Full text of A Framework for Assessing the Systemic Risk of Major Financial Institutions

The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.

Finance and Economics Discussion Series
Divisions of Research & Statistics and Monetary Affairs
Federal Reserve Board, Washington, D.C.

A Framework for Assessing the Systemic Risk of Major Financial
Institutions

Xin Huang, Hao Zhou, and Haibin Zhu
2009-37

NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary
materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth
are those of the authors and do not indicate concurrence by other members of the research staff or the
Board of Governors. References in publications to the Finance and Economics Discussion Series (other than
acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

A framework for assessing the systemic risk of major financial institutions†
Xin Huanga,∗ , Hao Zhoub and Haibin Zhuc
a

Department of Economics, University of Oklahoma
Risk Analysis Section, Federal Reserve Board
c
Bank for International Settlements
b

This version: May 2009

Abstract
In this paper we propose a framework for measuring and stress testing the systemic risk of
a group of major financial institutions. The systemic risk is measured by the price of insurance against financial distress, which is based on ex ante measures of default probabilities of
individual banks and forecasted asset return correlations. Importantly, using realized correlations estimated from high-frequency equity return data can significantly improve the accuracy
of forecasted correlations. Our stress testing methodology, using an integrated micro-macro
model, takes into account dynamic linkages between the health of major US banks and macrofinancial conditions. Our results suggest that the theoretical insurance premium that would
be charged to protect against losses that equal or exceed 15% of total liabilities of 12 major
US financial firms stood at $110 billion in March 2008 and had a projected upper bound of
$250 billion in July 2008.
JEL classification: G21 ; G28 ; G14 ; C13
Keywords: Systemic risk; Stress testing; Portfolio credit risk; Credit default swap; Highfrequency data
∗

Corresponding author. Tel.: 405 325 2643; fax: 405 325 2643.
E-mail addresses: xhuang@ou.edu (X. Huang), hao.zhou@frb.gov (H. Zhou) and haibin.zhu@bis.org
(H. Zhu).
†

We would like to thank Mark Carlson, Sean Campbell, Francis X. Diebold, Darrell Duffie, Robert Engle,
José L. Fillat, Michael Gibson, Brenda González-Hermosillo, Michael Gordy, Don Nakornthat, Nikola Tarashev, George Tauchen, and seminar participants at the Bank for International Settlements, the Hong Kong
Institute for Monetary Research, Federal Reserve Board Finance Forum, Hong Kong University, International
Monetary Fund, Federal Reserve Bank of Kansas City, and the conference participants at the Financial Econometrics and Vast Data Conference organized by the Oxford-Man Institute of Quantitative Finance, Federal
Reserve System Committee Meeting on Financial Structure and Regulation at Boston, Federal Reserve Bank
of Chicago’s 45th Annual Conference on Bank Structure and Competition, Shanghai Winter Finance Conference, BIS Second Asia Research Network Workshop on Financial Markets and Institutions, Stress Testing
Workshop sponsored by China’s Banking Regulatory Commission and International Finance Corporation. We
would also like to thank Clara Gacia for excellent data support. A grant by CAREFIN Bocconi Centre for
Applied Research in Finance is gratefully acknowledged. The views presented here are solely those of the
authors and do not necessarily represent those of the Federal Reserve Board or the Bank for International
Settlements.

1. Introduction
Banks have been the most important financial intermediaries in the economy, by providing
liquidity transformation and monitoring services. The mal-functioning of the banking system
can be extremely costly to the real economy, as illustrated in a number of financial crises
in both industrial and developing economies in the past few decades, including the current
global credit-liquidity turmoil. Therefore, financial regulators and central banks have devoted
much effort to monitoring and regulating the banking industry. Such regulation has been
traditionally focused on assuring the soundness of individual banks. More recently, there
has been a trend towards focusing on the stability of the banking system as a whole, which is
known as the macro-prudential perspective of banking regulation (see Borio (2003, 2006)). For
instance, Goodhart et al. (2005, 2006), Goodhart (2006) and Lehar (2005) propose measures of
financial fragility that apply at both the individual and aggregate levels. At the international
level, the Financial Sector Assessment Program (FSAP), a joint IMF and World Bank effort
introduced in May 1999, aims to increase the effectiveness of efforts to promote the soundness
of financial systems in their member countries.
In order to assess the health of a financial system, two related questions need to be addressed. First, how to measure the systemic risk of a financial system, where systemic risk
defined as multiple simultaneous defaults of large financial institutions? Second, how to assess
the vulnerability of the financial system to potential downside risks?
In answering the first question, traditional measures have focused on banks’ balance sheet
information, such as non-performing loan ratios, earnings and profitability, liquidity and capital adequacy ratios. However, given that balance sheet information is only available on a
relatively low-frequency (typically quarterly) basis and often with a significant lag, there have
been growing efforts recently to measure the soundness of a financial system based on information from financial markets. For example, Chan-Lau and Gravelle (2005) and Avesani et al.
(2006) suggest to treat a banking system as a portfolio and use the nth-to-default probability
to measure the systemic risk by employing liquid equity market or CDS market data with a
modern portfolio credit risk technology. Similarly, Lehar (2005) proposes to measure systemic
1

risk, defined as the probability of a given number of simultaneous bank defaults, from equity
return data. The market-based measures have two major advantages. First, they can be updated in a more timely fashion. Second, they are usually forward-looking, in that asset price
movements reflect changes in market anticipation on future performance of the underlying
entities.
In addressing the second question, stress-testing is a popular risk management tool to
evaluate the potential impact of an extreme event on a financial firm or a financial sector.1
The stress testing exercise typically consists of two major steps. In the first step, an economic
model is used to examine the dynamic linkages between the asset quality and underlying
driving factors (macro-financial variables or latent factors). In the second step, stress testing
scenarios (either historical or hypothetical ones), which are based on extreme movements of
the driving factors, are fed into the model to assess the resilience of the financial sector.
Avesani et al. (2006) and Basurto and Padilla (2006), among others, are examples of stress
testing exercises on the financial sector using market-based information.2
In this paper, we propose a framework for measuring and stress testing the systemic risk
of the banking sector. Our framework follows the direction of using market information, but
with interesting extensions that are designed to overcome a number of shortcomings in existing
studies.3
Echoing some earlier studies, we propose to construct the measure of systemic risk based on
forward-looking price information of two highly-liquid markets, the credit default swap (CDS)
spreads and the equity prices of individual banks. Both are available on a daily basis in real
time. We are able to derive two key default risk parameters, the (risk-neutral) probability of
1

See CGFS (2000, 2005) and Drehmann (2008a,b) for definitions of stress testing exercises and survey of
market practices. Stress testing can be implemented to assess the market risk, as in Alexander and Sheedy
(2008), or the credit risk, as in this paper.
2
In a recent related research, Hancock and Passmore (2008) propose a vector auto-regression in value-atrisk (VAR in VaR) approach, in which systemic and macroeconomic outlook shocks are first fed into a VAR
to compute subordinated debt return movements, and then these debt movements are translated into changes
in the bank market value using a Merton-type option pricing model. Finally they construct a VaR measure
to compute the amount of capital to protect banks against systemic risks.
3
Our methodology is based on publicly available market information. Our framework is not related to the
supervisory assessments that were conducted over February-April 2009, which relied on confidential supervisory
information to assess potential future losses.

2

default (PD) of individual banks and the asset return correlations, from the CDS spreads and
the co-movement of equity returns, respectively. This approach does not rely on the balance
sheet or accounting information that may be available only on a quarterly or longer time
frequency, with a significant reporting lag.
Similarly in the stress testing exercise, following the recent studies, we adopt an integrated
micro-macro model, which not only examines the impact of general market developments on
the performance of individual banks, but at the same time incorporates the feedback effect
from the banking system to the rest of the economy. More importantly the joint vector autoregression (VAR) system employs the financial market variables like market return, market
volatility, short rate, and yield spread, that are available at a daily frequency in real time.
Our main contribution is to propose to use a new indicator to assess the systemic risk of
the banking sector: the price of insurance against large default losses in the banking sector in
the coming 12 weeks. The new measure is economically intuitive, in that it is equivalent to
a theoretical premium to a risk-based deposit insurance scheme that guarantees against most
severe losses for the banking system. The new measure also has the property that it increases
in both PDs and asset return correlations. In other words, an increase in the indicator, or a
higher systemic risk, can reflect market participants’ perception of higher failure risk as well
as their view that the probability of common failings is higher (see Das et al. (2007) and Duffie
et al. (2008)).4 In addition, the new indicator reflects the various degrees of importance of
different banks in contributing to the systemic risk, in that banks are treated heterogeneously
based on their relative size.
We also propose a novel approach to estimating the asset return correlation, a key parameter to determine the risk profile of a portfolio. The approach employs an advanced technology
in the high-frequency literature, i.e. estimating realized correlation from the intra-day highfrequency co-movements in equity prices.5 This technique makes it possible to estimate the
4

