nep-rmg New Economics Papers
on Risk Management
Issue of 2023‒12‒11
twenty-two papers chosen by



  1. Tail Risk and Asset Prices in the Short-term By Caio Almeida; Gustavo Freire; René Garcia; Rodrigo Hizmeri
  2. A Risk Management Approach to Monetary Policy By James B. Bullard
  3. Long-Term Volatility Shapes the Stock Market’s Sensitivity to News By Christian Conrad; Julius Theodor Schoelkopf; Nikoleta Tushteva
  4. Forecasting Volatility with Machine Learning and Rough Volatility: Example from the Crypto-Winter By Siu Hin Tang; Mathieu Rosenbaum; Chao Zhou
  5. Recent Developments in Financial Risk and the Real Economy By Ian Dew-Becker; Stefano Giglio
  6. Listed Real Estate as an Inflation Hedge across Regimes By Jan Muckenhaupt; Martin Hoesli; Bing Zhu
  7. Neural Tangent Kernel in Implied Volatility Forecasting: A Nonlinear Functional Autoregression Approach By Chen, Ying; Grith, Maria; Lai, Hannah L. H.
  8. Common Risk Factors of REITs Returns Revisited By Alain Coen; Philippe Guardiola
  9. Law-Invariant Return and Star-Shaped Risk Measures By Roger J. A. Laeven; Emanuela Rosazza Gianin; Marco Zullino
  10. Bayesian Risk Assessment Technique for Economic Stress-Strength Models By Savchuk, Vladimir
  11. Housing in the Greater Paris Area as an Inflation Hedge? By Aya Nasreddine; Yasmine Essafi Zouari
  12. International portfolio frictions By Wenxin Du; Alessandro Fontana; Petr Jakubik; Ralph S J Koijen; Hyun Song Shin
  13. A multi-agent incomplete equilibrium model and its applications to reinsurance pricing and life-cycle investment (Forthcoming in "Insurance: Mathematics and Economics") By Keisuke Kizaki; Taiga Saito; Akihiko Takahashi
  14. A deep dive into the capital channel of risk sharing in the euro area By Martín Fuentes, Natalia; Born, Alexandra; Bremus, Franziska; Kastelein, Wieger; Lambert, Claudia
  15. Natural Hazard Exposure and REIT Equity Risk By Bing Zhu; Franz Fuerst
  16. Safety, in Numbers By Marilyn Pease; Mark Whitmeyer
  17. Robust Estimation of Realized Correlation: New Insight about Intraday Fluctuations in Market Betas By Peter Reinhard Hansen; Yiyao Luo
  18. Optimal dividend strategies for a catastrophe insurer By Hansjoerg Albrecher; Pablo Azcue; Nora Muler
  19. CDS and Credit: The Effect of the Bangs on Credit Insurance, Lending and Hedging By Yalin Gündüz; Steven Ongena; Gunseli Tumer-Alkan; Yuejuan Yu
  20. Getting the Right Tail Right: Modeling tails of health expenditure distributions By Karlsson, Martin; Wang, Yulong; Ziebarth, Nicolas R.
  21. Banking System Vulnerability: 2023 Update By Matteo Crosignani; Thomas M. Eisenbach; Fulvia Fringuellotti
  22. Fund fragility: the role of investor base By Allaire, Nolwenn; Breckenfelder, Johannes; Hoerova, Marie

  1. By: Caio Almeida (Princeton University); Gustavo Freire (Erasmus University Rotterdam); René Garcia (Université de Montréal); Rodrigo Hizmeri (University of Liverpool)
    Abstract: We combine high-frequency stock returns with risk-neutralization to extract the daily common component of tail risks perceived by investors in the cross-section of firms. Our tail risk measure significantly predicts the equity premium and variance risk premium at short-horizons. Furthermore, a long-short portfolio built by sorting stocks on their recent exposure to tail risk generates abnormal returns with respect to standard factor models and helps explain the momentum anomaly. Incorporating investors' preferences via risk-neutralization is fundamental to our findings.
    Keywords: Left tail risk, return predictability, factor models, risk-neutralization, high-frequency data
    JEL: C58 G12 G17
    Date: 2023–03
    URL: http://d.repec.org/n?u=RePEc:pri:econom:2023-06&r=rmg
  2. By: James B. Bullard
    Abstract: St. Louis Fed President Jim Bullard discusses a risk management approach to monetary policy that accounts for different inflation scenarios in 2022.
