Measuring Risks from Fat Tails, Tail Dependence, and Micro-Correlations

Resources For The Future Inc, Washington DC

Investigators

Abstract

Understanding how risks change under aggregation is critical for many fields, from financial markets, where assets are securitized, to insurance, where firms hold a portfolio of many individual policies. When individual risks are independent and sufficiently thin-tailed, bundling can lower overall risk levels. This project centers on three characteristics of risks that threaten the benefits obtained through aggregation: fat tails, tail dependence, and micro-correlations. This research develops new approaches for detecting, measuring, and analyzing these phenomena, with the aim of improving catastrophe risk management across a range of applications. Fat tailed distributions have been well studied since the early 1900s. Statistical estimators of tail indices, such as the Hill estimator, have been researched extensively, but have well known limitations, and variations continue to proliferate. We propose a new approach for measuring tail obesity based on the self-similarity of random aggregations. This has the benefit of focusing specifically on the properties of fat-tailed distributions that are of concern for securitization, rather than on hypothesized limit behavior. Tail dependence refers to the tendency for dependence between two variables to concentrate in the extreme values. While observable in datasets, such as damages from natural catastrophes, tail dependence is much less understood mathematically than fat tails. Empirically, tail dependence has been seen to grow with aggregation, raising concerns about securitizing or insuring tail dependent risks, but the theory lags far behind these observations. This research will provide risk managers with tools to understand and address tail dependence. Finally, global micro-correlations are small correlations which may be statistically insignificant when considered individually, but become dangerous when aggregated. Proof-of-concept analyses for detecting such correlations have been performed using flood and crop insurance claim data. The first stage of this new research requires collecting and standardizing historical loss data. After developing the appropriate datasets, the researchers will begin the analytical work that involves developing scalar measures for tail obesity in finite data sets, studying the conditions under which aggregation amplifies tail dependence, studying micro-covariation in fat tail distributions and their behavior under aggregation, and studying empirical distributions of aggregated losses. Finally, the third stage of the research focusing on dissemination: preparing publications for peer-reviewed journals, developing a set of online educational materials, and hosting a workshop.