The rather homogeneous sample of twelve large US banks and the turbulent period 2001-08, may be
coincide with similar movements of PDs and correlations. However, in an on-going research project focusing
on a diversified sample of Asian country banks, we find that the effects of PDs and correlation are quite
distinguishable.
5
Throughout this paper, “realized correlation” is a terminology that refers to correlations calculated from
high-frequency intra-day data. This is different from “historical correlation” as calculated from daily data and

3

asset return correlation in a very short time horizon (e.g. one week). Relatedly, we argue
that, to calculate the indicator of systemic risk, a forward-looking rather than a historical
measure of the asset return correlation is the appropriate default risk parameter to be used.
Importantly, we find that realized correlations in the short time horizon provide strong and
additional predicting power in forecasting the movement in asset return correlations, relative
to equity market and term structure variables.
We apply our approach to 12 major U.S. banks during the sample period 2001-08. We
produce a weekly time series of systemic risk indicators, that reflect time-varying market
perceptions on the systemic risk of the banking system in the United States. The indicator
was stable and at low levels at most times but exhibited substantial increases during market
turmoil, e.g. the 2002 credit market deterioration and more remarkably after the inception of
the subprime crisis in mid-2007.
Furthermore, the peaks of the systemic risk indicator align well with periods of major
adverse developments in the market, such as March 2008. In particular, the systemic risk
indicator, the theoretical insurance premium required to protect against default losses that
equal or exceed 15 % of total liabilities, stood at 110 billion USD in March 2008 and had a
projected upper bound of 250 billion USD in July 2008. Remarkably in terms of back testing,
in our in-sample quarterly horizon forecasting exercise, the realized systemic risk indicators lie
out of the 95% predicted confidence interval in approximately 3.5% (13 out of 375) of sample
weeks, which is a strong validation of our integrated micro-macro model.
The remainder of the paper is organized as follows. Section 2 outlines the methodology.
Section 3 introduces the data and Section 4 presents empirical results based on an illustrative
banking system that consists of twelve major commercial and investment banks in the U.S.
financial system. The last section concludes.
2. Methodology
Our framework for assessing and stress testing the systemic risk of a financial system consists of
the following major components. First, we estimate two major components that determine the
“observed correlation” (ex post observation of correlation).

4

risk profile of a portfolio, the probability of default and the asset return correlation. Second,
we construct an indicator of the systemic risk of a financial system, the price of insurance
against large losses of the banking sector, based on the forward-looking PDs and correlations
in the next period (a quarter). Third, for stress testing purpose we examine the dynamic
linkages between default risk factors and a number of macro-financial factors. An integrated
micro-macro model framework enables us to investigate the two-way linkages between the
banking sector and the macroeconomy. Lastly, we define stress testing scenarios and explore
their implications on the stability of the banking system. Below we explain the methodology
in detail.
2.1. Estimating risk-neutral PDs
The PD measure used in this study is derived from single-name CDS spreads. A CDS contract
offers protection against default losses of an underlying entity; in return, the protection buyer
agrees to make constant periodic premium payments. The CDS market has grown rapidly
in recent years, and the CDS spread is considered to be a superior measure of credit risk to
bond spreads (see Longstaff et al. (2005), Blanco et al. (2005), Zhu (2006) and Forte and
Peña (2009), for example) or loan spreads (see Norden and Wagner (2008)). Following Duffie
(1999) and Tarashev and Zhu (2008a), it is straightforward to derive the risk-neutral PD from
the observed CDS spread (si,t ):
P Di,t =
where at ≡

R t+T
t

e−rτ dτ and bt ≡

R t+T
t

at si,t
at LGDi,t + bt si,t

(1)

τ e−rτ dτ , LGD is the loss-given-default and r is the

risk-free rate. The assumptions required for the above characterization of risk neutral PDs
are: constant risk-free term structure, flat default intensity term structure, and recovery risk
independent of default risk.
There are three elements in the implied PD estimated from the CDS market: (1) the compensation for actual default losses; (2) default risk premium; (3) other premium components,
e.g. liquidity risk premium. Our systemic risk indicator incorporates the combined effects of
the above three elements on the price of insurance against distressed losses in the banking
5

system. Although there is no convincing quantitative framework to decompose these effects,
it is generally agreed that the default risk premium and liquidity risk premium explain the
majority of the increases in CDS spreads entering the subprime crisis. One piece of evidence
is that market estimates of actual default rates (e.g. EDF data provided by Moodys KMV)
only increased mildly during our sample period, suggesting the hike in CDS spreads is mainly
due to lower risk appetite, or concerns on counterparty risk and liquidity risk premium.6
Several remarks are worth noting. First, the PD implied from the CDS spread is a riskneutral measure, i.e. it reflects not only the actual default probability but also a risk premium
component as well.7 This has important implications on the choice of the appropriate indicator
of systemic risk. In particular, it might be misleading to use a nth-to-default indicator, as it
is typically considered to be a physical measure (see the discussion below).8
Second, the PD implied from the CDS market is a forward-looking measure, i.e., it reflects
the average risk-neutral PD of the underlying entity during the contract period. Hence, it
offers a market assessment from a different perspective from what most balance sheet variables
(such as bank profitability and non-performing loan ratios) do, which tell what has happened
rather than what will happen for the underlying firm. Under the efficient market hypothesis,
market prices should incorporate all relevant information including those from the accounting
books, especially for major indices and large firms.
Third, throughout this exercise we adopt the standard assumption of a flat term structure
of the default intensity (as reflected in equation 1). This assumption might be violated in
reality.9 However, some preliminary evidence suggests that this assumption only causes small
6

This is consistent with recent studies by Tang and Yan (2006) and Bongaerts et al. (2008).
There are extensive studies regarding the difference between the risk-neutral and physical PDs, see Amato
and Remolona (2003), Huang and Huang (2003), Eom et al. (2004), Berndt et al. (2005) and Driessen (2005),
among others.
8
If one is more interested in the physical measure of systemic risk, or the actual probability of bank distress,
one should use the physical PD measure(see Berndt et al. (2005) and Lehar (2005)). In contrast, our approach
is an internally consistent risk-neutral measure of the systemic financial distress.
9
In general, if the default intensity has an upward term structure, our assumption will lead to an overestimation of 1-year PD. On the contrary, if the default intensity has a downward term structure, our assumption will lead to an under-estimation of 1-year PD. Unfortunately, there is no consensus view on which
term structure is more appropriate (probably it is an important reason why the constant default intensity
assumption becomes a norm because of its simplicity).
7

6

bias and will not affect our major results.10
2.2. Forecasting asset return correlations
Regarding the other key dimension of portfolio credit risk, the default correlation, there exist
two popular approaches. One approach estimates it directly from historical data on defaults
(Daniels et al. (2005), Jarrow (2001), Das et al. (2007), and Duffie et al. (2008)). However,
this approach can lead to substantial estimation errors because defaults are rare events, particularly for portfolios comprising high credit-quality firms, like major U.S. commercial and
investment banks. The other approach derives the default correlation indirectly by estimating
the underlying asset return correlation from equity or credit market data. The logic behind
this approach is that equity (or debt) is a call (or put) option on underlying firm assets.
Hence, the comovement in equity prices (or CDS spreads) tends to reflect the comovement
among underlying asset values. In practice, Hull and White (2004) propose to use the equity return correlation as a proxy for the asset return correlation,11 the proprietary Global
Correlation model by Moody’s KMV derives the underlying asset value from equity market
data and firms’ balance sheet information, and then computes the asset return correlation
(see Crosbie (2005)), and Tarashev and Zhu (2008a) derive the asset return correlation from
the comovement of CDS spreads.
This paper follows the second approach and adopts the suggestion by Hull and White
(2004) to use the equity return correlation as a proxy for the asset return correlation. There
are two main reasons. First, equity is the the most liquid type of asset traded in the market.
Changes in market conditions and the default risk of an entity will be immediately reflected in
its stock price movements. Second, tick-by-tick data are only available in the equity market.
The advanced technology in the high-frequency literature makes it possible to compute reliable
10

One possible hint we can get is to compare between 1-year and 5-year CDS spreads of the sample entities.
They are highly correlated. At the beginning of our sample period when CDS spreads were generally low,
the 1-year CDS spreads were lower than 5-year CDS spreads, implying an upward default intensity curve.
However, since late 2007 – when the CDS spreads increased substantially – the 1-year CDS spreads have been
more or less in line with 5-year CDS spreads, supporting the constant default intensity assumption. Putting
together, the potential bias caused by the constant default intensity assumption tends to have only a small
effect on our results.
11
See Appendix A for a strict proof and the conditions under which the two correlations are equal.