    Keywords: monetary policy; inflation; risk management
    Date: 2021–12–02
    URL: http://d.repec.org/n?u=RePEc:fip:l00001:94051&r=rmg
  3. By: Christian Conrad (Heidelberg University, Department of Economics, Germany; KOF Swiss Economic Institute, Switzerland; Heidelberg Karlsruhe Strategic Partnership, Heidelberg University, Karlsruhe Institute of Technology, Germany; Rimini Centre for Economic Analysis); Julius Theodor Schoelkopf (Heidelberg University, Department of Economics, Germany); Nikoleta Tushteva (European Central Bank)
    Abstract: We show that the S&P 500’s instantaneous response to surprises in U.S. macroeconomic announcements depends on the level of long-term stock market volatility. When long-term volatility is high, stock returns are more sensitive to news, and there is a pronounced asymmetry in the response to good and bad news. We explain this by combining the Campbell-Shiller log-linear present value framework with a two-component volatility model for the conditional variance of cash flow news and allowing for volatility feedback. In our model, innovations to the long-term volatility component are the most important driver of discount rate news. Large announcement surprises lead to upward revisions in future required returns, which dampens/amplifies the effect of good/bad news.
    Keywords: event study, long- and short-term volatility, macroeconomic announcements, stock market response, time-varying risk premia, volatility feedback effect
    JEL: C58 E44 G12 G14
    Date: 2023–11
    URL: http://d.repec.org/n?u=RePEc:rim:rimwps:23-16&r=rmg
  4. By: Siu Hin Tang; Mathieu Rosenbaum; Chao Zhou
    Abstract: We extend the application and test the performance of a recently introduced volatility prediction framework encompassing LSTM and rough volatility. Our asset class of interest is cryptocurrencies, at the beginning of the "crypto-winter" in 2022. We first show that to forecast volatility, a universal LSTM approach trained on a pool of assets outperforms traditional models. We then consider a parsimonious parametric model based on rough volatility and Zumbach effect. We obtain similar prediction performances with only five parameters whose values are non-asset-dependent. Our findings provide further evidence on the universality of the mechanisms underlying the volatility formation process.
    Date: 2023–11
    URL: http://d.repec.org/n?u=RePEc:arx:papers:2311.04727&r=rmg
  5. By: Ian Dew-Becker; Stefano Giglio
    Abstract: This paper reviews recent developments in macro and finance on the relationship between financial risk and the real economy. We focus on three specific topics: the term structure of uncertainty, time variation - and specifically the long-term decline - in the variance risk premium, and time variation in conditional skewness. We also introduce two new data series: implied volatility from one-day options on grains for the period 1906-1936, and on cliquet options, which provide insurance against single-day crashes on the S&P 500, both of which give some context to the recent rise in trade in extremely short-dated options. Finally, we discuss new avenues for future research.
    JEL: E10 G10 G12 G13 N1 N2
    Date: 2023–11
    URL: http://d.repec.org/n?u=RePEc:nbr:nberwo:31878&r=rmg
  6. By: Jan Muckenhaupt; Martin Hoesli; Bing Zhu
    Abstract: This paper investigates the inflation hedging capability of listed real estate (LRE) companies from 1990 to 2021 in four economies: the US, the UK, Australia, and Japan. By using a Markov switching vector error correction model (MS-VECM), we identify that the short-term hedging ability moves towards being negative or zero during crisis periods. In non-crisis periods, LRE provides good protection against inflation. In the long term, LRE provides a good hedge against expected inflation, and shows a superior inflation hedging ability than stocks. Additionally, we propose inflation-hedging portfolios by minimizing the expected shortfall. This inflation-hedging portfolio allocation methodology suggests that listed real estate stocks should play a significant role in investor portfolios.
