An optimal investment strategy in bank management

This paper considers the application of stochastic optimization theory to asset and capital adequacy management in banking. The Basel II Capital Accord lays down regulations to control bank behaviour, and relies on regulatory ratios such as the capital adequacy ratio (CAR). In an attempt to address the problem of compliance to minimum CAR and under assumptions about retained earnings, loan‐loss reserves, the market and shareholder‐bank owner relationships, we construct a continuous‐time model of the Basel II CAR which is computed from the total risk‐weighted assets (TRWAs) and bank capital in a stochastic setting. In particular, we derive an optimal equity allocation strategy for the bank and monitor the performance of the Basel II CAR under the allocation strategy. Copyright © 2011 John Wiley & Sons, Ltd.     

Optimizing Asset and Capital Adequacy Management in Banking

This paper considers the application of stochastic optimization theory to asset and capital adequacy management in banking. Our study is motivated by new banking regulation that emphasizes risk minimization practices associated with assets and regulatory capital. Our analysis depends on the dynamics of the capital adequacy ratio (CAR), which we compute in a stochastic setting, by dividing regulatory bank capital (RBC) by risk weighted assets (RWAs). Furthermore, we demonstrate how the CAR can be optimized in terms of bank equity allocation and the rate at which additional debt and equity is raised. In either case, the dynamic programming algorithm for stochastic optimization is employed to verify the results. Also, we provide an illustration of aspects of bank management practice in relation to this regulation. Finally, we make a few concluding remarks and discuss possibilities for further research. The research was supported by a generous grant from the National Research Foundation of South Africa under GUN 2069031.     

A multiperiod model for estimating the cost of deposit insurance under the Basel III minimum capital requirement

Under the Basel III regime, a commercial bank is considered adequately capitalized if it maintains a ratio of capital to total risk-weighted assets or capital adequacy ratio (CAR) of at least 8%. We model a commercial bank that complies with Basel III's minimum capital requirement on an interval $[0,T]$ for $T>0$. The bank model is achieved via a specific rate of capital influx that fixes the bank's CAR at the minimum prescribed level of 8%. On the basis of this capital influx rate, we derive models for the bank's asset portfolio and capital dynamics required for maintaining the CAR at the minimum prescribed level. For the aforementioned bank, we further study a deposit insurance (DI) pricing problem with a coverage horizon equal to $T$ years. More specifically, we employ a multiperiod DI pricing model to approximate the cost of DI for the bank on the interval $[0,T]$, where the constant (minimum) CAR is maintained. We study the behaviours of the models leading to the constant (minimum) CAR, and the behaviour of the DI premium estimate by means of numerical simulations. In the simulation study pertaining to the DI premium estimate specifically, we determine the effects of changes in the bank's initial leverage level (deposit-to-asset ratio), the DI coverage horizon, and the volatility of the asset portfolio on the DI premium estimate.     

存款保险费率的敏感性分析及实证检验

资本充足率、存款保险费率是发达国家普遍采用的维持银行稳定的基本措施,一般来说资本充足率越高,则所需的存款保险费率越低,银行为减小成本,都希望在合理控制风险的前提下减少所缴纳的存款保险.本文使用根据期权思想建立的存款保险定价模型,推导了存款保险费率对资本充足率的敏感性系数;其次根据中国上市银行的数据进行测算,分别计算了14家银行每增加一个单位的资本充足率可降低存款保险费率的数额,并对实证的结果进行比较;最后给出相关结论.     

解读巴塞尔协议Ⅱ中内部评级法关于资本要求的计算

鉴于新巴塞尔协议中内部评级法关于资本要求的计算缺乏透明度,本文在归纳总结内部评级法关于资本要求计算的基础上,对资本要求计算的理论依据和统计含义进行了描述和分析。本文指出,资本要求计算的核心内容是Vasicek公式,它可以被解释为单一借款者的条件违约概率,或者单一个充分分散化贷款组合的风险价值。最后,我们对内部评级法关于资本要求计算中存在的一些问题作了简单讨论。     

