|
on Risk Management |
|
Issue of 2022‒12‒12
twenty-two papers chosen by |
| By: | Amit Chaudhary; Daniele Pinna |
| Abstract: | We assess the market risk of the 0VIX lending protocol using a multi-asset agent-based model to simulate ensembles of users subject to price-driven liquidation risk. Our multi-asset methodology shows that the protocol's systemic risk is small under stress and that enough collateral is always present to underwrite active loans. Our simulations use a wide variety of historical data to model market volatility and run the agent-based simulation to show that even if all the assets like ETH, BTC and MATIC increase their hourly volatility by more than ten times, the protocol carries less than 0.1\% default risk given suggested protocol parameter values for liquidation loan-to-value ratio and liquidation incentives. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.08870&r=rmg |
| By: | Storti, Giuseppe; Wang, Chao |
| Abstract: | A new multivariate semi-parametric risk forecasting framework is proposed, to enable the portfolio Value-at-Risk (VaR) and Expected Shortfall (ES) optimization and forecasting. The proposed framework accounts for the dependence structure among asset returns, without assuming their distribution. A simulation study is conducted to evaluate the finite sample properties of the employed estimator for the proposed model. An empirically motivated portfolio optimization method, that can be utilized to optimize the portfolio VaR and ES, is developed. A forecasting study on 2.5% level evaluates the performance of the model in risk forecasting and portfolio optimization, based on the components of the Dow Jones index for the out-of-sample period from December 2016 to September 2021. Comparing to the standard models in the literature, the empirical results are favorable for the proposed model class, in particular the effectiveness of the proposed framework in portfolio risk optimization is demonstrated. |
| Keywords: | semi-parametric; Value-at-Risk; Expected Shortfall; multivariate; portfolio optimization. |
| JEL: | C14 C32 C51 C58 G17 |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:115266&r=rmg |
| By: | Aleksander Schiffers (University of Warsaw, Faculty of Economic Sciences); Marcin Chlebus (University of Warsaw, Faculty of Economic Sciences) |
| Abstract: | There is an ongoing discussion, what is the most efficient approach to Value-at-Risk estimation. Subsequent studies and meta-analyzes show that there is no scientific consensus in this field and the necessity of further research is frequently underlined. In this study, authors try to assess the comparative performance of models used for Value-at-Risk estimations in changing market volatility regimes. The models considered are: the Historical Simulation, the Risk Metrics®, the GARCH(1,1)-n, the GARCH(1,1)-t, the GARCH(1,1)-st, the GARCH(1,1)-QML. GARCH models are additionally enriched with additional, exogenous regressors in the form of lagged commodity futures contracts returns. The analysis is conducted on a set of utility sector stock indices from six developed countries across the globe: WIG Energia (Poland), Dow Jones Utilities Average (USA), CAC Utilities (France), Tokyo SE Topix-17 Power & Gas (Japan), S&P ASX 200 Utilities (Australia), and DAX All Utilities (Germany). Three samples of different characteristics are distinguished from the last 10 years of data and one of them covers the upsurge in market volatility caused by the Covid-19 pandemic. In order to evaluate the VaR forecasts performance of each model, conditional/unconditional coverage tests of Kupiec and Christoffersen, Dynamic Quantile test, and Diebold-Marino test were used. Empirical results of the study indicate that in the volatile market periods, overall quality of forecasts deteriorates for all models to a varying degree. However, the GARCH(1,1)-st with external regressors is considered the most efficient and robust model due to its ability to capture stylized facts of data distribution. Exogenous variables are worth considering but their contribution to performance improvement may be model and market dependent. |
| Keywords: | risk management, market risk, Value-at-risk, GARCH, Historical Simulation, Risk Metrics®, risk modelling, benchmark, model quality assessment |
| JEL: | C51 C52 C53 C58 G15 G32 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:war:wpaper:2021-28&r=rmg |
| By: | Emma Kroell; Silvana M. Pesenti; Sebastian Jaimungal |