7

realized correlation over a very short time horizon (e.g., one week) that has been impossible
for daily observations.12 The short-term realized correlation turns out to add significant
predicting power on the future correlation movement.
The logic of using the equity return correlation as a proxy for the asset return correlation
lies in the fact that, when the firm leverage is constant, the asset return correlation equals
the equity return correlation. When the firm-leverage is time varying, this relationship breaks
down and the magnitude of the discrepancy depends on the comovements between asset
returns and leverages and comovements between changes in firm leverages as well. And
because this condition is more likely to hold approximately true in the short run, we compute
equity (asset) return correlations over time horizons that are not longer than one quarter.
For instance, using Moody’s KMV estimates of market values of equities and assets, we can
calculate time series of leverage (monthly) for each of the 12 banks. We test the hypothesis
that leverage is constant over a one-month (two/three/six months) window. The hypothesis is
not rejected for 11 (10/7/4) banks. This partly supports our claim that the constant leverage
assumption is reasonable in a short time horizon (less than one quarter).
Importantly, we deviate from previous studies by not relying merely on past correlation
measures, but using forecasted asset return correlations to measure portfolio credit risk. This
makes our correlation measure consistent with the PD measure, and therefore our indicator
of systemic risk will be forward-looking. In forecasting the asset return correlation over the
next period (one quarter), we derive the relationship between future realized correlation (ex
post observed) and current-period (quarterly and weekly) correlations and a number of other
explanatory variables:13
ρt,t+12 = c + k1 ρt−12,t +

l
X
i=1

k2i · ρt−i,t−i+1 + ηXt + νt

(2)

where ρ refers to the average asset return correlation and the subscript refers to the time
12
See Appendix B for detailed description on the estimation of realized correlation using high frequency
intraday data.
13
Driessen et al. (2006) derive a market-based, forward-looking correlation measure from the option market.
However, option-implied correlations can only be calculated for a portfolio for which both the index and
individual entities are actively traded in the option market. The application of their approach is quite limited
for the purpose of our exercise of measuring the systemic risk.

8

horizon (one week as one unit) to calculate the correlations, and X includes a list of financial
market variables as detailed in Section 4. Interestingly, we find that short-term (one-week)
correlations have significant and additional forecasting power on future (one-quarter) correlations.
2.3. Building an indicator of systemic risk
Once the two key portfolio credit risk parameters are known, we are able to use the portfolio
credit risk methodology (see Gibson (2004), Hull and White (2004), and Tarashev and Zhu
(2008a)) to come up with an appropriate indicator of the systemic risk for a pre-defined
group of banks. In this paper, we propose a “distress insurance premium” – the theoretical
price of insurance against financial distress. To compute the indicator, we first construct a
hypothetical portfolio that consists of debt instruments issued by member banks, weighted
by the liability size of each bank. The indicator of systemic risk is defined as the theoretical
insurance premium that protects against distressed losses of this portfolio in the coming 12
weeks. Technically, it is calculated as the risk-neutral expectation of portfolio credit losses
that equal or exceed a minimum share of the sector’s total liabilities.14
We choose this indicator over a few alternative measures, such as the probabilities of
joint defaults, credit value-at-risk (VaR) and expected shortfalls (see Avesani et al. (2006),
Inui and Kijima (2005), and Yamai and Yoshiba (2005)). One important reason is that our
PD measures, which are derived from the pricing of CDS contracts, are risk-neutral. This
implies that any indicator constructed based on them is also risk-neutral. However, the above
alternative measures are conventionally interpreted as physical rather than risk-neutral, and
hence are more likely to be misinterpreted by users.15 Even if the researcher is aware of the
difference, it is not straightforward to explain to the management how a risk-neutral measure
differs from a physical measure from a portfolio perspective. By contrast, our indicator of
14

The premium is represented as per unit of exposure to the hypothetical portfolio, therefore is unaffected
by the growing magnitude of the total liabilities in the banking sector. As a complementary measure, we also
report the total insurance cost in dollar term in the baseline example (see Section 4.1.2).
15
By contrast, the Lehar index refers to the physical (or actual) probability of joint defaults and is logically
intuitive. It is complimentary to our systemic risk indicator; and the combination of these information can shed
light on the important question whether the changes in our systemic risk indicator are driven by movements
in actual default rates or changes in the risk premium component.

9

systemic risk has a very intuitive economic interpretation: it is equivalent to the premium for
a hypothetical risk-based deposit insurance scheme, which covers all credit losses so long as
the loss exceeds a minimum share of the total liabilities of the banking system. Moreover, our
indicator has the property that it increases in both PDs and correlations, which is consistent
with the general impression that a higher systemic risk is either driven by higher failure rates
of individual banks or a higher exposure to the same risk factor.16 Lastly, the probability
of joint default measures treat all banks as equal and do not take into account differential
impacts of failures of different size banks.
In calculating this indicator, we rely on Monte Carlo simulations to estimate the unconditional (risk-neutral) probability distribution of portfolio credit losses.17 We assume that the
loss-given-default (LGD), the third dimension of credit risk components, follows a stochastic
distribution and is independent of the PD process. In particular, we assume that LGD follows
a symmetric triangular distribution with a mean of 0.55 and in the range of [0.1,1]. The mean
LGD of 0.55 is taken down from the Basel II IRB formula, which is also consistent with the
data. For instance, Markit provides both CDS spreads and the LGD parameters corresponding to each CDS spread. Previous studies (e.g. Tarashev and Zhu (2008a)) show that the
average LGD parameter used by market participants in the CDS market is about 60%.18
2.4. Designing stress testing scenarios
To implement a stress testing exercise, we first need to build the links between the macrofinancial part of the economy and the portfolio credit risk parameters, the PDs and correlations. Then we use either history or simulation to examine the impact of shock to the system,
and consequently the effects on our systemic risk indicator.
We design an integrated micro-macro model to examine the determinants of PDs and
correlations. The macro part of the model adopts a VAR framework that allows for dynamic
16

The nth-to-default probability does not have this property, see Section 4 for further discussion.
See Tarashev and Zhu (2008b), Appendix B, for the details of the Monte Carlo simulation procedure.
18
The adoption of symmetric triangular distribution follows Tarashev and Zhu (2008b) and is not essential
to our results. In a robustness check exercise, we assume that the LGD follows a beta distribution, another
popular choice in the credit risk literature, and find little changes in the systemic risk indicator (the results are
available upon request). However, using triangular distribution is computationally more efficient, especially
for the stress testing exercise (bootstrapping).
17

10

linkages between the credit risk factors of the banking system and a list of macro-financial
variables that reflect the developments of the macroeconomy and the general financial market.
In the VAR analysis, the health of the banking system is affected by the general market
conditions, and there is also a feedback effect in the opposite direction. The second (micro)
part of the model explains the determination of the default risk of individual banks by the
credit risk factors of the financial system and other financial market variables. To summarize,
the model estimation consists of two parts:
Xt = c 1 +

p
X
i=1

bi · Xt−i + t

P Di,t = c2i + ai · P Di,t−1 + γXt + µit

(3)
(4)

where equation (3) represents the macro-perspective of the model, in which X includes the
credit risk factors (average PD and one-week correlations) in the banking sector and macrofinancial variables. Equation (4) examines the movements of individual PDs in response to
changes in market conditions. The results, in combination with the forecasted correlations
as estimated from equation (2), form the whole dynamics of the economic system that are
relevant for the stress-testing exercise.
Our integrated micro-macro model is different from some existing studies, which rely on
analysis of latent factors that drive the comovements of default risk of individual banks (see
Avesani et al. (2006), for example). The major disadvantage of the latent factor framework
is that the hypothetical scenarios, which are based on the statistical distribution of latent
factors, lack a clear economic interpretation. On the other hand, a number of empirical
studies, including Amato and Luisi (2006), Ang and Piazzesi (2003), Duffie et al. (2007) and
Männasoo and Mayes (2009), have shown that default risk is closely related to the state of
the business cycle and the condition of the financial market. Our choice of using observed
macro-financial shocks in designing the stress testing scenarios is consistent with the latter
approach.
In the final part of the analysis, we design stress testing scenarios based on hypothetical
or historical shocks to variables within the VAR system. We feed the shocks into the dynamic

11

macro-micro system. And the resulting movements in state variables affect the forecasted
default risk of individual banks and the forecasts of correlations, which together change our
indicator of systemic risk of the banking system.
In designing the stress testing scenarios, we adopt two approaches. The first approach, a
purely hypothetical one, specifies the stress testing scenarios based on the statistical properties
of the shock variables in the model. In particular, we use the bootstrapping technique to
simulate the path of shock terms, including shocks in credit risk factors and macro-financial
factors (, µ, and ν in equations 3, 4 and 2) in the next 12 weeks. For each simulation, the
impact of the indicator of systemic risk is re-calculated. The simulation is implemented for
a large number of times, and the stress testing scenarios are defined as the set of scenarios
that generate the most remarkable increases in systemic risk—the 95% quantiles of the path
realizations.
The second approach uses historical scenarios, i.e. shocks that occurred during well-known
market turmoil periods. However, given that some data (CDS spreads and intraday equity
data) are only available in a recent short period, we have to rely on a smaller VAR model
that includes only macro-financial variables but can be estimated in a longer sample period
(back to 1986). The smaller VAR system includes all macro-financial factors that are included
in equation (3). The shocks in macro-financial factors are then fed into the system and the
impact on the systemic risk is examined.19
The two approaches are complementary and provide a general picture of the vulnerability
of the financial system, from both the statistical and the historical perspectives. The first approach is more generally a forecasting exercise and the results are richer in terms of describing
the possible movements—both improvements and deterioration in systemic risk. The second
approach, instead, focuses only on the downside risk, with a major advantage of being easily
interpretable and connected to major historical crises.
19

The shocks in credit factors are assumed to be zeros, as there are not actual observations of CDS spreads,
although other treatment may be viable for us to experiment in the future.

