Bank Capital Regulation of Trading Portfolios: An Assessment of the Basel Framework

In setting minimum capital requirements for trading portfolios, the Basel Committee on Banking Supervision (1996, 2011a, 2013) initially used Value‐at‐Risk (VaR), then both VaR and stressed VaR (SVaR), and most recently, stressed Conditional VaR (SCVaR). Accordingly, we examine the use of SCVaR to measure risk and set these requirements. Assuming elliptically distributed asset returns, we show that portfolios on the mean‐SCVaR frontier generally lie away from the mean‐variance (M‐V) frontier. In a plausible numerical example, we find that such portfolios tend to have considerably higher ratios of risk (measured by, e.g., standard deviation) to minimum capital requirement than those of portfolios on the M‐V frontier. Also, we find that requirements based on SCVaR are smaller than those based on both VaR and SVaR but exceed those based on just VaR. Finally, we find that requirements based on SCVaR are less procyclical than those based on either VaR or both VaR and SVaR. Overall, our paper suggests that the use of SCVaR to measure risk and set requirements is not a panacea.     

The Basel Committee proposals for a new capital accord: implications for Italian banks

Following a few general considerations on the recently proposed revision of the Basel Agreement on capital adequacy, this paper focuses on the first pillar of the Basel Committee proposals, the handling of capital requirements for credit risk in the banking book. The Basel Committee envisages an approach alternatively based on external ratings or on internal rating systems for the determination of the minimum capital requirement related to bank loan portfolios. This approach supports a system of capital requirements that is more sensitive to credit risk. On the basis of specific assumptions, these requirements provide a measure of the value at risk (VaR) produced by models used by major international banks. We first address the impact of the standardised and (internal ratings-based) IRB foundation approach using general data on Italian banks loans' portfolios default rates. We then simulate the impact of the proposed new rules on the corporate loan portfolios of Italian banks, using the unique data set of mortality rates recently published by the Bank of Italy. Three main conclusions emerge from the analysis: (i) the standardised approach implicitly penalizes Italian banks in their interbank funding as their rating is generally below AA/Aa, (ii) the average default rate experienced by Italian banks is higher than the one implied in the benchmark risk weight (BRW) proposed by the Basel Committee for the IRB foundation approach, thereby potentially leading to an increase in the regulatory risk weights, and (iii) the risk-weight is based on an average asset correlation that is significantly higher than the one historically recorded within the Italian banks' corporate borrowers. These findings support the need for a significant revision of the basic inputs and assumptions of the Basel proposals. Finally, in relation to the conditions that allow the capital market to effectively discipline banks, we comment on the proposals advanced in relation to the third pillar of the new capital adequacy scheme.     

Credit risk in the leasing industry

This paper is devoted to the credit risk modeling issues of retail lease portfolios. Using a re-sampling method, I estimate the probability density function of losses and VaR measures in a portfolio of 46,732 leases issued between 1990 and 2000 by a major European financial institution. My results show that physical collaterals play a major role in reducing the credit risk associated with lease portfolios. However, because of insufficient recognition of such collaterals under the new regulatory capital framework (Basel II), significant differences are observed between the estimated capital requirements and those calculated in accordance with the various Basel II approaches.     

Capital adequacy rules, catastrophic firm failure, and systemic risk

This paper studies capital adequacy rules based on Value-at-Risk (VaR), leverage ratios, and stress testing. VaR is the basis of Basel II, and all three approaches are proposed in Basel III. This paper makes three contributions to the literature. First, we prove that these three rules provide an incentive to increase the probability of catastrophic financial institution failure. Collectively, these rules provide an incentive to increase (not decrease) systemic risk. Second, we argue that an unintended consequence of the Basel II VaR capital adequacy rules was the 2007 credit crisis. Third, we argue that to reduce systemic risk, a new capital adequacy rule is needed. One that is based on a risk measure related to the conditional expected loss given insolvency.     

Capital shocks, bank asset allocation, and the revised Basel Accord

In contrast to the 1988 Basel Accord (Basel I), the revised risk-based capital standards (Basel II) propose regulatory capital requirements based on credit ratings. This paper develops a theoretical model to analyze how banks will adjust their low and high credit risk commercial loans under the proposed newer standard. Capital-constrained banks respond to an adverse capital shock by reducing high credit risk loans, while under certain circumstances, low credit risk loans may actually increase. When compared to Basel I, it is shown that high-risk loans are reduced more under Basel II, but whether a bank reduces total lending more under Basel I or under the revised standards depends on a complex interaction of factors.     

Capital requirements under the credit risk-based framework

This work aims to study the hypothesis of lower capitalization of banks under the risk-based rules introduced in Basel II. In this sense, an assessment of the impact of these rules on the capital requirements for non-financial firms’ credit risk is performed. A comparison with Basel I is presented and intervals of variation for the risk drivers such that capital requirements exceed the ones under Basel I are established. Data for a European country supports the hypothesis of a smaller capitalization of banks under the risk-based framework, as far as credit risk in concerned.     

Copula‐Based Formulas to Estimate Unexpected Credit Losses (The Future of Basel Accords?)

