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nep-rmg New Economics Papers
on Risk Management
Issue of 2021‒07‒12
nineteen papers chosen by



  1. Oil Tail Risks and the Forecastability of the Realized Variance of Oil-Price: Evidence from Over 150 Years of Data By Afees A. Salisu; Christian Pierdzioch; Rangan Gupta
  2. Option-Implied Spreads and Option Risk Premia By Christopher L. Culp; Mihir Gandhi; Yoshio Nozawa; Pietro Veronesi
  3. Evaluation of Volatility Spillovers and Quantile Hedging: a closer look to Brazilian agricultural markets By Baptista Palazzi, Rafael; Waldemar, Marcelo
  4. A liquidity risk early warning indicator for Italian banks: a machine learning approach By Maria Ludovica Drudi; Stefano Nobili
  5. Comparison of the accuracy in VaR forecasting for commodities using different methods of combining forecasts By Szymon Lis; Marcin Chlebus
  6. Quantifying time-varying forecast uncertainty and risk for the real price of oil By Knut Are Aastveit; Jamie Cross; Herman K. Djik
  7. Limits of stress-test based bank regulation By Tirupam Goel; Isha Agarwal
  8. Intergenerational risk sharing in a collective defined contribution pension system: a simulation study with Bayesian optimization By An Chen; Motonobu Kanagawa; Fangyuan Zhang
  9. Market Instability, Investor Sentiment, And Probability Judgment Error in Index Option Prices By Charles-Cadogan, G.
  10. Integration and Risk Transmission in the Market for Crude Oil: A Time-Varying Parameter Frequency Connectedness Approach By Ioannis Chatziantoniou; David Gabauer; Rangan Gupta
  11. Risk-adjusted return in sustainable finance: A comparative analysis of European positively screened and best-in-class ESG investment portfolios and the Euro Stoxx 50 index using the Sharpe Ratio By Gardenier, Julius; Lac, Visieu; Ashfaq, Muhammad
  12. Pricing and hedging contingent claims in a multi-asset binomial market By Jarek K\k{e}dra; Assaf Libman; Victoria Steblovskaya
  13. The efficient frontiers of mean-variance portfolio rules under distribution misspecification By Andrew Paskaramoorthy; Tim Gebbie; Terence van Zyl
  14. The incremental information in the yield curve about future interest rate risk By Bent Jesper Christensen; Mads Markvart Kjær; Bezirgen Veliyev
  15. Risk Perception & Behaviour Survey of Surveyors. Risk-SoS 2020 Preliminary results By Samuel Rufat; Iuliana Armaş; Wouter Botzen; Emeline Comby; Mariana de Brito; Alexander Fekete; Christian Kuhlicke; Peter Robinson
  16. The Identification of Non-Rational Risk Shocks By Böck, Maximilian
  17. Minimum variance hedging: Levels versus first differences By Prehn, Sören
  18. From Decision in Risk to Decision in Time - and Return: A Restatement of Probability Discounting By Marc-Arthur Diaye; André Lapidus; Christian Schmidt
  19. An Optimal Macroprudential Policy Mix for Segmented Credit Markets By Jelena Zivanovic

  1. By: Afees A. Salisu (Centre for Econometric and Allied Research, University of Ibadan, Ibadan, Nigeria); Christian Pierdzioch (Department of Economics, Helmut Schmidt University, Holstenhofweg 85, P.O.B. 700822, 22008 Hamburg, Germany); Rangan Gupta (Department of Economics, University of Pretoria, Private Bag X20, Hatfield, 0028, South Africa)
    Abstract: We examine the predictive value of tail risks of oil returns for the realized variance of oil returns using monthly data for the modern oil industry (1859:10-2020:10). The Conditional Autoregressive Value at Risk (CAViaR) framework is employed to generate the tail risks for both 1% and 5% VaRs across four variants of the CAViaR framework. We find evidence of both in-sample and out-of-sample predictability emanating from both 1% and 5% tail risks. Given the importance of real-time oil-price volatility forecasts, our results have important implications for investors and policymakers.
