nep-rmg New Economics Papers
on Risk Management
Issue of 2012‒11‒11
23 papers chosen by
Stan Miles
Thompson Rivers University

  1. The Risk Map: A New Tool for Validating Risk Models By Gilbert Colletaz; Christophe Hurlin; Christophe Pérignon
  2. Has the Basel Accord Improved Risk Management During the Global Financial Crisis? By Michael McAleer; Juan-Angel Jimenez-Martin; Teodosio Perez-Amaral
  3. A Theoretical and Empirical Comparison of Systemic Risk Measures By Sylvain Benoit; Gilbert Colletaz; Christophe Hurlin; Christophe Pérignon
  4. Credit risk in general equilibrium By Jürgen Eichberger; Klaus Rheinberger; Martin Summer
  5. Endogeneous Risk in Monopolistic Competition By Vladislav Damjanovic
  6. Bank ratings: what determines their quality? By Harald Hau; Sam Langfield; David Marqués-Ibáñez
  7. Margin Backtesting By Christophe Hurlin; Christophe Pérignon
  8. Common factors in credit defaults swaps markets By Yi-Hsuan Chen; Wolfgang Karl Härdle; ;
  9. Implied probabilities of default from Colombian money market spreads: The Merton Model under equity market informational constraints By Carlos León
  10. The role of the Model Validation function to manage and mitigate model risk By Alberto Elices
  11. The "A+B/u" rule for discrete and continuous time risk models with dependence By Christophe Dutang; Claude Lefèvre; Stéphane Loisel
  12. Uniqueness of Kusuoka Representations By Alois Pichler; Alexander Shapiro
  13. On bounding credit event risk premia By Jennie Bai; Pierre Collin-Dufresne; Robert S. Goldstein; Jean Helwege
  14. Covered bonds, core markets, and financial stability By Kartik Anand; James Chapman; Prasanna Gai;
  15. The Volatility-Return Relationship:Insights from Linear and Non-Linear Quantile Regressions By David E Allen; Abhay K Singh; Robert J Powell; Michael McAleer; James Taylor; Lyn Thomas
  16. Why ruin theory should be of interest for insurance practitioners and risk managers nowadays By Stéphane Loisel; Hans-U. Gerber
  17. Bailouts, Contagion, and Bank Risk-Taking By LEV RATNOVSKI; Giovanni Dell'Ariccia
  18. Challenges in Identifying and Measuring Systemic Risk By Lars Peter Hansen
  19. Clearing, counterparty risk and aggregate risk By Bruno Biais; Florian Heider; Marie Hoerova
  20. Trend Following, Risk Parity and Momentum in Commodity Futures By Andrew Clare, James Seaton, Peter N. Smith and Stephen Thomas
  21. Stochastic modeling of financing longevity risk in pension insurance By Ronkainen , Vesa
  22. The Zeeman Effect in Finance: Libor Spectroscopy and Basis Risk Management By Marco Bianchetti
  23. The full-tails gamma distribution applied to model extreme values By Joan del castillo; Jalila Daoudi; Isabel Serra

  1. By: Gilbert Colletaz (LEO - Laboratoire d'économie d'Orleans - CNRS : UMR6221 - Université d'Orléans); Christophe Hurlin (LEO - Laboratoire d'économie d'Orleans - CNRS : UMR6221 - Université d'Orléans); Christophe Pérignon (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - GROUPE HEC - CNRS : UMR2959)
    Abstract: This paper presents a new method to validate risk models: the Risk Map. This method jointly accounts for the number and the magnitude of extreme losses and graphically summarizes all information about the performance of a risk model. It relies on the concept of a super exception, which is de.ned as a situation in which the loss exceeds both the standard Value-at-Risk (VaR) and a VaR de.ned at an extremely low coverage probability. We then formally test whether the sequences of exceptions and super exceptions are rejected by standard model validation tests. We show that the Risk Map can be used to validate market, credit, operational, or systemic risk estimates (VaR, stressed VaR, expected shortfall, and CoVaR) or to assess the performance of the margin system of a clearing house.
