL classification numbers: C20, G14, G21.
Keywords: Systemic Market Risk, CoV aR, Value at Risk, Quantile Regression.
∗The authors thank Dairo Estrada and the staff of the Financial Stability Department at the Banco
de la Rep´ ublica (Central Bank of Colombia) for valuable comments. The views expressed in this paper
are those of the authors and do not necessarily reflect those of the Banco de la Rep´ ublica, nor of its
Board of Directors. The authors are solely responsible for any errors or omissions.
†The authors are, respectively, Senior Professional, Professional and Specialized Professional
of the Financial Stability Department at the Banco de la Rep´ ublica.
Negative shocks suffered by individual financial institutions can easily propagate and
affect other entities. Due to this, measuring and analyzing the phenomena derived from
systemic risk has been a common interest among policy makers. Moreover, since the
recent financial crisis, this analysis has gained even more importance.
Systemic risk may not be analyzed only by using individual risk measurements of
institutions. Herding behavior by financial entities may cause a high exposition to neg-
ative systemic events, even if individually all institutions have low risk measurements.
Additionally, the risk assumed by a systemic institution may cause negative spillovers
not internalized in risk requirements. To deal with these issues, several papers have ap-
proached systemic risk from different perspectives, according to what authors perceive
is more relevant to their analysis.
For Rochet and Tirole (1996) systemic risk is materialized when a bank’s economic
distress propagates to other economic agents linked to that bank through financial trans-
actions. This paper studies whether the flexibility offered by decentralized interbank
transactions can be maintained, while the corresponding financial authority can be pro-
tected against undesired rescue operations. If not, centralizing interbank systems would
be more efficient in terms of liquidity allocation and prudential control. In particular,
the authors analyze the “too big to fail”policy: proper authorities bail-out a bank with
short positions in the interbank market because the bank’s distress may affect solvent
According to Furfine (2003), there are two types of systemic risk: 1) the risk that
a financial shock causes a set of markets or institutions to simultaneously fail to func-
tion efficiently, and 2) the risk that failure of one or a small number of institutions will
be transmitted to others due to explicit financial linkages across institutions. To an-
alyze contagion, Furfine estimates it by examining federal funds exposures across U.S.
banks, which are used to simulate the impact of exogenous failure scenarios. This paper
concludes that, although the exposures are not large enough to cause a great risk of
contagion, illiquidity could pose a threat to the banking system.
For Acharya (2009) systemic risk, defined as joint failure risk, arises from the corre-
lation of banks’ assets returns. To analyze this, the author considers a model in which
banks invest in risky assets in various industries. The investment decision determines
the correlation among banks’ assets, which, in case it is high enough, results in a rising
exposition to systemic risk. The paper concludes that the effect of regulation of banks’
optimal investment decisions deserves careful scrutiny: requirements should depend both
on banks’ joint and individual risk.
On the other hand, Allen and Gale (2000) address systemic risk from a liquidity risk
perspective. They find that the resilience of the interbank market to adverse liquidity
shocks depends on the market’s structure.Similarly, Saade Ospina (2010) analyzes
the Colombian interbank collateralized market. He develops a centrality index using
cooperative game theory and concludes that when the interbank network is disconnected,
bid ask spreads are farther apart and their volatility is higher. This implies that banks
are more exposed to liquidity market risk under this scenario.
Nonetheless, in Colombia systemic risk has not been analyzed yet from a market risk
perspective. The exposition of financial institutions to this risk has increased since 2009
as lower rates and slower credit dynamics have caused asset restructuring. Treasury
bonds (TES) holdings and volatility in yields reached levels similar to the observed by
mid 2006, when a setback in this market caused the most important losses during the
past decade. In the context of the model proposed by Acharya (2009), this behavior has
increased the correlation of the different entities’ assets, especially among commercial
banks, which could cause a higher systemic risk. Due to these reasons, it is impera-
tive to analyze market risk codependence among Colombian commercial banks, pension
funds and financial institutions to identify which institutions have a high contribution
to systemic market risk.
