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on Risk Management |
| By: | Chia-Lin Chang (National Chung Hsing University, Taichung, Taiwan); Juan-Ángel Jiménez-Martín (Complutense University of Madrid, Spain); Esfandiar Maasoumi (Emory University, United States); Michael McAleer (National Tsing Hua University, Taiwan, Erasmus School of Economics, Erasmus University Rotterdam,Tinbergen Institute, The Netherlands, Complutense University of Madrid, Spain); Teodosio Pérez-Amaral (Complutense University of Madrid, Spain) |
| Abstract: | The Basel Committee on Banking Supervision (BCBS) (2013) recently proposed shifting the quantitative risk metrics system from Value-at-Risk (VaR) to Expected Shortfall (ES). The BCBS (2013) noted that “a number of weaknesses have been identified with using VaR for determining regulatory capital requirements, including its inability to capture tail risk” (p. 3). For this reason, the Basel Committee is considering the use of ES, which is a coherent risk measure and has already become common in the insurance industry, though not yet in the banking industry. While ES is mathematically superior to VaR in that it does not show “tail risk” and is a coherent risk measure in being subadditive, its practical implementation and large calculation requirements may pose operational challenges to financial firms. Moreover, previous empirical findings based only on means and standard deviations suggested that VaR and ES were very similar in most practical cases, while ES could be less precise because of its larger variance. In this paper we find that ES is computationally feasible using personal computers and, contrary to previous research, it is shown that there is a stochastic difference between the 97.5% ES and 99% VaR. In the Gaussian case, they are similar but not equal, while in other cases they can differ substantially: in fat-tailed conditional distributions, on the one hand, 97.5%-ES would imply higher risk forecasts, while on the other, it provides a smaller down-side risk than using the 99%-VaR. It is found that the empirical results in the paper generally support the proposals of the Basel Committee. |
| Keywords: | Stochastic dominance; Value-at-Risk; Expected Shortfall; Optimizing strategy; Basel III Accord |
| JEL: | C53 C22 G32 G11 G17 |
| Date: | 2015–05–18 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20150056&r=rmg |
| By: | Jon Danielsson; Chen Zhou |
| Abstract: | This paper analyzes the robustness of standard risk analysis techniques, with a special emphasis on the specifications in Basel III. We focus on the difference between Value– at–Risk and expected shortfall, the small sample properties of these risk measures and the impact of using an overlapping approach to construct data for longer holding periods. Overall, risk forecasts are extremely uncertain at low sample sizes. By comparing the estimation uncertainty, we find that Value–at–Risk is superior to expected shortfall and the time-scaling approach for risk forecasts with longer holding periods is preferable to using overlapping data. |
| Keywords: | value–at–risk; expected shortfall; finite sample properties; Basel II |
| JEL: | C10 C15 G18 |
| Date: | 2015–04–23 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:62002&r=rmg |
| By: | Muteba Mwamba, John; Mhlanga, Isaah |
| Abstract: | This paper empirically compares the static unconditional Value-at-Risk (VaR) and conditional Value-at-Risk (CVaR) estimates based on two extreme value theory (EVT) distributions: the generalized extreme value distribution (GEV) and the generalized Pareto distribution (GPD); and two other traditional methodologies: the historical simulation and the variance covariance method as a benchmark models. Using daily equity and exchange rate data from the United States, Japan, Europe, Brazil, Hong-Kong and South Africa covering the pre-crisis period (2004 to 2006), the crisis period (2007 to 2008) and the recovery period (2009 to 2011), we consider both the downside and upside risk to evaluate extreme losses for both long and short positions held by investors. The paper has several findings. Firstly, we find that the conditional GEV model outperforms all the other models at all the quantiles; however it overestimates risk especially the upside risk. Secondly, the conditional GPD does not perform significantly different from the unconditional historical simulation. Thirdly, as expected of models that ignore the fact that returns are fat tailed by assuming normally distributed returns, the unconditional variance-covariance model underestimates risk in both directions and at all quantiles. Fourthly, risk levels were highest during the crisis period, and decreased significantly in the recovery period however to levels still above the pre-crisis period. Lastly, regarding risk levels in advanced economies compared to emerging economies, a reverse of the pre- crisis period scenario occurred since the onset of the financial crisis, advanced economies are now riskier than emerging economies. |