The model used to estimate the capital required to cover unexpected credit losses in financial institutions (Basel II) has some drawbacks that reduce its ability to capture potential joint extreme losses in downturns. This paper suggests an alternative approach based on Copula Theory to overcome such flaws. Similarly to Basel II, the suggested model assumes that defaults are driven by a latent variable which varies as a response to an unobserved factor. On the other hand, the use of copulas allows the identification of asymmetric dependence between defaults which has been registered in the literature. As an example, a specific copula family (Clayton) is adopted to represent the association between the latent variables and a formula to estimate potential unexpected losses at a certain level of confidence is derived. Simulations reveal that, in most of the cases, the alternative model outperforms Basel II for portfolios with right‐tail‐dependent probabilities of default (supposedly, a good representation for real loan portfolios).     

Minimizing Basel III Capital Requirements with Unconditional Coverage Constraint

The new Basel III framework increases the banks’ market risk capital requirements. In this paper, we introduce a new risk management approach based on the unconditional coverage test to minimize the regulatory capital requirements. Portfolios optimized with our new minimum capital constraint successfully reduce the Basel III market risk capital requirements. In general, portfolios with value-at-risk and conditional-value-at-risk objective functions and underlying empirical distribution yield better portfolio risk profiles and have lower capital requirements. For the optimization we use the threshold-accepting heuristic and the common trust-region search method.     

Private equity and regulatory capital

Regulatory capital requirements for European banks have been put forward in the Basel II Capital Framework and subsequently in the capital requirements directive (CRD) of the EU. We provide a detailed discussion of the capital requirements for private equity investments under different approaches. For the internal model approach we present a structural model that we calibrate to a proprietary dataset. We modify the standard Merton structural model to make it applicable in practice and to capture stylized facts of private equity investments. We also implement the early default feature with a fast simulation algorithm. Our results support capital requirements lower than in Basel II, but not as low as in CRD, thereby giving adverse incentives to banks for using advanced risk models. A sensitivity analysis shows that this finding is robust to parameter uncertainty and stress scenarios.     

An Assessment of Basel II Procyclicality in Mortgage Portfolios

In this paper we develop a probability of default (PD) model for mortgage loans, taking advantage of the Spanish Credit Register, a comprehensive database on loan characteristics and credit quality. From that model, we calculate different types of PDs: point in time, PIT, through the cycle, TTC, average across the cycle and acyclical. Then, we compare capital requirements coming from the different Basel II approaches. We show that minimum regulatory capital under Basel II can be very sensitive to the risk measurement methodology employed. Thus, the procyclicality of regulatory capital requirements under Basel II is an open question, depending on the way internal rating systems are implemented and their output is utilised. We focus on the mortgage portfolio since it is one of the most under researched areas regarding the impact of Basel II and because it is one of the most important of banks’ portfolios.     

Extending the Basel II approach to estimate capital requirements for equity investments

Under the Basel II banking regulatory capital regime the capital requirements for credit exposures are calculated using the Asymptotic Single Risk Factor (ASRF) approach. The capital requirement is taken to be the contribution of an exposure to the unexpected loss on the bank’s diversified portfolio. Here we extend this approach to calculate capital requirements for equity investments. We show that in the case when asset values have a normal distribution an analytical formula for the unexpected loss contribution may be developed. We show that the capital requirements for equity investments are quite different to those of credit exposures, since equity investments can suffer substantial loss of value even when the underlying company has not defaulted.     

Financial crisis,Value-at-Risk forecasts and the puzzle of dependency modeling

Forecasting Value-at-Risk (VaR) for financial portfolios is a crucial task in applied financial risk management. In this paper, we compare VaR forecasts based on different models for return interdependencies: volatility spillover (Engle & Kroner, 1995), dynamic conditional correlations (Engle, 2002, 2009) and (elliptical) copulas (Embrechts et al., 2002). Moreover, competing models for marginal return distributions are applied. In particular, we apply extreme value theory (EVT) models to GARCH-filtered residuals to capture excess returns.Drawing on a sample of daily data covering both calm and turbulent market phases, we analyze portfolios consisting of German Stocks, national indices and FX-rates. VaR forecasts are evaluated using statistical backtesting and Basel II criteria. The extensive empirical application favors the elliptical copula approach combined with extreme value theory (EVT) models for individual returns. 99% VaR forecasts from the EVT-GARCH-copula model clearly outperform estimates from alternative models accounting for dynamic conditional correlations and volatility spillover for all asset classes in times of financial crisis.     

Stress testing credit risk: The Great Depression scenario

By employing Moody’s corporate default and rating transition data spanning the last 90 years we explore how much capital banks should hold against their corporate loan portfolios to withstand historical stress scenarios. Specifically, we will focus on the worst case scenario over the observation period, the Great Depression. We find that migration risk and the length of the investment horizon are critical factors when determining bank capital needs in a crisis. We show that capital may need to rise more than three times when the horizon is increased from 1 year, as required by current and future regulation, to 3 years. Increases are still important but of a lower magnitude when migration risk is introduced in the analysis. Further, we find that the new bank capital requirements under the so-called Basel 3 agreement would enable banks to absorb Great Depression-style losses. But, such losses would dent regulatory capital considerably and far beyond the capital buffers that have been proposed to ensure that banks survive crisis periods without government support.     