12

3. Data
The proposed methodology outlined in Section 2 is general and can apply to any portfolio
that consists of entities with publicly tradeable equity and CDS contracts in the market. For
illustrative purposes, we analyze the banking system in the United States over the period
2001-2008. Our banking group consists of 12 major banks in the United States, namely
Bank of America, Bank of New York, Bear Stearns, Citibank, Goldman Sachs, JP Morgan
Chase, Lehman Brothers, Merrill Lynch, Morgan Stanley, State Street Corp, Wachovia and
Wells Fargo. They represent the biggest commercial banks and security firms in the U.S. and
therefore their portfolio credit risk has a direct and major impact on the health of the U.S.
financial system.20
Our sample data cover the period from January 2000 to May 2008. We retrieve weekly CDS
spreads from Markit, compute realized correlations from high-frequency intraday equity price
data provided by Trade and Quote (TAQ) (see Appendix B for the methodology), and retrieve
a list of macro-financial variables that reflect the general condition of the macroeconomy and
the financial market (see Appendix C for details). See Table 1 for the summary statistics of
credit factor variables and financial market variables.
Given that no restriction has been imposed in the process of estimating realized correlations, the correlation estimate has a general correlation structure, i.e. without a factor-loading
structure. Although it does not impose any difficulty in computing the indicator of systemic
risk, it is impractical to forecast the correlation structure with all pairwise correlation coefficients to be freely determined. First, our sample data do not provide enough degrees of
freedom. Second, it is not guaranteed that the forecasted correlation matrix will be positive
definite. For these reasons, throughout this paper we assume the same pairwise correlation
coefficient across the correlation matrix.21
20

Our sample period ends in May 2008. In March 2008, the Federal Reserve facilitated the acquisition
of Bear Sterns by JP Morgan Chase. Subsequent acquisitions of Merrill Lynch, by Bank of America, and
Wachovia, by Wells Fargo, occurred after the end of our sample period.
21
The removal of dispersion in pairwise correlation coefficients only has a small effect on the magnitude of
the indicator of systemic risk, and almost negligible effects on the dynamics of the indicator. This is probably
due to the rather homogeneous banking system examined in this study.

13

The solid lines in Figure 1 plot the observed time series of our variables of interest. Average
risk-neutral PDs, implied from CDS spreads of individual banks and weighted by the size
of bank liabilities, peaked in March 2008 toward the end of the sample period. Average
correlations, on the other hand, are somewhat higher during both 2002-2003 and 2007-2008.22
The four panels in Figure 2 plot the weekly times series of financial market variables, including
the fed funds rate, the term spread (defined as the difference between 10-year and 3-month
constant maturity Treasury rates), the one-month return and implied volatility of the S&P
500 index.23
4. Empirical results
In this section, we report the empirical results for the banking group of interest, using the
methodology outlined in Section 2. We first illustrate the calculation of the indicator of
systemic risk of the banking system during the sample period, then assess its vulnerabilities
to extreme shocks in the stress testing exercise.
4.1. Constructing the indicator of systemic risk
In order to calculate the indicator of systemic risk of a banking system, we need to know the
PDs of individual banks and the corresponding asset return correlations in the future period
(one quarter). The risk-neutral PDs can be easily derived from the observed CDS spreads
(see equation (1)).24 The “future” asset return correlation, however, is not directly observable
and has to be estimated.
In all regressions here and below, PD and correlation variables are transformed so that
they can be defined in the range of all real numbers. We perform the Logit transformation on
22

The “future” correlation uses the observed realized correlation in the forthcoming quarter. It is an ex post
measure and therefore cannot be used directly to calculate the indicator of systemic risk ex ante.
23
We do not include macroeconomic variables because of their availability only at a lower frequency. In
a robustness exercise, we also include a longer list of financial variables, e.g. the whole term structure of
Treasury rates. We then use the principal components (see Allenspach and Monnin (2006)) in our model
analysis. This modification does not lead to improvement in the performance of our integrated micro-macro
model.
24
We set the LGD to be 55% in this exercise.

14

PD (between 0 and 1), i.e.
PD
)
P˜D = log(
1 − PD
Similarly, we perform the Fisher transformation for correlation coefficients ρ (between -1 and
1):
ρ̃ =

1
1+ρ
log(
)
2
1−ρ

4.1.1. Forecasted asset return correlations
Table 2 examines the determinants of future asset return correlations, measured by the equity
return correlations observed in the next quarter. We run three regressions to illustrate that
estimating realized correlations from the high-frequency data is helpful for the forecasting
exercise.25
In the first regression, the explanatory variables only include realized correlations estimated
over one-quarter and one-week time horizons. The one-week realized correlations are supposed
to incorporate very recent changes in the correlations and therefore are helpful to predict
future correlations. This is supported by the regression results: all explanatory variables
have significant and positive effects on the correlation in the next quarter, with an R2 of
0.54. This is quite striking given that the dependent variable and explanatory variables cover
non-over-lapping sample periods, indeed, with a lag of 12 weeks.
The second regression excludes the short-term (one-week) realized correlations, and, instead, includes a list of current-period market factors, including the fed fund rate, the term
spread, the S&P 500 return and implied volatility of the current quarter. It arguably represents the best effort one can achieve to explain future correlations without resorting to realized
correlation measures. It turns out that only lagged one-quarter correlation and current S&P
500 return are significant in explaining future correlations. It is also meaningful that correlation is persistent — high lagged correlation leads to high future correlation, and that low
25

A possible justification of using current-period asset return correlation as a proxy for future asset return
correlation, as adopted in existing studies, is that correlations may follow a random walk process. This
assumption, however, is not supported by the data in this sample, nor in the study by Driessen et al. (2006).

15

market returns lead to high comovement (high systemic risk). However, this regression is
similarly successful to the first one in term of R2 (0.55).
The third and last regression includes all explanatory variables mentioned above, which
reaches an R2 of 0.56 and maintains the sign and significance of lagged correlations and market
returns. The results provide evidence that movements in short-term realized correlations
incorporate important and additional information (compared to the macro-financial variables)
on the future movements in correlations.
The dash-dotted lines in Figure 1, in the lower two panels, plot in-sample predictions
of future asset return correlations. Although they are not perfect, they do catch the trend
of correlation movements and perform better than alternative estimates. For instance, our
predictions (the above third regression) yield a mean squared error of 0.0036, significantly
lower than the mean squared error of 0.0051 if the current-period asset return correlation is
directly used as a proxy.26
4.1.2. Indicator of systemic risk in the banking sector
Based on individual PDs and forecasted asset return correlations, we compute the indicator of
systemic risk, the theoretical price of insurance against distressed losses in the banking sector
over the next three months. As an example, we define “distress” as a situation in which at least
15% of total liabilities of the financial system are defaulted.27 Given that PDs of individual
banks are risk-neutral, the price of insurance against distress equals the expectation (under
the risk-neutral world) of portfolio credit losses that equal or exceed the pre-defined threshold.
For this purpose the latest portfolio credit risk technology is applied. In particular, we rely
on the Monte Carlo simulation method as outlined in Tarashev and Zhu (2008b), Appendix
B. The simulation method consists of two steps. In the first step, we simulate the joint default
scenarios based on the information of individual PDs and the asset return correlation. In the
second step, conditional on defaults occurring in the first step, we simulate the realization
26

The difference is statistically significant at the 95% level.
The 15% threshold is empirically chosen for illustrative purpose. We tried alternative threshold values
(e.g. 10%, 20% and 30%) and the results are very similar. In general, the choice of threshold values affects
the level of systemic risk indicators, but not their trend.
27