| Keywords: | Risk management; value-at-risk; conditional value-at-risk, extreme value theory; generalized extreme value distribution; generalized Pareto distribution, historical simulation; variance-covariance; fat-tails |
| JEL: | G1 G11 G15 G2 G23 |
| Date: | 2013–08–13 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:64387&r=rmg |
| By: | Dominique Guegan (Centre d'Economie de la Sorbonne); Bertrand K Hassani (Grupo Santander et Centre d'Economie de la Sorbonne) |
| Abstract: | This paper discusses the regulatory requirement (Basel Committee, ECB-SSM and EBA) to measure financial institutions' major risks, for instance Market, Credit and Operational, regarding the choice of the risk measures, the choice of the distributions used to model them and the level of confidence. We highlight and illustrate the paradoxes and the issues observed implementing an approach over another and the inconsistencies between the methodologies suggested and the goal to achieve. This paper make some recommendations to the supervisor and proposes alternative procedures to measure the risks |
| Keywords: | Risk measures; Sub-additivity; Level of confidence; Extreme value distributions; Financial regulation |
| JEL: | C1 C6 |
| Date: | 2015–05 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:15046&r=rmg |
| By: | Paul Glasserman (Office of Financial Research); Wanmo Kang (Korea Advanced Institute of Science and Technology) |
| Abstract: | Banking regulations set minimum levels of capital for banks. These requirements are generally formulated through a ratio of capital to risk-weighted assets. A risk-weighting scheme assigns a weight to each asset or category of assets and effectively functions as a linear constraint on a bank's portfolio choice; it also changes the incentives for banks to hold various kinds of assets. In this paper, we investigate the design of risk weights to align regulatory and private objectives in a simple mean-variance framework for portfolio selection. By setting risk weights proportional to profitability rather than risk, the regulator can induce a bank to reduce its overall level of risk without distorting its asset mix. Because the regulator is unlikely to know the true profitability of assets, we introduce an adaptive formulation in which the regulator sets weights by observing a bank's portfolio. The adaptive scheme converges to the same combination of weights and portfolio choice that would hold if the regulator knew the asset profitability. We also investigate other objectives, including steering banks to a target mix of assets, adding robustness, mitigating procyclicality, and reducing system-wide risk in a setting with multiple heterogeneous banks. |
| Keywords: | Risk Weights, Banking |
| Date: | 2014–08–19 |
| URL: | http://d.repec.org/n?u=RePEc:ofr:wpaper:14-06&r=rmg |
| By: | Makoto Takahashi (Graduate School of Economics, Osaka University); Toshiaki Watanabe (Institute of Economic Research, Hitotsubashi University); Yasuhiro Omori (Faculty of Economics, The University of Tokyo) |
| Abstract: | The predictive performance of the realized stochastic volatility model of Takahashi,　Omori, and Watanabe (2009), which incorporates the asymmetric stochastic volatility model with the realized volatility, is investigated. Considering well known characteristics of nancial returns, heavy tail and negative skewness, the model is extended by employing a wider class distribution, the generalized hyperbolic skew Student's t-distribution, for nancial returns. With the Bayesian estimation scheme via Markov chain Monte Carlo method, the model enables us to estimate the parameters in the return distribution and in the model jointly. It also makes it possible to forecast volatility and return quantiles by sampling from their posterior distributions jointly. The model　is applied to quantile forecasts of nancial returns such as value-at-risk and expected shortfall as well as volatility forecasts and those forecasts are evaluated by various tests　and performance measures. Empirical results with the US and Japanese stock indices, Dow Jones Industrial Average and Nikkei 225, show that the extended model improves　the volatility and quantile forecasts especially in some volatile periods. -- |
| Date: | 2015–05 |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2015cf975&r=rmg |
| By: | Robert Engle (New York University Stern School of Business); Emil Siriwardane (Office of Financial Research) |
| Abstract: | We propose a new model of volatility where financial leverage amplifies equity volatility by what we call the "leverage multiplier." The exact specification is motivated by standard structural models of credit; however, our parametrization departs from the classic Merton (1974) model and can accommodate environments where the firm's asset volatility is stochastic, asset returns can jump, and asset shocks are nonnormal. In addition, our specification nests both a standard GARCH and the Merton model, which allows for a statistical test of how leverage interacts with equity volatility. Empirically, the Structural GARCH model outperforms a standard asymmetric GARCH model for approximately 74 percent of the financial firms we analyze. We then apply the Structural GARCH model to two empirical applications: the leverage effect and systemic risk measurement. As a part of our systemic risk analysis, we define a new measure called "precautionary capital" that uses our model to quantify the advantages of regulation aimed at reducing financial firm leverage. |
