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on Risk Management |
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Issue of 2024‒05‒13
twenty papers chosen by |
| By: | Benjamin A. Jansen |
| Abstract: | This paper shows that theories focused solely on risk, and investors more generally, as the driver of asset returns may not be sufficiently reflecting relevant asset price inputs. This conclusion largely stems from prevalent asset pricing theories ignoring the firm side supply of value into their financial securities. |
| Keywords: | Asset Pricing, Cash Flow, Firms, Risk |
| JEL: | G12 G19 |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:mts:wpaper:202401&r=rmg |
| By: | Nichanan Sakolvieng (Martin de Tours School of Management and Economics, Assumption University, Thailand. Author-2-Name: Sutta Sornmayura Author-2-Workplace-Name: Martin de Tours School of Management and Economics, Assumption University, Thailand. Author-3-Name: Kaimook Numgaroonaroonroj Author-3-Workplace-Name: Martin de Tours School of Management and Economics, Assumption University, Thailand. Author-4-Name: Author-4-Workplace-Name: Author-5-Name: Author-5-Workplace-Name: Author-6-Name: Author-6-Workplace-Name: Author-7-Name: Author-7-Workplace-Name: Author-8-Name: Author-8-Workplace-Name:) |
| Abstract: | " Objective - This study aims to contribute to the field of cryptocurrency portfolio management and rebalancing strategies by empirically investigating the impact of different allocation frequencies and threshold percentages on the risk-adjusted returns of cryptocurrency portfolios. Methodology/Technique – Utilizing a simulation of 10, 000 cryptocurrency portfolios comprising seven assets, including Ethereum (ETH), Bitcoin (BTC), Tether (USDT), Litecoin (LTC), Solana (SOL), Dogecoin (DOGE), and Polygon (MATIC), this study examines and compares the effects of different allocation frequencies (daily, weekly, and monthly) in time-based rebalancing and various threshold percentages (5%, 10%, and 15%) in threshold-based strategies on the portfolios' risk-adjusted returns, using the Sharpe ratio. The performance of these strategies is also compared with a passive buy-and-hold strategy. Findings – The research reveals statistically significant differences in the risk-adjusted returns between the buy-and-hold strategy and the daily rebalancing and threshold-based strategies with 5% and 10% threshold percentages. The daily rebalancing strategy demonstrates a higher Sharpe ratio, while lower threshold percentages lead to better risk-adjusted returns. Novelty – These empirical findings, using a simulation of 10, 000 cryptocurrency portfolios, provide valuable insights into optimizing cryptocurrency portfolio performance through rebalancing strategies. Additionally, they highlight the effectiveness of implementing rebalancing techniques in cryptocurrency portfolios, contributing to the understanding of rebalancing optimization in this domain. Type of Paper - Empirical" |
| Keywords: | Cryptocurrency; Mean-Variance Optimization; Portfolio Management; Rebalancing Strategies; Risk-Adjusted Returns |
| JEL: | G11 G19 |
| Date: | 2024–03–31 |
| URL: | http://d.repec.org/n?u=RePEc:gtr:gatrjs:jfbr220&r=rmg |
| By: | Rene Schwaiger; Markus Strucks; Stefan Zeisberger |
| Abstract: | Narrow bracketing in combination with loss aversion has been shown to reduce individual risk-taking. This is known as myopic loss aversion (MLA) and has been corroborated by many studies. Recent evidence has contested this notion indicating that MLA’s applicability is confined to highly artificial settings. Given the impact of these findings, we reevaluated the evidence on MLA involving a total of 2, 245 university students, thereby achieving substantially higher statistical power than in almost all previous studies. To clarify inconsistencies in the literature, specifically under more realistic investment environments, we systematically modified the seminal study design by Gneezy and Potters (1997) to include five key adjustments. These involved realistic, down-scaled returns, return compounding, and extended investment horizons. Contrary to some prior studies that have raised doubts about the robustness of MLA, our results—which are highly robust to analytical heterogeneity—consistently document the presence of MLA across all experimental conditions. Our findings substantiate the widespread applicability of MLA and underscore the benefits of disclosing aggregated returns in practical financial decision-making contexts. |
| Keywords: | myopic loss aversion, narrow framing, risk-taking, meta science, replication |