中国银行系统的宏观审慎监管研究

全球金融危机爆发后,对银行系统实行审慎监管已成为国内外学者及相关监管机构的共识。但目前银行系统的监管研究多为微观审慎监管,宏观审慎监管研究缺乏,尤其是对中国银行网络系统进行动态建模并进行宏观审慎监管的定量研究未见。本文首先利用中国2008至2015年16家上市银行的实际数据构建动态的中国银行网络系统模型,然后使用Component VaR、Incremental VaR、Shapley value EL以及ΔCoVaR四种风险分配机制研究中国银行网络系统的宏观审慎监管方法。研究表明:对中国银行网络系统进行宏观审慎监管能够有效提升其稳定性,并且四种机制相比之下,ΔCoVaR的监管效果最为显著,而Incremental VaR则相对较差。此外,通过宏观审慎资本与银行指标之间的相关性分析,发现Incremental VaR、Shapley value EL以及Component VaR机制下的宏观审慎资本与银行的总资产具有一定的相关性,此时宏观审慎资本可以根据银行的总资产来设置;而ΔCoVaR机制下则不相关,因此宏观审慎资本可以依据各银行的系统性风险贡献大小来设置。     

Regulatory capital decisions in the Context of consumer loan portfolios

A topic of interest in recent literature is regulatory capital requirements for consumer loan portfolios. Banks are required to hold regulatory capital for unexpected losses, while expected losses are to be covered by either provisions or future income. In this paper, we show the set of efficient operating points in the market share and profit space for a portfolio manager operating under Basel II capital requirement and under capital constraints are a union of single-cutoff-score and double-cutoff-score operating points. For a portfolio manager to increase market-share beyond the maximum allowable under a single-cutoff score policy (eg, with binding capital constraints) requires granting loans to higher than optimal risk applicants. We show this result in greater portfolio risk but without an increase in regulatory capital requirement amount. The increase in forecasted losses is assumed to be absorbed by provisions or future margin income. Given portfolio managers take on higher risk under the same regulatory capital amount, our findings call for greater focus on provision amounts and future margin income under the supervisory review pillar of Basel II. This research raises the issue of whether the design of the regulatory formula for consumer loan portfolios is flawed.     

Modeling company failure: a longitudinal study of Turkish banks

Determining the factors related to the financial failure of a company is important. In this paper, we extend literature on bank failure prediction by modelling bank failures in Turkey from 1998 to 2000 using three statistical models combined with a principal component analysis on financial ratios. The three statistical models employed are a logistic regression, a logistic regression that takes serial correlation into account via generalized estimating equations and a marginalized transition model (MTM). Time and financial ratios that are related with capital adequacy and profitability, risk, non-interest income and Fx assets to Fx liabilities are found to be significant in classifying failed banks. Each of our methods achieves a correct classification rate of 93.3%. Among the three models, MTM, which is the soundest model in terms of statistical assumptions, shows slightly better model fit properties.     

Capital adequacy and risk management in banking industry

The present paper deals with the issue of bank capital adequacy and risk management within a stochastic dynamic setting. In particular, an explicit risk aggregation and capital expression is provided regarding the portfolio choice and capital requirements special context. Such a framework leads to a nonlinear stochastic optimal control problem whose solution may be determined by means of dynamic programming algorithm. The pertaining analysis relies heavily on the stochastic dynamic modeling of such balance sheet items as securities, loans, and regulatory capital with stochastic interest rates. In this respect, the special Kalman filter approach is used for the purpose of estimating the model parameters. The reached findings reveal well that the Tunisian bank, subject of study, generally exceeds the minimum requirements and is adequately capitalized to maintain the appropriate capital amount level commensurate with the aggregate risk. Besides, empirical evidence on the regulations' impact on driving bank capitalization and risk‐taking behavior has also been highlighted. Copyright © 2015 John Wiley & Sons, Ltd.     

Impact of insurance for operational risk: Is it worthwhile to insure or be insured for severe losses?

Under the Basel II standards, the Operational Risk (OpRisk) advanced measurement approach allows a provision for reduction of capital as a result of insurance mitigation of up to 20%. This paper studies different insurance policies in the context of capital reduction for a range of extreme loss models and insurance policy scenarios in a multi-period, multiple risk setting. A Loss Distributional Approach (LDA) for modeling of the annual loss process, involving homogeneous compound Poisson processes for the annual losses, with heavy-tailed severity models comprised of α-stable severities is considered. There has been little analysis of such models to date and it is believed insurance models will play more of a role in OpRisk mitigation and capital reduction in future. The first question of interest is when would it be equitable for a bank or financial institution to purchase insurance for heavy-tailed OpRisk losses under different insurance policy scenarios? The second question pertains to Solvency II and addresses quantification of insurer capital for such operational risk scenarios. Considering fundamental insurance policies available, in several two risk scenarios, we can provide both analytic results and extensive simulation studies of insurance mitigation for important basic policies, the intention being to address questions related to VaR reduction under Basel II, SCR under Solvency II and fair insurance premiums in OpRisk for different extreme loss scenarios. In the process we provide closed-form solutions for the distribution of loss processes and claims processes in an LDA structure as well as closed-form analytic solutions for the Expected Shortfall, SCR and MCR under Basel II and Solvency II. We also provide closed-form analytic solutions for the annual loss distribution of multiple risks including insurance mitigation.     

