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on Risk Management |
| By: | Toshinao Yoshiba (Director and Senior Economist, Institute for Monetary and Economic Studies, Bank of Japan (E-mail: toshinao.yoshiba@boj.or.jp)) |
| Abstract: | This paper surveys several applications of parametric copulas to market portfolios, credit portfolios, and enterprise risk management in the banking industry, focusing on how to capture stressed conditions. First, we show two simple applications for market portfolios: correlation structures for returns on three stock indices and a risk aggregation for a stock and bond portfolio. Second, we show two simple applications for credit portfolios: credit portfolio risk measurement in the banking industry and the application of copulas to CDO valuation, emphasizing the similarity to their application to market portfolios. In this way, we demonstrate the importance of capturing stressed conditions. Finally, we introduce practical applications to enterprise risk management for advanced banks and certain problems that remain open at this time. |
| Keywords: | copula, multivariate distribution, tail dependence, risk aggregation, economic capital |
| JEL: | G17 G21 G32 |
| Date: | 2015–01 |
| URL: | http://d.repec.org/n?u=RePEc:ime:imedps:15-e-01&r=rmg |
| By: | Makoto Nirei; Julián Caballero; Vladyslav Sushko |
| Abstract: | Loan syndication increases bank interconnectedness through co-lending relationships. We study the financial stability implications of such dependency on syndicate partners in the presence of shocks to banks' capital. Model simulations in a network setting show that such shocks can produce rare events in this market when banks have shared loan exposures while also relying on a common risk management tool such as value-at-risk (VaR). This is because a withdrawal of a bank from a syndicate can cause ripple effects through the market, as the loan arranger scrambles to commit more of its own funds by also pulling back from other syndicates or has to dissolve the syndicate it had arranged. However, simulations also show that the core-periphery structure observed in the empirical network may reduce the probability of such contagion. In addition, simulations with tighter VaR constraints show banks taking on less risk ex-ante. |
| Keywords: | Syndicated lending, systemic risk, network externalities, value at risk, bank capital shocks, rare event risk |
| Date: | 2015–01 |
| URL: | http://d.repec.org/n?u=RePEc:bis:biswps:484&r=rmg |
| By: | Ra\'ul Torres; Rosa E. Lillo; Henry Laniado |
| Abstract: | In economics, insurance and finance, value at risk (VaR) is a widely used measure of the risk of loss on a specific portfolio of financial assets. For a given portfolio, time horizon, and probability $\alpha$, the $100\alpha\%$ VaR is defined as a threshold loss value, such that the probability that the loss on the portfolio over the given time horizon exceeds this value is $\alpha$. That is to say, it is a quantile of the distribution of the losses, which has both good analytic properties and easy interpretation as a risk measure. However, its extension to the multivariate framework is not unique because a unique definition of multivariate quantile does not exist. In the current literature, the multivariate quantiles are related to a specific partial order considered in $\mathbb{R}^{n}$, or to a property of the univariate quantile that is desirable to be extended to $\mathbb{R}^{n}$. In this work, we introduce a multivariate value at risk as a vector-valued directional risk measure, based on a directional multivariate quantile, which has recently been introduced in the literature. The directional approach allows the manager to consider external information or risk preferences in her/his analysis. We have derived some properties of the risk measure and we have compared the univariate \textit{VaR} over the marginals with the components of the directional multivariate VaR. We have also analyzed the relationship between some families of copulas, for which it is possible to obtain closed forms of the multivariate VaR that we propose. Finally, comparisons with other alternative multivariate VaR given in the literature, are provided in terms of robustness. |
| Date: | 2015–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1502.00908&r=rmg |
| By: | Canals-Cerda, Jose J. (Federal Reserve Bank of Philadelphia); Kerr, Sougata (Federal Reserve Bank of Philadelphia) |
| Abstract: | The Great Recession offers a unique opportunity to analyze the performance of credit risk models under conditions of economic stress. We focus on the performance of models of credit risk applied to risk-segmented credit card portfolios. Specifically, we focus on models of default and loss and analyze three important sources of model risk: model selection, model specification, and sample selection. Forecast errors can be significant along any of these three model-risk dimensions. Simple linear regression models are not generally outperformed by more complex or stylized models. The impact of macroeconomic variables is heterogeneous across risk segments. Model specifications that do not consider this heterogeneity display large projection errors across risk segments. Prime segments are proportionally more severely impacted by a downturn in economic conditions relative to the subprime or near-prime segments. The sensitivity of modeled losses to macroeconomic factors is conditional on the model development sample. Models estimated over a period that does not incorporate a significant period of the Great Recession may fail to project default rates, or loss rates, consistent with those experienced during the Great Recession. |
