# Key Terms Explained

## Financial stability

There are numerous definitions of financial stability. Most of them have in common that financial stability is about the absence of system-wide episodes in which the financial system fails to function (crises). It is also about resilience of financial systems to stress.

A stable financial system is capable of efficiently allocating resources, assessing and managing financial risks, maintaining employment levels close to the economy’s natural rate, and eliminating relative price movements of real or financial assets that will affect monetary stability or employment levels. A financial system is in a range of stability when it dissipates financial imbalances that arise endogenously or as a result of significant adverse and unforeseen events. In stability, the system will absorb the shocks primarily via self-corrective mechanisms, preventing adverse events from having a disruptive effect on the real economy or on other financial systems. Financial stability is paramount for economic growth, as most transactions in the real economy are made through the financial system.

The true value of financial stability is best illustrated in its absence, in periods of financial instability. During these periods, banks are reluctant to finance profitable projects, asset prices deviate excessively from their intrinsic values, and payments may not arrive on time. Major instability can lead to bank runs, hyperinflation, or a stock market crash. It can severely shake confidence in the financial and economic system.

### Firm-level stability measures

A common measure of stability at the level of individual institutions is the z-score. It explicitly compares buffers (capitalization and returns) with risk (volatility of returns) to measure a bank’s solvency risk. The z-score is defined as z ≡ (k+µ)/σ, where k is equity capital as percent of assets, µ is return as percent of assets, and σ is standard deviation of return on assets as a proxy for return volatility. The popularity of the z-score stems from the fact that it has a clear (negative) relationship to the probability of a financial institution’s insolvency, that is, the probability that the value of its assets becomes lower than the value of its debt. A higher z-score therefore implies a lower probability of insolvency. Papers that used the z-score for analysis bank stability include Boyd and Runkle (1993); Beck, Demirgüç-Kunt, Levine (2007); Demirgüç-Kunt, Detragiache, and Tressel (2008); Laeven and Levine (2009); Čihák and Hesse (2010).

The z-score has several limitations as a measure of financial stability. Perhaps the most important limitation is that the z-scores are based purely on accounting data. They are thus only as good as the underlying accounting and auditing framework. If financial institutions are able to smooth out the reported data, the z-score may provide an overly positive assessment of the financial institutions’ stability. Also, the z-score looks at each financial institution separately, potentially overlooking the risk that a default in one financial institution may cause loss to other financial institutions in the system. An advantage of the z-score is that it can be also used for institutions for which more sophisticated, market based data are not available. Also, the z-scores allow comparing the risk of default in different groups of institutions, which may differ in their ownership or objectives, but face the risk of insolvency.

Other approaches to measuring institution-level stability are based on the Merton model. It is routinely used to ascertain a firm’s ability to meet its financial obligations and gauge the overall possibility of default. The Merton model (also called the asset value model) treats an institution’s equity as a call option on its held assets, taking into account the volatility of those assets. Put-call parity is used to price the value of the “put,” which is represented by the firm's credit risk. So, the model measures the value of the firm’s assets (weighting for volatility) at the time that the debtholders will “exercise their put option” by expecting repayment. The model defines default as when the value of a firm’s liabilities exceeds that of its assets (in different iterations of the model, the asset/liability level required to reach default is set at a different threshold). The Merton model can calculate the probability of credit default for the firm.

Merton’s model has been modified in subsequent research to capture a wider array of financial activity using credit default swap data. For example, it is part of the KMV model that Moody’s uses to both calculate the probability of credit default and as part of their credit risk management system. The Distance to Default (DD) is another market-based measure of corporate default risk based on Merton’s model. It measures both solvency risk and liquidity risk at the firm level.

### Systemic stability measures

To measure systemic stability, a number of studies attempt to aggregate firm-level stability measures (z-score and distance to default) into a system-wide evaluation of stability, by averaging or by weighting each measure by the institution’s relative size. The shortcoming of these aggregate measures is that they do not take into account the interconnectedness of financial institutions; that is, that one institution’s failure can be contagious.

The First-to-Default probability, or the probability of observing one default among a number of institutions, has been proposed as a measure of systemic risk for large financial institutions. It uses risk-neutral default probabilities from credit default swap spreads. The probability, unlike distance-to-default measures, recognizes that defaults among a number of institutions can be connected. However, studies focusing on probabilities of default tend to overlook the fact that a large institution failing causes bigger ripples than a small one.

Another assessment of financial system stability is Systemic Expected Shortfall (SES), which measures each institution’s individual contribution to systemic risk. SES takes the individual taking leverage and risk-taking into account and measures the externalities from the banking sector to the real economy when these institutions fail. The model is especially good at identifying which institutions are systemically relevant and would have the largest effects, if they fail, on the wider economy. One drawback of the SES method is that it is difficult to determine when the systemically-important institutions are likely to fail.

