Volume 33, Issue 3-4 - Special Issue: Systemic Risk: Data, Models and Metrics. Part 1. Guest Editors: Rama Cont and Michael Gordy

This paper concerns sequential computation of risk measures for financial data and asks how, given a risk measurement procedure, we can tell whether the answers it produces are ‘correct’. We draw the distinction between ‘external’ and ‘internal’ risk measures and concentrate on the latter, where we observe data in real time, make predictions and observe outcomes. It is argued that evaluation of such procedures is best addressed from the point of view of probability forecasting or Dawid’s theory of ‘prequential statistics’ [12]. We introduce a concept of ‘calibration’ of a risk measure in a dynamic setting, following the precepts of Dawid’s weak and strong prequential principles, and examine its application to quantile forecasting (VaR – value at risk) and to mean estimation (applicable to CVaR – expected shortfall). The relationship between these ideas and ‘elicitability’ [24] is examined. We show in particular that VaR has special properties not shared by any other risk measure. Turning to CVaR we argue that its main deficiency is the unquantifiable tail dependence of estimators. In a final section we show that a simple data-driven feedback algorithm can produce VaR estimates on financial data that easily pass both the consistency test and a further newly-introduced statistical test for independence of a binary sequence.

Financial institutions’ interconnectedness is a key component of systemic risk. However there is still no consensus on its measurement. Using a unique database of network of exposures of French financial institutions, we compare three strategies to measure interconnectedness: closeness of exposure distributions, identification of core-periphery structure and contagion models. The closeness of exposure distributions is adequate to identify outlier institutions. The “core-periphery” structure, usually applied to banking network, is still valid with insurance companies. However this approach is not immune to size effect. This result contrasts with previous analyses where size was not accounted for. Contagion-based stress-tests are the best suited to capture institutions’ systemic fragility, emphasizing their importance as a supervisory tool.

We develop a novel stress-test framework to monitor systemic risk in financial systems. The modular structure of the framework allows to accommodate for a variety of shock scenarios, methods to estimate interbank exposures and mechanisms of distress propagation. The main features are as follows. First, the framework allows to estimate and disentangle not only first-round effects (i.e. shock on external assets) and second-round effects (i.e. distress induced in the interbank network), but also third-round effects induced by possible fire sales. Second, it allows to monitor at the same time the impact of shocks on individual or groups of financial institutions as well as their vulnerability to shocks on counterparties or certain asset classes. Third, it includes estimates for loss distributions, thus combining network effects with familiar risk measures such as VaR and CVaR. Fourth, in order to perform robustness analyses and cope with incomplete data, the framework features a module for the generation of sets of networks of interbank exposures that are coherent with the total lending and borrowing of each bank. As an illustration, we carry out a stress-test exercise on a dataset of listed European banks over the years 2008–2013. We find that second-round and third-round effects dominate first-round effects, therefore suggesting that most current stress-test frameworks might lead to a severe underestimation of systemic risk.

This paper analyzes the topology of the network of common asset holdings, where nodes represent managed portfolios and edge weights capture the impact of liquidations. Asset holdings data is extracted from the 13F filings. We consider the degree centrality as the degree in the subnetwork of weak links, where weak links are those that lead to significant liquidations. We explore the applications of this network representation to clustering and forecasting. To validate the weight attribution and the threshold used to define the weak links, we show that the degree centrality is correlated with excess returns, and is significant after we control for the Carhart four factors. The network of weak links has a scale free structure, similar to financial networks of balance sheet exposures. Moreover, a small number of clusters, densely linked, concentrate a significant proportion of the portfolios.