16

of LGDs and the overall credit losses of the whole portfolio. Notice that this methodology
might be computationally burdensome, but has a major advantage that it is very general. In
particular, it fits the purpose of our exercise because the portfolio has the following characteristics: (i) PDs of constituent entities are heterogeneous; (ii) The underlying instruments are
unequally weighted; and (iii) LGDs are stochastic and independent of PDs.
Figure 3 plots the price of insurance against portfolio credit losses that equal or exceed 15%
of total liabilities of the banking system, with the top panel as per unit of overall exposures
(i.e. total liabilities) and the lower panel in dollar terms. The indicator started from about
10 basis points in the first half of 2001, increased and reached a peak of about 35 basis points
in the second half of 2002, when high corporate defaults were reported. The indicator then
trended downward and reached its lowest level in late 2006 and early 2007. Since August
2007, the indicator rose sharply and peaked around March 2008, and dropped dramatically
after the Federal Reserve facilitated the acquisition of Bear Sterns by JP Morgan Chase. In
dollar terms, the highest theoretical insurance premium was around $110 billion in March
2008, well exceeding the amount of the Federal Reserve’s $30 billion non-recourse loan to JP
Morgan Chase. Perhaps the market was anticipating a larger default, or it reflected the hike
in default risk premium during the market turmoil. Notice that the trend follows very closely
with the average PD series in the banking system (see Figure 1, the upper panel), but is
also substantially affected by the movement in correlations (though to a lesser extent). For
instance, the peak of the indicator coincides with the peak in both PDs and correlations. In
addition, comparing between early 2001 and early 2003, the indicator is higher in the second
period when the correlation is higher but the PD is more or less the same.
The impact of PDs and correlations on the indicators is more rigorously examined in the
regressions in Table 3. The regression shows that our indicator of systemic risk, the price of
insurance against distressed losses, increases in both PDs and correlations and the coefficients
are highly significant.28 This is consistent with the conventional view that higher default
28

Quantitatively, a one-standard-deviation increase in average PDs (0.0053) moves up the indicator by 11
basis points, and a one-standard-deviation increase in average correlations (0.0681) increases the indicator
by 2 basis points. It suggests that changes in PDs have a dominant effect on the indicator; the correlation
impact exists but plays a secondary role. Hence, although using realized correlations can improve the work, we

17

rates and higher exposures to common factors are both symptoms of higher systemic risk.
By contrast, the (risk-neutral) nth-to-default probability measure, another indicator used in
other studies (such as Avesani et al. (2006)), does not have this property. In fact, an nthto-default measure typically increases in PDs but may decrease in correlations (see Table
3). Therefore, using nth-to-default probability measures will produce at best unsatisfactory,
sometime misleading, indicators on the systemic risk of the banking system.29
These results are quite intuitive based on the knowledge of models of portfolio credit risk.
Essentially, our measure is similar to the spread of a senior tranche in a portfolio, when
there are only two tranches and the other tranche covers the losses up to the pre-specified
threshold. By contrast, the nth-to-default probability measures often correspond to some
mezzanine tranches in a multiple-tranche secularization structure. It is well known that,
when correlations increase, the probability of zero default and many defaults increases but
the probability of an intermediate number of defaults decreases. Therefore, the impact on
the mezzanine tranches, or equivalently the nth-to-default probabilities, is ambiguous. By
contrast, for a two-tranche structure, an increase in correlations will always lower the spread
of the equity tranche and increase the spread of the senior one.
4.2. Stress testing
We first report the regression results of the integrated micro-macro model, and then implement
the stress testing exercise.
4.2.1. VAR analysis (the “macro” part)
The “macro” part of the model refers to a VAR analysis, with the endogenous variables
consisting of two credit risk factors – average PDs and current-period correlations – and a
number of macro-financial factors. The optimal number of lags in the VAR system is chosen
consider a second-best solution in the application of our method is to use simpler correlation estimates. This
is particularly important if high-frequency data are not available in the banking system of interest. Indeed, in
a robustness check exercise we adopt historical correlations directly to recalculate the systemic risk indicator.
The indicators exhibit very similar dynamics although the levels can be different (the results are available
upon request.)
29
The results of (risk-neutral) probability of joint defaults are not reported here but are available upon
request.

18

by the Schwarz Information Criteria, which equals one period. Table 4 reports the regression
results and the dash-dotted lines in Figures 1 and 2 plot the in-sample prediction of endogenous
variables.
All endogenous variables are positively serial-correlated. In addition, there is strong evidence of dynamic linkages among the endogenous variables. The average PD is positively and
significantly affected by the average correlation and negatively and significantly affected by
the return in the market index. The results are intuitive. Higher systemic risk in the form
of elevated correlation leads to more default. The deterioration of the general market (lower
market returns) increases the probability of defaults.
The average correlations are negatively and significantly affected by the two interest rate
variables, the fed fund rate and the term spread. This may suggest that, when the monetary
policy is eased, most banks’ asset returns move together more closely. By contrast, when
the monetary policy is tightened, banks are affected to a different degree depending on their
position in liquidity and equity capital, and the composition of their assets and liabilities.
As expected, lower market returns are associated with higher correlations, as a phenomenon
of the downside risk. Finally, PDs have a positive effect on correlations, as it should be —
defaults are usually clustered (Das et al. (2007)).
While the VAR framework allows for a feedback effect from the banking system to the
macroeconomy and the general financial market, the evidence of the feedback effect is quite
weak during our sample period. One exception is that the average PD in the banking system
has a negative effect on federal funds rates, suggesting that the central bank’s interest rate
policy may be affected by financial stability concerns in practice. Finally, the positive effect
of average PD on the VIX index may be consistent with notion that VIX is regarded as the
“market gauge of fear” by practitioners.
4.2.2. Determination of PDs of individual banks (the “micro” part)
The “micro” part of the model investigates the determination of individual PDs, as a function
of lagged dependent variables and the current period market variables, including the average
PD and correlations in the banking system and the list of macro-financial factors. Table 5
19

summarizes the regression results.
For all banks, the individual PD series are positively serial-correlated. They are also
positively and significantly affected by the average PD in the banking system, and half of
the banks’ PDs are positively and significantly affected by the average correlation. Regarding
the macro-financial factors, the impacts are quite heterogeneous across banks. First, they
do not always have a significant impact on individual PDs. Second, when a macro-financial
factor has a significant impact on the PD of an individual bank, the sign is not always in the
same direction (except for the market return variable, which always has a negative impact if
significant). For instance, changes in fed fund rates have significantly positive impacts on four
banks but significantly negative impacts on three other banks. This may reflect the different
business models and the different balance sheets of the sample banks during the period under
review.
4.2.3. Stress testing
Based on the above regression results, the stress testing exercise can be implemented in three
steps. In the first step, we choose hypothetical stress testing scenarios based on the VAR
regression results. In the second step, these hypothetical shocks are fed into the model to
derive the future dynamic movements (up to twelve weeks) in all endogenous variables in the
VAR framework. By extension they will affect the future movements in risk-neutral PDs of
individual banks (regression results in equation 4) and forecasted correlations (equation 2).
In the third and last step, we construct future movements in the indicator of systemic risk
under the stress test scenario using the predicted PD and correlation measures.
As described in Section 2.4, there are two approaches to designing the stress testing scenarios. The first approach, a statistical one, adopts the bootstrapping technique to simulate
the shocks in the next 12 weeks based on the sample regression of model (including equations
2, 3 and 4). The simulation results are reflected in the future movements of the indicator of
systemic risk as shown in Figure 4. On average, 12 weeks after May 2008, the indicator is
forecasted to move up slightly to about 0.41%, roughly the levels of late 2007 and late 2002.
In the worst 2.5 percentile scenarios, the indicator will jump up above 1.11%, roughly the level
20

of March 2008 peak; and in the best 2.5 percentile scenarios, the indicator will move down to
0.09%.
The second approach uses historical scenarios, i.e. the shocks of macro-financial factors as
observed in two historical turmoil periods: the LTCM crisis (which uses the shocks between
July 3, 1998 and September 18, 1998) and the September 11 episode (which uses the shocks
between August 31, 2001 and November 16, 2001). The results are shown in Figure 5. In
both scenarios, the systemic risk indicator of the banking system increases and reaches a level
comparable to the January 2008 about 0.4-0.5% of the total liabilities. Overall, both results
suggest that the vulnerability of the banking system would rise ranging from moderately to
dramatically as of May 2008.
A major advantage of the bootstrapping stress testing exercise is that it can simulate the
distribution of future movements in the systemic risk, which can be used as a forecasting
tool. In Figure 6, we adopt such a bootstrap forecasting approach for the whole sample and
plot the mean and 95% confidence interval of the forecasted indicator 12 weeks ahead. It
is clear that the predicted mean (dash line) generally tracks well the realized systemic risk
indicator. The confidence interval band was wide from 2001 to 2004 with a local high in
late 2002 and the price tag then was about 1% of total liability (the upper bound). Then
the confidence band gradually narrowed until early 2007, when predicted mean also stayed
low. Of course, the mean prediction of the systemic risk indicator shot up since mid-2007
and the confidence interval band widened as well. The uncertainty peaked in March 2008,
then dropped significantly (though still at high levels) after the strong intervention of central
banks.
The in-sample performance of our model forecasts is extremely good, which is a strong
validation of our model for measuring and stress testing the systemic risk. Remarkably, out
of the 375 weeks of predictions, 13 weeks (3.5%) have the realized systemic risk indicators
lying outside of the 95% predicted confidence interval. The outliers were concentrated in two
periods, the inception (late July to mid September in 2007) and the peak (March 2008) of
the subprime crisis. The location of realized indicators within (or outside of) the confidence
interval bands is an indicator of the surprising component of the evolution of the systemic
21