| JEL: | D14 D81 G02 G11 |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:inn:wpaper:2024-05&r=rmg |
| By: | Zhaolin Li; Artem Prokhorov |
| Abstract: | We revisit the fundamental issue of tail behavior of accumulated random realizations when individual realizations are independent, and we develop new sharper bounds on the tail probability and expected linear loss. The underlying distribution is semi-parametric in the sense that it remains unrestricted other than the assumed mean and variance. Our sharp bounds complement well-established results in the literature, including those based on aggregation, which often fail to take full account of independence and use less elegant proofs. New insights include a proof that in the non-identical case, the distributions attaining the bounds have the equal range property, and that the impact of each random variable on the expected value of the sum can be isolated using an extension of the Korkine identity. We show that the new bounds not only complement the extant results but also open up abundant practical applications, including improved pricing of product bundles, more precise option pricing, more efficient insurance design, and better inventory management. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.02400&r=rmg |
| By: | Baptiste Lefort; Eric Benhamou; Jean-Jacques Ohana; David Saltiel; Beatrice Guez; Thomas Jacquot |
| Abstract: | This paper introduces a new risk-on risk-off strategy for the stock market, which combines a financial stress indicator with a sentiment analysis done by ChatGPT reading and interpreting Bloomberg daily market summaries. Forecasts of market stress derived from volatility and credit spreads are enhanced when combined with the financial news sentiment derived from GPT-4. As a result, the strategy shows improved performance, evidenced by higher Sharpe ratio and reduced maximum drawdowns. The improved performance is consistent across the NASDAQ, the S&P 500 and the six major equity markets, indicating that the method generalises across equities markets. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.00012&r=rmg |
| By: | Rodriguez, Harold; Colombo, Jefferson |
| Abstract: | Spot bitcoin ETFs have been recently approved in the U.S., increasing retail and institutional investors' attention to the crypto space. Still, empirical evidence on whether Bitcoin is an asset that protects investors against inflation is still inconclusive. To contribute to this debate, we analyze the effect of inflation shocks on bitcoin returns through the estimation and inference of Vector Autoregressive Models (VARs). Unlike previous research on the topic, we identify inflation shocks as surprises in the US’s CPI and Core PCE announcements: the difference between the announced inflation and the analysts’ consensus. The results, based on monthly data between August 2010 and January 2023, indicate that bitcoin returns increase significantly after a positive inflationary shock, corroborating empirical evidence that Bitcoin can act as an inflation hedge. However, we observe that bitcoin’s inflationary hedging property is sensitive to the price index -- it only holds for CPI shocks -- and to the period of analysis –- the hedging property stems primarily from sample periods before the increasing institutional adoption of BTC (``early days''). Thus, the inflation-hedging property of Bitcoin is context-specific and is likely to be diminishing as adoption increases. This research contributes to the still under-explored strand of literature that analyzes the hedging and safe-haven properties of Bitcoin and benefits asset managers, investors, and monetary authorities. |
| Keywords: | Bitcoin, Hedge against inflation, Unexpected inflation, surprises in CPI, surprises in PCE. |
| JEL: | E31 E44 G11 |
| Date: | 2024–03–06 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:120477&r=rmg |
| By: | Thorsten Hens (Department of Finance, University of Zurich, Department of Finance, Norwegian School of Economics, NHH, Institute of Economic Research, Kyoto University); Trine Nordlie (Department of Finance, Norwegian School of Economics, NHH, Bergen) |
| Abstract: | This study compares OpenAI's ChatGPT-4 and Google's Bard with bank experts in determining investors'risk profiles. We find that for half of the client cases used, there are no statistically significant differences in the risk profiles. Moreover, the economic relevance of the differences is small. |
| Keywords: | Large Language Models, ChatGPT, Bard, Risk Profiling |
| JEL: | D8 D14 D81 G51 |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:kyo:wpaper:1103&r=rmg |
