A Guide to IMF Stress Testing

Chapter 16. Introduction to the Equity Indicators–Based Approach to Stress Testing

Li Ong
Published Date:
December 2014
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Jorge A. Chan-Lau

For stress testing purposes, it is necessary to measure the default risk of individual financial and nonfinancial institutions and to assess how this risk changes under different scenarios. Once the default risk of individual institutions is measured, it is possible to analyze the credit exposures and potential losses and construct bottom-up measures of systemic risk under different stress scenarios.

The estimation of default risk is challenging because of limitations on data availability. One way around this challenge is to use income and balance sheet data to predict corporate bankruptcy, as is the case of the Altman Z-score (Altman, 1968). Although accounting data are readily available across jurisdictions, their use could be hampered by differences in standards, the risk that accounting figures may be manipulated, and, more important, the backward-looking nature of financial statements.

The shortcomings of using financial reporting data could be offset by using information extracted from security prices if secondary markets are judged adequately liquid and efficient. The preferred source of information should be the prices of securities with payoffs more directly related to the creditworthiness of the issuer, such as bonds and credit default swaps. In many instances, however, corporate bonds are rarely traded, so their prices and yields are unreliable. Credit default swaps, though liquid, cover only a relatively small subset of firms in advanced economies, but the coverage is increasing rapidly.

Equity prices are an alternative to bonds and credit default swaps. Unlike the markets in the last two instruments, stock markets tend to be relatively more liquid and cover a larger number of firms in a given jurisdiction. The usefulness of equity prices for estimating probabilities of default is established by the observation, first made by Black and Scholes (1973) and Merton (1974), that corporate securities are contingent claims on the asset value of the issuing firm. The observation can be illustrated in the case of a firm that issues one unit of equity and one unit of a zero-coupon bond with face value D and maturity T. At expiration, the value of debt, BT, and equity, ET, are given by

where VT is the asset value of the firm at maturity.

These equations state that bondholders get paid in full only if the firm’s assets exceed the face value of debt. Otherwise, the firm is liquidated, and its assets are used to compensate debt holders (partially). Equity holders are thus residual claimants in the firm and hold a call option on the asset value of the firm. Hence, option pricing can be used to calculate the risk-neutral default probability in period t for a horizon of T years as

where N is the cumulative normal distribution, Vt is the value of assets in period t, r is the risk-free rate, and (σA is the asset volatility.

The risk-neutral default probability then could be converted to a real-world default probability by using a number of techniques. For instance, Moody’s KMV maps the numerator of the previous equation, the distance to default, to default probabilities using historical data on defaults for a large panel of corporates. Alternatively, the risk-neutral default probability can be corrected for the risk premium obtained from an equity pricing model (Crouhy, Mark, and Galai, 2000). Empirical results by Moody’s KMV have shown that the distance to default does a good job in predicting corporate defaults. Furthermore, work by Chan-Lau, Jobert, and Kong (2004) and by Gropp, Vesala, and Vulpes (2006) shows that distance to default predicts banks’ downgrades in developed and emerging market countries.

Once default risk estimates are obtained, it is possible to use them to assess losses under different scenarios or to evaluate the level of systemic risk under stressed scenarios. There are several ways to accomplish this. For instance, standard linear and nonlinear econometric techniques could be used to evaluate how default risk responds to economic fundamentals, which could provide useful input for macro stress tests, as illustrated in the subpart of this book on contingent claims analysis.

The following chapters provide an example on how equity-based indicators can be used to evaluate the resilience of the banking system to a financial crisis and an example of the design of regulatory capital requirements for too-connected-to-fail institutions. The first example by Chan-Lau (Chapter 17) analyzes the impact of the 2008 global financial crisis on the Chilean banking system. The second example, also by Chan-Lau (Chapter 18), introduces the concept of the incremental contribution to systemic risk as a basic building block for the design of regulatory capital requirements. Both studies build from estimates of default probabilities from Moody’s KMV and use CoRisk analysis (see also Chan-Lau, 2009; and Chan-Lau and others, 2009), a variation of CoVaR (Adrian and Brunnermeier, 2008), to evaluate default risk spillovers across financial institutions, though the analyses can easily be extended using network analysis.


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