    Keywords: Inflation Hedging; Inflation-Hedging Portfolio; Listed Real Estate Companies; Markov-switching
    JEL: R3
    Date: 2023–01–01
    URL: http://d.repec.org/n?u=RePEc:arz:wpaper:eres2023_56&r=rmg
  7. By: Chen, Ying; Grith, Maria; Lai, Hannah L. H.
    Abstract: Implied volatility (IV) forecasting is inherently challenging due to its high dimensionality across various moneyness and maturity, and nonlinearity in both spatial and temporal aspects. We utilize implied volatility surfaces (IVS) to represent comprehensive spatial dependence and model the nonlinear temporal dependencies within a series of IVS. Leveraging advanced kernel-based machine learning techniques, we introduce the functional Neural Tangent Kernel (fNTK) estimator within the Nonlinear Functional Autoregression framework, specifically tailored to capture intricate relationships within implied volatilities. We establish the connection between fNTK and kernel regression, emphasizing its role in contemporary nonparametric statistical modeling. Empirically, we analyze S&P 500 Index options from January 2009 to December 2021, encompassing more than 6 million European calls and puts, thereby showcasing the superior forecast accuracy of fNTK.We demonstrate the significant economic value of having an accurate implied volatility forecaster within trading strategies. Notably, short delta-neutral straddle trading, supported by fNTK, achieves a Sharpe ratio ranging from 1.45 to 2.02, resulting in a relative enhancement in trading outcomes ranging from 77% to 583%.
    Keywords: Implied Volatility Surfaces; Neural Networks; Neural Tangent Kernel; Implied Volatility Forecasting; Nonlinear Functional Autoregression; Option Trading Strategies
    JEL: C14 C45 C58 G11 G13 G17
    Date: 2023–10–24
    URL: http://d.repec.org/n?u=RePEc:pra:mprapa:119022&r=rmg
  8. By: Alain Coen; Philippe Guardiola
    Abstract: In this article we analyze the dynamic returns of REITs and test multi-factor asset pricing models based on real estate specific risk exposure, including market risk, size, value momentum, cash flow volatility, leverage, investment growth, term risk, default risk, liquidity risk and common macroeconomic factors. We also focus on the role of idiosyncratic risk and higher moments and scrutinize their relative importance to explain the decomposition of listed property companies returns on U.S. financial markets. We suggest the use of a new parsimonious common factors model to improve REITs valuation and to define their cost of capital. Revisiting the previous literature devoted to the role of leverage in the real estate industry, our empirical (un-conditional and conditional) results shed new light on leverage risk and idiosyncratic risk for U.S. REITs returns over a long period (2000-2021) marked by important crises.
    Keywords: Asset Pricing; Leverage; Multifactor Models; REITs
    JEL: R3
    Date: 2023–01–01
    URL: http://d.repec.org/n?u=RePEc:arz:wpaper:eres2023_249&r=rmg
  9. By: Roger J. A. Laeven; Emanuela Rosazza Gianin; Marco Zullino
    Abstract: This paper presents novel characterization results for classes of law-invariant star-shaped functionals. We begin by establishing characterizations for positively homogeneous and star-shaped functionals that exhibit second- or convex-order stochastic dominance consistency. Building on these characterizations, we proceed to derive Kusuoka-type representations for these functionals, shedding light on their mathematical structure and intimate connections to Value-at-Risk and Expected Shortfall. Furthermore, we offer representations of general law-invariant star-shaped functionals as robustifications of Value-at-Risk. Notably, our results are versatile, accommodating settings that may, or may not, involve monotonicity and/or cash-additivity. All of these characterizations are developed within a general locally convex topological space of random variables, ensuring the broad applicability of our results in various financial, insurance and probabilistic contexts.
    Date: 2023–10
    URL: http://d.repec.org/n?u=RePEc:arx:papers:2310.19552&r=rmg
  10. By: Savchuk, Vladimir
    Abstract: This paper explores two areas of risk assessment modelling in economics and business: the Stress-Strength model and Bayesian techniques. The model assumes that the probability of stress exceeding strength is a measure of risk. The interpretation of stress and strength largely depends on the particular event or phenomenon being modelled. The use of the Stress-Strength model is demonstrated through the Gaussian assumption of probability distributions for random model parameters, particularly in assessing the risk of not achieving a required margin value. The concept of the capability function, representing the difference between strength and stress, is introduced in the modelling process. The probability distribution for the capability function is initially determined based on the Gaussian distribution of the random variables used in the model, allowing for evaluating the risk metric. The Bayesian approach is then applied to generalise the problem statement when dealing with unknown parameters of probability distributions for the Stress and Strength models. The uncertainty of these parameters is modelled through uniform probability distributions, and equations for calculating prior and posterior estimates are consistently obtained. Since multidimensional integrals are involved in these calculations, and solutions cannot be obtained in closed analytical form, Monte Carlo simulation is used to solve this computation problem.