The objective of this paper is to analyze market risk codependence among Colombian
financial institutions in order to identify institutions with the highest contribution to
systemic market risk. We define systemic market risk as the aggregate market risk of
the financial system. We follow the definition of CoV aR introduced by Adrian and
Brunnermeier (2009), which is measured as the Value at Risk (V aR) of a financial
institution or sector conditional on the V aR of another institution or sector. In this
way, if CoV aR increases relative to V aR, so does spillover risk among institutions.
By defining the difference between these measures as ∆CoV aR, we can estimate the
contribution of each institution to systemic market risk.
Additionally, since ∆CoV aR is not necessarily symmetric (that is, the contribution
that institution i’s V aR has on institution j’s market risk does not necessarily equals
the contribution of j’s V aR on i’s V aR), this measure can be used to analyze the risk
across the Colombian financial system. We focus on the public debt portfolio of financial
entities and define the portfolio of the financial system as the aggregate public debt
holdings of these institutions. Results suggest that risk codependence among entities
increases during distress periods.
As mentioned by Adrian and Brunnermeier (2009), one advantage of CoV aR is that it
can be applied with any other tail measure to analyze other risks. For instance, Chan-Lau
(2008) follows a similar approach and assesses systemic credit risk by measuring default
risk codependence among financial institutions through an analysis of CDS spreads of
25 entities in Europe, Japan and the US.
Also, Gauthier et al (2010) compare ∆CoV aR and other four approaches to assign
systemic capital requirements to individual banks based on each bank’s contribution to
systemic risk. The authors conclude that financial stability can be enhanced substantially
by implementing a system perspective on bank regulation.
Table 4: Conditional Risk Codependence Among Pension Funds
PF vs Sector
Sector vs PF
Source: Authors’ estimations.
Figure 7, Panel A, shows the interbank rate, which follows closely the intervention rate
of BR. In May 2006 BR began a monetary contraction by raising its intervention rate
from 6% to 10% during a time span close to two years. Due to the financial crisis, this
rate was lowered from 10% to 3.5% in less than one year, beginning in December 2008.
This behavior had a positive effect on the public debt market, as the TES index return
shows in figure 7, panel B.9This figure also shows that the TES crisis in 2006 and the
recent international financial crisis had a significant negative effect on the Colombian
Dynamics of Variables Used for PCA Estimation
By comparing panels A and C of figure 7 it can be concluded that periods of monetary
expansion match with periods of steep yield curves. This is observed both in COP-
denominated TES yield curve and in inflation-linked TES (UVR) yield curve. On the
other hand, periods with an increasing intervention rate have occurred at the same time
that yield curves have flattened. Additionally, by analyzing the difference between these
two yield curves, inflation expectations can be estimated. Panel D of figure 7 shows that
they have a decreasing trend in the analyzed period.
Panel F of figure 7 shows the weekly growth of the credit stock. On average, credit
has increased 0.3% each week. However, it has had a relatively high standard deviation of
0.5%. In particular, on the last week of January 2004 credit grew over 4% with respect to
the previous week. During 2009, however, the average weekly credit growth was 0.03%,
showing the slower dynamics credit stock had due to the economic turndown of Colombia
during that year. Finally, panels E, G and H of figure 7 show the EMBI+ for Colombia,
VIX and five-year CDS for Colombia, respectively. The dynamics of these indexes has
been closely related since the beginning of the recent financial international crisis. In
particular, the bankruptcy of Lehman Brothers was reflected in a historic increase in the
9For the construction of this index see Reveiz and Le´ on Rinc´ on (2008). We thank these authors for
supplying the index series.
Figure 7: Variables Used for PCA Estimation
A. Interbank RateB. Weekly Return for Different Markets
C. Slope of Yield CurvesD. Inflation Expectations
E. EMBI+ ColombiaF. Weekly Credit Growth
G. VIX H. Colombia 5 year CDS
Source: Banco de la Rep´ ublica, Bolsa de Valores de Colombia (Colombian Stock Market), Reveiz and
Le´ on Rinc´ on (2008), Bloomberg.