    Keywords: Financial Risk Management; Tail Risk; Basel III
    Date: 2012–10–28
  2. By: Michael McAleer (Econometric Institute Erasmus School of Economics Erasmus University Rotterdam and Tinbergen Institute The Netherlands and Institute of Economic Research Kyoto University and Department of Quantitative Economics Complutense University of Madrid); Juan-Angel Jimenez-Martin (Department of Quantitative Economics Complutense University of Madrid); Teodosio Perez-Amaral (Department of Quantitative Economics Complutense University of Madrid)
    Abstract: The Basel II Accord requires that banks and other Authorized Deposit-taking Institutions (ADIs) communicate their daily risk forecasts to the appropriate monetary authorities at the beginning of each trading day, using one or more risk models to measure Value-at-Risk (VaR). The risk estimates of these models are used to determine capital requirements and associated capital costs of ADIs, depending in part on the number of previous violations, whereby realised losses exceed the estimated VaR. In this paper we define risk management in terms of choosing from a variety of risk models, and discuss the selection of optimal risk models. A new approach to model selection for predicting VaR is proposed, consisting of combining alternative risk models, and we compare conservative and aggressive strategies for choosing between VaR models. We then examine how different risk management strategies performed during the 2008- 09 global financial crisis. These issues are illustrated using Standard and Poor’s 500 Composite Index.
    Keywords: Value-at-Risk (VaR), daily capital charges, violation penalties, optimizing strategy, risk forecasts, aggressive or conservative risk management strategies, Basel Accord, global financial crisis.
    JEL: G32 G11 G17 C53 C22
    Date: 2012–11
  3. By: Sylvain Benoit (LEO - Laboratoire d'économie d'Orleans - CNRS : UMR6221 - Université d'Orléans); Gilbert Colletaz (LEO - Laboratoire d'économie d'Orleans - CNRS : UMR6221 - Université d'Orléans); Christophe Hurlin (LEO - Laboratoire d'économie d'Orleans - CNRS : UMR6221 - Université d'Orléans); Christophe Pérignon (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - GROUPE HEC - CNRS : UMR2959)
    Abstract: We propose a theoretical and empirical comparison of the most popular systemic risk measures. To do so, we derive the systemic risk measures in a common framework and show that they can be expressed as linear transformations of firms' market risk (e.g., beta). We also derive conditions under which the different measures lead similar rankings of systemically important financial institutions (SIFIs). In an empirical analysis of US financial institutions, we show that (1) different systemic risk measures identify different SIFIs and that (2) firm rankings based on systemic risk estimates mirror rankings obtained by sorting firms on market risk or liabilities. One-factor linear models explain between 83% and 100% of the variability of the systemic risk estimates, which indicates that standard systemic risk measures fall short in capturing the multiple facets of systemic risk.
    Keywords: Banking Regulation; Systemically Important Financial Firms; Marginal Expected; Shortfall; SRISK; CoVaR; Systemic vs. Systematic Risk.
    Date: 2012–10–28
  4. By: Jürgen Eichberger (University of Heidelberg, Alfred-Weber-Institut für Wirtschaftswissenschaften); Klaus Rheinberger (University of Applied Sciences Vorarlberg, Research Center Process and Product Engineering); Martin Summer (Oesterreichische Nationalbank)
    Abstract: Credit risk models used in quantitative risk management treat credit risk analysis conceptually like a single person decision problem. From this perspective an exogenous source of risk drives the fundamental parameters of credit risk: probability of default, exposure at default and the recovery rate. In reality these parameters are the result of the interaction of many market participants: They are endogenous. We develop a general equilibrium model with endogenous credit risk that can be viewed as an extension of the capital asset pricing model. We analyze equilibrium prices of securities as well as equilibrium allocations in the presence of credit risk. We use the model to discuss the conceptual underpinnings of the approach to risk weight calibration for credit risk taken by the Basel Committee. JEL Classification: G32, G33, G01, D52.
    Keywords: Credit Risk, Endogenous Risk, Systemic Risk, Banking Regulation.
    Date: 2012–06
  5. By: Vladislav Damjanovic (Department of Economics, University of Exeter)
    Abstract: We consider a model of financial intermediation with a monopolistic competition market structure. A non-monotonic relationship between the risk measured as a probability of default and the degree of competition is established.
    Keywords: Competition and Risk, Risk in DSGE models, Bank competition; Bank failure, Default correlation, Risk-shifting effect, Margin effect.