    Keywords: Oil Tail Risks, Realized Variance of Oil-Price, Forecasting
    JEL: C22 C53 Q02
    Date: 2021–06
    URL: http://d.repec.org/n?u=RePEc:pre:wpaper:202146&r=
  2. By: Christopher L. Culp; Mihir Gandhi; Yoshio Nozawa; Pietro Veronesi
    Abstract: We propose implied spreads (IS) and normalized implied spreads (NIS) as simple measures to characterize option prices. IS is the credit spread of an option’s implied bond, the portfolio long a risk-free bond and short a put option. NIS normalizes IS by the risk-neutral default probability and reflects tail risk. IS and NIS are countercyclical and predict implied bond returns, while neither, like implied volatility, predicts put returns. These opposite predictability results are consistent with a stochastic volatility, stochastic jump intensity model, as put premia increase in volatility but decrease in jump intensity, while implied bond premia increase in both.
    JEL: G12 G13
    Date: 2021–06
    URL: http://d.repec.org/n?u=RePEc:nbr:nberwo:28941&r=
  3. By: Baptista Palazzi, Rafael; Waldemar, Marcelo
    Abstract: We evaluate the volatility spillovers among coffee, ethanol, soybeans, reformulated blendstock for oxygenate blending (RBOB) futures prices, and Brazilian spot prices from 2010 to 2020. Using the Diebold and Yilmaz volatility spillover analytical framework (DY), we estimate the total volatility spillover, the gross and net directional volatility spillover. We also analyze the optimal hedge ratio applying the linear quantile regression (QR) model, comparing the optimal hedge ratios with the minimum variance (MV) and error correction model (ECM). Results show an increasing trend in the total volatility spillover index, suggesting an increase in the Brazilian market's connectedness. In addition, we identify quantile ranges where the QR hedge is economical and statistically significant, particularly for extreme spot prices, lower-and-upper quantiles. The knowledge of the volatility spillover effect in agricultural commodity markets may provide additional information for efficient resource allocation decisions about harvesting, output, storage, commercialization, and hedging.
    Keywords: Demand and Price Analysis, Research Methods/ Statistical Methods
    Date: 2021–03
    URL: http://d.repec.org/n?u=RePEc:ags:aesc21:312073&r=
  4. By: Maria Ludovica Drudi (Bank of Italy); Stefano Nobili (Bank of Italy)
    Abstract: The paper develops an early warning system to identify banks that could face liquidity crises. To obtain a robust system for measuring banks’ liquidity vulnerabilities, we compare the predictive performance of three models – logistic LASSO, random forest and Extreme Gradient Boosting – and of their combination. Using a comprehensive dataset of liquidity crisis events between December 2014 and January 2020, our early warning models’ signals are calibrated according to the policymaker's preferences between type I and II errors. Unlike most of the literature, which focuses on default risk and typically proposes a forecast horizon ranging from 4 to 6 quarters, we analyse liquidity risk and we consider a 3-month forecast horizon. The key finding is that combining different estimation procedures improves model performance and yields accurate out-of-sample predictions. The results show that the combined models achieve an extremely low percentage of false negatives, lower than the values usually reported in the literature, while at the same time limiting the number of false positives.
    Keywords: banking crisis, early warning models, liquidity risk, lender of last resort, machine learning
    JEL: C52 C53 G21 E58
    Date: 2021–06
    URL: http://d.repec.org/n?u=RePEc:bdi:wptemi:td_1337_21&r=
  5. By: Szymon Lis (Faculty of Economic Sciences, University of Warsaw); Marcin Chlebus (Faculty of Economic Sciences, University of Warsaw)
    Abstract: No model dominates existing VaR forecasting comparisons. This problem may be solved by combine forecasts. This study investigates the daily volatility forecasting for commodities (gold, silver, oil, gas, copper) from 2000-2020 and identifies the source of performance improvements between individual GARCH models and combining forecasts methods (mean, the lowest, the highest, CQOM, quantile regression with the elastic net or LASSO regularization, random forests, gradient boosting, neural network) through the MCS. Results indicate that individual models achieve more accurate VaR forecasts for the confidence level of 0.975, but combined forecasts are more precise for 0.99. In most cases simple combining methods (mean or the lowest VaR) are the best. Such evidence demonstrates that combining forecasts is important to get better results from the existing models. The study shows that combining the forecasts allows for more accurate VaR forecasting, although it’s difficult to find accurate, complex methods.
