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Systemic Risk and Returns


I solve a consumption based model, with interfirm systemic risk, for a portfolio optimization with arbitrary return distributions and endogenous stochastic discount factor (sdf). The model highlights a new systemic risk: systemic allocation risk. In contrast to the case without systemic risk, the market and planner allocate capital differently. The externality causes the planner to reduce investment in the risky firm. The market, modeled as a representative agent, does not just ignore the externality and invest as if there were none. Instead, systemic risk increases the representative agent's investment in the systemically risky institution or industry, further increasing systemic risk. I introduce bailout of the financial industry and find it has a beneficial direct effect and a distortion effect. In some cases, investor moral hazard can make ex post optimal bailouts reduce ex ante utility - even when bailout does not benefit the financial industry's investors. I show that systemic risk, as opposed to systematic risk, can be characterized as a situation where the fundamental theorems of asset pricing do not apply.

Next I put the the model into a factor model, using the arbitrage pricing theory for market pricing of the firms. I use the model to distinguish between systematic and systemic risks. By directly including systemic risk, the potential of an interfirm or inter-industry externality, the model shows that including terms with fat tails in specifications for returns does not make them systemic risk if they still meet the definition of systematic risk (Systematic risk is risk within a firm's returns that is both non-causal and correlated with the stochastic discount factor - and therefore undiversifiable. In a factor model, systematic risk in the financial industry is the overall magnitude of firms loading onto systematic factors. The systematic factors do not need to be Gaussian.). The model shows why systematic risk is so often mistaken as systemic risk, why systematic risk in the financial industry is important, and why it should be considered along with systemic risk in regulatory efforts. The model is then used to delineate and outline the various types of risk. This vocabulary can facilitate communication and research in systemic risk. Finally, I derive a popular systemic risk measure directly in terms of the parameters of a pricing model. I test the one that attempts to include causality in its measure, CoVaR.

CoVaR seeks to use joint return data to measure a firm's contribution to systemic risk. To learn what comprehensive regulatory changes can do to systemic risk in general, and CoVaR in particular, Part 4 estimates the impact of the extensive and coincident U.S. regulatory changes of 1993 (including Prompt Corrective Action law and Basel I) on the systemic risk level of commercial banks, as measured by CoVaR. Investment banks not subject to the law are used as controls. In a difference-in-difference framework, the law is used as a treatment shock. Use of a novel CoVaR measure (unconditional rolling CoVaR) allows econometric assessment of exogenous changes and estimation of CoVaR standard errors. With high power, no effect is found. This eliminates from possibility one of two formerly widely held beliefs that are each the basis of a literature: 1. That PCA and concurrent regulation lowered systemic risk, or 2. That CoVaR measures systemic risk. The unique circumstances used for this test could also be exploited to assess other systemic risk metrics or inform other risk/regulation questions.

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