
on Risk Management 
By:  Eling, Martin; Pankoke, David 
Abstract:  This paper analyzes the equity risk module of Solvency II, the new regulatory framework in the European Union. The equity risk module contains a symmetric adjustment mechanism called equity dampener which shall reduce procyclicality of capital requirements and thus systemic risk in the insurance sector. We critically review the equity risk module in three steps: we first analyze the sensitivities of the equity risk module with respect to the underlying technical basis, then work out potential basis risk (i.e., deviations of the insurers actual equity risk from the Solvency II equity risk), and — based on these results — measure the impact of the symmetric adjustment mechanism on the goals of Solvency II. The equity risk module is backward looking in nature and a substantial basis risk exists if realistic equity portfolios of insurers are considered. Both results underline the importance of the own risk and solvency assessment (ORSA) under Solvency II. Moreover, we show that the equity dampener leads to substantial deviations from the proposed 99.5% confidence level and thereby reduces procyclicality of capital requirements. Our results are helpful for academics interested in regulation and risk management as well as for practitioners and regulators working on the implementation of such models. 
Keywords:  Solvency II, procyclicality, systemic risk, CoVaR, MES. 
JEL:  G22 G28 G32 
Date:  2013–02 
URL:  http://d.repec.org/n?u=RePEc:usg:sfwpfi:2013:06&r=rmg 
By:  Simon A. Broda 
Abstract:  Countless test statistics can be written as quadratic forms in certain random vectors, or ratios thereof. Consequently, their distribution has received considerable attention in the literature. Except for a few special cases, no closedform expression for the cdf exists, and one resorts to numerical methods. Traditionally the problem is analyzed under the assumption of joint Gaussianity; the algorithm that is usually employed is that of Imhof (1961). The present manuscript generalizes this result to the case of multivariate generalized hyperbolic (MGHyp) random vectors. The MGHyp is a very flexible distribution which nests, among others, the multivariate t, Laplace, and variance gamma distributions. An expression for the first partial moment is also obtained, which plays a vital role in financial risk management. The proof involves a generalization of the classic inversion formula due to GilPelaez (1951). Two applications are considered: first, the finitesample distribution of the 2SLS estimator of a structural parameter. Second, the Value at Risk and Expected Shortfall of a quadratic portfolio with heavytailed risk factors. 
Date:  2013–05–01 
URL:  http://d.repec.org/n?u=RePEc:ame:wpaper:1304&r=rmg 
By:  Hao Liu (CoFE, University of Konstanz, Germany); Winfried Pohlmeier (CoFE, University of Konstanz, Germany; ZEW, Germany; RCEA, Italy) 
Abstract:  This paper analyzes the estimation risk of efficient portfolio selection. We use the concept of certainty equivalent as the basis for a welldefined statistical loss function and a monetary measure to assess estimation risk. For given risk preferences we provide analytical results for different sources of estimation risk such as sample size, dimension of the portfolio choice problem and correlation structure of the return process. Our results show that theoretically suboptimal portfolio choice strategies turn out to be superior once estimation risk is taken into account. Since estimation risk crucially depends on risk preferences, the choice of the estimator for a given portfolio strategy becomes endogenous. We show that a shrinkage approach accounting for estimation risk in both, mean and covariance of the return vector, is generally superior to simple theoretically suboptimal strategies. Moreover, focusing on just one source of estimation risk, e.g. risk reduction in covariance estimation, can lead to suboptimal portfolios. 
Keywords:  efficient portfolio, estimation risk, certainty equivalent, shrinkage 
JEL:  G11 G12 G17 
Date:  2013–08 
URL:  http://d.repec.org/n?u=RePEc:rim:rimwps:47_13&r=rmg 
By:  Tolga Umut Kuzubas; Inci Omercikoglu; Burak Saltoglu 
Date:  2013–12 
URL:  http://d.repec.org/n?u=RePEc:bou:wpaper:2013/12&r=rmg 
By:  Ben Ammar, Semir; Eling, Martin 
Abstract:  The risk of infrastructure firms is driven by unique factors that cannot be well described by standard asset class factor models. We thus create a sevenfactor model based on infrastructurespecific risk exposure, i.e., market risk, cash flow volatility, leverage, investment growth, term risk, default risk, and regulatory risk. We empirically test our model on a large dataset of U.S. infrastructure stocks in different subsectors (utility, telecommunication, and transportation) and over a long period of time (1980 to 2011). The new factor model is able to capture the variation of infrastructure returns better than the Fama/French threefactor or the Carhart fourfactor models. Thus, our model helps to better determine the cost of capital of infrastructure firms, something that is increasingly relevant in light of the growing need for privately financed infrastructure projects. 
Keywords:  Infrastructure, Asset class, Factor model, Fama/French factors, Leverage, Cash ow volatility, Investment factor. 
