Public institutions have developed a wide range of methods to track systemic financial risk. What most of them have in common is reliance on financial market data. This implies that systemic risk indicators typically only show what the market has already priced, in form of correlation, volatility or value. They cannot anticipate market crises. Their main use is to predict when and how market turmoil begins to sap the functioning of the financial system. Some methods may be useful for macro trading. For example, Conditional Value-at-Risk can identify sources of systemic risk, such as specific institutions or market segments. Principal Components Analysis can indicate changing concentration of risk across securities and markets.

The post ties in with SRSV’s summary lecture on systemic risk management, particularly the section on “preparing crisis management”.

The below are quotes from the paper. Emphasis and cursive text have been added.

### Why so many different measures?

“__Systemic risk [ is] the risk that the financial system, or part of it, may become so impaired that severe negative consequences for overall economic activity would be inevitable__. This risk is…difficult to capture in a unique, compact framework…The multifaceted nature of systemic risk requires the deployment of a wide range of indicators in order to obtain reliable measures of its various features.”

“[*Systemic risk*] indicators that are…used…in macro-prudential analysis and policy [*of*] the International Monetary Fund, the European Systemic Risk Board (ESRB), the European Central Bank [*and other central banks*].”

“The features of systemic risk indicators that are most relevant from a regulatory perspective [*and for responsible macro trading*] are the capacity to anticipate systemic events, the simplicity of implementation and the possibility of updating them frequently…[*By contrast*] researchers…are interested in the theoretical foundations of the indicators and in the analytical techniques that are used.”

### What are the main measures?

**Conditional Value at Risk (CoVAR)**

“Conditional Value at Risk [*is*] the __Value at Risk (VaR) of the financial system conditional on an institution being in distress__. Its aim is to measure the systemic spillover from an individual institution to the whole financial system. While two institutions may be similar in terms of VaR, their contribution to systemic risk could differ substantially.

Intuitively, the CoVaR estimates the stock losses that the whole financial system would face with a certain confidence level conditional on the stock returns of an individual institution. In turn, __[ the change of] CoVaR estimates how the potential losses for the whole financial system would increase when the individual institution shifts from being in a normal condition to being in trouble__.”

“CoVaR has been widely used by public institutions…According to several stress tests, it is considered one of the most accurate systemic risk indicators. CoVaR is not simply a tail indicator like the VaR, but is a tail indicator conditional on a bad event. It is exactly that conditioning that __helps identifying as systemically significant some institutions that would have not been recognized as such otherwise__.”

“Since CoVaR is a bivariate indicator, it can be calculated for the financial system conditional on one institution at a time being in distress. [*The figure below*] displays the average CoVaR of the log stock returns of 52 European banks listed in the STOXX Europe 600 index. The shaded area shows the interval between the 5th and the 95th percentiles. The __indicator shows several troughs during the periods of major distress__…This highlights how the market was particularly sensitive to some institutions being in distress during those periods.”

**CoRisk**

“CoRisk is a __measure of risk interdependence across financial institutions that accounts for common risk factors and potential nonlinear effects__…Intuitively, CoRisk is the percentage difference between a default risk measure of an institution conditional on the default risk of another institution and some common drivers of default risk and its unconditional counterpart…CoRisk is estimated by running quantile regressions, that can capture potential non-linearities in the conditional distribution of default risk…CoRisk can be estimated using different datasets. IMF [*research*] uses CDS spreads. In particular, CDS spreads below the 5th quantile of their empirical distribution are assumed to indicate a very favourable regime, while CDS spreads above the 95th quantile are assumed to indicate a regime of distress.”

“[*The figure below*] shows the CoRisk estimates of a subset of systemically important US financial institutions in March 2008…The numbers reported next to the arrows are the CoRisk measures. For example, the risk of Wells Fargo conditional on the risk of AIG is almost five times (490 per cent) higher than the risk corresponding to the 95th percentile of the empirical distribution of Wells Fargo.”

**Systemic Expected Shortfall**

“The Systemic Expected Shortfall __measures how much a financial institution is undercapitalised when the whole financial system is undercapitalised__….[i.e.] how much a bank’s equity drops below a given fraction of its assets when the aggregate banking capital drops below a given fraction of the aggregate banking assets…The Systemic Expected Shortfall has two main components: the leverage and the marginal expected shortfall of the institution under consideration. The latter is defined as the losses of a firm ‘in the tail of the aggregate sector’s loss distribution’.”