| Keywords: | Structural GARCH, Volatility, Leverage |
| Date: | 2014–10–23 |
| URL: | http://d.repec.org/n?u=RePEc:ofr:wpaper:14-07&r=rmg |
| By: | Benoît Carmichael; Gilles Boevi Koumou; Kevin Moran |
| Abstract: | This paper extends the use of Rao(1982b)’s Quadratic Entropy (RQE) to modern portfolio theory. It argues that the RQE of a portfolio is a valid, flexible and unifying approach to measuring portfolio diversification. The paper demonstrates that portfolio’s RQE can encompass most existing measures, such as the portfolio variance, the diversification ratio, the normalized portfolio variance, the diversification return or excess growth rates, the Gini-Simpson indices, the return gaps, Markowitz’s utility function and Bouchaud’s general free utility. The paper also shows that assets selected under RQE can protect portfolios from mass destruction (systemic risk) and an empirical illustration suggests that this protection is substantial. |
| Keywords: | Portfolio Diversification, Rao’s Quadratic Entropy, Diversification Return, Diversification Ratio, Portfolio Variance Normalized, Gini-Simpson Index, Markowitz’s Utility Function, Bouchaud’s General Free Utility |
| JEL: | G11 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:lvl:lacicr:1508&r=rmg |
| By: | Philip Monin (Office of Financial Research); Thaleia Zariphopoulou (The University of Texas at Austin) |
| Abstract: | The theory of portfolio choice holds that investors balance risk and reward in their investment decisions. We explore the relationship between investors' attitudes towards taking risk and their objectives for managing the risk they take on. Working in a classical theoretical model, we calculate the distribution and density functions of an investor's optimal wealth process and prove new mathematical results for these functions under general risk preferences. By applying our results to a constant relative risk aversion investor who has a targeted value at risk or expected shortfall at a given future time, we are able to infer the investor's risk preferences and prescribe how to invest to achieve the desired goal. Then, drawing analogies to the option greeks, we define and derive closed-form expressions for "portfolio greeks," which measure the sensitivities of an investor's optimal wealth to changes in the cumulative excess stock return, time, and market parameters. Like option greeks, portfolio greeks can be used in the risk management of investors' portfolios. |
| Keywords: | expected utility, Merton problem, value at risk (VaR), expected shortfall, portfolio greeks |
| Date: | 2014–07–18 |
| URL: | http://d.repec.org/n?u=RePEc:ofr:discus:14-01&r=rmg |
| By: | Roman Horváth (Institute of Economic Studies, Faculty of Social Sciences, Charles University in Prague, Smetanovo nábreží 6, 111 01 Prague 1, Czech Republic; Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod Vodarenskou Vezi 4, 182 00, Prague, Czech Republic); Boril Sopov (Institute of Economic Studies, Faculty of Social Sciences, Charles University in Prague, Smetanovo nábreží 6, 111 01 Prague 1, Czech Republic) |
| Abstract: | We perform a large simulation study to examine the extent to which various generalized autoregressive conditional heteroskedasticity (GARCH) models capture extreme events in stock market returns. We estimate Hill's tail indexes for individual S&P 500 stock market returns ranging from 1995{2014. and compare these to the tail indexes produced by simulating GARCH models. Our results suggest that actual and simulated values differ greatly for GARCH models with normal conditional distributions, which underestimate the tail risk. By contrast, the GARCH models with Student's t conditional distributions capture the tail shape more accurately, with GARCH and GJR-GARCH being the top performers. |
| Keywords: | GARCH, extreme events, S&P 500 study, tail index |
| JEL: | C15 C58 G17 |
| Date: | 2015–05 |
| URL: | http://d.repec.org/n?u=RePEc:fau:wpaper:wp2015_09&r=rmg |
| By: | Phillip Monin (Office of Financial Research) |