    JEL: G21 G24 D43 E13 E43
    Date: 2012
  6. By: Harald Hau (University of Geneva); Sam Langfield (European Systemic Risk Board Secretariat; UK Financial Services Authority); David Marqués-Ibáñez (European Central Bank)
    Abstract: This paper examines the quality of credit ratings assigned to banks in Europe and the United States by the three largest rating agencies over the past two decades. We interpret credit ratings as relative assessments of creditworthiness, and define a new ordinal metric of rating error based on banks’ expected default frequencies. Our results suggest that rating agencies assign more positive ratings to large banks and to those institutions more likely to provide the rating agency with additional securities rating business (as indicated by private structured credit origination activity). These competitive distortions are economically significant and contribute to perpetuate the existence of ‘too-big-to-fail’ banks. We also show that, overall, differential risk weights recommended by the Basel accords for investment grade banks bear no significant relationship to empirical default probabilities. JEL Classification: G21, G23, G28
    Keywords: Rating agencies, credit ratings, conflicts of interest, prudential regulation
    Date: 2012–10
  7. By: Christophe Hurlin (LEO - Laboratoire d'économie d'Orleans - CNRS : UMR6221 - Université d'Orléans); Christophe Pérignon (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - GROUPE HEC - CNRS : UMR2959)
    Abstract: This paper presents a validation framework for collateral requirements or margins on a derivatives exchange. It can be used by investors, risk managers, and regulators to check the accuracy of a margining system. The statistical tests presented in this study are based either on the number, frequency, magnitude, or timing of margin exceedances, which are defined as situations in which the trading loss of a market participant exceeds his or her margin. We also propose an original way to validate globally the margining system by aggregating individual backtesting statistics obtained for each market participant.
    Keywords: Collateral Requirements; Futures Markets; Tail Risk; Derivatives Clearing
    Date: 2012–10–28
  8. By: Yi-Hsuan Chen; Wolfgang Karl Härdle; ;
    Abstract: We examine what are common factors that determine systematic credit risk and estimate and interpret the common risk factors. We also compare the contributions of common factors in explaining the changes of credit default swap (CDS) spreads during the pre-crisis, crisis and post-crisis period. Based on the testing result from the common principal components model, this study finds that the eigenstructures across the three subperiods are distinct and the determinants of risk factors differ from three subperiods. Furthermore, we analyze the predictive ability of dynamics in CDS indices changes by dynamic factor models.
    Keywords: credit default swaps; common factors; credit risk
    JEL: C38 G32 E43
    Date: 2012–10
  9. By: Carlos León
    Abstract: Informational constraints may turn the Merton Model for corporate credit risk impractical. Applying this framework to the Colombian financial sector is limited to four stock-market-listed firms; more than a hundred banking and non-banking firms are not listed. Within the same framework, firms’ debt spread over the risk-free rate may be considered as the market value of the sold put option that makes risky debt trade below default-risk-free debt. In this sense, under some supplementary but reasonable assumptions, this paper uses money market spreads implicit in sell/buy backs to infer default probabilities for local financial firms. Results comprise a richer set of (38) banking and non-banking firms. As expected, default probabilities are non-negligible, where the ratio of default-probability-to-leverage is lower for firms with access to lender-of-last-resort facilities. The approach is valuable since it allows for inferring forward-looking default probabilities in the absence of stock prices. Yet, two issues may limit the validity of results to serial and cross-section analysis: overvaluation of default probabilities due to (i) spreads containing non-credit risk factors, and (ii) systematic undervaluation of the firm’s value. However, cross-section assessments of default probabilities within a wider range of firms are vital for financial authorities’ decision making, and represent a major improvement in the implementation of the Merton Model in absence of equity market data.
    Keywords: Merton model, structural model, credit risk, probability of default, distance to default. Classification JEL: G2, G13, G33, G32
    Date: 2012–10
  10. By: Alberto Elices
    Abstract: This paper describes the current taxonomy of model risk, ways for its mitigation and management and the importance of the model validation function in collaboration with other departments to design and implement them.