| Abstract: | Stress testing, and in particular, reverse stress testing, is a prominent exercise in risk management practice. Reverse stress testing, in contrast to (forward) stress testing, aims to find an alternative but plausible model such that under that alternative model, specific adverse stresses (i.e. constraints) are satisfied. Here, we propose a reverse stress testing framework for dynamic models. Specifically, we consider a compound Poisson process over a finite time horizon and stresses composed of expected values of functions applied to the process at the terminal time. We then define the stressed model as the probability measure under which the process satisfies the constraints and which minimizes the Kullback-Leibler divergence to the reference compound Poisson model. We solve this optimization problem, prove existence and uniqueness of the stressed probability measure, and provide a characterization of the Radon-Nikodym derivative from the reference model to the stressed model. We find that under the stressed measure, the intensity and the severity distribution of the process depend on time and the state space. We illustrate the dynamic stress testing by considering stresses on VaR and both VaR and CVaR jointly and provide illustrations of how the stochastic process is altered under these stresses. We generalize the framework to multivariate compound Poisson processes and stresses at times other than the terminal time. We illustrate the applicability of our framework by considering "what if" scenarios, where we answer the question: What is the severity of a stress on a portfolio component at an earlier time such that the aggregate portfolio exceeds a risk threshold at the terminal time? Moreover, for general constraints, we provide a simulation algorithm to simulate sample paths under the stressed measure. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.03221&r=rmg |
| By: | Fabien Le Floc'h |
| Abstract: | What kind of implied volatility extrapolation is appropriate? Roger Lee proved that the Black-Scholes implied variance can not grow faster than linearly in log-moneyness. This paper investigates what happens in the Bachelier (or Normal) implied volatility world, making sure to cover the various aspects of vanilla option arbitrages. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.10232&r=rmg |
| By: | Jackson P. Lautier; Vladimir Pozdnyakov; Jun Yan |
| Abstract: | Risk-based pricing of loans is well-accepted. Left unstudied, however, is the conditional credit risk of a loan that remains current. Using large-sample statistics and asset-level consumer automobile asset-backed security data, we find that default risk conditional on survival converges for borrowers in disparate credit risk bands well before scheduled termination, a phenomenon we call credit risk convergence. We then use actuarial techniques to derive the conditional market-implied credit spread by credit risk band to estimate current deep subprime and subprime borrowers eventually overpay by annual percentage rates of 285-1,391 basis points. Our results are robust to various sensitivity tests. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.09176&r=rmg |
| By: | Marc S. Paolella (University of Zurich - Department of Banking and Finance; Swiss Finance Institute); Pawel Polak (Stony Brook University-Department of Applied Mathematics and Statistics) |
| Abstract: | The CCC-GARCH model, and its dynamic correlation extensions, form the most important model class for multivariate asset returns. For multivariate density and portfolio risk forecasting, a drawback of these models is the underlying assumption of Gaussianity. This paper considers the so-called COMFORT model class, which is the CCC-GARCH model but endowed with multivariate generalized hyperbolic innovations. The novelty of the model is that parameter estimation is conducted by joint maximum likelihood, of all model parameters, using an EM algorithm, and so is feasible for hundreds of assets. This paper demonstrates that (i) the new model is blatantly superior to its Gaussian counterpart in terms of forecasting ability, and (ii) also outperforms ad-hoc three step procedures common in the literature to augment the CCC and DCC models with a fat-tailed distribution. An extensive empirical study confirms the COMFORT model’s superiority in terms of multivariate density and Value-at-Risk forecasting. |
| Keywords: | GJR-GARCH, Multivariate Generalized Hyperbolic Distribution, Non-Ellipticity, Value-at-Risk. |
| JEL: | C51 C53 G11 G17 |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:chf:rpseri:rp2288&r=rmg |
| By: | Inaki Aldasoro; Luitgard A M Veraart |