risk. For instance, the severity of the rapid deterioration in market conditions during the two
outlier periods is well beyond market expectations. By contrast, the government intervention
and consequently the recovery of the market since late March 2008, although exceeding the
average of market expectations, are not extremely surprising.
5. Conclusions
In this paper we propose a framework for measuring the systemic risk of a group of major
financial institutions. The methodology is general and can apply to any pre-selected group of
firms with publicly tradeable equity and CDS contracts. Our approach adopts the advanced
high-frequency technique in estimating realized correlation, and shows that short-term realized
correlation helps to predict future movements in the asset return correlation. An indicator
of systemic risk, which is based on ex ante measures of risk-neutral PDs and correlations,
offers an insight on the market perception on the level of a theoretical insurance premium
that protects against distressed losses in the banking system. The indicator is higher when
the average failure rate increases or when the exposure to common factors increases.
The paper also proposes a framework for stress testing the stability of the banking system,
based on an integrated micro-macro model that takes into account dynamic linkages between
the health of the financial system and macro-financial conditions. The combination of historical and statistical scenarios offer a general picture of the vulnerability of the banking system
in the next quarter.
Our study is only a first step toward improving our understanding of the relationship
between financial stability, monetary policy and the real economy. The macro-prudential
view, which calls for a closer monitoring of asset prices and the stability of the financial
system, has become more widely accepted. However, its implementation largely depends on
the feasibility on the operational side. The methodology described in this paper may provide
a useful starting point along that direction.

22

Appendix
A. Relationship between equity and asset return correlations
In the framework of Merton (1974), suppose that the market value of a firm’s underlying
assets follows a stochastic process:
dV = µV dt + σV dW

(5)

where V is the firm’s asset value, µ, σ are the drift term and the volatility of the asset value,
W is a Wiener process.
The firm has only two types of liabilities, debt and equity. The debt has a book value of
X and is due at time T . Merton shows hat the equity value is determined by:
E = V N(d1 ) − e−rT XN(d2 )
2

where d1 ≡

V
)+(r+ σ2 )T
log( X
√
σ T

√
and d2 = d1 − σ T =

Under the condition that r, σ and

V
X

(6)
2

V
)+(r− σ2 )T
log( X
√
.
σ T

are all constant, it is straightforward that the equity

value is proportional to the asset value (because both d1 and d2 are constant and X is proportional to V ). Therefore, d(log(E)) = d(log(V )), where d(·) represents first difference. The
equity return correlation, under this condition, equals the asset return correlation:
cor[d(log(E1 )), d(log(E2 ))] = cor[d(log(V1 )), d(log(V2 ))]
B. Estimating equity return correlations from high frequency data
B.1. Data
The raw high-frequency data consist of all the tick-by-tick transaction data for the stocks of the
twelve banks traded in the major U.S. stock exchanges, including NYSE, Boston, Philadelphia,
Pacific and NASD. The trading time is from 9:30 to 16:00 Eastern Time. The data are
subject to market microstructure noise, such as non-synchronized trading and bid/ask spreads.
The impact of such noise on the realized correlation depends on our sampling frequency and
the market activity. For the twelve major banks studied in this paper, their markets are
23

quite deep. There are typically more than one trade per second. So following Andersen
et al. (2003), we use equally-spaced thirty-minute returns to construct our realized correlation
measure. This sampling frequency strikes a balance between mitigating the influence of market
microstructure noise and preserving the accuracy of the asymptotic theory underlying the
construction of our realized correlation measures.
We use previous tick method to construct thirty-minute price data from the tick data.
That is, the last price observation in the previous thirty-minute interval is taken as the price
of this thirty-minute mark. Then we compute the thirty-minute geometric returns by taking
the difference between two adjacent logarithmic prices.
B.2. Realized Correlation Construction
The vector of the logarithmic prices of the 12 stocks, p(t)12×1 , is assumed to be a 12-dimension
semi-martingale (SM) by the no-arbitrage condition. t ≥ 0 denotes the continuous time. Then
the log price can be written as
p(t) = a(t) + m(t)
where a(t) is the drift part with finite variation, and m(t) is the diffusion part. Notice that
m(t) is a local martingale with possible jump components.
Assume that there are M equally spaced observations for each h time period. In our study,
h can be a day, a week or a quarter. Corresponding to our thirty-minute sampling interval, M
takes the values of 12, 60 or 8640. Then i’th period j’th return is a 12 × 1 vector, computed
as
ri,j = p((i − 1)h +

h(j − 1)
hj
) − p((i − 1)h +
),
M
M

j = 1, 2, ..., M.

The realized correlation coefficient for the i’th period between stock k and l is
PM
j=1 r(k)j,i r(l)j,i
ρ̂(kl),j = qP
PM 2
M
2
j=1 r(k)j,i
j=1 r(l)j,i

(7)

Barndorff-Nielsen and Shephard (2004) proposed the asymptotic theory underlying the
above realized correlation measure. In particular, they show that ρ̂(kl),j is consistent for the

24

unobserved population correlation coefficient ρ(kl),j , as the sampling frequency goes to infinity.
ρ̂(kl),j

pρ(kl),j
M→∞

Additionally, if the price process is a continuous stochastic volatility semi-martingale, that
is, when there is no jump in the price process, then Barndorff-Nielsen and Shephard (2004)
show that ρ̂(kl),j is asymptotically conditionally normally distributed.
With the above well-defined asymptotics underlying the ρ̂ measure, we compute our realized correlation coefficient measure according to equation (7).
C. Data sources and definitions
Our analysis uses weekly data during the period 2001-2008. The list of variables and their
sources are:
1. CDS data are from Markit and include daily CDS spreads for each of the 12 sample
banks. The CDS quotes refer to 5-year, senior unsecured, no-restructuring clause and
US dollar denomination. We use end-of-week observations to construct weekly CDS
data.
2. Realized equity return correlations are calculated from high frequency intraday equity
price information of sample banks, using the methodology as described in Appendix
B. The tick-by-tick equity data are provided by TAQ. In each week, we calculate the
realized correlation measures over different time horizons, from one week to one quarter.
3. Financial variables. They include two variables on the performance of the general financial market, one-quarter return of the S&P 500 index and the implied volatility (VIX) of
the index, both of which are available from Bloomberg. In addition, we also include the
fed fund rate and the term structure, the latter defined as the difference between 10-year
and 3-month constant maturity Treasury rates. The interest rate data are available from
the Federal Reserve Board’s H.15 release.
4. Banks’ balance sheet information is available from Fitch IBCA. In particular, we retrieve
25

the annual information of total liabilities for each bank, and use the interpolated time
series (using linear interpolation) to decide on the weight of each bank in the portfolio.

26

References
Alexander, C., Sheedy, E., 2008. Developing a stress testing framework based on market risk
models. Journal of Banking and Finance 32, 2220–2236.
Allenspach, N., Monnin, P., 2006. International integration, common exposures and systemic
risk in the banking sector: An empirical investigation. Working paper, Swiss National Bank.
Amato, J., Luisi, M., 2006. Macro factors in the term structure of credit spreads. BIS Working
Paper No. 203.
Amato, J., Remolona, E., 2003. The credit premium puzzle. BIS Quarterly Review 2003-4,
51–63.
Andersen, T. G., Bollerslev, T., Diebold, F. X., Labys, P., 2003. Modeling and forecasting
realized volatility. Econometrica 71, 579–625.
Ang, A., Piazzesi, M., 2003. A no-arbitrage vector autoregression of term structure dynamics
with macroeconomic and latent variables. Journal of Monetary Economics 50, 745–787.
Avesani, R., Pascual, A. G., Li, J., 2006. A new risk indicator and stress testing tool: A
multifactor Nth-to-default CDS basket. IMF Working Paper No. 06/105.
Barndorff-Nielsen, O., Shephard, N., 2004. Econometric analysis of realized covariation: High frequency based covariance, regression, and correlation in financial economics.
Econometrica 72, 885–925.
Basurto, M. S., Padilla, P., 2006. Portfolio credit risk and macroeconomic shocks: Applications
to stress testing under data-restricted environments. IMF Working Paper No. 06/283.
Berndt, A., Douglas, R., Duffie, D., Ferguson, M., Schranz, D., 2005. Measuring default risk
premia from default swap rates and EDFs. Working paper, Stanford University.
Blanco, R., Brennan, S., March, I. W., 2005. An empirical analysis of the dynamic relationship
between investment-grade bonds and credit default swaps. Journal of Finance 60, 2255–
2281.
Bongaerts, D., de Jong, F., Driessen, J., 2008. Liquidity and liquidity risk premia in the CDS
market. Working paper, University of Amsterdam.
Borio, C., 2003. Towards a macro-prudential framework for financial supervision and regulation? BIS Working Paper No. 128.
Borio, C., 2006. Monetary and financial stability: Here to stay? Journal of Banking and
Finance 30, 3407–3414.

