A Review of Individual and Systemic Risk Measures in Terms of Applicability for Banking Regulations

The latest financial crisis has exposed substantial weaknesses in the bank risk models used by national regulators as well as the Basel Accords. The study is aimed at presenting the evolution and critique of risk measures and risk models in banking, with a special focus on the dynamically developing area of systemic risk measures. A discussion of the features of the respective measures allows us to draw conclusions for banking regulations based on the analyzed models and to present the main challenges for regulators in terms of bank risk measurement. The study shows that substantial challenges for regulators include compensating for the drawbacks of the Value at Risk (VaR) and expected shortfall risk models, resolving the pro-cyclicality in risk modeling, improving the techniques of stress testing, and addressing the fallacy of composition in banking (i.e., to model risk from a systemic point of view and not only from the perspective of an individual bank). As the discussion concerning proper risk measurement in regulatory frameworks, such as the Basel Accord or the European Banking Authority’s (EBA) rules is in progress, the topic seems to be of particular importance; moreover, measures of systemic risk are not yet a subject of regulation.


Introduction
For decades, bank risk modeling has been a challenge for managers of financial institutions and regulating authorities. The latest financial crisis has unleashed substantial weaknesses of the risk models used by national supervisors and the Basel Accords. These models are too arbitrary to evaluate the risk profiles of large banks. As such, they are prone to pro-cyclicality, which has contributed to incorrect risk measurement. Banking regulations derived from these models focus solely on individual bank risk without regard to the fallacy of composition problem; that is, even if individual banks function well, the banking system can fail. Hence, the focus of post-crisis regulations has shifted from a micro-prudential approach of banking supervision to a macro-prudential one.
in banking, with a special focus on the dynamically developing area of systemic risk measurement. The discussion of the features of each measure allows to draw conclusions for banking regulations that are based on the mentioned models and to present the main challenges for regulators in terms of bank risk measurement. Because the measures capable of counteracting systemic risk are currently not a subject of regulation, this topic seems to be of particular importance.
The paper is structured as follows: the first section reviews the individual bank risk measures, the second presents the risk models based on the mentioned measures, and the third section focuses on systemic risk measurement.

Review of risk measures
Banking risk includes credit risk, market risk (i.e., the risk of price changes), and operational risk (i.e., related to the banks general activity). The measurement and quantification of the various risk types has been a substantial challenge for academics, bank managers, and regulators.
In  While there is no definition of how to compute VaR, its estimation requires assumptions about the profit and loss density function. To estimate the potential loss on a portfolio, the probability distributions of individual risks, as well as their correlation and their effect on the value of the potential loss, have to be defined, resulting in arbitrary risk modeling. Three solutions are applied to address this problem: estimation based on past values of the parameters, Monte Carlo methods, which require an assumption about the distribution of the portfolio values, and analytic methods, which are based on assumptions about the return distribution parameters (Damodaran, 2010 Value at risk (CVaR), also known as expected shortfall.
The expected shortfall concept has substantial theoret-A review of individual and systemic risk measures in terms of applicability for banking regulations ical foundations (Acerbi & Tasche, 2002;Rockafellar & Uryasev, 2002;Yamai & Yoshiba, 2005). Its popularity among bank managers and regulators has increased.
Because of its coherence, the Basel Committee included this concept, rather than the VaR used over the last decade, in its new regulatory framework Basel III (Chen, 2014 2012). According to the Basel Committee, the methodology banks use to identify a stressed period that is relevant to their current portfolios is either formulaic or judgment-based, which enables them to make arbitrary choices. It has been stressed in the literature that past events and crises are not a good indicator of future bank performance (Chen, 2014). During a financial crisis, the volatility of market prices rises to extreme levels, which causes the correlation of returns used in the VaR methodology to deviate from historical values.
The concept of stressed VaR lacks theoretical underpinnings; consequently, its discussion in the academic literature is sparse.
The Basel Committee has tried to introduce a risk measure that would be resistant to fragility during periods of extreme financial stress and easily backtested.
In these terms, the concepts proposed in Basel 2.5 and in Basel III are contradictory; they highlight the conflict between the elicit VaR and coherent expected shortfall. (Chen, 2014). Alternative risk measures to VaR are considered to be technological leaders; as a consequence, their popularity in the banking sector has increased (BCBS, 2011).

Review of risk models in banking regulations
The risk measures discussed are the basis for risk modeling for financial institutions and regulating agencies.
A large number of risk models are derived from the Basel Accords.
The first Basel Accord from 1988 focuses on credit risk models attributed to the respective types of asset groups. The changes in the scope of banking activity enabled by deregulation make it apparent that regulators have to account for both credit and market risk. The Market Risk Amendment from 1996 introduces additional capital charges for banks' assets that are exposed to market risk. The capital requirements have been computed on the basis of two alternative models: the standardized approach or internal bank risk models. The former applies ready formulas for capital charges drawn from regulations, the latter uses VaR models that have been developed by the banks themselves and approved by the supervisory authorities. While the standardized approach is have seen in the subprime crisis, shocks tend to originate locally and spread globally (Slovik, 2012).
An additional challenge for regulators is the aggregation of risk types into risk indicators that allow for the formulation of capital requirements. One way to do this is to take the sum of the computed capital requirements for credit, market, and operational risk. This approach ignores portfolio invariance i.e., it does not account for diversification benefits. Another way is to estimate all the risks within an integrated framework that accounts for possible correlations and interactions (BCBS, 2011).
These empirical models are used for regulatory purposes and are abstract from the theoretically funded models prevalent in academic literature. Popular models that assess bank risk are accounting-based models (Altman, 1968;Ohlson, 1980) or the structural distance to default model (Merton, 1974). The academic models rely on the cost of debt, rather than default data, to assess the bankruptcy risk. The rationale behind this approach is that some banks never experi-ence bankruptcy. In addition, the lag between estimated and actual default can differ among banks such that quantifying default data may be problematic (Mansi, Maxwell & Zhang 2010).
The historically most significant model used for assessment of financial distress is the distance to default model (Merton 1974). The model extends the option pricing formula to predict company defaults. An advantage of this model is that it is not sensitive to the leverage ratio of other models that are aimed at estimating the probability of default (Mansi et al. 2010). Gropp, Vesala and Vulpes (2006)   If market players anticipate higher risk in the future, they will act upon this assumption, which contributes to market volatility. Patro, Qi, and Sun (2013) Acharya et al. (2010) Marginal expected shortfall-the average return of each institution, based on high frequency data, measured over the worst 5% of the sample period.

Systemic risk measures
Systemic expected shortfall-the propensity of an institution to be undercapitalized when the whole system is undercapitalized.
Leverage, expected loss. Expected capital shortage of a firm during a crisis as indication for the institutions' contribution to system wide capital shortage.
Leverage, size and marginal expected shortfall.
De Jonghe (2010) The tail beta i.e., the probability of a decrease in a bank's stock price in the case of a banking index crash computed via extreme value analysis.
Micro approach. The probability computed for each institution.