JEL:  G11 G12 G19 O18 
Date:  2013–05 
URL:  http://d.repec.org/n?u=RePEc:usg:sfwpfi:2013:07&r=rmg 
By:  Filip Zikes; Jozef Barunik 
Abstract:  This paper investigates how the conditional quantiles of future returns and volatility of financial assets vary with various measures of expost variation in asset prices as well as optionimplied volatility. We work in the flexible quantile regression framework and rely on recently developed modelfree measures of integrated variance, upside and downside semivariance, and jump variation. Our results for the S&P 500 and WTI Crude Oil futures contracts show that simple linear quantile regressions for returns and heterogenous quantile autoregressions for realized volatility perform very well in capturing the dynamics of the respective conditional distributions, both in absolute terms as well as relative to a couple of wellestablished benchmark models. The models can therefore serve as useful risk management tools for investors trading the futures contracts themselves or various derivative contracts written on realized volatility. 
Date:  2013–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1308.4276&r=rmg 
By:  Marius del Giudice Rodriguez; Thomas Wu 
Abstract:  Has the recent wave of capital controls and prudential foreign exchange (FX) measures been effective in promoting exchange rate stability? We tackle this question by studying a panel of 25 countries/currencies from July 1, 2009, to June 30, 2011. We calculate daily measures of exchange rate volatility, absolute crash risk, and tail risk implied in currency option prices, and we construct indices of capital controls and prudential FX measures taking into account the exact date when policy changes are implemented. Using a differenceindifferences approach, we find evidence that (i) tightening controls on nonresidents suppresses daily exchange rate fluctuations at the cost of increasing the frequency of outliers, (ii) easing controls on residents truly improves exchange rate stability over all dimensions, and (iii) tightening prudential FX measures not specific to derivative markets reduces absolute crash risk and tail risk, with no effect on volatility. 
Keywords:  Foreign exchange 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:fip:fedfwp:201320&r=rmg 
By:  D. S. Grebenkov; J. Serror 
Abstract:  We investigate how price variations of a stock are transformed into profits and losses (P&Ls) of a trend following strategy. In the frame of a Gaussian model, we derive the probability distribution of P&Ls and analyze its moments (mean, variance, skewness and kurtosis) and asymptotic behavior (quantiles). We show that the asymmetry of the distribution (with often small losses and less frequent but significant profits) is reminiscent to trend following strategies and less dependent on peculiarities of price variations. At short times, trend following strategies admit larger losses than one may anticipate from standard Gaussian estimates, while smaller losses are ensured at longer times. Simple explicit formulas characterizing the distribution of P&Ls illustrate the basic mechanisms of momentum trading, while general matrix representations can be applied to arbitrary Gaussian models. We also compute explicitly annualized risk adjusted P&L and strategy turnover to account for transaction costs. We deduce the trend following optimal timescale and its dependence on both autocorrelation level and transaction costs. Theoretical results are illustrated on the Dow Jones index. 
Date:  2013–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1308.5658&r=rmg 
By:  Su, EnDer 
Abstract:  This paper studies the risk hedging between stock index and underlying futures. The hedging ratios are optimized using the meanvariance utility function as considering the hedging cost. The trend of returns and variance are estimated by the model of regime switch on both vector autoregression (VAR) and GARCH(1,1) compared to three restricted models: VAR switch only, GARCH(1,1) switch only, and no switch. The hedge portfolio is constructed by Morgan Stanley Taiwan Index (MSTI) and Singapore Traded MSTI futures. The hedge horizon is set as a week to reduce the hedging cost and the weekly insample data cover from 08/09/2001 to 05/31/2007. The rolling window technique is used to evaluate the hedge performances of outofsample period spanning subprime, Greek debt, and postrisk durations. The subprime period indeed is evidenced very vital to achieve the hedge performance. All models perform surprisingly far above average during subprime period. The hedge ratios indeed are the tradeoff between maximum expected return and minimum variance. It is demonstrated challenging for all models to increase returns and reduce risk together. The hedge context is further classified into four hedge states: uu, ud, du, and dd (u and d denote respectively usual and down) using the state probabilities of series. The regime switch models are found to have much greater wealth increase when in dd state. It is decisive to hedge risk in dd state when volatility is extensively higher as observed recurrently in subprime period. Remarkably, the trend switch is found having larger wealth increase while the volatility switch is not found prominent between models. While the no switch model has larger utility increase in uu state as most observed in Greek debt or post risk period, its performance is far below average like other models. 
