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Fat Tails and (Un)happy Endings: Correlation Bias, Systemic Risk and Prudential Regulation

Journal 32: Applied Finance

Jorge A. Chan-Lau

The correlation bias refers to the fact that claim subordination in the capital structure of the firm influences claim holders’ preferred degree of asset correlation in portfolios held by the firm. Using the copula capital structure model, it is shown that the correlation bias shifts shareholder preferences towards highly correlated assets. For financial institutions, the correlation bias makes them more prone to fail and raises the level of systemic risk given their interconnectedness. The implications for systemic risk and prudential regulation are assessed under the prism of Basel III, and potential solutions involving changes to the prudential framework and corporate governance are suggested.

A firm or financial institution that holds a portfolio of diverse projects and/or assets is subject to correlation risk, or the risk arising from the correlation of cash flows accrued to the different projects/assets in the portfolio. Most firms and financial institutions finance their portfolios using a mix of claims, such as equity and debt, where each claim is differentiated by its seniority in the capital structure; for example, equity is subordinated to debt.

The correlation bias is the preference of different claim holders on the firm for different levels of projects/asset correlation in the firm’s portfolio. In particular, junior claim holders prefer portfolios where assets are highly correlated while senior claim holders would prefer a more uncorrelated portfolio. Since the control of the firm is usually exercised by managers that tend to act on behalf of the most junior claim holders, shareholders, the choice of portfolio assets would tend to be biased towards highly correlated assets. This bias leads to portfolio outcomes characterized by fat tails that increase the likelihood of observing scenarios with extreme upside and downside risks. In particular, the lack of diversity in the firm’s portfolio increases the likelihood that it may fail since all the assets in the portfolio will be equally affected by a negative shock.

The implications of the correlation bias are not circumscribed to individual institutions though. In a financial system where the correlation bias of junior claim holders is dominant and herd behavior prevalent, it would not be rare to observe “black swan” events often following on the heels of extended periods of tranquility [Taleb (2009)]. The stronger the bias of junior claim holders the more likely the financial system will oscillate between extreme periods of tranquility and financial disruption, contributing to increased procyclicality in the event of negative shocks. This is not just a mere theoretical implication: fat tail “tales” and their unhappy endings were dramatically illustrated by the recent global financial crisis originated by problems in the U.S. subprime mortgage market.

This paper argues that a copula approach to the capital structure, building on the copula pricing model first developed to analyze structured credit products, provides the right framework for understanding the correlation bias arising from the capital structure of the firm. Furthermore, the copula capital structure model is a natural generalization of the contingent claim approach to the capital structure of the firm first proposed by Black and Scholes (1973) and Merton (1974). Insights on the correlation bias derived from the copula pricing model are useful to understand how the bias interacts with systemic risk and whether recent financial regulatory reform could address these interactions effectively.

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