Pooling and Systematic Risk

This paper, for the first time, gives a general formulation of the systematic risk in a risk pool as portfolio's excess loss, and studies its relation with the principle of insurance (POI), and its extension, the principle of pooling (POP). We see that the systematic risk is secure if and only if POP holds. We call this proposition the fundamental theorem of pooling. Then, we show how the systematic risk can organically be measured. We present a variety of examples within the family of typological common shock models, covering homogeneous and heterogeneous risk pools, where we can identify the systematic risk, and measure it in different situations. Then we take a fresh look at the risk valuation from the systematic risk perspective. First, we study the valuation of the ex-ante policies and see that they are not independent of the pool, and need to be adjusted according to the relative systematic safety loading. Second, as we are exposed to systematic risk, we also study the ex-post policies and see that while in finite pools the relative safety loading is contingent on the common shock, for infinite pools it vanishes. In the end, we make an assessment of our theoretical models with reference to two real-world examples. First, we look at the UK Coronavirus (Covid-19) job retention case and second we use our theory to study the agricultural catastrophe risk. This way we propose a novel way to analyze events with large economic losses.