In this work, we present a methodology for measuring and optimizing the credit risk of a loan portfolio taking into account the non-normality of the credit loss distribution. In particular, we aim at modelling accurately joint default events for credit assets. In order to achieve this goal, we build the loss distribution of the loan portfolio by Monte Carlo simulation. The times until default of each obligor in portfolio are simulated following a copula-based approach. In particular, we study four different types of dependence structure for the credit assets in portfolio: the Gaussian copula, the Student's t-copula, the grouped t-copula and the Clayton n-copula (or Cook-Johnson copula). Our aim is to assess the impact of each type of copula on the value of different portfolio risk measures, such as expected loss, maximum loss, credit value at risk and expected shortfall. In addition, we want to verify whether and how the optimal portfolio composition may change utilizing various types of copula for describing the default dependence structure. In order to optimize portfolio credit risk, we minimize the conditional value at risk, a risk measure both relevant and tractable, by solving a simple linear programming problem subject to the traditional constraints of balance, portfolio expected return and trading. The outcomes, in terms of optimal portfolio compositions, obtained assuming different default dependence structures are compared with each other. The solution of the risk minimization problem may suggest us how to restructure the inefficient loan portfolios in order to obtain their best risk/return profile. In the absence of a developed secondary market for loans, we may follow the investment strategies indicated by the solution vector by utilizing credit default swaps.(J.E.L.: C61, C63, G11).
In this paper, we quantify the contribution to systemic risk of a single financial institution by utilizing a analytical framework based on the principles of Extreme Value Theory (EVT) for modelling the marginal distributions and on the properties of copula functions for describing the dependence structure between the financial system and the single financial institution. Among the several systemic risk measures proposed nowadays by academics and estimated by public data, we choose to adopt as systemic risk metric the Conditional Value‐at‐Risk (CoVaR). We select a co‐risk measure like the CoVaR because of its macro‐dimension that allows us to integrate the dependence structure of the single financial institution and of the whole financial system in the systemic risk measurement. While the copula functions have been utilized in some pioneer studies on this area, the EVT principles have not yet been implemented in such a context of systemic risk contribution measurement.
This work aims to illustrate an advanced quantitative methodology for measuring the credit risk of a loan portfolio allowing for diversification effects. Also, this methodology can allocate the credit capital coherently to each counterparty in the portfolio. The analytical approach used for estimating the portfolio credit risk is a binomial type based on a Monte Carlo Simulation. This method takes into account the default correlations among the credit counterparties in the portfolio by following a copula approach and utilizing the asset return correlations of the obligors, as estimated by rigorous statistical methods. Moreover, this model considers the recovery rates as stochastic and dependent on each other and on the time until defaults. The methodology utilized for coherently allocating credit capital in the portfolio estimates the marginal contributions of each obligor to the overall risk of the loan portfolio in terms of Expected Shortfall (ES), a risk measure more coherent and conservative than the traditional measure of Value-at-Risk (VaR). Finally, this advanced analytical structure is implemented to a hypothetical, but typical, loan portfolio of an Italian commercial bank operating across the overall national country. The national loan portfolio is composed of 17 sub-portfolios, or geographic clusters of credit exposures to 10,500 non-financial firms (or corporates) belonging to each geo-cluster or sub-portfolio. The outcomes, in terms of correlations, portfolio risk measures and capital allocations obtained from this advanced analytical framework, are compared with the results found by implementing the Internal Rating Based (IRB) approach of Basel II and III. Our chief conclusion is that the IRB model is unable to capture the real credit risk of loan portfolios because it does not take into account the actual dependence structure among the default events, and between the recovery rates and the default events. We underline that the adoption of this regulatory model can produce a dangerous underestimation of the portfolio credit risk, especially when the economic uncertainty and the volatility of the financial markets increase.
This research examines and compares the performances in terms of systemic risk ranking for three different systemic risk metrics based on daily frequency publicly available data, specifically: Marginal Expected Shortfall (ES), Component Expected Shortfall (CES) and Delta Conditional Value-at-Risk (ΔCoVaR). We compute ΔCoVaR, MES and CES by utilizing EVT principles for modelling marginal distributions and Student’s t copula for describing the dependence structure between every bank and the banking system. Our objective is to attest whether different systemic risk metrics detect the same banks as systemically dangerous institutions with refer to a sample of European banks over the time span 2004-2015. For each bank in the sample we also calculate three traditional market risk measures, like Market VaR, Sharpe’s beta and the correlation between every bank and the banking system (European STOXX 600 Banks Index). Another aim is to explore the existence of a link among systemic risk measures and traditional risk metrics. In addition, the classification results obtained by the different risk metrics are compared with the ranking in terms of systemic riskiness (for European banks) calculated by Financial Stability Board (2015) using end-2014 data and collected in its list of Global Systemically Important Banks (G-SIBs). With refer to the entire sample period, we find a good coherence of ranking results among the three different systemic risk metrics, in particular between CES and ΔCoVaR. Moreover, we find for MES and ΔCoVaR a strong linkage with beta and correlation metrics respectively. Finally, CES metric shows the highest level of concordance with the list of G-SIBs by FSB with refer to European banks.
In this work we propose a new prospective model for testing the economic hedge effectiveness. Our model is derived from the initial approach based on the measure of the relative risk reduction (RRR) where the risk is expressed by the standard deviation and a Normal world is assumed. Differently, our model estimates the RRR produced by the hedging strategy in terms of the new risk measures of the value at risk (VaR) and the expected shortfall (ES). Moreover, it fails the traditional hypothesis of a normal distribution for the risk factors generating their return scenarios by Monte Carlo simulation. Because the main hedging issue especially for financial institutions is the portfolio hedging, our model has been implemented to a market risk hedging strategy, the cross hedging, realized by combining a stock index future (short position) with a stock portfolio (long position). We underline that, while our results present a strong significance from an economic viewpoint, they may be utilized only in an experimental way for hedge accounting purposes.(J.E.L.: G17, G32, C15).
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