    Keywords: Stress-Strength model, capability function, Gaussian, Bayesian.
    JEL: M21
    Date: 2023–02–10
    URL: http://d.repec.org/n?u=RePEc:pra:mprapa:119078&r=rmg
  11. By: Aya Nasreddine; Yasmine Essafi Zouari
    Abstract: In this article, we use the framework of inflation beta to test the capacity of physical residential real estate to hedge against inflation and its components, and compare it to the inflation hedge ability of various financial assets. Specifically, the housing asset is represented by the residential market in the communes of the “Grand Paris” metropolis with the different components of inflation. We start by analyzing the residential market in this area, its fundamentals, characteristics and dynamic. Then, applying the hierarchical clustering technique, we divide the Greater Paris area into five homogenous groups of communes and test its hedging ability using both correlation and regression analysis. Residential assets are confirmed to be a hedge against inflation, particularly against its unexpected component and thanks to its capital return rather than the rental return. On the other hand, the listed real estate does not provide the same hedging properties and thus cannot be considered as a substitute for this aim.
    Keywords: Direct housing; Grand Paris Metropolis; Hedging ability; Inflation
    JEL: R3
    Date: 2023–01–01
    URL: http://d.repec.org/n?u=RePEc:arz:wpaper:eres2023_11&r=rmg
  12. By: Wenxin Du; Alessandro Fontana; Petr Jakubik; Ralph S J Koijen; Hyun Song Shin
    Abstract: We study patterns and implications of global asset allocations of European insurers and banks using newly available supervisory data. We show that the total assets of insurance companies and pension funds (ICPF) far exceed the amount of government bonds outstanding in Europe, and that countries with a large ICPF sector tend to have a large corporate bond market. Despite high levels of international investments, the characteristics of domestic financial markets still loom large in insurers’ and banks’ portfolio allocation, with two newly documented international portfolio frictions playing a prominent role. First, when investing abroad, insurers and banks do not offset attributes of the domestic markets (such as the composition of fixed-income markets, interest rates, and sovereign credit risk), which we label “domestic projection bias.” Second, subsidiaries of multinational groups act like local entities, which we label the “going native bias.” We propose a theoretical framework to explain our empirical findings and discuss the broader policy implications for European capital market deepening and integration, monetary policy transmission and financial stability, and a multi-sectoral approach to regulatory design.
    Keywords: Banks, insurance companies, pension funds, portfolio choice, fixed income, home bias
    JEL: G2 G11 G15 G21 G22 G28
    Date: 2023–10
    URL: http://d.repec.org/n?u=RePEc:bis:biswps:1137&r=rmg
  13. By: Keisuke Kizaki (Life Insurance Analytics Department, Mizuho-DL Financial Technology Co., Ltd.,); Taiga Saito (School of Commerce, Senshu University); Akihiko Takahashi (Graduate School of Economics, The University of Tokyo)
    Abstract: This paper develops an incomplete equilibrium model with multi-agents' different risk attitudes and heterogeneous income/payout pro les. Particularly, we apply its concrete and computationally tractable model to reinsurance derivatives pricing and life-cycle investment, which are important for insurance and asset management companies in practice. In numerical experiments, we explicitly obtain endogenously determined expected returns of the risky asset in equilibrium, agents' speci c reinsurance prices with their stochastic discount factors (SDF) and optimal life-cycle trading strategies. Moreover, we investigate how each agent's degree of risk aversion and income/payout pro le, and correlations between an insurance or economic factor and the risky asset price affect reinsurance claims pricing and optimal portfolios in life-cycle investment.
