A Systemic Risk Indicator

We now turn to our main objective, which is to model systemic risk. The importance of systemic risk is well understood; it manifests itself in the form of higher positive correlations between returns, thereby reducing benefits from diversification, which could lead to significant losses. We define a systemic event as the simultaneous failure of numerous markets or asset classes. For our purposes, we settle on a specific definition of a systemic risk event as one in which three or more of the five asset classes fail on any given day (that is, their returns all exceed their respective thresholds). We can also use the markets of countries to define systemic risk. For example, systemic risk could be defined as the simultaneous failure of three countries.

To describe this mathematically, the systemic event, y is a binary dependent variable that takes the value 1 on a day in which there is a systemic event, and zero otherwise. We use a logistic regression to model the relationship between the likelihood of the systemic event, y, conditional on our three covariates: volatility (specifically, the daily growth rate in the VIX as well as its daily change), default risk (AAA spread over the 10-year Treasury), and liquidity (TED spread). See Greene (2002) for an introduction to logit and probit models and Maddala (1983) on general limited dependent variable models. We therefore estimate the parameters of the following logistic function by maximum likelihood (qualitative ...

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