Principal components as a measure of systemic risk

The U. S. government's failure to provide adequate oversight and prudent regulation of the financial markets, together with excessive risk taking by some financial institutions, pushed the world financial system to the brink of systemic failure in 2008. As a consequence of this near catastrophe, both regulators and investors have become keenly interested in developing tools for monitoring systemic risk. But this is easier said than done. Securitization, private transacting, complexity, and “flexible” accounting prevent us from directly observing the many explicit linkages of financial institutions. As an alternative, we introduce a measure of implied systemic risk called the absorption ratio, which equals the fraction of the total variance of a set of asset returns explained or “absorbed” by a fixed number of eigenvectors. The absorption ratio captures the extent to which markets are unified or tightly coupled. When markets are tightly coupled, they are more fragile in the sense that negative shocks propagate more quickly and broadly than when markets are loosely linked. We offer persuasive evidence that the absorption ratio effectively captures market fragility.We show that: 1. Most significant U.S. stock market drawdowns were preceded by spikes in the absorption ratio. 2. Stock prices, on average, depreciated significantly following spikes in the absorption ratio and, on average, appreciated significantly in the wake of sharp declines in the absorption ratio. 3. The absorption ratio was a leading indicator of the U.S. housing market bubble. 4. The absorption ratio systematically rose in advance of market turbulence. 5. Important milestones throughout the global financial crisis coincided with shifts in the absorption ratio.We proceed as follows. In Part I we provide a literature review of systemic risk and related topics. In Part II we provide a formal description of the absorption ratio. In Part III we present historical estimates of the absorption ratio for a variety of asset markets, and we show how it relates to asset prices, financial turbulence, the global financial crisis, and financial contagion. We summarize in Part IV and suggest how regulators and investors might use the absorption ratio as an early warning signal of market stress