The optimal operational risk capital requirement by applying the advanced measurement approach

The purpose of this paper is to construct a risk quantification model to achieve the accurate operational risk management and gain the satisfying estimation and control of future possible extreme losses by using capital charges to assess operational risk. The paper takes a case bank as the research object and compares the differences under various circumstances engaging the Basic Indicator Approach, the Standardized Approach, and the Advanced Measurement Approach for the operational risk capital requirement of a bank. The results indicate that it is more appropriate to adopt the Advanced Measurement Approach to estimate the operational risk capital requirement; this way can help a bank enjoy a much lessened capital charge required and subsequently its available capital increases. Hence, it allows a bank to have sufficient funds in operations and reduce the burden of capital costs. Therefore, it will bring the positive benefits to the whole banking industry when enforcing the Advanced Measurement Approach.     

Integrated bank risk modeling: A bottom-up statistical framework

In the last few years, according to the evolution of financial markets and the enforcement of international supervisory requirements, an increasing interest has been devoted to risk integration. The original focus on individual risk estimation has been replaced by the growing prominence of top-down and bottom-up risk integration perspectives. Following this latter way, we bring together different approaches developed in the recent literature elaborating a general model to assess banking solvency in both the long-run (economic capital) as well as in the short period (liquidity mismatching). We consider banking capability to face credit, interest rate and liquidity risks associated to macro-economic shocks affecting both assets and liabilities. Following the perspective of commercial banks, we concentrate on information available in the risk management practice to propose an easy to implement statistical framework. We put in place this framework estimating its scenario generation parameters on Italian macro-economic time series from 1990 to 2009. Once applied to a stylized commercial bank, we compare the results of our approach to regulatory capital requirements. We emphasize the need for policy makers as well as risk managers, to take into account the entire balance sheet structure to assess banking solvency.     

The impact of Basel Accords on the lender’s profitability under different pricing decisions

In response to the deficiencies in financial regulation revealed by the global financial crisis a new capital regulatory standard, Basel III, has been introduced. This builds on the previous regulations known as Basel I and Basel II. We look at how the interest rate charged to maximise a lender’s profitability is affected by these three versions of the Basel Accord under three types of pricing: a fixed-price model, a two-price model and a variable risk-based pricing model. We investigate the result under two different scenarios. First, a fixed price of capital, and second, a fixed amount of equity capital available. We develop an iterative algorithm for solving the latter based on solution approaches to the former. The riskiness of the portfolio has more significance than the Basel Accord requirements but the move from Basel I to Basel II has more impact than that from Basel II to Basel III.     

Asset portfolio securitizations and cyclicality of regulatory capital

This paper analyzes the level and cyclicality of regulatory bank capital for asset portfolio securitizations in relation to the cyclicality of capital requirements for the underlying loan portfolio as under Basel II/III. We find that the cyclicality of capital requirements is higher for (i) asset portfolio securitizations relative to primary loan portfolios, (ii) Ratings Based Approach (RBA) relative to the Supervisory Formula Approach, (iii) given the RBA for a point-in-time rating methodology relative to a rate-and-forget rating methodology, and (iv) under the passive reinvestment rule relative to alternative rules. Capital requirements of the individual tranches reveal that the volatility of aggregated capital charges for the securitized portfolio is triggered by the most senior tranches. This is due to the fact that senior tranches are more sensitive to the macroeconomy. An empirical analysis provides evidence that current credit ratings are time-constant and that economic losses for securitizations have exceeded the required capital in the recent financial crisis.     

Estimation error in regulatory capital requirements: theoretical implications for consumer bank profitability

Despite the topic's societal importance and despite progress in bank research, a lack of consensus exists concerning either the desirability of bank regulation or its optimal design. Enforcement of minimum bank capital standards has been shown to enhance bank stability, but also serves as a potential source of incremental costs, some of which are subtle. Such widely ambiguous research results point to the need for theoretical research regarding capital regulation across diverse banking systems. Along the latter lines, consumer bank issues have been generally neglected. This paper theoretically examines the performance implications of misestimating the regulatory capital requirement for a stylised consumer bank. For our stylised consumer bank, we prove that misestimation, irrespective of its direction, results in lower economic profits and, hence, value. Conclusions and implications for future work are drawn.     