    Keywords: Combining forecasts, Econometric models, Finance, Financial markets, GARCH models, Neural networks, Regression, Time series, Risk, Value-at-Risk, Machine learning, Model Confidence Set
    JEL: C51 C52 C53 G32 Q01
    Date: 2021
    URL: http://d.repec.org/n?u=RePEc:war:wpaper:2021-11&r=
  6. By: Knut Are Aastveit; Jamie Cross; Herman K. Djik
    Abstract: We propose a novel and numerically efficient quantification approach to forecast uncertainty of the real price of oil using a combination of probabilistic individual model forecasts. Our combination method extends earlier approaches that have been applied to oil price forecasting, by allowing for sequentially updating of time-varying combination weights, estimation of time-varying forecast biases and facets of miscalibration of individual forecast densities and time-varying inter-dependencies among models. To illustrate the usefulness of the method, we present an extensive set of empirical results about time-varying forecast uncertainty and risk for the real price of oil over the period 1974-2018. We show that the combination approach systematically outperforms commonly used benchmark models and combination approaches, both in terms of point and density forecasts. The dynamic patterns of the estimated individual model weights are highly time-varying, reflecting a large time variation in the relative performance of the various individual models. The combination approach has built-in diagnostic information measures about forecast inaccuracy and/or model set incompleteness, which provide clear signals of model incompleteness during three crisis periods. To highlight that our approach also can be useful for policy analysis, we present a basic analysis of profit-loss and hedging against price risk.
    Keywords: Oil price, Forecast density combination, Bayesian forecasting, Instabilities, Model uncertainty
    Date: 2021–06
    URL: http://d.repec.org/n?u=RePEc:bny:wpaper:0099&r=
  7. By: Tirupam Goel; Isha Agarwal
    Abstract: Supervisory risk assessment tools, such as stress-tests, provide complementary information about bank-specific risk exposures. Recent empirical evidence, however, underscores the potential inaccuracies inherent in such assessments. We develop a model to investigate the regulatory implications of these inaccuracies. In the absence of such tools, the regulator sets the same requirement across banks. Risk assessment tools provide a noisy signal about banks' types, and enable bank specific capital surcharges, which can improve welfare. Yet, a noisy assessment can distort banks' ex ante incentives and lead to riskier banks. The optimal surcharge is zero when assessment accuracy is below a certain threshold, and increases with accuracy otherwise.
    Keywords: capital regulation; stress-tests; information asymmetry; adverse incentives; disclosure policy; Covid-19
    Date: 2021–07
    URL: http://d.repec.org/n?u=RePEc:bis:biswps:953&r=
  8. By: An Chen; Motonobu Kanagawa; Fangyuan Zhang
    Abstract: Pension reform is a crucial societal problem in many countries, and traditional pension schemes, such as Pay-As-You-Go and Defined-Benefit schemes, are being replaced by more sustainable ones. One challenge for a public pension system is the management of a systematic risk that affects all individuals in one generation (e.g., that caused by a worse economic situation). Such a risk cannot be diversified within one generation, but may be reduced by sharing with other (younger and/or older) generations, i.e., by intergenerational risk sharing (IRS). In this work, we investigate IRS in a Collective Defined-Contribution (CDC) pension system. We consider a CDC pension model with overlapping multiple generations, in which a funding-ratio-liked declaration rate is used as a means of IRS. We perform an extensive simulation study to investigate the mechanism of IRS. One of our main findings is that the IRS works particularly effectively for protecting pension participants in the worst scenarios of a tough financial market. Apart from these economic contributions, we make a simulation-methodological contribution for pension studies by employing Bayesian optimization, a modern machine learning approach to black-box optimization, in systematically searching for optimal parameters in our pension model.
    Date: 2021–06
    URL: http://d.repec.org/n?u=RePEc:arx:papers:2106.13644&r=
  9. By: Charles-Cadogan, G. (University of Leicester)
    Abstract: In a natural experiment with index option prices, we study how probability judgment error, and probabilistic risk attitudes, characterize investors’ sentiment about the ranking of index option attractiveness, the weight they place on each rank, and their ability to discriminate between prices. We introduce a novel behavioral process that (1) characterizes investor sentiment about tail events in index option prices over time and probability ranks, (2) provides early warning signals of market instability, and (3) crash probability estimates from a closed form expression for the time varying transition probability that a seemingly stable market state will become unstable and crash.
