Capital Adequacy Rules, Catastrophic Firm Failure, and Systemic Risk

Posted by R. Christopher Small, Co-editor, HLS Forum on Corporate Governance and Financial Regulation, on Friday August 31, 2012 at 9:09 am
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Editor’s Note: The following post comes to us from Robert Jarrow, Professor of Finance at Cornell University.

In the paper, Capital Adequacy Rules, Catastrophic Firm Failure, and Systemic Risk, which was recently made publicly available on SSRN, I study capital adequacy rules based on Value-at-Risk (VaR), leverage ratios, and stress testing. VaR is the basis of Basel II, and all three approaches are proposed in Basel III.

Due to the 2007 credit crisis, the need for increased regulatory capital has been addressed by newly enacted legislation in the Dodd Frank Wall Street Reform and Consumer Protection Act, and the Basel III capital proposals. The existing and proposed capital adequacy rules are based on three methodologies: Value- at-Risk (VaR), maximum leverage ratios, and stress testing. The purpose of this paper is to analyze the impact of these three rules on the likelihood of financial institution catastrophic failure, and systemic risk in the economy.

A related literature on bank capital concerns the impact of capital regulation on bank risk taking behavior and the business cycle. Kahane (1977), Kim and Santomero (1988), Furlong and Keeley (1989), Rochet (1992), and Blum (1999) study models to determine if capital regulations decrease the risk of insolvency. The answer is yes and no, depending upon the bank’s objective function and market structure. This paper differs from this literature in two ways. First, I am concerned with the probability of catastrophic failure, keeping the probability of insolvency fixed at a level determined by the regulators. Second, with the exception of Kahane (1977), banks are not able to short assets in these models. Shorting assets enables banks to create large left-tail loss distributions and is consistent with current banking practice. An essential element of our model structure is that we allow financial institutions to short risky assets.

The papers by Kashyap and Stein (2004) and Heid (2007), among others, study whether the Basel II capital regulations have an unintended consequence of accelerating the business cycle. The idea is that as the economy weakens, more bank capital is required by the regulations, thereby weakening the economy more. And as the economy improves, less capital is required, thereby accelerating economic growth. I study a related, but different issue, concerning systemic risk and capital regulation. The question I ask is whether the existing capital adequacy rules have an unintended consequence of increasing systemic risk in financial markets. I answer in the affirmative.

With respect to this literature, this paper makes three contributions.

  • I prove that VaR, stress-testing, and maximum leverage ratio capital adequacy rules provide an incentive for financial institutions to increase the probability of catastrophic failure. This is accomplished through a regulatory arbitrage opportunity that reduces required equity capital by shorting “far” left-tail risk while investing the proceeds in riskless securities. The short position does not increase VaR, nor does it affect change the firm’s leverage ratio or stress test outcomes. Collectively across financial institutions, these rules therefore increase (they do not decrease) systemic risk in the economy.
  • I argue that an unintended consequence of the Basel II VaR capital adequacy rules was to enable the regulatory arbitrage that caused the 2007 credit crisis. The regulatory arbitrage executed by financial institutions were the large short positions in credit default swaps (CDS) and the large long positions in highly rated credit debt obligations (CDOs/CDO^2s).
  • I argue that to reduce catastrophic failure and systemic risk, a new capital adequacy rule is needed. The new rule must be based on a risk measure related to the conditional expected loss. Two such measures are suggested: (1) expected shortfall, and (2) the put premium risk measure.

The full paper is available for download here.

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