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Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Journal of International Money and Finance, Available online 31 January 2014
This study examines the Value-at-Risk for ten euro-zone equity markets individually and also divided into two groups: PIIGS (Portugal, Italy, Ireland, Greece and Spain) and the Core (Austria, Finland, France, Germany and the Netherlands), employing four VaR estimation and evaluation methods considered over the full period and the pre- and post-global crisis subperiods 1 and 2. The backtesting results are also evaluated according to the Basel capital requirements. The results demonstrate that the CEVT methods meet all the statistical criteria the best for most individual equity indices over the full period, but these results over the two subperiods for those two methods are mixed compared to those the DPOT methods. Moreover, the two optimal group portfolios for the PIIGS and the Core as well as the grand portfolio that combines the ten indices do not show much diversification benefits. The PIIGS portfolio selects Spain’s IBEX only, while that of the Core opts for Austria’s ATX only in the full period and subperiod 1. However, Germany’s DAX overwhelmingly dominates both the Core and the Grand portfolios in subperiod 2.
The recent financial turmoil in the euro-zone countries has brought into focus the importance of financial risk management in those countries. The euro-zone debt crisis has affected their stock markets which are highly correlated because of increasing integration and harmonization in this area over time. The mounting risk and uncertainty resulting from the crisis have confounded investors, portfolio managers and policy-makers in the euro-zone as well as in other countries. In such an environment, it will be valuable and useful to examine the downside risk for these equity markets and figure out ways to diversify away risks under different time periods. It will also be particularly important to estimate risks during periods of extreme events like the 2007/2008 financial crisis that affected essentially all asset markets. We will examine the equity risk for the pre- and post-global financial crisis subperiods as well as the full period under consideration. Under such crisis circumstances, significant and extreme drops in prices and returns of these assets have become highly probable, with potentially damaging consequences on portfolios of individuals and institutions. These circumstances have also made risk management strategies for highly volatile markets become more challenging, particularly when the percentages of violations of confidence targets have compounded. The quantification of the size of potential losses and the assessment of risk levels for individual markets and their portfolios are fundamental in designing prudent risk management and portfolio strategies. Value-at-risk (VaR) models have become an important instrument within the financial markets for quantifying and assessing downside market risks associated with asset price fluctuations. They determine the maximum expected loss an asset or a portfolio can generate over a certain holding period, with a pre-determined probability value. Therefore, a VaR model can be used to evaluate the performance of individual asset and portfolio managers by providing downside risk quantification. It can also help investors and portfolio managers determine the most effective risk management strategy for a given situation. Moreover, quantification of the extreme losses in those asset markets is important in the current market environment. Extreme value theory (EVT) provides a comprehensive theoretical forum through which statistical models describing extreme scenarios can be developed. There is a cost for inaccurate estimation of the VaR in equity markets, which affects the efficiency and accuracy of risk assessments. Surprisingly, despite the increasing importance and rising correlation and risk and the need for more portfolio diversification in the euro-zone markets, there are only few studies that analyze the VaRs, the VaR-based optimal portfolio constructions and their efficient VaR frontiers for these markets. The studies that examine European portfolio diversification emphasize diversification through industries instead of countries. In our paper, we assess the significance of diversification of the equity markets for portfolio combinations of two groups of the ten countries in the euro-zone as well as for all ten countries combined as a grand group. The two groups are: the PIIGS which includes Portugal, Ireland, Italy, Greece and Spain, and the Core which consists of Germany, France, Austria, Finland and the Netherlands. The risk in these countries of the two groups will be investigated for the full period and before and after the crisis for comparison purposes. It will be the subject of our future research to examine expanded portfolios of these euro-zone countries by diversifying the equity portfolios with other asset classes such as commodities. Our current study expands the spectrum of equity diversifications in the euro-zone and deals with events that are more extreme than the regular behavior dynamics of the stock indices over different periods. Therefore, it constructs VaR-based optimal portfolios, examines their characteristics and performances for this zone, and ranks those optimal portfolios using VaR-based risk performance measures.1 The objective of this paper is to fill this gap in the financial risk management for the euro-zone equity markets and construct optimal portfolio strategies by using more up-to-date techniques that take into account the volatility asymmetry and clustering in the pre- and post-global financial crisis periods. This topic has not been researched adequately for the seemingly harmonious euro-zone, despite the global crisis and its implications for diversification within broad investment portfolios and hedging capability. To achieve these objectives, this paper computes VaRs for the ten individual euro-zone market indices and their grouping into PIIGS and Core, using four estimation methods including RiskMetrics, Duration-based Peak-Over-Threshold (DPOT), and conditional extreme value theory (CEVT) ( for both the normal and skewed t-distributions) under different periods. Several portfolios have been constructed from the markets in the two groups as