27

CGFS, 2000. Stress testing by large financial institutions: Current practice and aggregation
issues. Committee on the Global Financial System Report (14), Bank for International
Settlements.
CGFS, 2005. Stress testing at major financial institutions: Survey results and practice. Committee on the Global Financial System Report (24), Bank for International Settlements.
Chan-Lau, J. A., Gravelle, T., 2005. The End: A new indicator of financial and nonfinancial
corporate sector vulnerability. IMF Working Paper No. 05/231.
Crosbie, P., 2005. Global correlation factor structure: Modeling methodology. Moody’s KMV
Documents.
Daniels, R., Koopman, S. J., Lucas, A., 2005. A non-Gaussian panel time series model for
estimating and decomposing default risk. DNB Working Paper No. 55.
Das, S., Duffie, D., Kapadia, N., Saita, L., 2007. Common failings: How corporate defaults
are correlated. Journal of Finance 62, 93–117.
Drehmann, M., 2008a. Macroeconomic stress testing banks: A survey of methodologies.
Working paper, Bank for International Settlements.
Drehmann, M., 2008b. Stress tests: Objectives, challenges and modelling choices. Sveriges
Riksbank Economic Review 2/2008, 60–92.
Driessen, J., 2005. Is default event risk priced in corporate bond?
Studies 18, 165–195.

Review of Financial

Driessen, J., Maenhout, P., Vilkov, G., 2006. Option-implied correlation and the price of
correlation risk. Working paper, INSEAD.
Duffie, D., 1999. Credit swap valuation. Financial Analysts Journal 55, 73–87.
Duffie, D., Eckner, A., Horel, G., Saita, L., 2008. Frailty correlated default. Journal of
Finance, forthcoming.
Duffie, D., Saita, L., Wang, K., 2007. Multi-period corporate default prediction with stochastic
covariates. Journal of Financial Economics 83, 635–665.
Eom, Y. H., Helwege, J., Huang, J., 2004. Structural models of corporate bond pricing: An
empirical analysis. Review of Financial Studies 17, 499–544.
Forte, S., Peña, J. I., 2009. Credit spreads: An empirical analysis on the informational content
of stocks, bonds, and CDS. Journal of Banking and Finance, forthcoming.
Gibson, M., 2004. Understanding the risk of synthetic CDOs. Working paper, Board of
Governors of the Federal Reserve System.
28

Goodhart, C., 2006. A framework for assessing financial stability? Journal of Banking and
Finance 30, 3415–3422.
Goodhart, C., Sunirand, P., Tsomocos, D., 2005. A risk assessment model for banks. Annals
of Finance 1, 197–224.
Goodhart, C., Sunirand, P., Tsomocos, D., 2006. A model to analyse financial fragility.
Economic Theory 27, 107–142.
Hancock, D., Passmore, W., 2008. Financial stability and the capital adequacy of large U.S.
banking organizations: A VAR in VaR approach. Working paper, Board of Governors of
the Federal Reserve System.
Huang, J., Huang, M., 2003. How much of the corporate-treasury yield spread is due to credit
risk? Working paper, Penn State University.
Hull, J., White, A., 2004. Valuation of a CDO and an n-th to default CDS without Monte
Carlo simulation. Journal of Derivatives 12, 8–23.
Inui, K., Kijima, M., 2005. On the significance of expected shortfall as a coherent risk measure.
Journal of Banking and Finance 29, 853–864.
Jarrow, R., 2001. Default parameter estimation using market prices. Financial Analysts
Journal 57, 75–92.
Lehar, A., 2005. Measuring systemic risk: A risk management approach. Journal of Banking
and Finance 29, 2577–2603.
Longstaff, F., Mithal, S., Neis, E., 2005. Corporate yield spreads: Default risk or liquidity?
New evidence from the credit-default-swap market. Journal of Finance 60, 2213–2253.
Männasoo, K., Mayes, D. G., 2009. Explaining bank distress in Eastern European transition
economies. Journal of Banking and Finance 33, 244–253.
Merton, R., 1974. On the pricing of corporate debt: The risk structure of interest rates.
Journal of Finance 29, 449–470.
Norden, L., Wagner, W., 2008. Credit derivatives and loan pricing. Journal of Banking and
Finance 32, 2560–2569.
Tang, D. Y., Yan, H., 2006. Liquidity, liquidity spillover, and credit default swap spreads.
Working paper, Kennesaw State University.
Tarashev, N., Zhu, H., 2008a. The pricing of portfolio credit risk: Evidence from the credit
derivatives market. Journal of Fixed Income 18, 5–24.

29

Tarashev, N., Zhu, H., 2008b. Specification and calibration errors in measures of portfolio
credit risk: The case of the ASRF model. International Journal of Central Banking 4,
129–174.
Yamai, Y., Yoshiba, T., 2005. Value-at-risk versus expected shortfall: A practical perspective.
Journal of Banking and Finance 29, 997–1015.
Zhu, H., 2006. An empirical comparison of credit spreads between the bond market and the
credit default swap market. Journal of Financial Services Research 29, 211–235.

30

Table and Figure Legends
Table 1: This table describes the summary statistics of credit factor variables and financial
market variables.
Table 2: The dependent variable is the observed asset return correlation in the next quarter
(between period t and t + 12), with the Fisher transformation applied. Explanatory variables
include the current period one-quarter and one-week asset return correlations and financial
market variables. The reported t-statistics (in the parenthesis) are based on Newey-West HAC
covariance matrix with the truncation lag of 20. ** and * represent significance of coefficients
at the 95% and 90% confidence levels respectively.
Table 3: The dependent variables are indicators of systemic risk in the banking group, including our measure of the insurance premium against distressed losses and nth-to-default
probability measures with n = 1, n = 2 and n ≥ 1. Explanatory variables are average PDs
and (forward-looking) correlations ρ̄ that are used to calculate these indicators. t-statistics
are in the parenthesis and ** represents significance at the 95% confidence level.
Table 4: The results are based on a VAR analysis in which the number of lags, which equals
one, is determined by the Schwarz Information Criteria. Endogenous variables include average
PDs (Logit transformation applied), average one-week correlations (Fisher transformation applied), fed fund rates, term spreads, one-month returns and implied volatility of the S&P500
index. t-statistics are in the brackets. ** and * represent significance of coefficients at the
95% and 90% confidence levels respectively.
Table 5: The results show the impacts of explanatory variables, including credit risk factors
and financial market variables, on PDs of individual banks (Logit transformation applied).
** and * represent significance of coefficients at the 95% and 90% confidence levels respectively.
Figure 1: This figure plots the time series of (weighted-average) risk-neutral PDs, average
1-week realized correlations and average 1-quarter future correlations. The solid lines refer to
the observed data. The dash-dotted lines refer to in-sample predictions based on: (1) a VAR
analysis that consists of credit risk factors (average PDs and 1-week realized correlations)
and financial market variables (fed fund rates, term spreads, S&P500 one-month returns and
implied volatility), as shown in Table 4; (2) regressions of individual PDs on the lagged own
variable and the current-period market variables (Table 5); and (3) a regression of future
(one-quarter) correlations on the current-period 1-quarter correlations, weekly correlations
and other market factors (Table 2, Regression 3).
Figure 2: This figure plots the time series of fed fund rates, term spreads, S&P500 one-month
returns and implied volatility (VIX). The solid lines refer to the observed data. The dash-

31

dotted lines refer to in-sample predictions as described in Figure 1.
Figure 3: The indicator refers to the price of insurance against banking distresses, i.e. the
risk-neutral expectation of credit losses that equal or exceed 15% of the corresponding banking
sector’s liabilities. The prices are shown as the cost per unit of exposure to these liabilities in
the upper panel and are shown in dollar term in the lower panel. The indicators are calculated
based on individual risk-neutral PDs implied from CDS spreads and forecasted one-quarter
asset return correlations.
Figure 4: This graph plots the movements in the indicator of systemic risk, defined as the
price of insurance against banking distresses (credit losses exceed 15% of total liabilities of
the banking sector), under stress testing scenarios. The stress testing adopts hypothetical
scenarios based on the statistical properties of error terms in the model (described in Figure
1). In particular, the bootstrapping technique is used to simulate the future path of shock
terms. The simulation is repeated 1,000 times and in each time the corresponding indicator
of systemic risk is calculated. The lines plot the mean and 95% percentile distributions of the
indicator.
Figure 5: This graph plots the movements in the indicator of systemic risk, defined as the
price of insurance against banking distresses (credit losses exceed 15% of total liabilities of the
banking sector), under stress testing scenarios. The stress testing adopts historical scenarios,
i.e. using shocks in macro-financial factors as observed during the LTCM crisis (dotted line)
and the September 11 episode (dashed line). The model framework is the same as the one
specified in Figure 1 except that the VAR model only includes the four financial market variables.
Figure 6: The bootstrapping stress testing technique, described in Figure 4, is adopted to
forecast the movements of the indicator of systemic risk (defined as in Figure 4) 12 weeks into
the future. The dashed line plots the predicted average of the indicator and the dash-dotted
lines the 95% confidence interval of the predicted values. The solid line refers to the ex post
realization of these measures.