| Abstract: | Financial institutions commonly face the risk that large trades will execute at unfavorable prices due to price impact effects from insufficient market liquidity. A typical method to manage these price impact effects is to split a given order into smaller pieces and to trade these pieces sequentially over time. Such a strategy, however, is exposed to market risk. Unlike price impact, market risk can be hedged. This paper explores the market risk management of the liquidation of a large trade that is subject to price impact. Specifically, we consider an investor, such as a large financial institution or a broker-dealer, who must a priori liquidate a large position in a primary risky asset whose price is influenced by the investor's liquidation strategy. The investor hedges the market risk involved with liquidation by simultaneously taking a position in a liquid proxy asset that is imperfectly correlated with the primary asset. We show that the optimal strategies for an investor with a finite investment horizon and constant absolute risk aversion are deterministic and we find them explicitly using the calculus of variations. We find that the liquidation strategy for an investor able to hedge market risk is the same as the liquidation strategy of a less risk-averse investor without such a hedge. Similarly, the liquidation strategy for an investor able to hedge market risk is the same as for an investor facing higher price impact effects but without the ability to hedge market risk. |
| Keywords: | optimal liquidation, optimal execution, hedging market risk, block trades, indifference price, price spread |
| Date: | 2014–11–13 |
| URL: | http://d.repec.org/n?u=RePEc:ofr:wpaper:14-08&r=rmg |
| By: | Suarez, Ronny |
| Abstract: | In this paper the impact of political risk is model through the quantification of the decline in the (net) present value of cash flows due to the occurrence of a political event. |
| Keywords: | Political Risk |
| JEL: | C00 G3 |
| Date: | 2015–05–25 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:64559&r=rmg |
| By: | Romeil Sandhu; Tryphon Georgiou; Allen Tannenbaum |
| Abstract: | Measuring systemic risk or fragility of financial systems is a ubiquitous task of fundamental importance in analyzing market efficiency, portfolio allocation, and containment of financial contagions. Recent attempts have shown that representing such systems as a weighted graph characterizing the complex web of interacting agents over some information flow (e.g., debt, stock returns, shareholder ownership) may provide certain keen insights. Here, we show that fragility, or the ability of system to be prone to failures in the face of random perturbations, is negatively correlated with geometric notion of Ricci curvature. The key ingredient relating fragility and curvature is entropy. As a proof of concept, we examine returns from a set of stocks comprising the S\&P 500 over a 15 year span to show that financial crashes are more robust compared to normal "business as usual" fragile market behavior - i.e., Ricci curvature is a "crash hallmark." Perhaps more importantly, this work lays the foundation of understanding of how to design systems and policy regulations in a manner that can combat financial instabilities exposed during the 2007-2008 crisis. |
| Date: | 2015–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1505.05182&r=rmg |
| By: | Zhou, Richard |
| Abstract: | Path dependent counterparty credit risk exposure modeling poses challenges. In this paper, we present models for consistent and accurate estimation of counterparty credit exposure involving barrier option and European swaption under the general Monte Carlo simulation framework. In particular, we discuss how to consistently estimate the pathwise swaption exercise probability and accurate monitoring of barrier crossing. We present exact formulation for standalone expected exposure and potential future exposure for swap, swaption and barrier option without monte carlo simulation. The exact formulation is of practical importance to computing standalone exposure profiles, exposure model validation and system benchmarking. |
| Keywords: | Counterparty credit exposure, expected exposure, PFE, swap, swaption, barrier option, monte carlo |
| JEL: | C6 C60 |
| Date: | 2015–05–25 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:64647&r=rmg |
| By: | Runhuan Feng; Hans W. Volkmer |
| Abstract: | Conditional Asian options are recent market innovations, which offer cheaper and long-dated alternatives to regular Asian options. In contrast with payoffs from regular Asian options which are based on average asset prices, the payoffs from conditional Asian options are determined only by average prices above certain threshold. Due to the limited inclusion of prices, conditional Asian options further reduce the volatility in the payoffs than their regular counterparts and have been promoted in the market as viable hedging and risk management instruments for equity-linked life insurance products. There has been no previous academic literature on this subject and practitioners have only been known to price these products by simulations. We propose the first analytical approach to computing prices and deltas of conditional Asian options in comparison with regular Asian options. In the numerical examples, we put to the test some cost-benefit claims by practitioners. As a by-product, the work also presents some distributional properties of the occupation time and the time-integral of geometric Brownian motion during the occupation time. |
| Date: | 2015–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1505.06946&r=rmg |
| By: | Eduardo Astorino; Fernando Chague, Bruno Cara Giovannetti, Marcos Eugênio da Silva |
