Financial stability

Firm-level stability measures

The 1968 Altman's z‐score is extensively used in empirical research as a measure of firm-level stability for its high correlation with the probability of default. This measure contrasts buffers (capitalization and returns) with risk (volatility of returns) and has done well at predicting bankruptcies within two years. Despite development of alternative models to predict financial stability, Altman's model remains the most widely used.

An alternate model used to measure institution-level stability is the Merton model (also called the asset value model). It builds on Black-Scholes option pricing theory, and evaluates a firm's ability to meet its financial obligations and gauges the overall possibility of default. In this model, an institution's equity is treated 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 implied “put” option, which represents the firm's credit risk. Ultimately, the model measures the value of the firm's assets (weighted for volatility) at the time that the debtholders exercises their “put option” by expecting repayment. The model estimates distance to default from the gap between a firm's market-valued assets and its liabilities, adjusted for volatility in asset values. In this implementation, the option's strike price is set equal to the firm's current book value of debt.

In subsequent research, the Merton model has been modified to capture a wider array of financial activity using credit default swap data. For example, Moody's KMV-Merton model developed in 1993 by KMV LLC and acquired by Moody's in 2002, applies Merton both to calculate the probability of credit default and as part of their credit risk management system. Distance-to-default (DD) is a market-based measure of default risk derived from Merton's model and popularized by KMV, which KMV used with a proprietary database to map it to real-world probability of default (Expected Default Frequency). Distance-to-default estimates how far the market value of a firm's assets is from the value of its liabilities, adjusted for asset volatility. It has been shown that a naïve DD can be used without solving for an implied probability of default (which involves solving two non-linear equations), and it performs just as well as the computationally intensive KMV iterative approximation method despite less complexity and being transparent since it doesn't require KMV's black-box proprietary data.

Systemic stability measures

There is not yet a singular, standardized model for assessing financial system stability and for examining policies. This is in contrast to most macroeconomic or monetary policy objectives (such as unemployment, economic growth, external or budgetary equilibrium, price stability, etc.) which have widely accepted measurable sets of indicators that define and measure deviations from the objective, such as inflation for price stability.

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, either by taking a simple average or weighing each measure by the institution's relative size. However, these aggregate measures fail to account for correlated risks among financial institutions. In other words, the model fails to consider the inter-connectedness between institutions, and that one institution's failure can lead to a contagion.

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 a group of large financial institutions. This measure looks at risk-neutral default probabilities from credit default swap spreads. Unlike distance-to-default measures, the probability recognizes the interconnectedness among defaults of different institutions. However, studies focusing on probabilities of default tend to overlook the ripper effect caused by the failing of a large institution.

Another assessment of financial system stability is Systemic Expected Shortfall (SES), which measures the contribution to systemic risk by individual institutions. SES considers individual leverage level and measures the externalities created from the banking sector when these institutions fail. The model is especially apt at identifying which institutions are systemically relevant and would impact the most on the economy when it fails. One drawback of the SES method is that it is difficult to determine when the systemically important institutions are likely to fail.

To enhance predictive power, the retrospective SES measure was extended and modified in later research. The enhanced model is called SRISK, which evaluates the expected capital shortfall for a firm in a crisis scenario. To calculate this SRISK, one should first determine the Long-Run Marginal Expected Shortfall (LRMES), which measures the relationship between a firm's equity returns and the market's return (estimated using asymmetric volatility, correlation, and copula). Then, the model estimates the drop in the firm's equity value if the aggregate market experiences a 40% or larger fall in a six-month period to determine how much capital is needed in order to achieve an 8% capital to asset value ratio. In other words, SRISK gives insights into the firm's percentage of total financial sector capital shortfall. A high SRISK % indicates the biggest losers when a crisis strikes. One implication of the SES indicator is that a firm is considered “systemically risky” if it faces a high probability of capital shortage when the financial sector is weak.

Another gauge of financial stability is the distribution of systemic loss, which attempts to fill some of the gaps of the aforementioned measures. This measure incorporates three key elements: each individual institution's probability of default, the size of loss given a default, and the contagion resulting from defaults interconnected institutions.