    Date: 2012–10
  11. By: Christophe Dutang (SAF - Laboratoire de Sciences Actuarielle et Financière - Université Claude Bernard - Lyon I : EA2429, IRMA - Institut de Recherche Mathématique Avancée - CNRS : UMR7501 - Université de Strasbourg); Claude Lefèvre (Département de Mathématique - Université Libre de Bruxelles); Stéphane Loisel (SAF - Laboratoire de Sciences Actuarielle et Financière - Université Claude Bernard - Lyon I : EA2429)
    Abstract: The purpose of this paper is to point out that an asymptotic rule "A+B/u" for the ultimate ruin probability applies to a wide class of dependent risk models, in discrete and continuous time. Dependence is incorporated through a mixing approach among claim amounts or claim inter-arrival times, leading to a systemic risk behavior. Ruin corresponds here either to classical ruin, or to stopping the activity after realizing that it is not pro table at all, when one has little possibility to increase premium income rate. Several special cases for which closed formulas are derived, are also investigated in some detail.
    Date: 2012–10–01
  12. By: Alois Pichler; Alexander Shapiro
    Abstract: This paper addresses law invariant coherent risk measures and their Kusuoka representations. By elaborating the existence of a minimal representation we show that every Kusuoka representation can be reduced to its minimal representation. Uniqueness -- in a sense specified in the paper -- of the risk measure's Kusuoka representation is derived from this initial result. Further, stochastic order relations are employed to identify the minimal Kusuoka representation. It is shown that measures in the minimal representation are extremal with respect to the order relations. The tools are finally employed to provide the minimal representation for important practical examples. Although the Kusuoka representation is usually given only for nonatomic probability spaces, this presentation closes the gap to spaces with atoms.
    Date: 2012–10
  13. By: Jennie Bai; Pierre Collin-Dufresne; Robert S. Goldstein; Jean Helwege
    Abstract: Reduced-form models of default that attribute a large fraction of credit spreads to compensation for credit event risk typically preclude the most plausible economic justification for such risk to be priced--namely, a “contagious” response of the market portfolio during the credit event. When this channel is introduced within a general equilibrium framework for an economy comprised of a large number of firms, credit event risk premia have an upper bound of just a few basis points and are dwarfed by the contagion premium. We provide empirical evidence supporting the view that credit event risk premia are minuscule.
    Keywords: Default (Finance) ; Credit ; Risk ; Financial crises
    Date: 2012
  14. By: Kartik Anand; James Chapman; Prasanna Gai;
    Abstract: We examine the financial stability implications of covered bonds. Banks issue covered bonds by encumbering assets on their balance sheet and placing them within a dynamic ring fence. As more assets are encumbered, jittery unsecured creditors may run, leading to a banking crisis. We provide conditions for such a crisis to occur. We examine how different over-the-counter market network structures influence the liquidity of secured funding markets and crisis dynamics. We draw on the framework to consider several policy measures aimed at mitigating systemic risk, including caps on asset encumbrance, global legal entity identifiers, and swaps of good for bad collateral by central banks.
    Keywords: covered bonds, over-the-counter markets, systemic risk, asset encumbrance, legal entity identifiers, velocity of collateral
    JEL: G01 G18 G21
    Date: 2012–10
  15. By: David E Allen (School of Accouting Finance & Economics, Edith Cowan University, Australia); Abhay K Singh (School of Accouting Finance & Economics, Edith Cowan University, Australia); Robert J Powell (School of Accouting Finance & Economics, Edith Cowan University, Australia); Michael McAleer (Erasmus School of Economics, Erasmus University Rotterdam, Institute for Economic Research,Kyoto University, and Department of Quantitative Economics, Complutense University of Madrid); James Taylor (Said Business School, University of Oxford, Oxford); Lyn Thomas (Southampton Management School, University of Southampton, Southampton)
    Abstract: This paper examines the asymmetric relationship between price and implied volatility and the associated extreme quantile dependence using a linear and non- linear quantile regression approach. Our goal is to demonstrate that the relationship between the volatility and market return, as quantied by Ordinary Least Square (OLS) regression, is not uniform across the distribution of the volatility-price re- turn pairs using quantile regressions. We examine the bivariate relationships of six volatility-return pairs, namely: CBOE VIX and S&P 500, FTSE 100 Volatility and FTSE 100, NASDAQ 100 Volatility (VXN) and NASDAQ, DAX Volatility (VDAX) and DAX 30, CAC Volatility (VCAC) and CAC 40, and STOXX Volatility (VS- TOXX) and STOXX. The assumption of a normal distribution in the return series is not appropriate when the distribution is skewed, and hence OLS may not capture a complete picture of the relationship. Quantile regression, on the other hand, can be set up with various loss functions, both parametric and non-parametric (linear case) and can be evaluated with skewed marginal-based copulas (for the non-linear case), which is helpful in evaluating the non-normal and non-linear nature of the relationship between price and volatility. In the empirical analysis we compare the results from linear quantile regression (LQR) and copula based non-linear quantile regression known as copula quantile regression (CQR). The discussion of the prop- erties of the volatility series and empirical ndings in this paper have signicance for portfolio optimization, hedging strategies, trading strategies and risk management, in general.
