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on Risk Management |
| By: | John Cotter (University College Dublin) |
| Abstract: | Accurate forecasting of risk is the key to successful risk management techniques. Using the largest stock index futures from twelve European bourses, this paper presents VaR measures based on their unconditional and conditional distributions for single and multi-period settings. These measures underpinned by extreme value theory are statistically robust explicitly allowing for fat-tailed densities. Conditional tail estimates are obtained by adjusting the unconditional extreme value procedure with GARCH filtered returns. The conditional modelling results in iid returns allowing for the use of a simple and efficient multi-period extreme value scaling law. The paper examines the properties of these distinct conditional and unconditional trading models. The paper finds that the biases inherent in unconditional single and multi-period estimates assuming normality extend to the conditional setting. |
| Keywords: | extreme value theory; GARCH filter; conditional risk |
| JEL: | G1 G10 |
| Date: | 2011–07–21 |
| URL: | http://d.repec.org/n?u=RePEc:ucd:wpaper:200419&r=rmg |
| By: | Michael McAleer (Erasmus University Rotterdam, Tinbergen Institute, The Netherlands, Complutense University of Madrid, and Institute of Economic Research, Kyoto University); Roberto Casarin (Department of Economics Ca’Foscari University of Venice); Chia-Lin Chang (Department of Applied Economics Department of Finance National Chung Hsing University Taichung, Taiwan); Juan-Ángel Jiménez-Martín (Department of Quantitative Economics Complutense University of Madrid); Teodosio Pérez-Amaral (Department of Quantitative Economics Complutense University of Madrid) |
| Abstract: | It is well known that the Basel II Accord requires banks and other Authorized Deposit-taking Institutions (ADIs) to communicate their daily risk forecasts to the appropriate monetary authorities at the beginning of each trading day, using one or more risk models, whether individually or as combinations, to measure Value-at-Risk (VaR). The risk estimates of these models are used to determine capital requirements and associated capital costs of ADIs, depending in part on the number of previous violations, whereby realised losses exceed the estimated VaR. McAleer et al. (2009) proposed a new approach to model selection for predicting VaR, consisting of combining alternative risk models, and comparing conservative and aggressive strategies for choosing between VaR models. This paper addresses the question of risk management of risk, namely VaR of VIX futures prices, and extends the approaches given in McAleer et al. (2009) and Chang et al. (2011) to examine how different risk management strategies performed during the 2008-09 global financial crisis (GFC). The empirical results suggest that an aggressive strategy of choosing the Supremum of single model forecasts, as compared with Bayesian and non-Bayesian combinations of models, is preferred to other alternatives, and is robust during the GFC. However, this strategy implies relatively high numbers of violations and accumulated losses, which are admissible under the Basel II Accord. |
| Keywords: | Median strategy, Value-at-Risk, daily capital charges, violation penalties, aggressive risk management, conservative risk management, Basel Accord, VIX futures, Bayesian strategy, quantiles, forecast densities. |
| JEL: | G32 C53 C22 C11 |
| Date: | 2011–07 |
| URL: | http://d.repec.org/n?u=RePEc:kyo:wpaper:784&r=rmg |
| By: | Paulo Araújo Santos (Escola Superior de Gestão e Tecnologia de Santarém and Center of Statistics and Applications, University of Lisbon); Juan-Ángel Jiménez-Martín (Departamento de Economía Cuantitativa (Department of Quantitative Economics), Facultad de Ciencias Económicas y Empresariales (Faculty of Economics and Business), Universidad Complutense de Madrid); Michael McAleer (Econometrisch Instituut (Econometric Institute), Faculteit der Economische Wetenschappen (Erasmus School of Economics), Erasmus Universiteit, Tinbergen Instituut (Tinbergen Institute).); Teodosio Pérez Amaral (Departamento de Economía Cuantitativa (Department of Quantitative Economics), Facultad de Ciencias Económicas y Empresariales (Faculty of Economics and Business), Universidad Complutense de Madrid) |
| Abstract: | In McAleer et al. (2010b), a robust risk management strategy to the Global Financial Crisis (GFC) was proposed under the Basel II Accord by selecting a Value-at-Risk (VaR) forecast that combines the forecasts of different VaR models. The robust forecast was based on the median of the point VaR forecasts of a set of conditional volatility models. In this paper we provide further evidence on the suitability of the median as a GFC-robust strategy by using an additional set of new extreme value forecasting models and by extending the sample period for comparison. These extreme value models include DPOT and Conditional EVT. Such models might be expected to be useful in explaining financial data, especially in the presence of extreme shocks that arise during a GFC. Our empirical results confirm that the median remains GFC-robust even in the presence of these new extreme value models. This is illustrated by using the S&P500 index before, during and after the 2008-09 GFC. We investigate the performance of a variety of single and combined VaR forecasts in terms of daily capital requirements and violation penalties under the Basel II Accord, as well as other criteria, including several tests for independence of the violations. The strategy based on the median, or more generally, on combined forecasts of single models, is straightforward to incorporate into existing computer software packages that are used by banks and other financial institutions. |