| Abstract: | We provide a framework for modelling risk and quantifying payment shortfalls in cleared markets with multiple central counterparties (CCPs). Building on the stylised fact that clearing membership is shared among CCPs, we show how this can transmit stress across markets through multiple CCPs. We provide stylised examples to lay out how such stress transmission can take place, as well as empirical evidence to illustrate that the mechanisms we study could be relevant in practice. Furthermore, we show how stress mitigation mechanisms such as variation margin gains haircutting by one CCP can have spillover effects on other CCPs. The framework can be used to enhance CCP stress-testing, which currently relies on the "Cover 2" standard requiring CCPs to be able to withstand the default of their two largest clearing members. We show that who these two clearing members are can be significantly affected by higher-order effects arising from interconnectedness through shared clearing membership. Looking at the full network of CCPs and shared clearing members is therefore important from a financial stability perspective. |
| Keywords: | central counterparties, systemic risk, contagion, stress testing, Cover 2. |
| JEL: | C60 C62 G18 G21 G23 |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:bis:biswps:1052&r=rmg |
| By: | Leonie Bräuer; Harald Hau |
| Abstract: | Over the last decade foreign bond portfolio positions in US dollar assets have risen above the reciprocal US investor positions in foreign currencies. In periods of increased economic uncertainty, institutional investors hedge their international bond positions, which creates a net hedging demand for dollar assets that depreciates USD rates in both the forward and spot markets. We document the time-varying nature of this net hedging demand and show how it relates to eco-nomic uncertainty and the US net foreign bond position in various currencies. Based on a parsimonious VAR model, we find that changes in FX hedging pressure can account for approximately 30% of all monthly variation in the seven most important dollar exchange rates from 2012 to 2022. |
| Keywords: | exchange rate, hedging channel, institutional investors |
| JEL: | E44 F31 F32 G11 G15 G23 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_10065&r=rmg |
| By: | Best, Stefan |
| Abstract: | Im Januar 2019 veröffentlichte der Baseler Ausschuss für Bankenaufsicht eine revidierte Fassung der Mindestanforderungen an Eigenkapital für Marktrisiken, die am 01.01.2023 in Kraft treten wird. Diese Arbeit beschäftigt sich mit dem auf Sensitivitäten basierenden Standardansatz und dem Vereinfachten Standardansatz. Neben der Darstellung und kritischen Analyse beider Ansätze wird untersucht, wie sich die Ansätze in ihren Auswirkungen auf die Eigenkapitalanforderungen unterscheiden. Zudem werden die Ergebnisse für Instrumente mit Ausfallrisiko mit denen des Standardansatzes des Bankbuchs verglichen. Insbesondere wird gezeigt, dass der auf Sensitivitäten basierende Standardansatz konzeptionelle und technische Schwachstellen aufweist. Er ist zudem unnötig kompliziert und läuft so der vom Baseler Ausschuss selbst formulierten Forderung nach mehr Transparenz und Vereinfachung zuwider. |
| Keywords: | Basel III,Standardized Approach,Market Risk,Minimum capital requirements |
| JEL: | G21 G28 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:wifinw:102021&r=rmg |
| By: | Sebastian Calcetero Vanegas; Andrei L. Badescu; X. Sheldon Lin |
| Abstract: | Credibility, experience rating and more recently the so-called a posteriori ratemaking in insurance consists in the determination of premiums that account for both the policyholders' attributes and their claim history. The models designed for such purposes are known as credibility models and fall under the same framework of Bayesian inference in statistics. Most of the data-driven models used for this task are mathematically intractable due to their complex structure, and therefore credibility premiums must be obtained via numerical methods e.g simulation via Markov Chain Monte Carlo. However, such methods are computationally expensive and even prohibitive for large portfolios when these must be applied at the policyholder level. In addition, these computations are "black-box" procedures for actuaries as there is no clear expression showing how the claim history of policyholders is used to upgrade their premiums. In this paper, we address these challenges and propose a methodology to derive a closed-form expression to compute credibility premiums for any given Bayesian model. We do so by introducing a credibility index, that works as an efficient summary statistic of the claim history of a policyholder, and illustrate how it can be used as the main input to approximate any credibility formula. The closed-form solution can be used to reduce the computational burden of a posteriori ratemaking for large portfolios via the same idea of surrogate modeling, and also provides a transparent way of computing premiums from which practical interpretations and risk assessments can be performed. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.06568&r=rmg |