| By: | Yupeng Cao; Zhi Chen; Qingyun Pei; Fabrizio Dimino; Lorenzo Ausiello; Prashant Kumar; K. P. Subbalakshmi; Papa Momar Ndiaye |
| Abstract: | The integration of Artificial Intelligence (AI) techniques, particularly large language models (LLMs), in finance has garnered increasing academic attention. Despite progress, existing studies predominantly focus on tasks like financial text summarization, question-answering (Q$\&$A), and stock movement prediction (binary classification), with a notable gap in the application of LLMs for financial risk prediction. Addressing this gap, in this paper, we introduce \textbf{RiskLabs}, a novel framework that leverages LLMs to analyze and predict financial risks. RiskLabs uniquely combines different types of financial data, including textual and vocal information from Earnings Conference Calls (ECCs), market-related time series data, and contextual news data surrounding ECC release dates. Our approach involves a multi-stage process: initially extracting and analyzing ECC data using LLMs, followed by gathering and processing time-series data before the ECC dates to model and understand risk over different timeframes. Using multimodal fusion techniques, RiskLabs amalgamates these varied data features for comprehensive multi-task financial risk prediction. Empirical experiment results demonstrate RiskLab's effectiveness in forecasting both volatility and variance in financial markets. Through comparative experiments, we demonstrate how different data sources contribute to financial risk assessment and discuss the critical role of LLMs in this context. Our findings not only contribute to the AI in finance application but also open new avenues for applying LLMs in financial risk assessment. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.07452&r=rmg |
| By: | Serena Merrino; Ilias Chondrogiannis |
| Abstract: | We examine the effect of post-2010 banking regulation in South Africa on financial stability, macroeconomic variables and bank performance. We focus on risk spillovers and increased network and tail connectedness between banks, using a sample of nine listed South African banks in 20082023. The implementation of Basel III regulation, particularly capital adequacy ratios, has reduced connectedness-related risks but there is weak evidence of an effect of regulation on bank performance. |
| Date: | 2024–04–15 |
| URL: | http://d.repec.org/n?u=RePEc:rbz:wpaper:11060&r=rmg |
| By: | Hirbod Assa; Peng Liu |
| Abstract: | This paper introduces and studies factor risk measures. While risk measures only rely on the distribution of a loss random variable, in many cases risk needs to be measured relative to some major factors. In this paper, we introduce a double-argument mapping as a risk measure to assess the risk relative to a vector of factors, called factor risk measure. The factor risk measure only depends on the joint distribution of the risk and the factors. A set of natural axioms are discussed, and particularly distortion, quantile, linear and coherent factor risk measures are introduced and characterized. Moreover, we introduce a large set of concrete factor risk measures and many of them are new to the literature, which are interpreted in the context of regulatory capital requirement. Finally, the distortion factor risk measures are applied in the risk-sharing problem and some numerical examples are presented to show the difference between the Value-at-Risk and the quantile factor risk measures. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.08475&r=rmg |
| By: | David Xiao |
| Abstract: | A Hedge Fund Index is very useful for tracking the performance of hedge fund investments, especially the timing of fund redemption. This paper presents a methodology for constructing a hedge fund index that is more like a quantitative fund of fund, rather than a weighted sum of a number of early replicable market indices, which are re-balanced periodically. The constructed index allows hedge funds to directly hedge their exposures to index-linked products. That is important given that hedge funds are an asset class with reduced transparency, and the returns are traditionally difficult to replicate using liquid instruments. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.15925&r=rmg |
| By: | Afees A. Salisu (Centre for Econometrics & Applied Research, Ibadan, Nigeria; Department of Economics, University of Pretoria, Private Bag X20, Hatfield 0028, South Africa); Ahamuefula E. Ogbonna (Centre for Econometrics & Applied Research, Ibadan, Nigeria); Rangan Gupta (Department of Economics, University of Pretoria, Private Bag X20, Hatfield 0028, South Africa); Qiang Ji (Institutes of Science and Development, Chinese Academy of Sciences, Beijing, China; School of Public Policy and Management, University of Chinese Academy of Sciences, Beijing, China) |