    Keywords: sentiment ; crash risk ; probability weighting function ; index option prices ; market instability JEL codes: C02 ; C44 ; D03 ; D81 ; G01 ; G12
    Date: 2021
    URL: http://d.repec.org/n?u=RePEc:wrk:wcreta:71&r=
  10. By: Ioannis Chatziantoniou (Economics and Finance Subject Group, University of Portsmouth, Portsmouth Business School, Portland Street, Portsmouth, PO1 3DE, United Kingdom); David Gabauer (Data Analysis Systems, Software Competence Center Hagenberg, Hagenberg, Austria); Rangan Gupta (Department of Economics, University of Pretoria, Pretoria, South Africa)
    Abstract: In this study, we investigate dynamic integration and risk transmission among a set of six well-established crude oil markets by combining frequency connectedness (Barunik and Krehlik, 2018) with the time-varying parameter connectedness approach (Antonakakis et al., 2020). Our study covers the period from May 1996 to December 2020 and focuses on crude oil price volatility. We measure connectedness for both a high and a low-frequency band. Findings are suggestive of relatively strong co-movements over time. For the most part of the sample period, connectedness occurs in the short-run; nonetheless, starting approximately in 2010, long-run connectedness gains much prominence until at least the end of 2015. Long-run connectedness is also prevalent at the beginning of 2020 caused by the COVID pandemic. We opine that periods of increased long-run connectedness relate to deeper changes in the market for crude oil that bring about new dynamics and associations within the specific network.
    Keywords: World crude oil market, TVP-VAR, volatility spillovers, frequency connectedness
    JEL: C32 F30 G10 Q43
    Date: 2021–06
    URL: http://d.repec.org/n?u=RePEc:pre:wpaper:202147&r=
  11. By: Gardenier, Julius; Lac, Visieu; Ashfaq, Muhammad
    Abstract: This discussion paper aims at describing the risk-adjusted return of European sustainable and conventional investment portfolios and comparing them to determine whether sustainable investment portfolios generate superior risk-adjusted returns. The paper is based on the bachelor thesis of Julius Gardenier. In fulfilling this aim, we actively construct sustainable positively screenedand best-in-class portfolios using the Sustainalytics ESG risk rating with the help of modern portfolio theory. In a second step, the Sharpe Ratios of these portfolios are compared with those of the Euro Stoxx 50, as a proxy for a conventional portfolio, for the time horizon between 2005 and 2019 thatis divided into ten instances on whose SharpeRatios paired sample t-tests are applied. Results show a statistically significant higher mean Sharpe Ratio for both types of sustainable portfolios when compared to the Euro Stoxx 50 for the periodunder investigation. Additionally, it was found that best-in-class portfolios yielded higher mean Sharpe Ratios. We conclude that, under reference to the paper's limitations, sustainable investments yielded superior risk-adjusted returns when compared to the conventional investment portfolio. Furthermore, the paper's findings identify recommendations for future research and may contribute to the growing body of academic literature in the field of sustainable finance.
    Keywords: Sustainable finance,modern portfolio theory,Sharpe Ratio,ESG risk rating
    JEL: G11 Q56
    Date: 2021
    URL: http://d.repec.org/n?u=RePEc:zbw:iubhbm:72021&r=
  12. By: Jarek K\k{e}dra; Assaf Libman; Victoria Steblovskaya
    Abstract: We consider an incomplete multi-asset binomial market model. We prove that for a wide class of contingent claims the extremal multi-step martingale measure is a power of the corresponding single-step extremal martingale measure. This allows for closed form formulas for the bounds of a no-arbitrage contingent claim price interval. We construct a feasible algorithm for computing those boundaries as well as for the corresponding hedging strategies. Our results apply, for example, to European basket call and put options and Asian arithmetic average options.