Keywords:  stock index, regime switch, hedging cost, hedging ratio 
JEL:  C13 C51 
Date:  2013–01–09 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:49190&r=rmg 
By:  Su, EnDer 
Abstract:  In this paper, three copula GARCH models i.e. Gaussian, Studentt, and Clayton are used to estimate and test the tail dependence measured by Kendall’s tau between six stock indices. Since the contagion risk spreads from large markets to small markets, the tail dependence is studied for smaller Taiwanese and South Korean stock markets, i.e. Taiex and Kospi against four larger stock markets, i.e. S&P500, Nikkei, MSCI China, and MSCI Europe. The vector autoregression result indicates that S&P500 and MSCI China indeed impact mostly and significantly to the other four stock markets. However, the tail dependence of both Taiex and Kospi against S&P500 and MSCI Chia are lower due to unilateral impacts from US and China. Using Clayton copula GARCH, the threshold tests of Kendall’s tau between most stock markets except China are significant during both subprime and Greek debt crises. The tests of Studentt copula GARCH estimated Kendall’s taus are only acceptable for subprime crisis but not for Greek debt crisis. Thus, Clayton copula GARCH is found appropriate to estimate Kendall’s taus as tested by threshold regression. 
Keywords:  contagion risk, tail dependence, copula GARCH, threshold test 
JEL:  C0 C13 
Date:  2013–01–30 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:48444&r=rmg 
By:  Soumik Pal; TingKam Leonard Wong 
Abstract:  We introduce a framework to analyze the relative performance of a portfolio with respect to a benchmark market index. We show that this relative performance has three components: a term that can be interpreted as energy coming from the market fluctuations, a relative entropy term that measures "distance" between the portfolio holdings and the market capital distribution, and another entropy term that can be controlled by the trader by choosing a suitable strategy. The first aids growth in the portfolio value, and the second poses as relative risk of being too far from the market. We give several explicit controls of the third term that allows one to outperform a diverse volatile market in the long run. Named energyentropy portfolios, these strategies work in both discrete and continuous time, and require essentially no probabilistic or structural assumptions. They are wellsuited to analyze a hierarchical portfolio of portfolios and attribute relative risk and reward to different levels of the hierarchy. We also consider functionally generated portfolios (introduced by Fernholz) in the case of two assets and the binary tree model and give a novel explanation of their efficacy. 
Date:  2013–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1308.5376&r=rmg 
By:  Ilya Tkachev; Alessandro Abate 
Abstract:  We study the ruin problem over a risk process described by a discretetime Markov model. In contrast to previous studies that focused on the asymptotic behaviour of ruin probabilities for large values of the initial capital, we provide a new technique to compute the quantity of interest for any initial value, and with any given precision. Rather than focusing on a particular model for risk processes, we give a general characterization of the ruin probability by providing corresponding recursions and fixpoint equations. Since such equations for the ruin probability are illposed in the sense that they do not allow for unique solutions, we approximate the ruin probability by a twobarrier ruin probability, for which fixpoint equations are wellposed. We also show how good the introduced approximation is by providing an explicit bound on the error and by characterizing the cases when the error converges to zero. The presented technique and results are supported by two computational examples over models known in the literature, one of which is extremely heavytailed. 
Date:  2013–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1308.5152&r=rmg 
By:  KyongHui Kim; MyongGuk Sin 
Abstract:  An investor faced with a contingent claim may eliminate risk by perfect hedging, but as it is often quite expensive, he seeks partial hedging (quantile hedging or efficient hedging) that requires less capital and reduces the risk. Efficient hedging for European call option was considered in the standard BlackScholes model with constant drift and volatility coefficients. In this paper we considered the efficient hedging for European call option in general BlackScholes model $dX_t=X_t(m(t)dt+\sigma (t)dw(t))$ with timevarying drift and volatility coefficients and in fractional BlackScholes model $dX_t=X_t(mdt+\sigma dB_H(t))$ with constant coefficients. 
Date:  2013–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1308.6387&r=rmg 
By:  Peter Fuleky (UHERO, University of Hawaii at Manoa); Luigi Ventura (Department of Economics and Law, Sapienza, University of Rome); Qianxue Zhao (UHERO, University of Hawaii at Manoa) 
Abstract:  Existing studies of risk pooling among groups of countries are predicated upon the highly restrictive assumption that all countries have symmetric responses to aggregate shocks. We show that the conventional risk sharing test fails to isolate idiosyncratic fluctuations within countries and produces spurious results. To avoid these problems, we propose an alternative form of the risk sharing test that is robust to heterogeneous country characteristics. In our empirical example, we provide estimates using the proposed approach for various groupings of 158 countries. 