“The figure below shows the systemic shortfall risk of Bank of America Corp and Deutsche Bank AG over the period July 2008 – July 2016.”

**Distress Insurance Premium**

“The Distress Insurance Premium (DIP) is equivalent to __a theoretical premium to a risk-based deposit insurance scheme that guarantees against most severe losses for the banking system__. The indicator represents the expected value of portfolio credit losses that are equal or exceed a minimum share of the total liabilities in the banking sector. Two components are necessary to calculate the DIP: the probability of default for individual banks and the correlation of asset returns. __Probabilities of default are derived from single-name CDS spreads, while asset return correlations are derived from the co-movements of equity returns__.”

“[*The figure below*] shows the DIP, the theoretical insurance premium against a credit loss of at least 15 per cent of the banking sector’s liabilities in the United States over the period 2001-08.”

**Principal Component Analysis (PCA)**

“PCA decomposes the stock return volatility of a sample of financial institutions into different components. The __number of components which are necessary to explain a given fraction of stock return volatility becomes lower as the interconnection among financial institutions increases__.”

“[*The figure below*] displays 36-month rolling windows for the cumulative risk fraction [of the first principal component as a yellow area] over the period January 1994 – 2008. The financial institutions used in the sample are the hedge funds included the Lipper TASS database, and the banks, brokers/dealers, and insurers in the University of Chicago’s Center for Research Database.”

**Option-implied probability of default**

“The option-implied probability of default is a __market-based indicator that measures the probability of default for an institution based on the prices of its equity options__…The probability of default is defined as the probability that the value of a firm’s assets drop below a threshold level (the default barrier). To estimate this probability, both the default barrier and the density function of the asset value are needed…The model is based on Merton’s balance sheet approach according to which __the value of equity can be seen as a call option on the firm’s assets with strike price value equal to the on-balance sheet liabilities__.”

**Joint Distress Indicators**

“Joint distress indicators that are built upon the concept of the Banking System Multivariate Density (BSMD). In particular, __they treat the banking system as a portfolio of banks and they estimate its multivariate density__. From the latter they calculate four indicators of joint distress:

- The
**Joint Probability of Distress**(JPoD), which measures `the probability of all banks in the system (portfolio) becoming distressed, i.e. the tail risk of the system’; - The
**Banking Stability Index**(BSI), which `reflects the expected number of banks becoming distressed given that at least one bank has become distressed’; - The
**Distress Dependence Matrix**(DiDe), which is a matrix that `contains the probability of distress for the bank specified in the row given that the bank specified in the column becomes distressed’; - The
**Probability of Cascade Effects**(PCE), which is the probability that `at least one bank becomes distressed, given that a specific bank becomes distressed’.”

“A major advantage of these indicators is that they are able to capture both linear and non-linear distress dependencies among the banks in the system. In addition, the linear and non-linear dependencies are allowed to change throughout the economic cycle. “

[*The figures below*] show the Joint Probability of Distress and the Banking Stability Index of a sample of large international banks over the period 1 January 2010 – 31 October 2011.

**Systemic Contingent Claim Analysis**

“Systemic Contingent Claim Analysis was proposed…as a new__ measure of systemic risk founded on two main theories: contingent claim analysis and extreme value theory__…Contingent claim analysis is a generalization of the option pricing theory… which is necessary in order to estimate each firm’s expected losses. Extreme value theory is used to combine the individual firms’ expected losses through a dependence measure in order to derive the joint expected losses as a measurement of systemic riskiness.”

“More in detail, __contingent claim analysis is a risk-adjusted balance-sheet framework__ based on three main principles: i) the values of liabilities can be derived from the value of assets; ii) assets follow a stochastic process; and iii) liabilities have different seniorities. These principles allow one to compute the value of equity as the value of an implicit call option on assets, and the value of risky debt as the difference between default-free debt and a guarantee against default. This guarantee can be calculated as the value of a put option on assets.”

“The main strengths of Systemic Contingent Claim Analysis are that it can be used to derive market-implied expected losses and that it endogenizes the loss given default. On the other hand, the major drawbacks are that it is not easy to calculate and that it relies on the specification of the option pricing model.”