| Keywords: | Value-at-Risk (VaR), DPOT, daily capital charges, robust forecasts, violation penalties, optimizing strategy, aggressive risk management, conservative risk management, Basel, global financial crisis. |
| JEL: | G32 G11 C53 C22 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:ucm:doicae:1127&r=rmg |
| By: | John Cotter (University College Dublin); Jim Hanly (Dublin Institute of Technology) |
| Abstract: | We examine whether hedging effectiveness is affected by asymmetry in the return distribution by applying tail specific metrics to compare the hedging effectiveness of short and long hedgers using crude oil futures contracts. The metrics used include Lower Partial Moments (LPM), Value at Risk (VaR) and Conditional Value at Risk (CVAR). Comparisons are applied to a number of hedging strategies including OLS and both Symmetric and Asymmetric GARCH models. Our findings show that asymmetry reduces in-sample hedging performance and that there are significant differences in hedging performance between short and long hedgers. Thus, tail specific performance metrics should be applied in evaluating hedging effectiveness. We also find that the Ordinary Least Squares (OLS) model provides consistently good performance across different measures of hedging effectiveness and estimation methods irrespective of the characteristics of the underlying distribution. |
| Keywords: | Hedging Performance; Asymmetry; Lower Partial Moments, Value at Risk, Conditional Value at Risk. |
| JEL: | G10 G12 G15 |
| Date: | 2011–07–21 |
| URL: | http://d.repec.org/n?u=RePEc:ucd:wpaper:200843&r=rmg |
| By: | John Cotter (University College Dublin); Francois Longin (ESSEC Graduate Business School, France) |
| Abstract: | Value at risk (VaR) is a risk measure that has been widely implemented by financial institutions. This paper measures the correlation among asset price changes implied from VaR calculation. Empirical results using US and UK equity indexes show that implied correlation is not constant but tends to be higher for events in the left tails (crashes) than in the right tails (booms). |
| Keywords: | Implied Correlation, Value at Risk |
| JEL: | G12 |
| Date: | 2011–07–21 |
| URL: | http://d.repec.org/n?u=RePEc:ucd:wpaper:200618&r=rmg |
| By: | John Cotter (University College Dublin) |
| Abstract: | Key to the imposition of appropriate minimum capital requirements on a daily basis requires accurate volatility estimation. Here, measures are presented based on discrete estimation of aggregated high frequency UK futures realisations underpinned by a continuous time framework. Squared and absolute returns are incorporated into the measurement process so as to rely on the quadratic variation of a diffusion process and be robust in the presence of fat tails. The realized volatility estimates incorporate the long memory property. The dynamics of the volatility variable are adequately captured. Resulting rescaled returns are applied to minimum capital requirement calculations. |
| Date: | 2011–07–21 |
| URL: | http://d.repec.org/n?u=RePEc:ucd:wpaper:200418&r=rmg |
| By: | John Cotter (University College Dublin) |
| Abstract: | This paper empirically analyses risk in the Euro relative to other currencies. Comparisons are made between a sub period encompassing the final transitional stage to full monetary union with a sub period prior to this. Stability in the face of speculative attack is examined using Extreme Value Theory to obtain estimates of tail exchange rate changes. The findings are encouraging. The Euro’s common risk measures do not deviate substantially from other currencies. Also, the Euro is stable in the face of speculative pressure. For example, the findings consistently show the Euro being less risky than the Yen, and having similar inherent risk to the Deutsche Mark, the currency that it is essentially replacing. |
| Keywords: | Extreme Value Theory; Tail Behaviour; GARCH; The Euro |
| JEL: | G15 F31 |
| Date: | 2011–07–21 |
| URL: | http://d.repec.org/n?u=RePEc:ucd:wpaper:200417&r=rmg |
| By: | Angelo Baglioni (DISCE, Università Cattolica); Umberto Cherubini |
| Abstract: | We propose a new index for measuring the systemic risk of default of the banking sector, which is based on a homogeneous version of multivariate intensity based models (Cuadras – Augé distribution). We compute the index for 10 European countries, exploiting the information incorporated in the CDS premia of 44 large banks over the period January 2007 – September 2010. In this way, we provide a market based measure of the liability incurred by the Governments, due to the implicit bail-out guarantees they provide to the financial sector. We find that during the financial crisis the systemic component of the default risk in the banking sector has significantly increased in all countries, with the exception of Germany and the Netherlands. As a consequence, the Governments’ liability implicit in the bail out guarantee amounts to a quite relevant share of GDP in several countries: it is huge for Ireland, lower but still important for the other PIIGS (Italy is the least affected within this group) and for the UK. Finally, our estimate is very close to the overall amount of money already committed in the rescue plans adopted in Europe between Octo ber 2008 and March 2010, despite strong cross-country differences: in particular, Germany and Ireland seem to have committed an amount of resources much larger than needed; to the contrary, the Italian Government has committed much less than it should. |
| Keywords: | bank bail out, Government budget, systemic risk, financial crisis |
| JEL: | G21 H63 |
| Date: | 2011–07 |
| URL: | http://d.repec.org/n?u=RePEc:ctc:serie3:ief0103&r=rmg |