In further research, the retrospective SES measure was extended to be somewhat predictive. The predictive measure is SRISK. SRISK evaluates the expected capital shortfall for a firm if there is another crisis. To calculate this predictive systemic risk measure, one must first find the Long-Run Marginal Expected Shortfal (LRMES), which measures the relation between a firm’s equity returns and the returns of the broader market (estimated using asymmetric volatility, correlation, and copula). The model estimates the drop in equity value of the firm if the aggregate market falls more than 40 percent in a six-month window to determine how much capital is needed during the simulated crisis in order to achieve an 8 percent capital to asset value ratio. SRISK% measures the firm’s percentage of total financial sector capital shortfall. A high SRISK% simultaneously indicates the biggest losers and contributors to the hypothetical crisis. One of the assumptions of the SES indicator is that a firm is “systemically risky” if it is especially likely to face a capital shortage when the financial sector is weak overall.

Another gauge of financial stability is the distribution of systemic loss, which attempts to fill some of the gaps of the previously-discussed measures. This combines three key elements: each individual institution’s probability of default, the size of loss given default, and the “contagious” nature of defaults across the institutions due to their interconnectedness.

There is also a range of indicators of financial soundness. These include the ratio of regulatory capital to risk-weighted assets and the ratio nonperforming loans to total gross loans. These are reported as part of the “financial soundness indicators” (fsi.imf.org). Variables such as the nonperforming loan ratios may be better known than the z-score, but they are also known to be lagging indicators of soundness (Čihák and Schaeck (2010).

Another alternative indicator of financial instability is “excessive” credit growth, with the emphasis on excessive. A well-developing financial sector is likely to grow. But very rapid growth in credit is one of the most robust common factors associated with banking crises (Demirgüc-Kunt and Detragiache 1997, Kaminsky and Reinhart 1999). Indeed, about 75 percent of credit booms in emerging markets end in banking crises. The credit growth measure also has pros and cons: Although it is easy to measure credit growth, it is difficult to assess ex-ante whether the growth is excessive.

For financial markets, the most commonly used proxy variable for stability is market volatility. Another proxy is the skewness of stock returns, because a market with a more negative skewed distribution of stock returns is likely to deliver large negative returns, and likely to be prone to less stability. Another variable is vulnerability to earnings manipulation, which is derived from certain characteristics of information reported in the financial statements of companies that can be indicative of manipulation. It is defined as the percentage of firms listed on the stock exchange that are susceptible to such manipulation. In the United States, France, and most other high-income economies, less than 10 percent of firms have issues concerning earnings manipulation; in Zimbabwe, in contrast, almost all firms may experience manipulation of their accounting statements. In Turkey, the number is close to 40 percent. Other variables approximating volatility in the stock market are the price-to-earnings ratio and duration, which is a refined version of the price-to-earnings ratio that takes into account factors such as long-term growth and interest rates.

##### Suggested reading:

Beck, Thorsten, Asli Demirgüç-Kunt, and Ross Levine. 2007. "Finance, Inequality and the Poor," *Journal of Economic Growth* 12(1): 27–49.

Boyd, John, and David Runkle. 1993. “Size and Performance of Banking Firms: Testing the Predictions of Theory,” *Journal of Monetary Economics* 31: 47–67.

Čihák, Martin. 2007. “Systemic Loss: A Measure of Financial Stability” *Czech Journal of Economics and Finance*, 57 (1-2): 5-26.

Čihák, Martin, and Heiko Hesse. 2010. "Islamic Banks and Financial Stability: An Empirical Analysis",* Journal of Financial Services Research,* 38 (2-3): 95–113.

Čihák, Martin, Asli Demirgüç-Kunt, Erik Feyen, and Ross Levine. 2012. “Benchmarking Financial Development Around the World.” Policy Research Working Paper 6175, World Bank, Washington, DC.

Cihák, Martin and Schaeck, Klaus, 2010. "How well do aggregate prudential ratios identify banking system problems?" *Journal of Financial Stability*, 6(3): 130-144.

Demirgüç-Kunt, Asli and Enrica Detragiache, 1997, "The Determinants of Banking Crises in Developing and Developed Countries," *IMF Staff Papers*, 45: 81–109.

Demirgüç-Kunt, Asli, Enrica Detragiache, and Thierry Tressel. 2008. "Banking on the Principles: Compliance with Basel Core Principles and Bank Soundness," *Journal of Financial Intermediation* 17(4): 511–42.

Kaminsky, Graciela, and Carmen Reinhart, 1999, “The Twin Crises: The Causes of Banking and Balance of Payments Problems,” *The American Economic Review* 89 (3): 473–500.

Laeven, Luc and Ross Levine, 2009, “Bank Governance, Regulation, and Risk Taking” *Journal of Financial Economics* 93(2): 259–275.

World Bank. 2012. *Global Financial Development Report 2013: Rethinking the Role of the State in Finance*. World Bank, Washington, DC (http://www.worldbank.org/financialdevelopment).