| By: | Kuntal K. Das (University of Canterbury); Mona Yaghoubi (University of Canterbury) |
| Abstract: | Exploiting a novel measure of firm-level political risk based on earnings conference calls, we examine the effect of firm-level political risk on stock liquidity. We show that liquidity decreases significantly more in firms that are exposed to political risk. An increase in firm-level political risk by one standard deviation lowers liquidity by around 3.64%. We further investigate whether the effect of firm-level political risk on stock liquidity can be mitigated or exacerbated by the political environment of the U.S. economy and find some evidence of the Democratic liquidity premium. Our results are robust to alternative measures of (il)liquidity, and an estimation method. |
| Keywords: | Stock liquidity, political risk |
| JEL: | G11 G14 |
| Date: | 2022–11–01 |
| URL: | http://d.repec.org/n?u=RePEc:cbt:econwp:22/18&r=rmg |
| By: | George Samartzis; Nikitas Pittis |
| Abstract: | We derive a closed-form expression capturing the degree of Relative Risk Aversion (RRA) of investors for non-"fair" lotteries. We argue that our formula is superior to earlier methods that have been proposed, as it is a function of only three variables. Namely, the Treasury yields, the returns and the market capitalization of a specific market index. Our formula, is tested on CAC 40, EURO, S&P 500 and STOXX 600, with respect to the market capitalization of each index, for different time periods. We deduce that the investors in these markets exhibit Decreasing Absolute Risk Aversion (DARA) through all the different time periods that we consider, while the degree of RRA has altered between being constant, decreasing or increasing. Furthermore, we propose a simple and intuitive way to measure the degree to which a wrong assumption with respect to the utility function of an investor will affect the structure of his portfolio. Our method is built on a two asset portfolio framework. Namely, a portfolio consisting of one risky and one risk-free asset. Applying our method, the empirical findings indicate that the weight invested in the risky asset varies substantially even among utility functions with similar characteristics. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.03604&r=rmg |
| By: | M. Reza Bradrania; Maurice Peat; Stephen Satchell |
| Abstract: | This paper considers liquidity as an explanation for the positive association between expected idiosyncratic volatility (IV) and expected stock returns. Liquidity costs may affect the stock returns, through bid-ask bounce and other microstructure-induced noise, which will affect the estimation of IV. We use a novel method (developed by Weaver, 1991) to eliminate microstructure influences from stock closing price-based returns and then estimate IV. We show that there is a premium for IV in value-weighted portfolios, but this premium is less strong after correcting returns for microstructure bias. We further show that this premium is driven by liquidity in the prior month after correcting returns for microstructure noise. The pricing results from equally-weighted portfolios indicate that IV does not predict returns either before or after controlling for liquidity costs. These findings are robust after controlling for common risk factors as well as analysing double-sorted portfolios based on IV and liquidity. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.04695&r=rmg |
| By: | Ferraz, Eduardo; Mantilla, Cesar |
| Abstract: | We use a three-period model adopting a recursive definition of consumption to explore the optimal delegation that a present self, aware that her near-future self is present-biased but better informed, will make to protect her far-future self against income shocks. The model captures the present self's trade-off between using commitment mechanisms, restricting the near-future self's agency through illiquid savings, and profiting from the near-future self's better information about future shocks. Our main result states that agents with higher risk aversion can cover better against utility losses from time-inconsistent consumption through the commitment mechanism. Given the evidence of women being more risk-averse than men, this result provides the micro-foundation for the gender gap in adopting financial commitment devices, especially among single individuals. |
| Date: | 2022–09–10 |
| URL: | http://d.repec.org/n?u=RePEc:osf:osfxxx:xbsn8&r=rmg |
| By: | Sangmin Oh; Ishita Sen; Ana-Maria Tenekedjieva |