    Date: 2021–06
    URL: http://d.repec.org/n?u=RePEc:arx:papers:2106.13283&r=
  13. By: Andrew Paskaramoorthy; Tim Gebbie; Terence van Zyl
    Abstract: Mean-variance portfolio decisions that combine prediction and optimisation have been shown to have poor empirical performance. Here, we consider the performance of various shrinkage methods by their efficient frontiers under different distributional assumptions to study the impact of reasonable departures from Normality. Namely, we investigate the impact of first-order auto-correlation, second-order auto-correlation, skewness, and excess kurtosis. We show that the shrinkage methods tend to re-scale the sample efficient frontier, which can change based on the nature of local perturbations from Normality. This re-scaling implies that the standard approach of comparing decision rules for a fixed level of risk aversion is problematic, and more so in a dynamic market setting. Our results suggest that comparing efficient frontiers has serious implications which oppose the prevailing thinking in the literature. Namely, that sample estimators out-perform Stein type estimators of the mean, and that improving the prediction of the covariance has greater importance than improving that of the means.
    Date: 2021–06
    URL: http://d.repec.org/n?u=RePEc:arx:papers:2106.10491&r=
  14. By: Bent Jesper Christensen (Aarhus University and CREATES and the Dale T. Mortensen Center); Mads Markvart Kjær (Aarhus University and CREATES); Bezirgen Veliyev (Aarhus University and CREATES and the Danish Finance Institute)
    Abstract: Using high-frequency intraday futures prices to measure yield volatility at selected maturities, we find that daily yield curves carry incremental information about future interest rate risk at the long end, relative to that contained in the time series of historical volatilities. Some of the information in the yield curves is not captured by standard affine models. At the short end, time series based forecasts outperform yield curve based forecasts. Both provide utility to a risk averse investor in longerterm instruments, not in short, relative to a random walk. Our results point to the existence of an unspanned volatility factor.
    Keywords: Term structure models, Volatility, Forecasting, Kalman filtering, Yield curve
    JEL: C58 E43 G12
    Date: 2021–07–01
    URL: http://d.repec.org/n?u=RePEc:aah:create:2021-11&r=
  15. By: Samuel Rufat (IUF - Institut Universitaire de France - M.E.N.E.S.R. - Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche, MRTE - Laboratoire Mobilités, Réseaux, Territoires, Environnements - CY - CY Cergy Paris Université); Iuliana Armaş (UniBuc - University of Bucharest); Wouter Botzen (Institute for Environmental Studies (IVM) - VU University Amsterdam); Emeline Comby (EVS - Environnement Ville Société - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées - CNRS - Centre National de la Recherche Scientifique - ENSAL - École nationale supérieure d'architecture de Lyon - Mines Saint-Étienne MSE - École des Mines de Saint-Étienne - IMT - Institut Mines-Télécom [Paris] - ENTPE - École Nationale des Travaux Publics de l'État - UJM - Université Jean Monnet [Saint-Étienne] - UJML - Université Jean Moulin - Lyon 3 - Université de Lyon - UL2 - Université Lumière - Lyon 2 - ENS Lyon - École normale supérieure - Lyon); Mariana de Brito (UFZ - Helmholtz Centre for Environmental Research); Alexander Fekete (THK - Institute of Rescue Engineering and Civil Protection, University of Applied Sciences Cologne); Christian Kuhlicke (UFZ - Helmholtz Centre for Environmental Research); Peter Robinson (Institute for Environmental Studies (IVM) - VU University Amsterdam)
    Abstract: One of the key challenges in risk, vulnerability and resilience is how to address the role of risk perceptions and how perceptions influence behaviour. A central question is why people still fail to act in an adaptive manner to reduce future losses, even when there are ever richer risk information provided by several communication channels (e.g. websites, social media, mobile applications, television, and print news). The current fragmentation of the field makes it an uphill battle to cross-validate the results of the current collection of independent case studies. This, in turn, hinders comparability and transferability across scales and contexts, and hampers giving recommendations for policy and risk management. While we obviously cannot all run the very same questionnaire or focus groups because we have different research interests, our ability to work together and build cumulative knowledge could be significantly improved by having: (1) a common list of minimal requirements to compare studies and surveys, (2) shared criteria to address context-specific aspects of countries and regions, (3) a selection of survey questions or themes allowing for comparability and long-term monitoring. Following the First European Conference on Risk Perception, Behaviour, Management and Response , the aim of the Risk Perception & Behaviour Survey of Surveyors (SoS) was to provide answers to move towards this direction.