    Date: 2023–11
    URL: http://d.repec.org/n?u=RePEc:cfi:fseres:cf576&r=rmg
  14. By: Martín Fuentes, Natalia; Born, Alexandra; Bremus, Franziska; Kastelein, Wieger; Lambert, Claudia
    Abstract: This paper investigates the contribution of capital markets to international risk sharing in the euro area over the 2000Q1-2021Q1 period. It provides three main contributions: First, the estimation of country-specific vector autoregressions (VAR) shows that shock absorption through capital markets remains modest, particularly in the southern euro area. Second, we analyse the geographical patterns of the capital channel. While risk sharing between southern and northern euro area countries led the improvements in income smoothing at the beginning of the 2000s, intra-regional capital flows supported income smoothing in the recent past. Third, based on a panel threshold VAR, we analyse how the composition of external capital positions impacts the capital channel. Long-term portfolio debt assets and liabilities as well as equity liabilities significantly improved income smoothing. The effect is more pronounced for northern countries, in line with their larger cross-border portfolios, when compared to the southern countries. Regarding foreign direct investment, only northern countries benefited from inward positions. JEL Classification: C23, E62, G11, G15
    Keywords: capital channel, CMU, external financial structure, international risk sharing, panel threshold vector autoregression (TVAR) model
    Date: 2023–11
    URL: http://d.repec.org/n?u=RePEc:ecb:ecbwps:20232864&r=rmg
  15. By: Bing Zhu; Franz Fuerst
    Abstract: This paper investigates if exposure to natural hazards in its underlying assets affects the equity risk of a real estate fund. In a panel dataset of 139 distinct Real Estate Investment Trusts (REITs) over the period of 2004 to 2021, we find that REITs with a higher natural hazard exposure show a higher market beta. This finding persists even when possible endogenous market selection is taken into account, using historical hurricanes as a natural experiment and an instrumental variables approach. The increased systematic risk is explained by the increased cost of debt and reduced rental income. Assets in more resilient communities, more green buildings in the portfolio, and higher ESG performance are all shown to attenuate the impact of natural hazard risk on the market beta of a REIT. Investors seeking to lower their exposure to climate risk can use the proposed metrics at various levels of spatial aggregation to gauge the resilience of their investments.
    Keywords: Asset Pricing Model; Market Beta; Natural Hazard Risk; REITs
    JEL: R3
    Date: 2023–01–01
    URL: http://d.repec.org/n?u=RePEc:arz:wpaper:eres2023_64&r=rmg
  16. By: Marilyn Pease; Mark Whitmeyer
    Abstract: We introduce a way to compare actions in decision problems. An action is safer than another if the set of beliefs at which the decision-maker prefers the safer action increases in size (in the set inclusion sense) as the decision-maker becomes more risk averse. We provide a full characterization of this relation and discuss applications to robust belief elicitation, contracting, Bayesian persuasion, game theory, and investment hedging.
    Date: 2023–10
    URL: http://d.repec.org/n?u=RePEc:arx:papers:2310.17517&r=rmg
  17. By: Peter Reinhard Hansen; Yiyao Luo
    Abstract: Time-varying volatility is an inherent feature of most economic time-series, which causes standard correlation estimators to be inconsistent. The quadrant correlation estimator is consistent but very inefficient. We propose a novel subsampled quadrant estimator that improves efficiency while preserving consistency and robustness. This estimator is particularly well-suited for high-frequency financial data and we apply it to a large panel of US stocks. Our empirical analysis sheds new light on intra-day fluctuations in market betas by decomposing them into time-varying correlations and relative volatility changes. Our results show that intraday variation in betas is primarily driven by intraday variation in correlations.
    Date: 2023–10
    URL: http://d.repec.org/n?u=RePEc:arx:papers:2310.19992&r=rmg
  18. By: Hansjoerg Albrecher; Pablo Azcue; Nora Muler
    Abstract: In this paper we study the problem of optimally paying out dividends from an insurance portfolio, when the criterion is to maximize the expected discounted dividends over the lifetime of the company and the portfolio contains claims due to natural catastrophes, modelled by a shot-noise Cox claim number process. The optimal value function of the resulting two-dimensional stochastic control problem is shown to be the smallest viscosity supersolution of a corresponding Hamilton-Jacobi-Bellman equation, and we prove that it can be uniformly approximated through a discretization of the space of the free surplus of the portfolio and the current claim intensity level. We implement the resulting numerical scheme to identify optimal dividend strategies for such a natural catastrophe insurer, and it is shown that the nature of the barrier and band strategies known from the classical models with constant Poisson claim intensity carry over in a certain way to this more general situation, leading to action and non-action regions for the dividend payments as a function of the current surplus and intensity level. We also discuss some interpretations in terms of upward potential for shareholders when including a catastrophe sector in the portfolio.