Keywords:  Panel data, Crosssectional dependence, International risk sharing, Consumption insurance 
JEL:  C23 C51 E21 F36 
Date:  2013–03 
URL:  http://d.repec.org/n?u=RePEc:hae:wpaper:20133r&r=rmg 
By:  Daniele Bianchi (Bocconi University); Massimo Guidolin (IGIER Bocconi University); Francesco Ravazzolo (Norges Bank (Central Bank of Norway) and BI Norwegian Business School) 
Abstract:  This paper proposes a Bayesian estimation framework for a typical multifactor model with timevarying risk exposures to macroeconomic risk factors and corresponding premia to price U.S. stocks and bonds. The model assumes that risk exposures and idiosynchratic volatility follow a breakpoint latent process, allowing for changes at any point in time but not restricting them to change at all points. An empirical application to 40 years of U.S. data and 23 portfolios shows that the approach yields sensible results compared to previous twostep methods based on naive recursive estimation schemes, as well as a set of alternative model restrictions. A variance decomposition test shows that although most of the predictable variation comes from the market risk premium, a number of additional macroeconomic risks, including real output and inflation shocks, are significantly priced in the crosssection. A Bayes factor analysis decisively favors the proposed changepoint model. 
Keywords:  Changepoint model, Stochastic volatility, Multifactor linear models 
JEL:  G11 C53 
Date:  2013–08–22 
URL:  http://d.repec.org/n?u=RePEc:bno:worpap:2013_19&r=rmg 
By:  Ammann, Manuel; Buesser, Ralf 
Abstract:  Based on the theory of static replication of variance swaps we assess the sign and magnitude of variance risk premiums in foreign exchange markets. We find significantly negative risk premiums when realized variance is computed from intraday data with low frequency. As a likely consequence of microstructure effects however, the evidence is ambiguous when realized variance is based on highfrequency data. Common to all estimates, variance risk premiums are highly timevarying and inversely related to the riskneutral expectation of future variance. When we test whether variance risk premiums can be attributed to classic risk factors or fear of jump risk, we find that conditional premiums remain significantly negative. However, we observe a strong relationship between the size of log variance risk premiums and the VIX, the TED spread and the general shape of the implied volatility function of the corresponding currency pair. Overall, we conclude that there is a separately priced variance risk factor which commands a highly timevarying premium. 
Keywords:  Foreign exchange, variance risk premium, variance swap, intraday data, risk neutral expectation, jump risk. 
JEL:  C12 C13 F31 G12 G13 G15 
Date:  2013–04 
URL:  http://d.repec.org/n?u=RePEc:usg:sfwpfi:2013:04&r=rmg 
By:  Olivier Bruno (GREDEG  Groupe de Recherche en Droit, Economie et Gestion  CNRS : UMR7321  Université Nice Sophia Antipolis [UNS]); André Cartapanis (CHERPA  Croyance, Histoire, Espace, Régulation Politique et Administrative  Institut d'Études Politiques [IEP]  AixenProvence  AixMarseille Université  AMU); Eric Nasica (GREDEG  Groupe de Recherche en Droit, Economie et Gestion  CNRS : UMR7321  Université Nice Sophia Antipolis [UNS]) 
Abstract:  We analyse the determinants of banks' balancesheet and leverageratio dynamics and their role in increasing financial fragility. Our results are twofold. First, we show that there is a value of bank's leverage that minimises financial fragility. Second, we show that this value depends on the overall business climate, the expected value of the collateral and the riskless interest rate. This result leads us to advocate the establishment of anadjustableleverage ratio, depending on economic conditions, rather than the fixed ratio provided for under the new Basel III regulation. 
Keywords:  Bank Leverage, Leverage ratios, Financial Instability, Prudential Regulation 
Date:  2013–08–23 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:halshs00853701&r=rmg 
By:  Morgan, Peter J. (Asian Development Bank Institute); Pontines, Victor (Asian Development Bank Institute) 
Abstract:  The purpose of this study is to better understand the likely impact on Asian economies and financial institutions of various recent global financial reforms, including Basel III capital adequacy and liquidity rules. Overall, the authors find that the Basel III capital adequacy rules are likely to have limited impacts on economic growth in Asia, but other financial regulations, including liquidity standards and rules for overthecounter (OTC) derivatives, could have stunting effects on financial development in the region. 
Keywords:  asian economies; financial institutions; global financial reforms; basel iii; capital adequacy rules; liquidity rules; otc derivatives 
JEL:  E17 G01 G18 G21 
Date:  2013–08–22 
URL:  http://d.repec.org/n?u=RePEc:ris:adbiwp:0433&r=rmg 
By:  Marcello Basili; Luca Pratelli 
Abstract:  We consider an aggregation scheme of opinions expressed through different probability distributions or multiple priors decision model. The decisionmaker adopts entropy maximization as a measure of risk diversification and a rational form of prudence for valuing uncertain outcomes. We show a new aggregation rule formalization based on the idea that the decisionmaker has a more reliable set of outcomes called ordinary and two fat tails that include more ambiguous and extreme events. 
Keywords:  Ambiguity, Aggregation, Entropy, Multiple Priors, Quantiles 
JEL:  D81 
Date:  2013–06 
URL:  http://d.repec.org/n?u=RePEc:usi:wpaper:677&r=rmg 