Backtesting value-at-risk based on tail losses

Extreme losses caused by leverage and financial derivatives highlight the need to backtest Value-at-Risk (VaR) based on the sizes of tail losses, because the risk measure currently used disregards losses beyond the VaR boundary. While Basel II backtests VaR by counting the number of exceptions, this paper proposes to use the saddlepoint technique by summing the sizes of tail losses. Monte Carlo simulations show that the technique is extremely accurate and powerful, even for small samples. Empirical applications for the proposed backtest find substantial downside tail risks in S&P 500, and demonstrate that risk models which account for jumps, skewed and fat-tailed distributions failed to capture the tail risk during the 1987 stock market crash. Finally, the saddlepoint technique is used to derive a multiplication factor for any risk capital requirement that is responsive to the sizes of tail losses.     

Loan pricing under Basel capital requirements

We analyze the loan pricing implications of the reform of bank capital regulation known as Basel II. We consider a perfectly competitive market for business loans where, as in the model underlying the internal ratings based (IRB) approach of Basel II, a single risk factor explains the correlation in defaults across firms. Our loan pricing equation implies that low risk firms will achieve reductions in their loan rates by borrowing from banks adopting the IRB approach, while high risk firms will avoid increases in their loan rates by borrowing from banks that adopt the less risk-sensitive standardized approach of Basel II. We also show that only a very high social cost of bank failure might justify the proposed IRB capital charges, partly because the net interest income from performing loans is not counted as a buffer against credit losses. A net interest income correction for IRB capital requirements is proposed.     

Bank size and risk-taking under Basel II

We analyze the relationship between bank size and risk-taking under the Basel II Capital Accord. Using a model with imperfect competition and moral hazard, we show that the introduction of an internal ratings based (IRB) approach improves upon flat capital requirements if the approach is applied uniformly across banks and if the costs of implementation are not too high. However, the banks’ right to choose between the standardized and the IRB approaches under Basel II gives larger banks a competitive advantage and, due to fiercer competition, pushes smaller banks to take higher risks. This may even lead to higher aggregate risk-taking.     

An analysis of VaR-based capital requirements

We study the behavior of a financial institution subject to capital requirements based on self-reported VaR measures, as in the Basel Committee's Internal Models Approach. We view these capital requirements and the associated backtesting procedure as a mechanism designed to induce financial institutions to reveal the risk of their investments and to support this risk with adequate levels of capital. Accordingly, we consider the simultaneous choice of an optimal dynamic reporting and investment strategy. Overall, we find that VaR-based capital requirements can be very effective not only in curbing portfolio risk but also in inducing revelation of this risk.     

Empirical analysis of the average asset correlation for real estate investment trusts

The credit risk capital requirements within the current Basel II Accord are based on the asymptotic single risk factor (ASRF) approach. The asset correlation parameter, defined as an obligor's sensitivity to the ASRF, is a key driver within this approach, and its average values for different types of obligors are to be set by regulators. Specifically, for commercial real estate (CRE) lending, the average asset correlations are to be determined using formulas for either income-producing real estate or high-volatility commercial real estate. In this paper, the value of this parameter was empirically examined using portfolios of U.S. publicly-traded real estate investment trusts (REITs) as a proxy for CRE lending more generally. CRE lending as a whole was found to have the same calibrated average asset correlation as corporate lending, providing support for the recent U.S. regulatory decision to treat these two lending categories similarly for regulatory capital purposes. However, the calibrated values for CRE categories, such as multi-family residential or office lending, varied in important ways. The comparison of calibrated and regulatory values of the average asset correlations for these categories suggests that the current regulatory formulas generate parameter values that may be too high in most cases.     

Ratings-based credit risk modelling: An empirical analysis

Banks have recently developed new techniques for gauging the credit risk associated with portfolios of illiquid and defaultable instruments. These techniques could revolutionise banks' management of credit risk and could in the longer term serve as a more risk-sensitive basis for calculating regulatory capital on banks' loan books than in Basel 2, the new regulatory capital framework. In this paper we implement a popular credit risk model that exploits the information in credit ratings to determine a portfolio's value-at-risk. Using price data on large eurobond portfolios, we assess, on an out-of-sample basis, how well the model tracks the risks it is supposed to measure.     

Capital Allocation for Portfolio Credit Risk

Capital allocation rules are derived that maximize leverage while maintaining a target solvency rate for credit portfolios where risk is driven by a single common factor and idiosyncratic risk is fully diversified. Equilibrium conditions ensure that capital allocations depend on interest earnings as well as credits’ probability of default, endogenous loss given default, and asset correlation. Capitalization rates exceed those estimated using Gaussian credit loss models. Results demonstrate that credit risk is undercapitalized by the Basel II AIRB approach in part because of ambiguities regarding the definition of loss given default. An alternative proposed capital rule removes this bias.