    Keywords: Return Volatility relationship, quantile regression, copula, copula quantile regression, volatility index, tail dependence
    JEL: C14 C58 G11
    Date: 2012–11
  16. By: Stéphane Loisel (SAF - Laboratoire de Sciences Actuarielle et Financière - Université Claude Bernard - Lyon I : EA2429); Hans-U. Gerber (UNIL - Université de Lausanne - Université de Lausanne)
    Abstract: We present applications of risk theory to contemporary problems related to the implemented of Solvency II related concepts, like the Own Risk and Solvency Assessment.
    Date: 2012
  17. By: LEV RATNOVSKI (International Monetary Fund); Giovanni Dell'Ariccia (IMF)
    Abstract: We revisit the link between bailouts and bank risk taking. The expectation of government support to failing banks (bailout) creates moral hazard and encourages risk-taking. However, when a bank's success depends on both its idiosyncratic risk and the overall stability of the banking system, a government's commitment to shield banks from contagion may increase their incentives to invest prudently. We explore these issues in a simple model of financial intermediation where a bank's survival depends on another bank's success. We show that the positive effect from systemic insurance dominates the classical moral hazard effect when the risk of contagion is high.
    Date: 2012
  18. By: Lars Peter Hansen
    Abstract: Sparked by the recent “great recession” and the role of financial markets, considerable interest exists among researchers within both the academic community and the public sector in modeling and measuring systemic risk. In this essay I draw on experiences with other measurement agendas to place in perspective the challenge of quantifying systemic risk, or more generally, of providing empirical constructs that can enhance our understanding of linkages between financial markets and the macroeconomy.
    JEL: E44
    Date: 2012–11
  19. By: Bruno Biais (Toulouse School of Economics (TSE)); Florian Heider (European Central Bank); Marie Hoerova (European Central Bank)
    Abstract: We study the optimal design of clearing systems. We analyze how counterparty risk should be allocated, whether traders should be fully insured against that risk, and how moral hazard affects the optimal allocation of risk. The main advantage of centralized clearing, as opposed to no or decentralized clearing, is the mutualization of risk. While mutualization fully insures idiosyncratic risk, it cannot provide insurance against aggregate risk. When the latter is significant, it is efficient that protection buyers exert effort to find robust counterparties, whose low default risk makes it possible for the clearing system to withstand aggregate shocks. When this effort is unobservable, incentive compatibility requires that protection buyers retain some exposure to counterparty risk even with centralized clearing. JEL Classification: G22, G28, D82
    Keywords: Risk-sharing, moral hazard, optimal contracting, counterparty risk, central clearing counterparty, mutualization, aggregate and idiosyncratic risk
    Date: 2012–10
  20. By: Andrew Clare, James Seaton, Peter N. Smith and Stephen Thomas
    Abstract: We show that combining momentum and trend following strategies for individual commodity futures can lead to portfolios which offer attractive risk adjusted returns which are superior to simple momentum strategies; when we expose these returns to a wide array of sources of systematic risk we find that robust alpha survives. Experimenting with risk parity portfolio weightings has limited impact on our results though in particular is beneficial to long-short strategies; the marginal impact of applying trend following methods far outweighs momentum and risk parity adjustments in terms of risk-adjusted returns and limiting downside risk.Overall this leads to an attractive strategy for investing in commodity futures and emphasises the importance of trend following as an investment strategy in the commodity futures context.
    Keywords: trend following, momentum, risk parity, equally-weighted, portfolios, commodity futures.