32

Table 1: Summary statistics
Variables

Mean

Std. Dev.

Min

Max

CDS spread (bps): bank 1
CDS spread (bps): bank 2
CDS spread (bps): bank 3
CDS spread (bps): bank 4
CDS spread (bps): bank 5
CDS spread (bps): bank 6
CDS spread (bps): bank 7
CDS spread (bps): bank 8
CDS spread (bps): bank 9
CDS spread (bps): bank 10
CDS spread (bps): bank 11
CDS spread (bps): bank 12
CDS spread (bps): weighted average
1-Week realized correlation
1-Quarter realized correlation
Fed fund rate (%)
Term spread (%)
1-Month SP500 return (%)
SP500 implied volatility (%)

25.34
30.40
58.18
34.06
46.48
39.57
62.92
56.59
51.00
35.18
39.82
28.45
44.16
0.51
0.53
4.86
1.58
0.66
20.39

20.45
22.62
59.21
33.06
29.69
24.16
60.49
54.03
42.79
25.99
48.08
22.30
34.42
0.13
0.09
2.13
1.17
4.18
7.65

9.25
7.66
18.03
6.80
17.79
10.87
17.70
14.63
17.97
13.58
9.07
5.93
12.72
0.12
0.27
0.96
-0.82
-26.47
9.04

112.50
149.45
723.61
225.02
230.52
172.61
438.00
334.07
330.62
158.54
327.04
151.72
259.50
0.82
0.71
9.90
3.84
13.97
98.81

33

Table 2: Forecasting asset return correlations

ρ̃t−12,t
ρ̃t−1,t

Regression 1
0.52**
(5.4)
0.18**
(4.7)

FFRt
TERMt
SP500 rett
VIXt
constant
Adjusted R2
Observations

0.19**
(3.6)
0.54
415

34

Regression 2
0.63**
(6.1)

-0.030
(-1.2)
-0.038
(-1.2)
-0.0046**
(-3.6)
0.0015
(0.9)
0.36**
(2.5)
0.55
415

Regression 3
0.52**
(4.7)
0.12**
(3.8)
-0.026
(-1.1)
-0.033
(-1.1)
-0.0036**
(-2.9)
0.0012
(0.8)
0.33**
(2.3)
0.56
415

Table 3: Impacts of PDs and correlations on indicators of systemic risk
Indicators of systemic risk

P Dt
ρ̄t
constant
Adjusted R2
Observations

Price of insurance

n=1

n=2

n≥1

0.2077**
(84.0)
0.0029**
(12.7)
-0.0021**
(-17.6)

1.0994**
(87.9)
-0.0204**
(-17.8)
0.0145**
(24.5)

0.3085**
(159.7)
0.0008**
(4.4)
-0.0005**
(-5.9)

1.6952**
(157.5)
-0.0157**
(-15.9)
0.0110**
(21.7)

0.97
387

0.96
387

0.99
387

0.99
387

35

Table 4: VAR analysis

P˜D(-1)
ρ̃W (-1)
FFR(-1)
Term(-1)
SP500 ret(-1)
VIX(-1)
Constant
Adjusted R2
Observations

P˜D

ρ̃W

FFR

Term

SP500 ret

VIX

0.98**
(66.8)
0.083**
(2.4)
0.010
(0.9)
0.012
(0.8)
-0.0025**
(-2.0)
-0.00084
(-0.8)
-0.18
(-1.5)

0.055**
(2.8)
0.49**
(10.7)
-0.054**
(-3.9)
-0.071**
(-3.9)
-0.0029*
(-1.7)
0.0012
(0.9)
0.85**
(5.4)

-0.037*
(-1.8)
-0.031
(-0.6)
0.94**
(64.4)
-0.064**
(-3.4)
-0.00063
(-0.4)
-0.0011
(-0.8)
0.14
(0.8)

0.033
(1.5)
0.026
(0.5)
-0.012
(-0.8)
0.97**
(47.8)
-0.00047
(-0.2)
0.0024
(1.6)
0.20
(1.2)

-0.34
(-0.8)
0.11
(0.1)
-0.38
(-1.2)
-0.47
(-1.1)
0.73**
(18.6)
0.030
(1.0)
-0.44
(-0.1)

0.66*
(1.8)
-0.22
(-0.3)
0.084
(0.3)
0.097
(0.3)
0.0048
(0.1)
0.92**
(35.5)
4.70
(1.5)

0.97
386

0.43
386

0.99
386

0.99
386

0.53
386

0.91
386

36

Table 5: Determinants of individual PDs

37

Factors

Bank 1

Bank 2

Bank 3

Bank 4

Bank 5

Bank 6

Bank 7

Bank 8

Bank 9

Bank 10

Bank 11

Bank 12

P˜Di,t−1
P˜D
ρ̃W
FFR
TERM
SP500 ret
VIX
constant

0.70**
0.25**
-0.04
-0.02
-0.02
0.0004
0.0002
-0.27

0.63**
0.39**
-0.004
0.03**
0.04
-0.005**
-0.003**
-0.09

0.68**
0.36**
0.15**
0.10**
0.08
-0.006**
-0.004**
-0.17

0.51**
0.63**
0.01
-0.03**
-0.04
-0.006**
-0.004 **
0.78**

0.38**
0.50**
0.11**
0.003
-0.01
0.001
0.002**
-0.64**

0.71**
0.23**
0.13**
-0.03**
-0.02*
-0.005**
0.001
-0.31**

0.45**
0.63**
0.10**
0.08**
0.05
-0.003**
-0.004**
0.27**

0.57**
0.50**
0.15**
-0.02
-0.03
-0.004**
-0.004**
0.51**

0.38**
0.61**
0.17**
-0.03**
-0.06
-0.001
-0.003**
0.20*

0.81**
0.10**
0.02
-0.0003
0.01
0.002
0.004**
-0.57**

0.79**
0.29**
0.03
0.02**
0.01
-0.003**
-0.003**
0.33**

0.68**
0.35**
0.05
0.0000
0.02
-0.004**
-0.004**
0.006

Adj-R2
Obs.

0.92
274

0.98
381

0.98
386

0.98
386

0.97
386

0.97
385

0.99
386

0.98
386

0.97
386

0.91
363

0.98
386

0.97
386

Figure 1: Portfolio credit risk and macro-financial factors

Average PDs
5
4

Observed data
In−sample prediction

%

3
2
1
0

Jan02

Jan04
Date

Jan06

Jan08

Jan06

Jan08

Jan06

Jan08

1−week realized correlations
100
80

%

60
40
20
0

Jan02

Jan04
Date
1−quarter realized correlations

80
70

%

60
50
40
30
20

Jan02

Jan04
Date

38

Figure 2: Financial market factors

Fed fund rates

Term spread

8

5
Observed data
In−sample prediction

4

6

%

%

3
4

2
1

2
0
0

Jan02

Jan04
Date

Jan06

−1

Jan08

Jan02

Jan06

Jan08

Jan06

Jan08

VIX

20

50

10

40
30

0

%

%

S&P500 monthly return

Jan04
Date

20
−10
10
−20
Jan02

Jan04
Date

Jan06

0

Jan08

39

Jan02

Jan04
Date

Figure 3: Indicator of systemic risk in the banking sector

Price of insurance against distresses (>=15% losses)
1.2
Telecom bubble burst

subprime
crisis

unit price (%)

1
0.8

Credit market
deterioration

0.6

Argentina
crisis

0.4
0.2
0
Jan01

Ford / GM
episode
Iraq war

9.11

Jan02

Jan03

Jan04

Jan05
Date

Jan06

Jan07

Jan08

Price of insurance against distresses (>=15% losses)
120
100
bn USD

80
60
40
20
0
Jan01

Jan02

Jan03

Jan04

40

Jan05
Date

Jan06

Jan07

Jan08

Figure 4: Stress testing exercises based on statistical scenarios

1.5
In−sample
Predicted mean
Predicted interval 95%

41

%

1

0.5

0
Jan01

Jan02

Jan03

Jan04

Jan05
Date

Jan06

Jan07

Jan08

Figure 5: Stress testing exercises based on historical scenarios

1.5
In−sample
LTCM
9.11

42

%

1

0.5

0
Jan01

Jan02

Jan03

Jan04

Jan05
Date

Jan06

Jan07

Jan08

Figure 6: Forecasting the systemic risk indicator

Price of insurance against distresses (>=15% losses)
2.5
In−sample
Predicted mean
Predicted 95% interval
2

1.5

%

43
1

0.5

0
Jan01

Jan02

Jan03

Jan04

Jan05
Date

Jan06

Jan07

Jan08