| Abstract: | In this paper, we employ the generalized autoregressive conditional heteroscedasticity-mixed data sampling (GARCH-MIDAS) framework to forecast the daily volatility of 19 dollar-based exchange rate returns based on monthly metrics of oil price uncertainty (OPU), and relatively broader global and country-specific energy market-related uncertainty indexes (EUI) over the daily period of January, 1996 to September, 2022. We find that the global EUIs tend to perform better than the OPU, in terms of their respective GARCH-MIDAS-based forecast performances relative to the benchmark (GARCH-MIDAS-realized volatility (RV)) model, highlighting the need to look beyond the oil market to capture energy related uncertainties. This line of reasoning is further enhanced when we observe the relative (to the United States) country-specific EUIs to outperform the benchmark in a statistically significant manner for at least 14 currencies across the short-, medium-, and long-term forecasting horizons. Our findings have important implications for currency traders. |
| Keywords: | Monthly Oil Price and Energy Market Uncertainties, Daily Exchange Rate Returns Volatility, GARCH-MIDAS, Forecasting |
| JEL: | C32 C53 F31 F37 Q02 |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:pre:wpaper:202418&r=rmg |
| By: | Cañon, Carlos (Bank of England); Gerba, Eddie (Bank of England); Pambira, Alberto (Bank of England); Stoja, Evarist (University of Bristol) |
| Abstract: | We examine how the tail risk of currency returns of nine countries, from 2000 to 2020, were impacted by central bank monetary and liquidity measures across the globe with an original and unique dataset that we make publicly available. Using a standard factor model, we derive theoretical measures of tail risks of currency returns which we then relate to the various policy instruments employed by central banks. We find empirical evidence for the existence of a cross-border transmission channel of central bank policy through the FX market. The tail impact is particularly sizeable for asset purchases and swap lines. The effects last for up to one month, and are proportionally higher in a hypothetical joint QE action scenario. This cross-border source of tail risk is largely undiversifiable, even after controlling for the US dollar dominance and the effects of its own monetary policy stance. |
| Keywords: | Unconventional and conventional monetary policy; liquidity measures; currency tail risk; systematic and idiosyncratic components of tail risk |
| JEL: | E44 E52 G12 G15 |
| Date: | 2024–04–05 |
| URL: | http://d.repec.org/n?u=RePEc:boe:boeewp:1068&r=rmg |
| By: | Ariel Neufeld; Julian Sester |
| Abstract: | In this article we present a general framework for non-concave distributionally robust stochastic control problems in a discrete time finite horizon setting. Our framework allows to consider a variety of different path-dependent ambiguity sets of probability measures comprising, as a natural example, the ambiguity set defined via Wasserstein-balls around path-dependent reference measures, as well as parametric classes of probability distributions. We establish a dynamic programming principle which allows to derive both optimal control and worst-case measure by solving recursively a sequence of one-step optimization problems. As a concrete application, we study the robust hedging problem of a financial derivative under an asymmetric (and non-convex) loss function accounting for different preferences of sell- and buy side when it comes to the hedging of financial derivatives. As our entirely data-driven ambiguity set of probability measures, we consider Wasserstein-balls around the empirical measure derived from real financial data. We demonstrate that during adverse scenarios such as a financial crisis, our robust approach outperforms typical model-based hedging strategies such as the classical Delta-hedging strategy as well as the hedging strategy obtained in the non-robust setting with respect to the empirical measure and therefore overcomes the problem of model misspecification in such critical periods. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.05230&r=rmg |