well as the ten index euro-zone group. Based on the four backtesting evaluation criteria, the results show that the two CEVT methods stand out as the best models for satisfying the backtesting properties for the ten euro-zone equity indices for the full period but compete with DPOT in the subperiods. The RiskMetrics method performs the worst under the full period but performs better under the crisis period (subperiod 2) than the other two periods. The DPOT yields better performance for the Core countries than for the countries in the PIIGS group. The results also show that the VaR-based risk adjusted return ratio for the optimal portfolios for the PIIGS, the Core and the 10 index euro-zone groups varies over the three periods. This ratio is the greatest for subperiod 1 relative to the full period and subperiod 2 for the portfolios of the three groups. Additionally, the optimal diversification results suggest that each of the two well-integrated euro-zone groups should have mainly one euro-zone equity index in its optimal portfolio. Spain’s IBEX index strongly dominates the PIIGS portfolio for the three periods, while Austria’s ATX index overwhelms the Core and the expanded ten index equity (euro-zone) portfolios under the full period and subperiod 1. However, in subperiod 2 Germany’s DAX dominates the Core and the euro-zone portfolios probably because Germany has acquired a great deal of firepower in this crisis period. There is also slightly more room for portfolio diversification for the three groups’ portfolios under subperiod 1 than under the full period, reflecting less harmonization and integration over the shorter period. The results of the average daily capital charges for the two subperiods are different than for the full period. They are considerably lower in subperiod 1 than in the full period for both PIIGS and Core groups. On the other hand, those capital requirements are higher for some countries in subperiod 2 than the full period and subperiod 1. The paper is organized as follows. After this introduction, Section 2 presents a review of the VaR literature on euro-zone and Europe. Section 3 provides the VaR estimation methods and the construction of the optimal portfolios for the euro-zone. Section 4 discusses the data and the empirical results for the three periods under consideration. Section 5 constructs the optimal portfolios for the three groups under the three periods. Section 6 concludes.
نتیجه گیری انگلیسی
Using the recent daily data from 2001 to 2013, we explore the downside risks for ten individual equity indices in the euro-zone countries. These countries are divided into two groups: the PIIGS countries (Portugal, Italy, Ireland, Greece and Spain) and the Core countries (Austria, Finland, France, Germany and the Netherlands) and also all combined in one grand group. The backtesting is estimated for the individual countries using four VaR estimation methods: RiskMetrics, DPOT, CEVT-normal and CEVT-student t and evaluated utilizing four evaluation criteria (percentage of violations, unconditional coverage, conditional coverage and maximum median), in addition to computing the daily capital charges as specified in the Basel Accord. The sample period is classified into three periods: the full period, the pre-crisis period (subperiod 1) and the post-crisis period (subperiod 2). We also explore the downside risk for optimal portfolios of the two groups as well as for the ten index (euro-zone) portfolio for the three periods. We test for the most appropriate value-at-risk (VaR) method for the individual market indices under the three periods. Given the evidence we collected for the individual equity index VaR forecasts, the basktesting evaluation criteria imply that the CEVT methods are the best performer among all the estimation methods for the full period. On the other hand, the RiskMetrics method performs the worst under the full period but performs better under the crisis period (subperiod 2) than the other two periods. The DPOT yields better performance for the Core countries than for the countries in the PIIGS group and it competes with the CEVT methods in the subperiods. If the minimum capital requirement is the only concern, the RiskMetrics method gives the lowest mean capital requirement for the individual indices, which rewards the financial institutions who apply this method the opportunity to earn higher profits than other institutions who utilize different advanced VaR estimation methods such the CEVT methods. However, the probability that this risk management strategy would succeed is low because this model has the worst performance in terms of the number of entries in the red zone (which happens in 8 out of the 10 cases for the full period). With employing the RiskMetrics model, the probability of entering in the red zone is high and the consequences of this entering can be severe and damaging. We examine portfolio diversifications across the ten equity indices. By assessing the historical performance of the VaR-based equity portfolios for the PIIGS and Core groups, the results demonstrate that the optimal portfolio is overwhelmingly dominated by one index for each group for the three subperiods, which implies limited diversification benefits within the euro-zone. We find that the optimal PIIGS portfolio is comprised of over 99% and 98% of the Spanish IBEX index, respectively, over the full period and subperiod 1 which has less harmonization and integration. Similarly, the optimal Core portfolio consists of about 99% of the Austrian ATX index in full period and 95% in subperiod 1, respectively. However, in subperiod 2 the countries in the PIIGS group have slightly drifted apart from each other under the pressure of the debt crisis and have a tad of more room for diversification as the dominance of IBEX dropped to 97.7%. The interesting thing about subperiod 2 is that DAX has replaced ATX as the dominant index in the Core and the grand euro-zone portfolios over this subperiod. During this crisis period, Germany holds all the punches and persists to be the strongest and most stable economy in Europe. Thus, any diversification within the euro-zone markets is not expected to produce great diversification gains. Consequently, any diversification with other asset classes such as commodities like oil and gold should give greater diversification benefits. This conclusion will be our next research project.