    JEL: G10 G11 G12
    Date: 2012–10
  21. By: Ronkainen , Vesa (Financial Supervisory Authority)
    Abstract: This work studies and develops tools to quantify and manage the risks and uncertainty relating to the pricing of annuities in the long run. To this end, an idealized Monte-Carlo simulation model is formulated, estimated and implemented, which enables one to investigate some typical pension and life insurance products. The main risks in pension insurance relate to investment performance and mortality/longevity development. We first develop stochastic models for equity and bond returns. The S&P 500 yearly total return is modeled by an uncorrelated and Normally distributed process to which exogenous Gamma distributed negative shocks arrive with Geometrically distributed interarrival times. This regime switching jump model takes into account the empirical observations of infrequent exceptionally large losses. The 5-year US government bond yearly total return is modeled as an ARMA(1,1) process after suitably log-transforming the returns. This model is able to generate long term interest rate cycles and allows rapid year-to-year corrections in the returns. We also address the parameter uncertainty in these models. <p> We then develop a stochastic model for mortality. The chosen mortality forecasting model is the well-known model of Lee and Carter (1992), in which we use the Bayesian MCMC methods in the inference concerning the time index. Our analysis with a local version of the model showed that the assumptions of the Lee-Carter model are not fully compatible with Finnish mortality data. In particular we found that mortality has been lower than average for the cohort born in wartime. However, because the forecasts of these two models were not significantly different, we chose the more parsimonious Lee-Carter model. Although our main focus is on the total population data, we also analysed the data for males and females separately. Finally we build a flexible model for the dependence structure that allows us to generate stochastic scenarios in which mortality and economic processes are either uncorrelated, correlated or shock-correlated. <p> By using the simulation model to generate stochastic pension cash-flows, we are then able to analyse the financing of longevity risk in pension insurance and the resulting risk management issues. This is accomplished via three case studies. Two of these concentrate on the pricing and solvency questions of a pension portfolio. The first study covers a single cohort of different sizes, and the second allows for multiple cohorts of annuitants. The final case study discusses individual pension insurance from the customer and long-term points of view. <p> Realistic statistical long-term risk measurement is the key theme of this work, and so we compare our simulation results with the Value-at-Risk or VaR approach. The results show that the limitations of basic VaR approach must be carefully accounted for in applications. The VaR approach is the most commonly used risk measurement methodology in insurance and finance applications. For instance, it underlies the solvency capital requirement in Solvency II, which we also discuss in this work.
    Keywords: equities; stocks; jump model; bond; longevity; Lee-Carter model; stochastic mortality; cohort mortality; dependence model; asymmetric dependence; parameter uncertainty; stochastic annuity; pension; cohort size; solvency; internal model
    JEL: G12 J11
    Date: 2012–05–25
  22. By: Marco Bianchetti
    Abstract: Once upon a time there was a classical financial world in which all the Libors were equal. Standard textbooks taught that simple relations held, such that, for example, a 6 months Libor Deposit was replicable with a 3 months Libor Deposits plus a 3x6 months Forward Rate Agreement (FRA), and that Libor was a good proxy of the risk free rate required as basic building block of no-arbitrage pricing theory. Nowadays, in the modern financial world after the credit crunch, some Libors are more equal than others, depending on their rate tenor, and classical formulas are history. Banks are not anymore too "big to fail", Libors are fixed by panels of risky banks, and they are risky rates themselves. These simple empirical facts carry very important consequences in derivative's trading and risk management, such as, for example, basis risk, collateralization and regulatory pressure in favour of Central Counterparties. Something that should be carefully considered by anyone managing even a single plain vanilla Swap. In this qualitative note we review the problem trying to shed some light on this modern animal farm, recurring to an analogy with quantum physics, the Zeeman effect.
    Date: 2012–10
  23. By: Joan del castillo; Jalila Daoudi; Isabel Serra
    Abstract: In this article we show the relationship between the Pareto distribution and the gamma distribution. This shows that the second one, appropriately extended, explains some anomalies that arise in the practical use of extreme value theory. The results are useful to certain phenomena that are fitted by the Pareto distribution but, at the same time, they present a deviation from this law for very large values. Two examples of data analysis with the new model are provided. The first one is on the influence of climate variability on the occurrence of tropical cyclones. The second one on the analysis of aggregate loss distributions associated to operational risk management.
    Date: 2012–11

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