“[*The figure below*] exhibits the total contingent liabilities of thirty-six US financial institutions. The blue line shows the total level of contingent liabilities, which reflects `the concurrent realization of individual distress at an average degree of severity.”

**Network Analysis**

“Network analysis is a __useful approach for identifying financial interlinkages among institutions, as well as for tracking the reverberation of a credit and/or funding event throughout the system__. It is a valuable tool for identifying both the most systemic institutions – the ones that trigger the stronger domino effects in case of default – and the most vulnerable institutions – those that are most seriously affected by the default of other institutions.”

“[*This approach*] requires access to data on inter-institution exposures, which are usually only available to supervisors.”

“[*The figure below*] represents how network analysis can be used to track the reverberation of a possible credit event throughout the banking system. It shows the contagion path triggered by the hypothetical default of Italy’s cross-border interbank loans.”

**Default Intensity Model**

“[*This is*] a __reduced-form statistical model of the timing of banking default events__…In brief, the default rate is modelled as a continuous time process which jumps at default events, thus reflecting the increased likelihood of further default events due to spillover effects. The jump size specification guarantees that the impact of an event increases with the default rate prevailing at the time of the event. This is consistent with the clustering behaviour of defaults…”

“While the advantage of this model is that it captures both direct and indirect linkages among financial institutions, it is not able to disentangle between the two.”

“[*The figure below*] shows a time series of quarterly forecasts for the one-year distributions of the number of defaults in the US banking sector estimated from the model for the banking-wide default rate.”

**Markov-Regime Switching Model**

“A Markov regime __switching autoregressive conditional heteroskedastic model (SWARCH) [ can be used] for assessing financial volatility and the likelihood of a crisis__. In particular, they model the dynamics of proxies for global market conditions such as the VIX index, the TED spread and the EUR-USD forex swap as ARCH models with state-dependent parameters. This allows them to differentiate between states of low, medium, and high volatility. The probability of switching from one state to another is modelled as a Markov chain.”

“[*The figure below*] shows the results of a daily SWARCH model for the VIX index over the period 1998-2008. A probability of being in the high state equal to 1 is reached for the Russian and LTCM defaults in 1998, for the WorldCom scandal and Brazil’s election in 2003, and for Lehman’s collapse in 2008.”

**Composite Indicator of Systemic Stress (CISS)**

“The CISS is a composite indicator built to __`measure the current state of instability, i.e. the current level of frictions, stresses and strains (or the absence thereof) in the financial system__ and to summarize it in a single statistic’.”

“It is designed not only to identify systemic risk within the financial system (the `horizontal view’, according to which systemic risk pervades the whole financial system), but also to consider systemic risk stemming from the interaction between the financial system and the real economy (the `vertical view’, according to which systemic risk spills over into the real sector)…__Five categories within the financial system are considered: the equity market, the bond market, the money market, the foreign exchange market, and the financial intermediaries’ sector__.”

“The euro-area CISS is included in the ECB’s analytical toolkit…[*The figure below*] exhibits the CISS (the black line) for the euro-area members.”

**Risk Assessment Model for Systemic Institutions (RAMSI)**

“RAMSI is a __quantitative model of financial stability that aims to assess institution-specific and system-wide vulnerabilities__…RAMSI relies on a modular approach where a macroeconomic model is combined with models that describe how the risk profiles of key financial institutions respond to changes in macroeconomic conditions.

In particular, RAMSI __adopts a balance sheet approach and integrates it with a network model in order to account for interaction and contagion among banks__. The model allows for macro-credit risk, interest and non-interest income risk, network interaction and feedback effects emerging on both the asset and the liability side of the balance sheet. Systemic risk arises because of the feedback loop that may be triggered by the failure of a bank heavily connected with the rest of the system. As a result of counterparty risk, fire sales and confidence contagion, the failure of one bank spills over to other banks, thus generating a cascade effect.”

“While the relationship between a deterioration in bank fundamentals and an increase in funding costs is roughly linear during normal times, it becomes non-linear in times of crisis. This __non-linearity is included in RAMSI through bank ratings__.”

“[*The figure below*] shows the modular structure of RAMSI. A macroeconomic or financial shock is transmitted to the system via several feedback channels, which act through balance sheet interdependencies and network effects.”