| Keywords: | Credit cards; Credit risk; Stress test; Risk segmentation; |
| JEL: | G20 G32 G33 |
| Date: | 2015–02–01 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedpwp:15-8&r=rmg |
| By: | Perignon , Christophe; Yeung , Stanley; Hurlin, Christophe; Iseli, Grégoire |
| Abstract: | As most Exchange-Traded Funds (ETFs) engage in securities lending or are based on total return swaps, they expose their investors to counterparty risk. To mitigate the funds' exposure, their counterparties must pledge collateral. In this paper, the authors present a framework to study collateral risk and provide empirical estimates for the $40.9 billion collateral portfolios of 164 funds managed by a leading ETF issuer. Overall, our findings contradict the allegations made by international agencies about the high collateral risk of ETFs. Finally, the authors theoretically show how to construct an optimal collateral portfolio for an ETF. |
| Keywords: | Asset management; passive investment; derivatives; optimal collateral portfolio; systemic risk |
| JEL: | G20 G23 |
| Date: | 2014–08–10 |
| URL: | http://d.repec.org/n?u=RePEc:ebg:heccah:1050&r=rmg |
| By: | Jinbeom Kim; Tim Leung |
| Abstract: | This paper studies a valuation framework for financial contracts subject to reference and counterparty default risks with collateralization requirement. We propose a fixed point approach to analyze the mark-to-market contract value with counterparty risk provision, and show that it is a unique bounded and continuous fixed point via contraction mapping. This leads us to develop an accurate iterative numerical scheme for valuation. Specifically, we solve a sequence of linear inhomogeneous PDEs, whose solutions converge to the fixed point price function. We apply our methodology to compute the bid and ask prices for both defaultable equity and fixed-income derivatives, and illustrate the non-trivial effects of counterparty risk, collateralization ratio and liquidation convention on the bid-ask spreads. |
| Date: | 2015–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1501.06221&r=rmg |
| By: | Iosifidi, Maria; Kokas, Sotirios |
| Abstract: | This paper exploits a unique data set on bank-firm relationships based on syndicated loan deals to examine the effect of banks’ credit risk and capital on firms’ risk and performance. Our data set is a multilevel cross-section, which essentially allows controlling for all bank and firm characteristics through respective fixed effects, thus avoiding concerns regarding omitted variables. We find that banks with higher credit risk are associated with more risky firms, with lower profitability and market value. In turn, we find that banks with higher risk-weighted capital ratios lend to riskier firms with less market value. Our results are indicative of a strong adverse selection mechanism and highlight the need to monitor the risky banks more closely, especially as we consider large and influential syndicated loan deals. |
| Keywords: | Bank-firm relationships; Risk; Performance; Syndicated loans |
| JEL: | G20 G21 G30 G32 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:61942&r=rmg |
| By: | Izhar, Hylmun (The Islamic Research and Teaching Institute (IRTI)) |
| Abstract: | The aim of the paper is to propose a model, namely Delta-Gamma Sensitivity Analysis- Extreme Value Theory (DGSA-EVT). DGSA-EVT is a model to measure HF-LS and LF-HS type of operational risks. The first leg of the proposed model, namely DGSA, is a methodology that deals with propagation of errors in the value adding activities which works by using measures of fluctuations in the activities. The sensitivities of the output, hence, are deployed to estimate the performance volatility. Furthermore, the second leg of the proposed model, Extreme Value Theory (EVT), is a technique to cater for an excess operational loss over a defined threshold which is normally characterised by low frequency and high severity (LF-HS) type of loss. |
| Date: | 2015–01–20 |
| URL: | http://d.repec.org/n?u=RePEc:ris:irtiwp:1432_003&r=rmg |
| By: | Paolo Tasca; Stefano Battiston |
| Abstract: | This paper contributes to a growing literature on the pitfalls of diversification by shedding light on a new mechanism under which, full risk diversification can be sub-optimal. In particular, banks must choose the optimal level of diversification in a market where returns display a bimodal distribution. This feature results from the combination of two opposite economic trends that are weighted by the probability of being either in a bad or in a good state of the world. Banks have also interlocked balance sheets, with interbank claims marked-to-market according to the individual default probability of the obligor. Default is determined by extending the Black and Cox (1976) first-passage-time approach to a network context. We find that, even in the absence of transaction costs, the optimal level of risk diversification is interior. Moreover, in the presence of market externalities, individual incentives favor a banking system that is over-diversified with respect to the level of socially desirable diversification. |
