###### Systemic Risk

### ARCH

This is the acronym corresponding to the Auto-Regressive Conditional Heteroscedasticity model in which current volatility is modeled as a function of past shocks only. In its seminal version, inflation was the variable of interest. Rapidly, this model has been applied to asset return data.

### Beta

This is a measure of exposure of a bank to aggregate market variations. It is exactly the same beta as the one used in the CAPM and results from an OLS regression of a bank's returns on the market returns. To allow for time varying beta's we have used the approach consisting of estimating with a DCC variances and covariances of a bank's returns and of the market's returns and then to reconstruct the beta. Negative beta are very rare. A bank with a beta of 1 moves like the entire stock market. A bank whose beta is for instance 2 will see its equity return fall by -10% if the market return falls by an amount of -5%.

### Capital shortfall

This number measures the amount of capital that a bank would require in the case that the market fall.

### Correlation

Correlation is a measure of dependence of the central parts of distributions. It measures the average deviations from the mean of one series in comparison with similar deviations from another series scaled in such a manner that the correlation belongs to the interval -1 to 1. A correlation of -1 means that two assets' returns move in opposite directions. A correlation of +1 means that the two assets' returns move in parallel, a rare instance, for instance because a relation exists between assets, one being a derivative of the other.

### Conditional Correlation

This is a measure of how correlation evolves over time. The model that is used to obtain this measure is the DCC. Exactly like correlation, this number lies between -1 and 1. In the figures representing conditional correlation, we represent the conditional correlation between a bank and the entire market. An increase of the correlation may be seen as a bad signal since the bank becomes more exposed to economy wide risk.

### DCC

This acronym stands for Dynamic Conditional Correlation and represents a multivariate model, which allows the modeling of time varying correlation. Since correlation is also shown to be evolving over time, this extension to a multivariate setting of GARCH models is very important. The DCC also allows a modeling of covariances. Since covariances are a key ingredient for OLS regressions, the DCC model allows for an efficient estimation of time varying parameter models.

### Equity Loss

This measures the loss in the equity value of a financial institution if risk factor such as the market falls by a certain amount, say 2% .

### GARCH

This is the generalization of the ARCH model of Robert Engle. Current volatility is not only affected by past shocks but also by the level of past volatility. Such a model yields volatility which is relatively smooth.

### Leverage

The liability side of banks consists of debt and equity. The number represented by the total value of a bank divided by the equity is called leverage. We define quasi leverage as the total value of a bank divided by the market value of equity (the market capitalization).

### Marginal Expected Shortfall (MES)

This is the expected equity loss of a financial institution when the market declines beyond a given threshold over a given time period. Since capital requirement is related to the equity value of a financial institution, the MES provides a measure of financial fragility.

### Relatif Capital Shortfall

This is the capital shortfall of a bank expressed in percent of the total market capital shortfall. Those financial institutions with the highest relative capital shortfall are also the ones whose default would be the most costly to the government (in case of a bailout).

### Systemic Risk (SRISK)

Federal Reserve Governor Daniel Tarullo defined Systemic Risk as the risk that a firm fails to meet its obligations to creditors and customers. The word systemic comes from the medical literature where a systemic disease is one affecting several organs often leading to severe complications for the patient. SRISK is an econometric measure of systemic risk. Financial institutions that have the highest SRISK are those that contribute the most to market undercapitalization in a crisis. For those financial institutions to survive a crisis either the government provides massive help or new capital needs to be found in financial markets.

### TARCH

This model represents an extension of the GARCH model. Past negative shocks can have a different impact on current volatility than positive shocks of the same level. This model allows the capturing of asymmetries in volatility. Many different specifications exist, but in the end most models provide rather similar volatility predictions.

### Volatility

This is the variability of an asset. Statistically volatility corresponds to a standard deviation. Since this characteristic may change over time, models are required that describe volatility in a satisfactory model. One type of model with great success are those models belonging to the ARCH class. Volatility is also the square root of variance. Multiplied by 100 and the square root of 250, one gets the annual volatility in percent, a number of about 20%-30%.

### Variance

This is also a measure of variability of an asset. Statistically variance corresponds to an average of squared deviations from the mean. Since this characteristic may change over time, models are required that describe volatility in a satisfactory model. One type of model with great success are those models belonging to the ARCH class. Such a model produces a time series of Daily Conditional Variances.