A Discussion on Recent Risk Measures with Application to Credit Risk: Calculating Risk Contributions and Identifying Risk Concentrations

Abstract

In both financial theory and practice, Value-at-risk (VaR) has become the predominant risk measure in the last two decades. Nevertheless, there is a lively and controverse on-going discussion about possible alternatives. Against this background, our first objective is to provide a current overview of related competitors with the focus on credit risk management which includes definition, references, striking properties and classification. The second part is dedicated to the measurement of risk concentrations of credit portfolios. Typically, credit portfolio models are used to calculate the overall risk (measure) of a portfolio. Subsequently, Euler's allocation scheme is applied to break the portfolio risk down to single counterparties (or different subportfolios) in order to identify risk concentrations. We first carry together the Euler formulae for the risk measures under consideration. In two cases (Median Shortfall and Range-VaR), explicit formulae are presented for the first time. Afterwards, we present a comprehensive study for a benchmark portfolio according to Duellmann and Masschelein (2007) and nine different risk measures in conjunction with the Euler allocation. It is empirically shown that-in principle-all risk measures are capable of identifying both sectoral and single-name concentration. However, both complexity of IT implementation and sensitivity of the risk figures w.r.t. changes of portfolio quality vary across the specific risk measures.

The Truncated Burr X-G Family of Distributions: Properties and Applications to Actuarial and Financial Data

“…Furthermore, the series expansions determined in Equations ( 14) and ( 15) can be used to provide sum approximations of these risk measures. We refer the reader to [42,43] for a detailed description of them.…”

“…The graphical demonstration of the models in Figures 10 and 11 also reveals that the proposed model is heavier than the BX, EE, EW, W, and E models. See [43,47] for a detailed discussion of VaR q and ES q and their calculation using the R-Statistical Computing Environment.…”

A Comprehensive Stability Indicator for Banks

“…The z-score (Laeven and Levine 2009;Lepetit and Strobel 2013;Doumpos et al 2015) includes capital to assets (leverage) and return on assets (ROA), a far lower number of indicators (two) than those of the IMF. Value at Risk (VaR), which measures maximum losses at a given level of confidence has become a predominant measure of risk among banks given its incorporation into Basel Regulatory requirements (see (Fischer et al 2018) for a comprehensive evaluation of VaR techniques). (Powell 2017) compares small and large banks from Malaysia to the overall ASEAN region using NPLs and conditional distance to default CDD (a tail risk measure of default) to show that larger banks are generally of lower risk than smaller banks.…”

Quantifying Risk in Traditional Energy and Sustainable Investments

“…It is therefore important to model these price fluctuations and implement an effective tool for managing energy price risk. VaR has become a popular risk measure in the financial industry among many other alternative risk measures (e.g., [3,4]). The internal model approach under the Basel II framework proposes VaR as a risk measure to gauge the amount of assets needed to cover possible losses, that is, the minimum regulatory capital requirements.…”