Sustainable investing is growing fast and investors are increasingly integrating environmental, social, and governance (ESG) criteria. However, ESG ratings are derived using heterogeneous methodologies and can be quite divergent across providers, which suggests the need for a formal statistical...

The global minimum variance portfolio computed using the sample covariance matrix is known to be negatively affected by parameter uncertainty, an important component of model risk. Using a robust approach, we introduce a portfolio rule for investors who wish to invest in the global minimum...

We propose a widely applicable bootstrap based test of the null hypothesis of equality of two firms' Risk Measures (RMs) at a single point in time. The test can be applied to any market-based measure. In an iterative procedure, we can identify a complete grouped ranking of the RMs, with...

We show how to reverse-engineer banks' risk disclosures, such as Value-at-Risk, to obtain an implied measure of their exposures to equity, interest rate, foreign exchange, and commodity risks. Factor Implied Risk Exposures (FIRE) are obtained by breaking down a change in risk disclosure into a...

This paper presents a new method to validate risk models: the Risk Map. This method jointly accounts for the number and the magnitude of extreme losses and graphically summarizes all information about the performance of a risk model. It relies on the concept of a super exception, which is...