| By: | Onur Polat (Department of Public Finance, Bilecik Seyh Edebali University, Bilecik, Turkiye); Rangan Gupta (Department of Economics, University of Pretoria, Private Bag X20, Hatfield 0028, South Africa); Oguzhan Cepni (Copenhagen Business School, Department of Economics, Porcelænshaven 16A, Frederiksberg DK-2000, Denmark; Ostim Technical University, Ankara, Turkiye); Qiang Ji (Institutes of Science and Development, Chinese Academy of Sciences, Beijing, China; School of Public Policy and Management, University of Chinese Academy of Sciences, Beijing, China) |
| Abstract: | Using daily data on municipal bonds and equity returns from the 50 US states over the period from May 2, 2006, to February 9, 2024, we find that barring extreme periods of financial, macroeconomic, and health crises, the underlying conditional correlation between these two assets is negative, as derived from the Asymmetric Dynamic Conditional Correlations (ADCC)-Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model. When we utilize the Quantile-on-Quantile (QQ) regression model to capture the effect of climate risk quantiles on the entire conditional distribution of the underlying time-varying stock-bond correlation, we generally observe a negative impact at different levels of climate risks, although this could turn positive in the event of extreme climate disasters. In summary, the role of municipal bonds as a hedge against climate risks cannot be denied, carrying important portfolio allocation implications for investors. |
| Keywords: | Stocks and bonds returns, Time-varying conditional correlation, ADCC-GARCH, Climate risks, QQ regressions, US states |
| JEL: | C22 C32 G10 G12 Q54 |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:pre:wpaper:202419&r=rmg |
| By: | Vassilios Babalos (Department of Accounting and Finance, University of Peloponnese, Antikalamos, 24100 Kalamata, Greece); Elie Bouri (School of Business, Lebanese American University, Lebanon); Rangan Gupta (Department of Economics, University of Pretoria, Private Bag X20, Hatfield 0028, South Africa) |
| Abstract: | This paper provides first empirical evidence on whether the introduction of US spot Bitcoin ETFs affected the returns and volatility of major cryptocurrencies. Using data from December 18, 2017 to March 15, 2024 and applying various Generalized Autoregressive Conditional Heteroskedasticity (GARCH) with exogenous predictors (X), i.e., GARCH-X models, the main results show that the volatility of major cryptocurrencies, namely Ethereum, Ripple, and Litecoin, decreased following the SEC approval, which supports the stabilization hypothesis. No impact is noticed for the Bitcoin spot market, whereas the returns of Grayscale Bitcoin Trust (which represents the first publicly-traded Bitcoin fund in the US) increased following the introduction of Bitcoin ETFs. Further analysis on the returns and volatility of Bitcoin futures and Ethereum futures indicate an insignificant impact by the launch of US spot Bitcoin ETFs. Our findings enhance the limited understanding on the price discovery and functioning of the cryptocurrency markets, which could be useful for investors, regulators, and policymakers. |
| Keywords: | US spot Bitcoin ETFs introduction, SEC approval, Cryptocurrency spot returns and volatility, GARCH-X models |
| JEL: | C32 G00 |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:pre:wpaper:202416&r=rmg |
| By: | rao, amar; Dagar, Vishal; dagher, leila; Shobande, Olatunji |
| Abstract: | This study aims to investigate the spillover effects from geopolitical risks (proxied by the geopolitical risk index) and cryptocurrencies-related uncertainty (proxied by the Cryptocurrency Uncertainty Index) to cryptocurrencies. We utilize the Baruník and Křehlík (2018) framework to detect time-frequency connectedness. Our investigation for the period 2017 to 2022 discovers significant spillover effects from both indices to cryptocurrencies. Utilizing the information transmission theory and network graphs, our findings reveal that some cryptocurrencies function as net receivers of spillovers from geopolitical risks and uncertainty in the short-term, while over longer time horizons they transform into net transmitters of spillovers to uncertainty. The study contributes to better understanding how uncertainty due to various factors (geopolitical, policy changes, regulatory changes, etc.) could affect the cryptocurrencies’ markets. |
| Keywords: | cryptocurrencies; geopolitical risk; market uncertainty; time–frequency connectedness |
| JEL: | C58 G15 |
| Date: | 2024 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:120582&r=rmg |
| By: | Nikitas Stamatopoulos; B. David Clader; Stefan Woerner; William J. Zeng |