    Date: 2023–11
    URL: http://d.repec.org/n?u=RePEc:arx:papers:2311.05781&r=rmg
  19. By: Yalin Gündüz (Deutsche Bundesbank); Steven Ongena (University of Zurich; KU Leuven; NTNU Business School; Swiss Finance Institute; CEPR); Gunseli Tumer-Alkan (VU University Amsterdam); Yuejuan Yu (Shandong University)
    Abstract: We assess the differential impact of the “Big Bang” and “Small Bang” contract and convention changes on market participants across CDS markets. We couple comprehensive bank-firm level CDS trading data from DTCC to the German credit register containing bilateral bank-firm credit exposures. We find that after the Bangs, the cost of buying CDS contracts becomes lower for non dealer banks, and that – because of this decrease in insurance cost – these banks extend relatively more credit to CDS traded and affected firms compared to dealers, and hedge more effectively. Hence, standardization lowers the cost of credit insurance and increases credit availability.
    Keywords: Credit default swaps, credit exposure, hedging, bank lending, Depository Trust and Clearing Corporation (DTCC)
    JEL: G21
    Date: 2023–11
    URL: http://d.repec.org/n?u=RePEc:chf:rpseri:rp23102&r=rmg
  20. By: Karlsson, Martin; Wang, Yulong; Ziebarth, Nicolas R.
    Abstract: Health expenditure data almost always include extreme values, implying that the underlying distribution has heavy tails. This may result in infinite variances as well as higher-order moments and bias the commonly used least squares methods. To accommodate extreme values, we propose an estimation method that recovers the right tail of health expenditure distributions. It extends the popular two-part model to develop a novel three-part model. We apply the proposed method to claims data from one of the biggest German private health insurers. Our findings show that the estimated age gradient in health care spending differs substantially from the standard least squares method.
    Keywords: heavy tails, health expenditures, claims data, nonlinear model
    JEL: C10 C13 I10 I13
    Date: 2023
    URL: http://d.repec.org/n?u=RePEc:zbw:zewdip:279812&r=rmg
  21. By: Matteo Crosignani; Thomas M. Eisenbach; Fulvia Fringuellotti
    Abstract: The bank failures that occurred in March 2023 highlighted how unrealized losses on securities can make banks vulnerable to a sudden loss of funding. This risk, which materialized following the rapid rise in interest rates that began in early 2022, underscores the importance of monitoring the vulnerabilities of the banking system. In this post, as in previous years, we provide an update of four analytical models aimed at capturing different aspects of vulnerability of the U.S. banking system, with data through the second quarter of 2023. In addition, we discuss changes made to the methodology based on the lessons from March 2023 and assess how the system-level vulnerability has evolved.
    Keywords: banks; capital; fire sales; liquiditiy; runs
    JEL: G2
    Date: 2023–11–06
    URL: http://d.repec.org/n?u=RePEc:fip:fednls:97313&r=rmg
  22. By: Allaire, Nolwenn; Breckenfelder, Johannes; Hoerova, Marie
    Abstract: Using security-by-security data on investor holdings in the euro area, we study run dynamics across different fund-shares of the same fund during the unprecedented liquidity crisis in March 2020. For an average bond or equity mutual fund-share, households, other euro area funds, and the foreign sector each represent about a quarter of the total holdings. Insurance companies hold another 14%, with all other investors combined (banks, non-financial corporations, pension funds, etc.) accounting for less than 10% of holdings. Analyzing bond funds, we show that fund-shares with higher ownership by other funds suffered substantially higher outflows (by 6 percentage points), while fund-shares with higher ownership by households had substantially lower outflows (by 5 percentage points) compared to the other fund-shares within the same fund. This gap is not driven by time-varying differences in fund performance. Results for equity funds are similar, although they faced substantially smaller outflows, coupled with much larger declines in performance, compared to bond funds. Our findings suggest that a collective “dash for cash” by consumers and firms in need of liquidity at the outset of the COVID-19 pandemic was not the source of mutual fund fragility. Instead, the most run-prone investor type turned out to be the fund sector itself. JEL Classification: G01, G10, G21, G23
    Keywords: investor type, liquidity, March 2020 liquidity crisis, mutual funds, runs
    Date: 2023–11
    URL: http://d.repec.org/n?u=RePEc:ecb:ecbwps:20232874&r=rmg

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