| Abstract: | Homeowners’ insurance, a $15 trillion market by coverage, provides households financial protection from climate losses. Insurance premiums (rates) are subject to significant regulations at a state level in the United States. Using novel data on filings made by insurers to regulators, we propose a metric to quantify the extent of regulation in individual states. We provide evidence of decoupling of insurance rates from their underlying risks and identify regulation as a driving force behind this pattern. Rates are least reflective of risk in states we classify as "high friction", i.e. states where regulations appear most restrictive. We identify two sources behind the decoupling. First, in high friction states, rates have not adequately adjusted in response to the growth in losses. Second, insurers have cross-subsidized high friction states by raising rates in low friction states. Our results imply that households in low friction states are disproportionately bearing the risks of households in high friction states. More broadly, our findings question whether insurance rates can play a useful role in steering climate adaptation and whether households will have continued access to insurance. |
| Keywords: | Climate Risk; Cross-subsidies; Homeowners' Insurance; Insurance Availability; Rate Regulation |
| JEL: | G22 G52 G28 G32 Q54 |
| Date: | 2022–10–03 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedgfe:2022-64&r=rmg |
| By: | Prendergast, Michael |
| Abstract: | This paper describes an empirical analysis of optimized portfolios and safe return rates across multiple investment time horizons using Telser’s Safety-First method. The analysis uses thirty years of historical monthly data for 81 different Fidelity® mutual funds and a blended money market fund rate. The Fidelity® funds represent a wide variety of investment factors, strategies and asset types, including bonds, stocks, commodities and convertible securities. A large synthetic return dataset was generated from this data by a Monte-Carlo random walk using cointegrated bootstrapping of investment returns and yields. Portfolio optimization was then performed on this synthetic dataset for safety factors varying from 60% to 99% and time horizons varying from one month to ten years. Results from portfolio analyses include the following: 1) there are no risk-free investments available to Fidelity® mutual fund investors, as even money market funds have risk due to yield fluctuations, 2) optimized portfolios are sensitive to both investment time horizons and safety factor confidence levels, 3) conservative, short-term investors are better off leaving their money in a money market fund than investing in securities, 4) optimized portfolios for longer term, more aggressive investors consist of a blend of both value and growth equities, and 5) the funds most often represented in optimized portfolios are those that have the best risk/reward ratios, although this rule is not universal. Two practical applications of this optimization approach are also presented. |
| Date: | 2022–09–30 |
| URL: | http://d.repec.org/n?u=RePEc:osf:osfxxx:dypw6&r=rmg |
| By: | Vladim\'ir Hol\'y |
| Abstract: | We develop a novel observation-driven model for high-frequency prices. We account for irregularly spaced observations, simultaneous transactions, discreteness of prices, and market microstructure noise. The relation between trade durations and price volatility, as well as intraday patterns of trade durations and price volatility, is captured using smoothing splines. The dynamic model is based on the zero-inflated Skellam distribution with time-varying volatility in a score-driven framework. Market microstructure noise if filtered by including a moving average component. The model is estimated by the maximum likelihood method. In an empirical study of the IBM stock, we demonstrate that the model provides a good fit to the data. Besides modeling intraday volatility, it can also be used to measure daily realized volatility. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.12376&r=rmg |
| By: | Kamil Korzeń (Faculty of Economic Sciences, University of Warsaw); Robert Ślepaczuk (Faculty of Economic Sciences, University of Warsaw) |
| Abstract: | The following research paper’s main goal is to create an algorithmically managed ETF, which tracks the SPX index and provides a Smart Beta exposure. Authors apply the following simple index replication methods: partial correlation, non-negative least squares, beta coefficient, and dynamic time warping. First, authors are trying to reverse engineer the Index Tracking process in an automated and fair manner - taking into account e.g. transaction costs. Additionally, authors apply a constraint to the total number of assets used in the replication process, which is limited to the certain N. Then, authors develop a Smart Beta framework based on limiting the negative tail-risk. The positive excess return (alpha) is captured and used to