WP/16/158 
            Measuring Concentration Risk  A Partial Portfolio 
                                                Approach 
                                by Pierpaolo Grippa and Lucyna Gornicka 
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                    © 2016 International Monetary Fund                                                        WP/16/158 
                                                          IMF Working Paper 
                                              Monetary and Capital Markets Department 
                            MEASURING CONCENTRATION RISK - A PARTIAL PORTFOLIO APPROACH 
                                                                                                1
                                          Prepared by Pierpaolo Grippa and Lucyna Gornicka  
                                           Authorized for distribution by Michaela Erbenova 
                                                               August 2016 
                    IMF Working Papers describe research in progress by the author(s) and are published 
                    to elicit comments and to encourage debate. The views expressed in IMF Working Papers 
                    are those of the author(s) and do not necessarily represent the views of the IMF, its Executive 
                    Board, or IMF management. 
                                                                ABSTRACT 
                    Concentration risk is an important feature of many banking sectors, especially in emerging and 
                    small economies. Under the Basel Framework, Pillar 1 capital requirements for credit risk do not 
                    cover concentration risk, and those calculated under the Internal Ratings Based (IRB) approach 
                    explicitly exclude it. Banks are expected to compensate for this by autonomously estimating and 
                    setting aside appropriate capital buffers, which supervisors are required to assess and possibly 
                    challenge within the Pillar 2 process. Inadequate reflection of this risk can lead to insufficient 
                    capital levels even when the capital ratios seem high. We propose a flexible technique, based on 
                    a combination of “full” credit portfolio modeling and asymptotic results, to calculate capital 
                    requirements for name and sector concentration risk in banks’ portfolios. The proposed approach 
                    lends itself to be used in bilateral surveillance, as a potential area for technical assistance on 
                    banking supervision, and as a policy tool to gauge the degree of concentration risk in different 
                    banking systems. 
                    JEL Classification Numbers: E44, G21, G32 
                    Keywords: concentration risk, Basel capital requirements, Pillar 2, Credit VaR. 
                    Authors’ E-Mail Address: pgrippa@imf.org, lgornicka@imf.org. 
                    1 The authors wish to thank Andre O. Santos for stimulating the initial work on which this paper is based, as well as 
                    participants of two internal IMF seminars for their useful comments. We also thank Michaela Erbenova for her constant 
                    support throughout this research project. We are grateful to Mr. Som-lok Leung (IACPM) for providing the IACPM-ISDA 
                    dataset and useful instructions, and to Nirmaleen Jayawardane and Rebecca Shyam for their assistance.  
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                Content  Page
                             
        I. Introduction ........................................................................................................................... 4 
        II. Concentration Risk in the Basel Capital Framework ........................................................... 6 
         A. The Asymptotic Single Risk Factor Approach ................................................................ 6 
         B. Name Concentration ......................................................................................................... 8 
         C. Sector Concentration ...................................................................................................... 10 
         D. Treatment of Concentration Risk under Basel II and Basel III ...................................... 10 
        III. A Partial Portfolio Approach to Concentration Risk ........................................................ 12 
        IV. Testing the Approach ........................................................................................................ 13 
         A. Application to a Synthetic Portfolio............................................................................... 13 
         B. Application to Semi-Hypothetical Portfolios ................................................................. 18 
        V. Conclusions ........................................................................................................................ 28 
        References ............................................................................................................................... 30 
         
        Figures 
        1. Partial Portfolio Approach: Credit VaR for Varying m ...................................................... 16 
        2. Granularity Adjustment of Partial Portfolio and G&L (2013) Methods............................. 17 
        3. Partial Portfolio Approach: Credit VaR for Varying m and Different LGD Assumptions 18 
        4. Share of Non-Granular Part of Loan Portfolios .................................................................. 20 
        5. Partial Portfolio Approach for Semi-Hypothetical Portfolios ............................................ 23 
        6. Granularity Adjustment: Partial Portfolio Approach and Gordy and Lütkebohmert ......... 24 
        7. Granularity Adjustment: Partial Portfolio Approach and HHI ........................................... 25 
        8. Distribution of Sectoral Adjustments Across the Semi-Hypothetical Portfolios................ 26 
        9. Sectoral Adjustment and Weighted Average Difference between MKMV and IRB-Based 
           Asset Correlation ............................................................................................................ 27 
        10. Sectoral Adjustments with and without Correlated Draws in the Simulation .................. 27 
         