A classification problem of credit risk rating investigated and solved by optimisation of the ROC curve

Estimation of probability of default has considerable importance in risk management applications where default risk is referred to as credit risk. Basel II (Committee on Banking Supervision) proposes a revision to the international capital accord that implies a more prominent role for internal credit risk assessments based on the determination of default probability of borrowers. In our study, we classify borrower firms into rating classes with respect to their default probability. The classification of firms into rating classes necessitates the finding of threshold values separating the rating classes. We aim at solving two problems: to distinguish the defaults from non-defaults, and to put the firms in an order based on their credit quality and classify them into sub-rating classes. For using a model to obtain the probability of default of each firm, Receiver Operating Characteristics (ROC) analysis is employed to assess the distinction power of our model. In our new functional approach, we optimise the area under the ROC curve for a balanced choice of the thresholds; and we include accuracy of the solution into the program. Thus, a constrained optimisation problem on the area under the curve (or its complement) is carefully modelled, discretised and turned into a penalized sum-of-squares problem of nonlinear regression; we apply the Levenberg–Marquardt algorithm. We present numerical evaluations and their interpretations based on real-world data from firms in the Turkish manufacturing sector. We conclude with a discussion of structural frontiers, parametrical and computational features, and an invitation to future work.     

Downturn Loss Given Default: Mixture distribution estimation

The internal estimates of Loss Given Default (LGD) must reflect economic downturn conditions, thus estimating the “downturn LGD”, as the new Basel Capital Accord Basel II establishes. We suggest a methodology to estimate the downturn LGD distribution to overcome the arbitrariness of the methods suggested by Basel II. We assume that LGD is a mixture of an expansion and recession distribution. In this work, we propose an accurate parametric model for LGD and we estimate its parameters by the EM algorithm. Finally, we apply the proposed model to empirical data on Italian bank loans.     

Precautionary measures for credit risk management in jump models

Sustaining efficiency and stability by properly controlling the equity to asset ratio is one of the most important and difficult challenges in bank management. Due to unexpected and abrupt decline of asset values, a bank must closely monitor its net worth as well as market conditions, and one of its important concerns is when to raise more capital so as not to violate capital adequacy requirements. In this paper, we model the trade-off between avoiding costs of delay and premature capital raising, and solve the corresponding optimal stopping problem. In order to model defaults in a bank's loan/credit business portfolios, we represent its net worth by Lévy processes, and solve explicitly for the double exponential jump-diffusion process and for a general spectrally negative Lévy process.     

网络结构、资本缓冲与银行系统性风险传染效应——来自2007~2017年中国14个上市商业银行数据

银行体系稳健运行对国民经济健康发展具有重要意义。选取2007~2017年中国14个上市商业银行数据,利用债务矩阵构建银行网络,运用无残差完全分解模型将其分解为网络结构和资本缓冲两个因素,对我国银行系统性风险传染效应研究。结果表明:网络结构与银行系统性风险存在复杂的关联性,而资本缓冲与银行系统性风险有显著负相关关系;在金融危机期间,网络结构是诱导银行系统性风险波动的决定性因素,资本缓冲对降低银行系统性风险有重要作用。此外国有商业银行与其他银行债务关系更为紧密,对系统性金融风险贡献较大,中国银行处于网络结构中重要位置,中国工商银行和中国建设银行处于次重要位置。该结果为资本监管政策和宏观审慎政策有效实施提供了理论依据。     

Assessing performance factors in the UK banking sector: A multicriteria methodology

Further consolidation takes place not only among UK banks but also across borders, since some banks see size as a key factor in remaining competitive in international markets. Therefore, it is interesting to investigate the effectiveness and performance of UK banks. Based on their assets, banks are distinguished into small and large ones and a classification of UK banks in a multivariate environment for the period 1998–2002 takes place. The PAIRCLAS multicriteria methodology is employed to investigate the performance of UK small and large banks over multiple criteria, such as asset quality, capital adequacy, liquidity and efficiency/profitability. A comparison with discriminant analysis (DA) and logistic regression (LR) facilitates the investigation of the relative performance of PAIRCLAS against them. The results of the study determine the key factors that specify the classification of a bank as small or large and provide us with the responsible banking decision makers for future readjustments.