| Abstract: | We introduce two quantum algorithms to compute the Value at Risk (VaR) and Conditional Value at Risk (CVaR) of financial derivatives using quantum computers: the first by applying existing ideas from quantum risk analysis to derivative pricing, and the second based on a novel approach using Quantum Signal Processing (QSP). Previous work in the literature has shown that quantum advantage is possible in the context of individual derivative pricing and that advantage can be leveraged in a straightforward manner in the estimation of the VaR and CVaR. The algorithms we introduce in this work aim to provide an additional advantage by encoding the derivative price over multiple market scenarios in superposition and computing the desired values by applying appropriate transformations to the quantum system. We perform complexity and error analysis of both algorithms, and show that while the two algorithms have the same asymptotic scaling the QSP-based approach requires significantly fewer quantum resources for the same target accuracy. Additionally, by numerically simulating both quantum and classical VaR algorithms, we demonstrate that the quantum algorithm can extract additional advantage from a quantum computer compared to individual derivative pricing. Specifically, we show that under certain conditions VaR estimation can lower the latest published estimates of the logical clock rate required for quantum advantage in derivative pricing by up to $\sim 30$x. In light of these results, we are encouraged that our formulation of derivative pricing in the QSP framework may be further leveraged for quantum advantage in other relevant financial applications, and that quantum computers could be harnessed more efficiently by considering problems in the financial sector at a higher level. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.10088&r=rmg |
| By: | Stefano Colonnello (Department of Economics, Ca’ Foscari University of Venice); Giuliano Curatola (University of Siena; Leibniz Institute for Financial Research SAFE); Shuo Xia (Leipzig University; Halle Institute for Economic Research (IWH)) |
| Abstract: | To contain bankers' risk-shifting behavior, policymakers use a variety of tools. Among them, mandating the use of default-linked (i.e., debt-like) pay features prominently, typically in the form of bonus deferrals. In our model, a risk-neutral manager is in charge of choosing bank-level asset risk, receiving in exchange a compensation package consisting of a bonus and a default-linked component. In the spirit of existing regulation and widespread industry practices, we give the manager discretion over the allocation of the personal default-linked account between own bank's shares and an alternative asset. The possibility for the manager to tie the value of default-linked pay to equity weakens its debt-like feature and, in the same way, its ability to rein in excessive risk-taking. Bank leverage and bailout expectations appear to exacerbate these effects, which may be further aggravated by the endogenous shareholders' choice to design a more convex bonus as a response to mandatory default-linked pay. Our analysis raises concerns on the robustness of the theoretical foundations of some recent regulatory efforts. |
| Keywords: | Bank Risk-Taking, Banking Regulation, Default-Linked Compensation |
| JEL: | G21 G28 G34 M12 |
| Date: | 2024 |
| URL: | http://d.repec.org/n?u=RePEc:ven:wpaper:2024:07&r=rmg |
| By: | Simon Firestone; Nathan Y. Godin; Akos Horvath; Jacob Sagi |
| Abstract: | We use model-implied volatility to proxy for property risk perceptions in the commercial real estate lending market. Although loan-to-value ratios (LTVs) unconditionally decreased following the Global Financial Crisis, LTVs conditioned on implied volatility and other theoretically motivated fundamental determinants of optimal leverage show no conclusive trend before or after the crisis. Taking reported property and loan attributes at face value, we find no clear pattern of unwarranted credit being extended to commercial real estate assets. We conclude that systematically higher LTV decisions pre-crisis would have primarily stemmed from risk misperceptions rather than imprudent practices. Our findings suggest that the aggregate LTV level should be interpreted as a proxy for lending standards only after controlling for aggregate risk perceptions, among a host of asset and lending market factors. Our findings also highlight the importance of measuring and tracking aggregate risk perceptions in informing regulators and policymakers. |
| Keywords: | Loan underwriting; Lending standards; Global Financial Crisis; Mortgages; Real estate finance; Implied volatility |
| JEL: | C22 D80 G01 G10 G18 G21 R38 |
| Date: | 2024–04–10 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedgfe:2024-19&r=rmg |