compensate for the underperformance of the replicated Index or paid in a form of a dividend. Moreover, with the enhancement methods applied (Kurtosis/Skewness and Excess Return Cushion (ERC) enhancements), the authors’ main goal is to keep the Tracking Error (TE) on a fixed level, although with a significant overweight on the Positive TE and underweight on the Negative TE. In the research paper, the data from 04-Jan-2016 to 31-Dec-2020 is used as the training window, while the first quarter of the year 2021 (Q1 2021) is used as an out-of-sample and out-of-time testing period. Additionally, the authors measure the replicated Index’s performance compared to the SPY, VOO, and IVV ETFs. Authors find a piece of empirical evidence that it is possible to track the SPX Index within the limits of 4-5% TE with the limited number of assets. Moreover, after the implementation of alpha accumulation, the authors outperform the benchmark ETFs in terms of minimizing the TE but did not succeed in providing statistically significant returns better than the SPX Index. |
| Keywords: | exchange-traded funds, enhanced index replication methods, smart beta, asset allocation, partial correlation, non-negative least squares, dynamic time warping |
| JEL: | C4 C14 C45 C53 C58 G13 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:war:wpaper:2021-18&r=rmg |
| By: | Yuchen Li; Zongxia Liang; Shunzhi Pang |
| Abstract: | As classical mean-variance preferences have the shortcoming of non-monotonicity, portfolio selection theory based on monotone mean-variance preferences is becoming an important research topic recently. In continuous-time Cram\'er-Lundberg insurance and Black-Scholes financial market model, we solve the optimal reinsurance-investment strategies of insurers under mean-variance preferences and monotone mean-variance preferences by the HJB equation and the HJBI equation, respectively. We prove the validity of verification theorems and find that the optimal strategies under the two preferences are the same. This illustrates that neither the continuity nor the completeness of the market is necessary for the consistency of two optimal strategies. We make detailed explanations for this result. Thus, we develop the existing theory of portfolio selection problems under the monotone mean-variance criterion. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.12168&r=rmg |
| By: | Sebastian Doerr; Gazi Kabas; Steven Ongena |
| Abstract: | What are the implications of an aging population for financial stability? To examine this question, we exploit geographic variation in aging across U.S. counties. We establish that banks with higher exposure to aging counties increase loan-to-income ratios, especially where they operate no branches. Laxer lending standards also lead to higher nonperforming loans during downturns, suggesting higher credit risk. Inspecting the mechanism shows that aging drives risk-taking through two contemporaneous channels: deposit in ows due to seniors' propensity to save in deposits; and depressed local investment opportunities due to seniors' lower credit demand. Banks thus look for riskier clients in no-branch counties. |
| Keywords: | risk-taking, financial stability, low interest rates, population aging, demographics. |
| JEL: | E51 G21 |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:bis:biswps:1050&r=rmg |
| By: | Mario Cerrato; Hormoz Ramian; Shengfeng Mei |
| Abstract: | We show that European firms, at the peak of the COVID-19 shock in 2020:Q2, went into a “panic borrowing” status and drew down €87bn in a very short period. We show that firms with less stringent solvency and liquidity constraints drew down their credit lines and accumulated cash. Our study exploits the implications of the social distancing policies to corporate operations across Europe. It proposes a novel empirical framework that identifies panic borrowing while accounting for the endogeneity between credit line drawdowns and an underlying borrowing ability during the COVID-19 shock. We use COVID-19 infection data and proxies for social distancing policies in Europe to study if the increase in risk following the COVID-19 shock can explain the panic borrowing while accounting for possible endogenous credit lines drawdowns. Finally, we show that European corporate drawdowns during the pandemic crisis increased drawdowns, on average, by 3.35 percentage points in response to an unexpected one percentage point fall in their cash flows but only when firms’ earnings are negative. This result is driven by the lockdown policies introduced in Europe |
| Keywords: | Corporate credit lines, cash holding, investment, default risk |
| JEL: | G21 G32 G33 |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:gla:glaewp:2022_12&r=rmg |