The crisis, Fed, Quants and stochastic optimal control

Abstract

The Dodd–Frank (D–F) Financial Reform Bill authorizes the Federal Reserve to monitor the financial services marketplace to identify potential threats to the stability of the US financial system. Alan Greenspan's retrospective indicates what he has learned from the crisis. He argues that the crisis, the housing price bubble, was unpredictable and unavoidable. Greenspan now focuses on desirable capital requirements, or leverage, for banks and financial intermediaries. I explain why the Fed's and Greenspan's views stem from a lack of the appropriate tools of analysis of what is an excessive debt or leverage. The Quants who devised the highly leveraged financial derivatives ignored systemic risk. My theme is that the application of stochastic optimal control (SOC) is an effective approach to implement what the D–F bill is authorizing. I explain: first, what is the optimal capital requirement/leverage that balances expected return against risk. Second, what is a theoretically derived early warning signal of a crisis. Third, I derive an excess debt ratio, equal to the difference between the actual and optimal ratios. The probability of a debt crisis is directly related to the excess debt ratio. The excess debt ratio starting from 2004–05 indicated that a crisis was most likely. The Fed should use this SOC analysis in implementing the Dodd–Frank bill.