| Keywords: | naive diversification; leverage; default probability |
| JEL: | F3 G3 |
| Date: | 2014–01–20 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:59297&r=rmg |
| By: | Guillaume Plantin (Sciences Po Paris and Centre for Economic Policy Research and Hong Kong Institute for Monetary Research) |
| Abstract: | Banks are subject to capital requirements because their privately optimal leverage is higher than the socially optimal one. This is in turn because banks fail to internalize all the costs that their insolvency creates for the non-financial agents using their money-like liabilities to settle transactions. If banks can bypass capital regulation in an opaque shadow-banking system, it may be optimal to relax capital requirements so that liquidity dries up in the shadow-banking system. Tightening capital requirements may spur a surge in shadow-banking activity that leads to an overall larger risk on the money-like liabilities of the formal and shadow banking institutions. |
| Date: | 2014–12 |
| URL: | http://d.repec.org/n?u=RePEc:hkm:wpaper:322014&r=rmg |
| By: | Vilsmeier, Johannes |
| Abstract: | In this paper we 'update' the option implied probability of default (option iPoD) approach recently suggested in the literature. First, a numerically more stable objective function for the estimation of the risk neutral density is derived whose integrals can be solved analytically. Second, it is reasoned that the originally proposed approach for the estimation of the PoD produces arbitrary results and hence an alternative procedure is suggested that is based on the Lagrange multipliers. Based on numerical evaluations and an illustrative empirical application we conclude that the framework provides very promising results. |
| Keywords: | Option Implied Probability of Default,Risk Neutral Density,Cross Entropy |
| JEL: | C51 C52 C61 G12 G24 G32 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:bubdps:432014&r=rmg |
| By: | Oliver Janke; Qinghua Li |
| Abstract: | This paper solves a utility maximization problem under utility-based shortfall risk constraint, by proposing an approach using Lagrange multiplier and convex duality. Under mild conditions on the asymptotic elasticity of the utility function and the loss function, we find an optimal wealth process for the constrained problem and characterize the bi-dual relation between the respective value functions of the constrained problem and its dual. This approach applies to both complete and incomplete markets. Moreover, we give a few examples of utility and loss functions in the Black-Scholes market where the solutions have explicit forms. Finally, the extension to more complicated cases is illustrated by solving the problem with a consumption process added. |
| Date: | 2015–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1501.07480&r=rmg |
| By: | Clerc, Laurent; Derviz, Alexis; Mendicino, Caterina; Moyen, Stéphane; Nikolov, Kalin; Stracca, Livio; Suarez, Javier; Vardoulakis, Alexandros |
| Abstract: | We develop a dynamic general equilibrium model for the positive and normative analysis of macroprudential policies. Optimizing financial intermediaries allocate their scarce net worth together with funds raised from saving households across two lending activities, mortgage and corporate lending. For all borrowers (households, firms, and banks) external financing takes the form of debt which is subject to default risk. This "3D model" shows the interplay between three interconnected net worth channels that cause financial amplification and the distortions due to deposit insurance. We apply it to the analysis of capital regulation. |
| Keywords: | Default risk; Financial frictions; Macroprudential policy |
| JEL: | E3 E44 G01 G21 |
| Date: | 2014–12 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:10316&r=rmg |
| By: | Nassim Nicholas Taleb (School of Engineering - New-York University); Raphaël Douady (Centre d'Economie de la Sorbonne et Riskdata) |
| Abstract: | We provide a mathematical definition of fragility and antifragility as negative or positive sensitivity to a semi-measure of dispersion and volatility (a variant of negative or positive "vega") and examine the link to nonlinear effects. We integrate model error (and biases) into the fragile or antifragile context. Unlike risk, which is linked to psychological notions such as subjective preferences (hence cannot apply to a coffee cup) we offer a measure that is universal and concerns any object that has a probability distribution (whether such distribution is known or, critically, unknown). We propose a detection of fragility, robustness, and antifragility using a single "fast-and-frugal", model-free, probability free heuristic that also picks up exposure to model error. The heuristic lends itself to immediate implementation, and uncovers hidden risks related to company size, forecasting problems, and bank tail exposures (it explains the forecasting biases). While simple to implement, it improves on stress testing and bypasses the cillib flaws in Value-at-Risk. |
| Keywords: | Stress testing, fragility, impulse response, Jensen inequality. |
| JEL: | C00 C14 C65 |
| Date: | 2014–12 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:14093&r=rmg |