        Tables 
        1. Characteristics of the IACPM-ISDA Portfolio ................................................................... 14 
        2. Regulatory Capital: Partial Portfolio Method versus IRB Model ....................................... 15 
        3. Characteristics of Semi-Hypothetical Portfolios ................................................................ 19 
        4. Bank Funding of Domestic Companies in Semi-Hypothetical Portfolios .......................... 19 
         
        Appendix ................................................................................................................................. 32 
          
         
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                       I.   INTRODUCTION 
        The concentration risk in banks’ credit portfolios arises mainly from two types of imperfect 
        diversification: “name” and sector concentrations (BCBS, 2006b). Name concentration 
        happens when the idiosyncratic risk cannot be perfectly diversified due to large (relative to 
        the size of the portfolio) exposures to individual borrowers. Sector concentration emerges 
        when the portfolio is not perfectly diversified across sectoral factors, corresponding to 
        systematic components of risk. 
        Concentration risk is relevant for the stability of both individual institutions and whole 
        financial systems. Exposures to large borrowers like Enron and WorldCom contributed to 
        financial problems of several U.S. banks in the early 2000s. A housing crisis combined with 
        concentrated mortgage portfolios resulted in a number of bank failures in Scandinavian 
        countries in the 1990s, and contributed to the global financial crisis of 2007/08.  
        The Internal Ratings Based approach (IRB) of the Basel capital framework is aimed at 
        capturing general credit risk, but does not incorporate explicitly the concentration risk. The 
        IRB formula is based on the Asymptotic Single Risk Factor (ASRF) model derived from the 
        Vasicek (2002) model, which is—in turn—an extension of the Merton (1974) model of 
        firms’ default. The ASRF model has the advantage of being portfolio-invariant, i.e., the 
        capital required for any given loan only depends on the risk of that loan, regardless of the 
        portfolio it is added to. From a regulatory perspective, this property allows the capital charge 
        to be estimated without the need to rely on credit portfolio models. The downside of the 
        model is that it ignores the concentration of exposures in real-world bank portfolios, as the 
        idiosyncratic risk is assumed to be fully diversified. Specifically, the capital charge derived 
        from the ASRF model is the same for banks with different levels of the concentration risk (all 
        other things equal).  In Basel II and in Basel III the concentration risk is covered under Pillar 
        2, focused on interaction between banks’ own evaluations of their capital adequacy (ICAAP) 
        and supervisors’ subsequent review (SREP). Pillar 2 provides a general framework for 
        dealing with concentration risk (and other types of risk not captured by the ASRF model), but 
        banks and regulators have a large degree of freedom in choosing the quantitative tools to 
        measure the additional capital required to cover concentration risk. 
        Several model-based and simulation-based methods for calculating capital charges for 
        concentration risk have been proposed over the years. The model-based techniques, usually 
        use second-order approximations of generalized ASRF formulas, are generally conceptually 
        complex, and are based on analytical results that are strongly dependent on the assumptions 
        made. The simulation-based methods, while relatively straightforward in application, are 
        heavily computer-intensive: in order to obtain stable quantile loss estimates, millions of 
        Monte Carlo (MC) iterations are often needed. 
        In this paper we propose an alternative, “partial portfolio” approach, which tries to extract the 
        best features of the two “worlds” of realistic—but cumbersome—full-portfolio simulations 
        and parsimonious—but inflexible—ASRF approximations. Specifically, within a MC 
        simulation, we maintain the ASRF assumption of diversified idiosyncratic risk for the part of