Anatomy of Systematic Risk in Pools

While the 2008 financial crisis brought systemic risk to the forefront of risk management research, the COVID-19 pandemic has further highlighted the importance of studying systematic risk. This study seeks to examine the anatomy of systematic risk of a pool in a theoretical framework. Our vision is guided by the principle that systematic risk should remain consistent regardless of size, transformation, scaling, and changes in finite members of the pool. To accomplish this, various new concepts are introduced and explored. In particular, we can better understand and distinguish concepts such as systematic uncertainty and systematic risk. Based on this analysis, we propose the fundamental theorem of pooling, that indicates how under no-systematic-uncertainty assumption a systematic hedging strategy is optimal to manage the risk of the pool regardless of the risk measure we choose. This gives rise to a natural way of measuring systematic risk that is discussed in more details in the paper. We also identify and study several examples from the literature within the context of a unifying framework of common shock models, which we introduce in this paper