| By: | Peter Christoffersen (University of Toronto, Rotman School of Management and CREATES); Xuhui (Nick) Pan (Tulane University, A.B. Freeman School of Business) |
| Abstract: | We survey the recent academic literature that uses option-implied information to construct equity portfolios. Studies show that equity managers can earn a positive alpha by using information in individual equity options, by using stocks' exposure to information in market index options, and by using stocks' exposure to crude oil option information. Option-implied information can also help construct better mean-variance portfolios and better estimates of market beta. |
| Keywords: | option-implied volatility, commodity futures, cross-section of stocks, option-implied beta, mean-variance optimization. |
| JEL: | G12 |
| Date: | 2014–04–02 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2015-05&r=rmg |
| By: | Conrad, Christian; Mammen , Enno |
| Abstract: | In this paper we develop an asymptotic theory for the parametric GARCH-in-Mean model. The asymptotics is based on a study of the volatility as a process of the model parameters. The proof makes use of stochastic recurrence equations for this random function and uses exponential inequalities to localize the problem. Our results show why the asymptotics for this specification is quite complex although it is a rather standard parametric model. Nevertheless, our theory does not yet treat all standard specifications of the mean function. |
| Keywords: | GARCH-in-Mean; stochastic recurrence equations; risk-return relationship |
| Date: | 2015–01–19 |
| URL: | http://d.repec.org/n?u=RePEc:awi:wpaper:0579&r=rmg |
| By: | Catalina Bolancé (Riskcenter-IREA, Department of Econometrics. University of Barcelona); Zuhair Bahraoui (Riskcenter-IREA, Department of Econometrics. University of Barcelona); Ramon Alemany (Riskcenter-IREA, Department of Econometrics. University of Barcelona) |
| Abstract: | We propose a new kernel estimation of the cumulative distribution function based on transformation and on bias reducing techniques. We derive the optimal bandwidth that minimises the asymptotic integrated mean squared error. The simulation results show that our proposed kernel estimation improves alternative approaches when the variable has an extreme value distribution with heavy tail and the sample size is small. |
| Keywords: | Transformed kernel estimation, cumulative distribution function, extreme value distribution. |
| Date: | 2015–01 |
| URL: | http://d.repec.org/n?u=RePEc:xrp:wpaper:xreap2015-01&r=rmg |
| By: | Nikolaos Sgouropoulos; Qiwei Yao; Claudia Yastremiz |
| Abstract: | Motivated by the problem of selecting representative portfolios for backtesting counterparty credit risks, we propose a matching quantiles estimation (MQE) method for matching a target distribution by that of a linear combination of a set of random variables. An iterative procedure based on the ordinary least squares estimation (OLS) is proposed to compute MQE. MQE can be easily modified by adding a LASSO penalty term if a sparse representation is desired, or by restricting the matching within certain range of quantiles to match a part of the target distribution. The convergence of the algorithm and the asymptotic properties of the estimation, both with or without LASSO, are established. A measure and an associated statistical test are proposed to assess the goodness-of-match. The finite sample properties are illustrated by simulation. An application in selecting a counterparty representative portfolio with a real data set is reported. The proposed MQE also finds applications in portfolio tracking, which demonstrates the usefulness of combining MQE with LASSO. |
| Keywords: | goodness\-of\-match; LASSO; ordinary least squares estimation; portfolio tracking; representative portfolio; sample quantile |
| JEL: | C1 E6 |
| Date: | 2014–05–25 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:57221&r=rmg |
| By: | Michael Ho; Zheng Sun; Jack Xin |
| Abstract: | It is well known that the out-of-sample performance of Markowitz's mean-variance portfolio criterion can be negatively affected by estimation errors in the mean and covariance. In this paper we address the problem by regularizing the mean-variance objective function with a weighted elastic net penalty. We show that the use of this penalty can be motivated by a robust reformulation of the mean-variance criterion that directly accounts for parameter uncertainty. With this interpretation of the weighted elastic net penalty we derive data driven techniques for calibrating the weighting parameters based on the level of uncertainty in the parameter estimates. We test our proposed technique on US stock return data and our results show that the calibrated weighted elastic net penalized portfolio outperforms both the unpenalized portfolio and uniformly weighted elastic net penalized portfolio. This paper also introduces a novel Adaptive Support Split-Bregman approach which leverages the sparse nature of $\ell_{1}$ penalized portfolios to efficiently compute a solution of our proposed portfolio criterion. Numerical results show that this modification to the Split-Bregman algorithm results in significant improvements in computational speed compared with other techniques. |
| Date: | 2015–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1502.01658&r=rmg |