    Keywords: Climate Change Adaptation,Disaster Risk Reduction,Disaster Risk Management,Disaster Communications,Disaster Awareness,Risk perception drivers,Risk perceptions,Adaptive behavior,Survey
    Date: 2021
    URL: http://d.repec.org/n?u=RePEc:hal:journl:hal-03228369&r=
  16. By: Böck, Maximilian
    Abstract: This paper studies how non-rational risk shocks affect the macroeconomy. Using a novel identification design which exploits survey data on expectations of financial executives in the US, I identify non-rational risk shocks via distortions in beliefs. Belief distortions are measured through surprises in beliefs of credit spreads, defined as the difference between subjective and objective forecasts. They are then used as a proxy for exogenous variation in the risk premium. Belief distortions elicit due to overreaction of credit spreads, eventually leading to exaggerated beliefs on financial markets. Results indicate that the constructed shocks have statistically and economically meaningful effects. This has sizeable consequences for the U.S. economy: A positive non-rational risk shock moves credit spreads remarkably while real activity and the stock market decline.
    Keywords: Business Cycles, Risk Shocks, Belief Distortions
    Date: 2021–06
    URL: http://d.repec.org/n?u=RePEc:wiw:wus005:8197&r=
  17. By: Prehn, Sören
    Abstract: Nowadays it is widely accepted to estimate minimum variance hedge ratio regressions in first differences. There are both statistical and economic reasons for a first difference approach. However, no study has ever analyzed whether the first difference approach is also consistent with the theory of minimum variance hedging. In this paper we show, on the basis of a simulation study, that the first difference model with intercept does not provide hedge ratio estimates that are in line with the theory of minimum variance hedging. Only a linear regression model in levels provides theoretically consistent results.
    Keywords: Agricultural Finance, Research Methods/ Statistical Methods
    Date: 2021–03
    URL: http://d.repec.org/n?u=RePEc:ags:aesc21:312051&r=
  18. By: Marc-Arthur Diaye (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique); André Lapidus (PHARE - Philosophie, Histoire et Analyse des Représentations Économiques - UP1 - Université Paris 1 Panthéon-Sorbonne); Christian Schmidt (PHARE - Philosophie, Histoire et Analyse des Représentations Économiques - UP1 - Université Paris 1 Panthéon-Sorbonne)
    Abstract: This paper aims at restating, in a decision theory framework, the results of some signicant contributions of the literature on probability discounting that followed the publication of the pioneering article by Rachlin et al. (1991). We provide a restatement of probability discounting in terms of rank-dependent utility, in which the utilities of the outcomes of n-issues lotteries are weighted by probabilities transformed after their transposition into time-delays. This formalism makes the typical cases of rationality in time and in risk mutually exclusive, but allows looser types of rationality. The resulting attitude toward probability and toward risk are then determined in relation to the values of the two parameters involved in the procedure of probability discounting.
    Keywords: time discounting,Probability discounting,logarithmic time perception,rank-dependent utility,rationality,attitude toward probabilities,attitude toward risk
    Date: 2021–06–10
    URL: http://d.repec.org/n?u=RePEc:hal:wpaper:hal-03256606&r=
  19. By: Jelena Zivanovic
    Abstract: This paper analyzes the design of simple macroprudential rules for bank and non-bank credit markets in a medium-scale dynamic stochastic general equilibrium model. In the model, mutual funds support corporate bond issuance by rms with access to capital markets; a banking sector supplies loans to the remaining producers. This model is used to study the optimal design of monetary and macroprudential rules and to address whether financial stability in the banking and bond markets is welfare improving. First, in response to aggregate productivity and financial shocks, the welfare-maximizing monetary policy rule implies near price stability, while the optimal macroprudential policy rule stabilizes bank credit and bond volumes. Second, there is no trade-off between price and financial stability. Third, if the central bank cannot correctly identify a sector-specific financial shock, responding optimally as if the shock affects both sectors, then welfare outcomes are negligibly worse than those under the optimal policy.
    Keywords: Business fluctuations and cycles; Credit and credit aggregates; Credit risk management; Financial stability; Financial system regulation and policies
    JEL: E30 E44 E50
    Date: 2021–06
    URL: http://d.repec.org/n?u=RePEc:bca:bocawp:21-31&r=

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