| Abstract: | We propose an implied volatility index for Brazil that we name "IVol-BR". The index is based on daily market prices of options over IBOVESPA -- an option market with relatively low liquidity and few option strikes. Our methodology combines standard international methodology used in high-liquidity markets with adjustments that take into account the low liquidity in Brazilian option markets. We then do a number of empirical tests to validate the IVol-BR. First, we show that the IVol-BR has significant predictive power over future volatility of equity returns not contained in traditional volatility forecasting variables. Second, we decompose the squared IVol-BR into (i) the expected variance of stock returns and (ii) the equity variance premium. This decomposition is of interest since the equity variance premium directly relates to the representative investor risk aversion. Finally, assuming Bollerslev et al. (2009) functional form, we produce a time-varying risk aversion measure for the Brazilian investor. We empirically show that risk aversion is positively related to expected returns, as theory suggests. |
| Keywords: | IVol-BR; Variance Risk Premium; Risk-aversion |
| JEL: | G12 G13 G17 |
| Date: | 2015–05–18 |
| URL: | http://d.repec.org/n?u=RePEc:spa:wpaper:2015wpecon8&r=rmg |
| By: | Stefano Puddu (Institute of economic research IRENE, Faculty of Economics, University of Neuchâtel, Switzerland); Andreas Waelchli (Studienzentrum Gerzensee (Study Center Gerzensee), Schweizerische Nationalbank (SNB) (Swiss National Bank); Department of Econometrics and Political Economy DEEP, Faculty of Economics, University of Lausanne, Switzerland) |
| Abstract: | Using a unique bank-level dataset, we assess the impact of the Term Auction Facility program on bank liquidity risk. The change in the US housing price index at state levels between 2002:Q1 and 2006:Q3 is the exclusion restriction to control for potential selection bias. On average, TAF banks exhibit higher ex ante levels of liquidity risk and they drastically reduce funding liquidity risk in the periods after the rst time they received TAF funds. TAF banks show larger reductions in liquidity and they are more likely to be headquartered in US states that experienced sharper housing price appreciation before 2007. |
| Keywords: | Term Auction Facility, Liquidity Risk, Financial Crisis, Unconventional Monetary Policies |
| JEL: | G21 G28 G32 |
| URL: | http://d.repec.org/n?u=RePEc:irn:wpaper:15-07&r=rmg |
| By: | Rick Bookstaber (Office of Financial Research); Jill Cetina (Office of Financial Research); Greg Feldberg (Office of Financial Research); Mark Flood (Office of Financial Research); Paul Glasserman (Columbia Business School, Columbia University) |
| Abstract: | Stress testing, which has its roots in risk management, should be adapted to support financial stability monitoring and to incorporate the interconnections and dynamics of the financial system. Since the 2008 financial crisis, bank supervisors have honed their financial stability monitoring tools and significantly expanded the use of stress testing in the supervision of the largest financial institutions. This article describes areas in which further research could contribute to the development of best practices in stress testing and how bank supervisory stress tests can be made more useful for macroprudential supervision. We discuss both near-term and longer-term objectives. |
| Keywords: | Stress Tests, Financial Stability |
| Date: | 2013–07–18 |
| URL: | http://d.repec.org/n?u=RePEc:ofr:wpaper:13-07&r=rmg |
| By: | Rick Bookstaber (Office of Financial Research); Mark Paddrik (Office of Financial Research); Brian Tivnan (MITRE Corporation) |
| Abstract: | This paper describes an agent-based model for analyzing the vulnerability of the financial system to asset- and funding-based fire sales. The model views the dynamic interactions of agents in the financial system extending from the suppliers of funding through the intermediation and transformation functions of the bank/dealer to the financial institutions that use the funds to trade in the asset markets, and that pass collateral in the opposite direction. The model focuses on the intermediation functions of the bank/dealers in order to trace the path of shocks that come from sudden price declines, as well as shocks that come from the various agents, namely funding restrictions imposed by the cash providers, erosion of the credit of the bank/dealers, and investor redemptions by the buy-side financial institutions. The model demonstrates that it is the reaction to initial losses rather than the losses themselves that determine the extent of a crisis. By building on a detailed mapping of the transformations and dynamics of the financial system, the agent-based model provides an avenue toward risk management that can illuminate the pathways for the propagation of key crisis dynamics such as fire sales and funding runs. |
| Keywords: | Agent-based model, Financial Vulnerability |
| Date: | 2014–07–29 |
| URL: | http://d.repec.org/n?u=RePEc:ofr:wpaper:14-05&r=rmg |